my sapce

इन्क्रेअसिंग storms

2008-02-05T16:13:00.000-08:00

Are rising temperatures favouring more and stronger hurricanes? A study published in Nature this week attempts to quantify the relationship between Atlantic hurricane activity and ocean temperature to help answer this question. Nature News examines where we are in the debate and what it means for us.
Have hurricanes become more frequent and fierce?

Yes. The number of major — category 4 or 5 — hurricanes (or cyclones, as hurricanes are called in the Pacific region) has increased worldwide by around 75% since 1970. The largest increases were in the North Pacific, Indian and Southwest Pacific Oceans. There is also a global trend since the mid-1970s towards longer storm duration.

In the North Atlantic, Caribbean Sea and the Gulf of Mexico, hurricane activity was below average in the 1970s and 1980s, but increased substantially after 1995. The number of North Atlantic hurricanes has been above normal in 9 of the last 11 years, reaching a peak in 2005 — a record number of 15 hurricanes formed between June and December 2005, making it the most active hurricane season on record.
What is behind the increase?

It is difficult to attribute the observed changes to specific causes because of the large natural variability in hurricane activity, which is typical of many atmospheric and oceanic processes.

It is now widely accepted, however, that rising sea surface temperatures play the main role. Hurricanes can only form from pre-existing atmospheric disturbances in regions where sea surface temperatures exceed 26 °Celsius. The warmer the water, the more moisture and energy is available for intense storms to develop.

Between June and August of 2005, sea surface temperatures in the tropical North Atlantic hurricane-development region were 0.9 °Celsius above the 1901 to 1970 average — one of many record-breaking figures of this season. Atmospheric conditions were also favourable for hurricanes that season.

Kerry Emanuel, a leading hurricane researcher at the Massachusetts Institute of Technology in Cambridge, showed that the strength of hurricanes is correlated with sea surface temperature and that hurricanes have grown more intense over the past 30 years1.
What does this new paper tell us?

Mark Saunders and Adam Lea of University College London, UK, have quantified, for the first time, the contribution of sea warming to the increase in hurricane activity. They found that local sea surface warming was responsible for around 40% of the rise in number of storms between 1996 and 2005 (compared to the 1950-2000 average) in the North Atlantic2.

Saunders and Lea used a statistical model to disentangle the two main hurricane predictors: sea surface temperature and near-surface trade wind speed. Together, these two variables explain about 80% of the variance observed in tropical Atlantic hurricane activity between 1965 and 2005.

Their result indicates that a 0.5 °Celsius increase in August-September sea surface temperature should result in an average 40% increase in hurricane activity — a measure including both number and severity of storms.
How much have the seas warmed?

Globally, the world's oceans have warmed by around 0.5 °Celsius since 1970, and scientists believe that they will continue to warm throughout the century. In the tropical North Atlantic, sea surface temperatures in the 1996-2005 period were 0.27 °Celsius above average, the highest ten-year anomaly since records began in 1950. Computer models suggest that sea surface temperatures in the Atlantic hurricane-forming region could warm by 2 °Celsius by 2100.
So can we expect an ever growing number of severe hurricanes in a warmer future?

Not necessarily. Natural variability continues to play a role in hurricane activity. And some scientists think that as the sea continues to warm, atmospheric conditions in a warmer climate might become more unfavourable for hurricanes.

As the speed of near-surface trade winds increases, so-called shear wind force (caused by the difference between wind speeds at different altitudes) over hurricane track regions might increase as well. Once wind shear gets strong enough, it will suppress the cyclonic rotation of winds. If, and at what point, this might outweigh the impact of rising sea temperatures is unknown and hotly contested. At last week’s annual meeting of the American Meteorological Society, a new study proposing that global warming may eventually decrease the number of hurricanes in this way created quite a stir.
Will climate change result in more hurricanes reaching land, causing more damage?

The proportion of storms that hit the land versus those that stay at sea is unlikely to change. But the area of ocean surface warm enough to form hurricanes is likely to expand, making more coastline susceptible to these storms.
If these waters warm by 2 °Celsius by 2100, maximum wind speeds of hurricanes could increase by 6%3. That might not seem like much, but damage from hurricanes rises in proportion to the cube of the wind speed.
Has debate over the link between climate change and hurricanes died down in the United States?

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No. Political debate may have taken a break during a relative lull after Hurricane Katrina in 2005, but the link is still hotly contested in the scientific community.
Are hurricanes bad for the planet?

Hurricanes are bad news for people who find themselves in harm’s way. But hurricanes contribute to the functioning of the planet much as do wildfires, volcanic eruptions or tectonic movements. They play an important role in mixing the oceans, and during past hotter climates they may have helped to cool down the otherwise excessively hot tropics.

*
References
1. Emanuel, K. Nature 436, 686-688 (2005). | Article | PubMed | ISI | ChemPort |
2. Saunders, M. A. & Lea, A. S. Nature 451, 557-560 (2008). | Article |
3. Knutson, T. R. & Tuleya, R. E. J. Climate 17, 3477-3495 (2004). | Article |

2008-01-30T14:57:00.001-08:00

2008-01-30T14:50:00.001-08:00

Light Still Shines On The Fair

2008-01-28T07:58:00.001-08:00

Light Still Shines On The Fair, originally uploaded by Alec Feld.

sencond order debet

2008-01-27T17:34:00.000-08:00

▀ 次级债危机溯源

He shang

2008-01-26T14:08:00.001-08:00

inflation in china

2008-01-13T09:07:00.000-08:00

大约在两年前，我就说中国一定会通货膨胀，当时有很多人攻击我，大家在网络上看文章就可以知道。我当时在九一一时说美国经济已经走出低谷了，但中国要走下坡路，而这下坡路就是说中国的经济要进入一个通货膨胀的经济年代。到了去年的十一月份，在中美的第二轨道会议< 中美关系会谈> ，其中中国人民币升值与贬值就讨论的很多，会议中专门邀请全球的经济学家和金融专家开了一个属下的会议讨论人民币的升值与贬值，当时我就谈了我的观点：对国内，人民币不能升值，只能贬值，当时他们都觉得我这观念不对，认为现在人民币都被逼着升值，怎么会贬值？为甚么你要说中国会通货膨胀，人民币贬值，这道理在哪里？

　　其实道理很简单，中国对外贸易是有固定的汇率的，这汇率是８. ２８。例如，我有１００瓶水，我卖给你之后，赚得的美元比你多的时候，应该这个人民币相对就要升值了，但是中国却维持８. ２８不升不动。实际上人民币兑海外的美元是升值了，应该要升值，因为中国施行的是与美元汇率挂钩，就是美元涨多少，人民币的币值随着美元调整。美元与人民币之间也应该是按照相互货币量来调整，哪有一个商品几年保持一个价格而不变化的？

　　在五十年前，世界上都以黄金储备发行钞票，就是有多少黄金发多少钞票。后来美元改为国家信用，国家本位，以国家信用和资源来发钞票。但中国现在不是以黄金，也不是以国家信用，是以甚么呢？以美元为本位，所以美元升值，中国跟着升值，美元降，中国跟着降。但是大家想想，中国的外贸出口，赚的是美元，美元多了人民币就该升，原来我有人民币１０００元，现在又赚进来１５美元，人民币当然要升值，升值是理所当然的。

　　但中国人民币为甚么不升值？政府担心中国的信用，一旦中国汇率自由化，就意味着货币要自由交易，就是美元的自由流通，在中国就很有可能取代人民币。而这种美元取代人民币的结果就是海外的银行在中国正常营业。这种情况下，中国老百姓就可能不愿意将自己的钱全部存人民币，而愿意存一部份美元，那时候大量的人民币就会被换成美元，造成中国国有银行人民币储蓄大量抽逃，中国银行的内债和外债亏损整个就暴露出来了，而中国四大国有银行坏帐率高达７０％，只要中国百姓将自己的储蓄的一半拿出来换成美元，中国国有银行就会无法支撑，就会倒闭。但中國政府不可能让四大国有银行倒闭，那样会造成中国的整个社会崩溃，怎么办？就只有印钞票。造成人民币反过来贬值，这样一来，中国经济体系就会被冲击垮掉。所以现在中国大陆宁肯承受人民币升值压力，而不愿放开汇率，最根本的一点就在这里，他们担心中国金融界的内部亏损暴露出来，进而冲击中国的整个社会稳定。

　　其实还有一种原因，这就是欺骗性。人民币对外好像升值，实际上对内是贬值，为甚么对内贬值呢？原因在哪里？这是固定汇率造成的，任何东西自由买卖的时候都是平等的交换，美元与人民币的兑换也是物品交易。美元多了，人民币自然就要升值，美元少了，人民币就会贬值。这是一个自由交换的过程，但一旦固定下来后，等于卡了一条线，这条线使整个中国和国外的交易不是公平交易，而是国家控制和垄断的。

　　中國政府之所以愿意采取这个策略就是因为中国的人民币实际上是以美元为基准的货币。比如说外汇储备增长一块美金的时候，对国内就要发８. ２８块人民币，政府随着美元储备越多，发的新货币就越多。从今年的数据来看，一月到十月的时候，人民币增发了四万亿，大家想想四万亿是甚么概念？中国大陆国民总产值去年一年十万亿，今年预计达到十二万亿。十二万亿人民币的ＧＤＰ，国家要新增加四万亿的人民币，你说这人民币是不是贬值了？肯定贬值了，因为你外币多了，外币进入中国一定要兑换成人民币才能流通，所以一定要发货币，增发货币的结果是甚么呢？大家可以看到中国大陆官方统计的数据，就是M ２统计数据（M ２指：Broad money ，广义货币供给的一种形式或口径，包括交易货币（M １）、银行储蓄帐户，还有其他类似交易货币的替代性资产。），它是从十八万亿的总量上增长到二十二万亿的总量，所以一下子增加了四万亿，这四万亿整个投放市场，大家可以看到一个最明显的现象，就是所有物价上涨。

　　中国大陆公布的十月份数据，中国大陆的通货膨胀率是４. ３% ，按照常规的经济学观点讲的，５% 以内的通货膨胀是温和通货膨胀，是合理的。可是中共官方又有数据公布，就是粮食、石油、煤、铁，这些数据增长了多少呢？准确数据是２４. １% ，基础行业的价格涨了２４. １% ，可他讲整个社会的通货膨胀率４. ３% ，其实就可以看出来４. ３% 这个数据是非常的不真实。其实不光是粮食等涨价，钢铁和煤、石油涨价，不仅身上穿的衣服，装水的塑料瓶，其它的统统都要涨价。它涨２４. １% ，怎么可能社会上整个的通货膨胀率只有４. ３% ？根据中国官方公布的中国恩格尔系数是３７，也就是说中国百姓用于食品生活的开支占其收入的３７％，这３７％的消费涨价了２４. １% ，即使其他的部份都不涨价，这个数据也不对啊。

　　我没办法相信这个数据，如果这个通涨指数是真实的话，因为原材料成本只能上涨不可能被压缩，很有一种可能就是整个国民的工资收入被压缩了，既使压缩也不可能压缩二十个百分点吧！因为中国大陆本身的工资成本的总额大约只占了成本的１５%~２０% 左右，压缩了二十就没了，大家没有工资了怎么生活？这是不可能的事情，所以说这数据是欺骗。

　　在这种情况下，中国大陆的通货膨胀实际上是非常严重、非常厉害的情况，大家看到中国大陆的物价涨得很快，而且一个最明显的情况是房子涨得很快，在这种经济通货膨胀的情况下，对中國政府却有好处。货币增发之后就等于人民币贬值，无形中就等于向百姓抽取钱财。通货膨胀２０% ，这个２０% 等于让老百姓平均承担下来了，这种情况下政府的坏帐就被消减了。今年的统计数据没有出来，出来的时候大家可能会看到大约中国的金融坏帐会降低１０% 左右。这个数据哪来的？就是我从今年中国大陆的通货膨胀数据推算出来的。就这点来说，中国大陆保持固定汇率的作用，一是怕自己银行体系崩溃；另一个就是想靠通货膨胀来维持这个政府，从而消灭政府本身的坏帐。

　　根据凯恩思的经济理论，通货膨胀产生的环境是一个封闭的环境，如果流通的话，没办法形成通货膨胀的。你这里东西贵了，便宜的东西会进来的，物价马上就会被压下来。这东西少了，马上别国的东西又进来。流通就不会产生通货膨胀。

　　事实上，最近几十年来，全球没有发生恶性的通货膨胀，反而是因为全球化，产生了不少次的通货紧缩。而未来，全球各个国家所面临的只能是通货紧缩，而不会是通货膨胀。中国大陆产生通货膨涨的情况就是因为政府用汇率这条线把流通给卡住。在加入WTO 之后，中共认识到关税不起作用了，他所以用汇率从经济上进行一刀切，切的情况就是为了销减坏帐。人民币升值，国民财富增加了，以前买进口汽车需要二十万人民币，现在就需要十五万人民币了，为甚么不好？但中共先削减政府坏帐，不开放私人金融业，还不让国有金融机构倒台，所以这方面的宣传和控制是具有非常大的欺骗性。

　　大家可能看到，中国的房价为甚么涨？就是最近有国内经济界发出一个阴谋论，说的是摩根斯坦利银行，大摩银行怎么会一方面喊着中国经济要崩溃，另一方面为甚么又拿巨资去投资中国的房地产？他们认为摩根斯坦利银行对中国有阴谋，要整垮中国，其实他们理解错了。因为现在中國政府认为说有近亿美元要阻击中国人民币，其实上如果真的要买人民币换美元的话，一定会陪本，人民币要贬值嘛，摩根斯坦利银行不是傻瓜。所以西方国家，摩根斯坦利银行这些大企业之所以进军中国买房地产，是因为看到在中国，人民币要贬值，房地产的价值是永不会变的。随着人民币的贬值，他会增值，至少是保值，是目前中国最能保值的产品。在这种情况下，买房地产是因为看出人民币要贬值，而不是证明说海外银行和金融资本要狙击人民币。虽然中国的房地产价高，但是他们认为这个钱要进入中国之后，要汇出的话，汇不出来，因为中国有个规定，企业赚的纯利润不想交税的话要留在中国，所以把这笔钱买了房地产，房地产的上涨保值的机会远远高于人民币。在表面上看，这个现象很模糊，普通百姓看不出来，但实际分析起来，整个的欧洲企业，包括美国金融企业，完全是在看空人民币，也就是说看到了中国未来的整个经济会走上通货膨胀，海外企业不愿意在手中留有人民币，要将人民币变成能保值的产品。

　　通货膨胀的最大问题是延缓了现在的问题，而将问题留给了未来，在没有配套的全方位改革的情况下，通货膨胀将严重地冲击将来中国整个经济与社会，虽然把眼前的这个坏帐解决了。但没有一个好的社会保障体系的情况下施行通货膨胀手段，在未来的几年对整个中国的社会损伤还是非常大，会引发经济问题和社会动乱。

　　我们从这一点上可以看出，中國政府在整个经济走向上，不是走一个平稳的路线，也不是全面考虑，先解决社会保障机制和政治改革，建立司法公平。而是急于解决目前的执政安全问题。当年的江朱政府就是如此，原来讲积极的财政政策，我在当时就写文章反对这个积极的财政政策，反对了六，七年，结果到了胡溫的时候又一刀切了。不要积极的财政政策，要施行宏观调控，也就是说取消积极扩张的财政政策。现在换了政府领导人，就从一个极端改成另一个极端，我在半年前也写文章反对胡溫的宏观调控。

　　经济不是变魔术，想变就变。这需要时间，是缓慢的，不是马上就会起作用的。在这种情况下，就又看到一点，不管谁上台，只要我在位的时候保持稳定，树立我的统治权威，我就不管后面的，我想怎么办就怎么办。没有政策的延续性和稳定性，中國政府在现在的状况情况下还依然如此，未来还是如此。

　　从中国的经济还可以看出一点，中共以经济繁荣来支持这个政权的合法性。比如中共经常说的，我们为人民谋了多少福利，维持了中国社会的进步。其实从根本上看完全是虚假的东西，中共往往用一些虚假的，似是而非的东西掩盖真正的本质。

　　我这里讲一点，有很多人说中国现在实行资本主义了，其实最根本一点就是很多人并不理解甚么叫资本主义。最近，中國政府在世界上一直强调要美国承认中国是一个自由的市场经济国家，美国并不承认他，为甚么？因为自由的市场经济这几个词含义非常深，字典上解释说：市场经济需要自由公平交易。

　　大家可能看到这个解释会说，中国都是资本主义了，都是私有社会了，都有私人工厂，也是自由交易，政府也不干涉企业买卖，他怎么不算是自由市场经济？其实这样的理解不对，市场经济最根本的一点就是要自由、要公平。东西要有拥有权才能交换。中国是实行的公有制，矿山、土地都是国家的，你交换甚么呢？不是我的，不是我私人的怎么和你交换？你能拿不是你拥有的东西去和别人交换吗？那是盗窃。

　　公平，甚么叫公平？这就需要建立公平法律制度体系，大家有问题可以申诉，可以得到公平的保障。中共的法律有公平吗？

　　再说自由，举个例子，在美国要交税。为甚么要交税？是政府要雇佣一批人，维持我们社会安定。如果说今天在蒙市，市政府的官员搞得乱七八糟的话，我们不交税，我们投票选他下台，这是个交换，我们为甚么交了钱不能换回我们满意的服务？这种情况下，中國政府，老百姓交很多税，但没有办法选官员，这就不是自由，也没有公平。中国官员不是我们百姓选的，他是赖着不走。这种情况下，自由没有办法实现，公平没有办法实现，交换也没有办法实现。

　　现在百姓信仰基督教，这是一种交换，因为我信仰了之后有身心上的满足，这与我们去电影院花钱看电影得到精神上的满足是一个事情。比如说，信仰基督教，精神上有寄托。这也是用金钱、时间去交换，这是在法律上公平地交换。如果这点都做不到的话，自由市场经济更没办法搞了，中国现在的政权怎么会是市场经济？在这点上中共宣传的所谓的资本主义道路和海外资本主义国家里的私人企业的自由市场经济，实际上本质上相差十万八千里。

　　很多人误解说中共愿意走资本主义道路其实是不对的，他走的只是一个表象，真正本质上没有。就像香港的郎咸平教授讲，为甚么我们看到中国的国有企业都让少数人瓜分光了，因为这企业表面上是人民的，或者说是他爸爸的东西，但儿子私下和别人讲，把这房子卖了算了，你给我五块钱，我就卖他的房子，这合不合理？讲不通嘛，你爸爸的房子你怎么能卖？他不是你的财产嘛。在美国，你能把你邻居的房子卖了吗？打工的员工能把你老板的公司卖了吗？大陆是全民共有财产，大家的财产我们几个人怎么能私下讲一讲就把它卖掉了？主人还不知道，知道了反抗也不行，这是甚么世道？这不是强盗吗？这和到大街上抢劫有甚么区别？

　　从根本上来讲，目前中共所有制度都是带有虚假的东西，他表面上学习，实施资本主义，实际上根本上没有。中共的欺骗性是非常大的。中国经济表面上发展的很好，让世人觉得中国盖了很多高楼大厦，经济繁荣，人民生活增长，这都是一个假象。他动用一个极大社会公共资源去维持一个虚假的东西，损害的是百姓的切身利益。

　　比如说现在政府对大家说：“你们都买房子吧！”老百姓都试图去买房子，可大家想一想那房子，土地是谁的？宪法规定是全体人民的，但实际上是政府的，你买了房子，七十年后政府可以把你赶走！中國政府规定土地只有七十年使用权，就我所知，中共正在讨论实行物业税，因为土地不是购屋者的，是政府自己的，中共不能像美国那样征收土地税，他要改收物业税，参照香港和美国的办法，每年向房主收７%-８% 。大家想一想，土地不是我的，买了房子只能住七十年，还要收我七十年的物业税，这是甚么政府？在美国，谁敢制定法律，让百姓买房子要一次交清七十年的土地租金？中共就是这样先骗你钱，然后再变相再把老百姓的钱骗一次，反覆地掠夺，而这些钱拿出去做政府开支。

　　今年大陆现在已有征收上来的财政收入两万亿，今年计划总的征收量是３.４万亿。大家知道，中国今年ＧＤＰ只有１２万亿，再讲讲利润，利润可能只有１０%-２０% 。２０% 好了，就２. ４万亿。而中共拿的税是多少？３. ４万亿，这个ＧＤＰ当中有多大比例是税收啊！

　　大家想想，美国政府拿的税也很多，但美国政府的税有三分之二的开销是用于政府的，三分之一是用是社安基金的。中國政府税收开支几乎完全是政府开销，没有多少用在社安基金上的。你知道中国社安基金有多少呢？四年期间，用于救济最贫困人口只有９２亿人民币，当时的财政收入四年累计将近８万亿人民币，只拿了９２亿元，而地方政府拿了１５１亿。中國政府的财政收入相对中国百姓的救济是非常非常少的，关键是绝大部份用于政府开支。开支用于甚么呢？大家知道到中国去，喝酒吃饭，还有小姐陪……至少我是参加过宴请ＸＸＸ副总理吃饭的，做生意没办法。请了二桌，大家可能想像不到，化掉了２７万人民币，十年前在北京的一个大酒楼，折合３万美金请了二十个人，在美国我没有这样花过钱，拿三万美金去请二十个人吃饭。这儿没有，但北京有！中国就是这样的。现在中國政府开销是非常大的。所以，看经济问题一定要看本质，目前的中国经济的现象是共產黨造成的，中国多少代人的经济积累也被挖空了

smater bomb

2008-01-12T15:36:00.001-08:00

10 Creepiest Old Ads

2008-01-10T06:35:00.001-08:00

The one with the pig is just disturbing.

read more | digg story

El Niño and Global Warming

2008-01-09T08:14:00.001-08:00

The relationship between ENSO and Global Warming, plus short introduction of El Nino and La Nina.

read more | digg story

China Invests $1.4 Billion on Nuclear Fusion

2008-01-09T02:27:00.001-08:00

China has tossed down a $1.4 billion bet on the world energy roulette wheel. China's stake is 10% of a research project, the International Thermonuclear Experimental Reactor, trying to unlock the secret to nuclear fusion, a potentially boundless, clean and cheap form of energy.

read more | digg story

What are gravitational waves

2008-01-09T02:22:00.001-08:00

A proffesional explantion about what are gravitational waves and what they have to do with us.

read more | digg story

数学家们的逸闻趣事

2008-01-07T13:54:00.001-08:00

Bernoulli 家族
　　
　　Euler停止了生命，也就停止了计算。
　　——de Condorcet
　　
　　这是一个生产数学家和物理学家的部落，有着十几位优秀的科学家都拥有这个令人骄傲的姓氏。
　　
　　1． John Bernoulli在1696年把最速降线问题在一个叫做《教师学报》的杂志上面提出，公开挑战主要是针对他的哥哥Jacobi.Bernoulli,这两个人在学术让一直相互不忿，据说当年John求悬链线的方程，熬了一夜就搞定了，Jacobi做了一年还认为悬链线应该是抛物线，实在是很没面子。那个杂志好像是Leibniz搞得，很牛，欧洲的牛人们都来做这个东西。到最后，Jhon收的了5份答案，有他自己的，Leibniz的,还有一个L.Hospital侯爵的（我们比较喜欢的那个L.Hospital法则好像是他雇人做的，是个有钱人）然后是他哥哥Jacobi的，最后一份是盖着英国邮戳的，必然是Newton的，John自己说“我从它的利爪上认出了这头狮子．”据说当年Newton从造币厂回去，看到了Bernoulli的题，感觉浑身不爽，熬夜到凌晨4点，就搞定了。这么多解答当中，John的应该是最漂亮的，类比了Fermat原理，用光学一下做了出来。但是从影响来说，Jacobi的做法真正体现了变分思想。
　　
　　2． Bernoulli一家在欧洲享有盛誉，有一个传说，讲的是Daniel Bernoulli（他是John Bernoulli的儿子）有一次正在做穿过欧洲的旅行，他与一个陌生人聊天，他很谦虚的自我介绍：“我是Daniel Bernoullis。"那个人当时就怒了，说：“我是还是Issac Newton 呢。”Daniel从此之后在很多的场合深情的回忆起这一次经历把他当作他曾经听过的最衷心的赞扬。
　　
　　3． John & Jacobi这两个Bernoulli人，都算不出来自然数倒数的平方和这个级数，Euler从他老师John那里知道的，并且给出了π2/6这个正确的答案。
　　4．法国有一个哲学家，叫做Denis Diderot，中文的名字叫做狄德罗，是个无神论者，这个让叶卡捷琳娜女皇不爽，于是他请Euler来教育一下Diderot，其实Euler本来是弄神学的，他老爸就是的，后来是好几个叫Bernoulli的去劝他父亲，才让Euler做数学了。Euler邀请Diderot来了皇宫，他这次的工作是证明上帝的存在性，然后，在众人面前说：“ 先生，( a + bn ) / n = x, 因此上帝存在；请回答!”Diderot自然不懂代数，于是被羞辱，显然他面对的是欧洲最伟大的数学家，他不得不离开圣彼得堡，回到了巴黎……
　　
　　四色定理
　　
　　证明是一个偶像，数学家在这个偶像前折磨自己。
　　——A.Eddington
　　
　　1．一次拓扑课，Minkowski向学生们自负的宣称：“这个定理没有证明的最要的原因是至今只有一些三流的数学家在这上面花过时间。下面我就来证明它。”…….这节课结束的时候，没有证完，到下一次课的时候，Minkowski继续证明，一直几个星期过去了……一个阴霾的早上，Minkowski跨入教室，那时候，恰好一道闪电划过长空，雷声震耳，Minko wski很严肃的说：“上天被我的骄傲激怒了，我的证明是不完全的……"
　　
　　2． 1942年的时候，Lefschetz去Havard做了个报告，Birkhoff是他的好朋友，讲座结束之后，就问他最近在Princeton有没有什么有意思的东西。Lefschetz说有一个人刚刚证明了四色猜想。Birkhoff严重的不相信，说要是这是真的，就用手和膝盖，直接爬到Princeton的Fine Hall去。
　　
　　
　　做数论的人
　　
　　从实用的观点来判断，我的数学生涯的价值等于零。
　　——Hardy
　　
　　1． Lev Landau这位俄国最伟大的物理学家惊叹道：“为什么素数要相加呢？素数是用来相乘而不是相加的。”据说这是Landau看了Goldbach(哥德巴赫)猜想之后的感觉。术业有专攻呀......
　　
　　2． Graham说：“我知道一数论学家，他仅在素数的日子和妻子同房：在月初，这是挺不错的，2，3，5，7；但是到月终的日子就显得难过了，先是素数变稀，19，23，然后是一个大的间隙，一下子就蹦到了29，……”
　　
　　3．由于Fermat大定理的名声，在New York的地铁车站出现了乱涂在墙上的话： x^n + y^n = z^n 没有解对此我已经发现了一种真正美妙的证明，可惜我现在没时间写出来，因为我的火车正在开来。
　　
　　4. Hilbert曾有一个学生，给了他一篇论文来证明Riemann猜想，尽管其中有个无法挽回的错误，Hilbert还是被深深的吸引了。第二年，这个学生不知道怎么回事死了，Hilbert要求在葬礼上做一个
　　演说。那天，风雨瑟瑟，这个学生的家属们哀不胜收。Hilbert开始致词，首先指出，这样的天才这么早离开我们实在是痛惜呀，众人同感，哭得越来越凶。接下来，Hilbert说，尽管这个人的证明有错，但是如果按照这条路走，应该有可能证明Riemann猜想，再接下来，Hilbert继续热烈的冒雨讲道：“事实上，让我们考虑一个单变量的复函数.....”众人皆倒。
　　
　　5．有一个人叫做Paul Wolfskehl,大学读过数学，痴狂的迷恋一个漂亮的女孩子，令他沮丧的是他被无数次被拒绝。感到无所依靠，于是定下了自杀的日子，决定在午夜钟声响起的时候，告别这个世界，再也不理会尘世间的事。Wolfskehl在剩下的日子里依然努力的工作，当然不是数学，而是一些商业的东西，最后一天，他写了遗嘱，并且给他所有的朋友亲戚写了信。由于他的效率比较高的缘故，在午夜之前，他就搞定了所有的事情，剩下的几个小时，他就跑到了图书馆，随便翻起了数学书。很快,被Kummer解释Cauchy等前人做Fermat大定理为什么不行的一篇论文吸引住了。那是一篇伟大的论文，适合要自杀的数学家最后的时刻阅读。Wolfskehl竟然发现了Kummer的一个bug，一直到黎明的时候，他做出了这个证明。他自己狂骄傲不止，于是一切皆成烟云……这样他重新立了遗嘱，把他财产的一大部分设为一个奖，讲给第一个证明Fermat定理的人10万马克… …这就是Wolfskehl奖的来历。
　　
　　Gottingen的传说
　　
　　Gottingen市政厅底层的墙上
　　言不讳的镌刻着：
　　“Gottingen以外没有生活。”
　　
　　1． 1854年，Riemann为了在Gottingen获得一个讲师的席位，发表了他划时代的关于几何学的演说。由于当时听这个演说的人很多是学校里的行政官员，对于数学根本就不懂，Riemann在演说中仅仅只用了一个数学公式。Weber的回忆说，当演说结束后，Gauss怀着少见的表情激动的称赞Riemann的想法。如果读读Riemann的讲稿，就会发现那几乎就是哲学，尽管这样子，当时的观众中只有一个人可以理解Riemann,那就是Gauss。而整个数学界,为了完善消化Riemann的这些想法，却话了将近100年的时间。有人说Riemann的著作，更接近于哲学而不是数学，甚至在一开始，欧洲的很多数学家认为Riemann的东西是一种家庭出版物，更接近物理学家的看法，与数学家没有关系。一次，Helmholz和Weiestrass一起外出度假，Weiestrass随身带了一篇Riemann的博士论文，以便能在一个山清水秀的环境里静静的研究这篇他认为是复杂又宏伟的工作。但是Helmholz大惑不解，他认为，Riemann的文章再明白不过了，为什么Weiestrass作为数学家要这么化功夫呢？
　　
　　2． Klein上了年纪之后，在Gottingen的地位几乎就和神一般，大家对之敬畏有加。那里流行一个关于Klein的笑话，说Gottingen有两种数学家，一种数学家做他们自己要做但不是Klein要他们做的事；另一类数学家做Klein要做但不是他们自己要做的事。这样Klein不属于第一类，也不属于第二类，于是Klein不是数学家。
　　
　　3． Wiener去Gottingen拜访这位老人家，他在门口见到女管家时，问道教授先生在么？女管家训斥道，枢密官先生在家。一个枢密官在德国科学界的地位就相当于一个被封爵的数学家在英国科学界的地位，譬如说Newton。Wiener见到Klein的时候，感觉就像去拜佛，后者高高在上，Wiener的描述是“对他而言时间已经变得不再有任何意义”。
　　
　　4．关于Klein还有一个故事，当初王诗宬老师请了一个法国的拓扑学家来北大做报告，他讲的东西和双曲几何有些关系，半路上，突然讲到了Klein和Poincare的故事，说是Klein和Poincare都在研究自守函数什么的，对于2维的的情况，Poincare把自己的结果用Fuchs的名字来命名，因为这个人的东西他曾经看过，并且有很大的影响，Klein感到特别的不爽，他也得到了这样的结果然而Fuchs本人对此却一无所知，如此冠名，他自然觉的很不妥。后来，他和Poincare分别做3维的情况，无奈自己不是Poincare那样的天才，用功过度，体力不支，身体都垮了，从此结束了自己创造性的数学生涯。Poincare自己也不在乎这么东西，于是把3维自己得到的群命名为Klein群。当时王老师也特别想将这个故事，自己踌躇了半天，后来说这个东西是法国人很有面子的一件事情，还是让这个法国人讲了。
　　开始讲D.Hilbert吧
　　
　　5． David Hilbert并不是Gottingen毕业的。19世纪80年代，Berlin大学的博士论文答辩，需要2名学生作为对手，他们向你不停的发问。Hilbert的一个对手是Emil Wiechert(埃米尔.魏恰特),后来是最著名的地震学家。那时候，德国（也许叫做普鲁士）的大学教授特别少。Berlin之后3名数学教授，一般的大学至多2个。 Hilbert的博士宣誓仪式，校长主持：“我庄严的要你回答，宣誓是否能使你用真诚的良心承担如下的许诺和保证：你讲勇敢的去捍卫真正的科学，将其开拓，为之添彩；既不为厚禄所驱，也不为虚名所赶，只求上帝真理的神辉普照大地，发扬光大。”欧很想知道现在北大的授予博士仪式是不是也有类似的话
　　
　　6． Hilbert上了年纪的时候，一次听到一群年轻人正在谈论一个他知道数学家。那时候，Minkowski这些他很熟的人，有很多都已经故去。他特别关心正在被谈论的这个人，当大家说完这个人有几个孩子之类的事情之后，他就问说：“...他还‘存在'么.…….”
　　
　　7．一次在Hilbert的讨论班上，一个年轻人报告，其中用了一个很漂亮的定理，Hilbert说 :“这真是一个妙不可言（wunderbaschon）的定理呀,是谁发现的？”那个年轻人茫然的站了很久，对Hilbert说：“是你.……”。
　　
　　8． Gottingen广为流传的一个关于Minkowski的故事，说是他在街上散步，发现一个年轻人正在默默想着某个很重要的问题，于是Minkowski轻轻的拍拍他的肩膀，告诉他“收敛是肯定的”，年轻人感激而笑。
　　
　　9． H.刚去Gottingen的时候,被拒之“圈”外。所谓的圈，是指Toeplitz, Schmidt, Hecke和Haar等一
　　群年轻人，大家一起谈论数学物理，很有贵族的感觉。一次，大家在等待Hilbert来上课，Toeplitz指着远处的Weyl说：“看那边的那个家伙，他就是Weyl先生。他也是那种考虑数学的人。”就这样子，Weyl就不属于“圈”这个集合了。这个故事是Courant讲的，Haar当时是Hilbert的助手，Gottingen当时的人们无一不认为他将是那种不朽的数学家。但是事实证明，Weyl的伟大无人能比，尽管Haar在测度论上贡献突出，但是Courant还是说他和Weyl“根本没法相比”。
　　
　　10． von Karman（冯.卡门）通过Haar的介绍来到Gottingen,等到Haar去了匈牙利之后，他很快成为“圈”内的领袖。圈外人Weyl再一次证明了他的优秀，他和Karman同时爱上了才貌双全的一个女孩，并且展开了一场竞争。最终圈内人都感到特别的沮丧，因为那个女孩子选择了Weyl。
　　
　　Gottingen讲得太多了吧
　　先停几次，多讲几件烂事
　　然后再讲
　　
　　先介绍一个人，L.V.Ahlfors, 和另一个美国的数学家共同分享了第一届的Feilds奖。欧知道他的一部分工作，就是展示给大家复分析和双曲几何之间的深刻联系，把曲率之类的几何概念引入了复分析，给出了Schwarz引理的几何上的漂亮解释。他还在共形映射，Riemann曲面领域都是贡献非凡。下面是一个很传奇的事情，欧希望那些认为数学没有“用”的看看数学家是如何认为数学有用的。hehe
　　
　　L.V.Ahlfors说这些话的时候，正是二战受封锁的时候 “Feilds奖章给了我一个很实在的好处，当被允许从芬兰去瑞典的时候，我想搭火车去见一下我的妻子，可是身上只有10元钱。我翻出了Fields奖章，把它拿到当铺当了，（！！！！）从而有了足够的路费…… 我确信那是唯一一个在当铺呆过的Feilds奖章……”
　　
　　在讲几个小事情，都是蛮有意思的那种
　　明天继续Gottingen
　　
　　这一个是因果循环的
　　
　　Hilbert写的第一篇关于Dirichlet原理的文章，希望Fredholm能够欣赏，但是Fredhold根本就没看；F.Riesz写了很多文章，希望Hilbert能够欣赏，但是Hilbert根本就没看；M.Riesz写了很多文章，希望F.Riesz能够欣赏，但是F.Riesz根本就没看……
　　再来一个苏联大牛的
　　
　　39年的时候，Kolmogorov决定在冰水中游泳，结果以住院告终，医生一致认为他差点点死掉；但是，70岁的时候，突然决定到莫斯科河里游泳，仍然是冰水，这一次却没有事情。
　　
　　Gottingen 的传说
　　开始讲一下Edmund Landau的故事。
　　
　　11． E.Landau是后来的Gottingen的数学系系主任，此人不仅解析数论超强，而且超级有钱。曾有人问他怎么能在Gottingen找到他，他很轻描淡写的说：“这个没有任何困难，它是城里最好的那座房子。”
　　
　　12． Gottingen 1909-1934年的数学系主任是Edmund Landau。Landau的工作习惯很奇怪，用6个小时工作，6个小时休息，如此交替。他收到过无穷多关于证明了Fermat大定理的信件，后来实在没有精力处理，就印了一批卡片，样子大概是这个样子的:
　　
　　---------------------------------------------------------
　　亲爱的_____
　　谢谢您寄来的关于Fermat大定理的证明。
　　第一个错误在
　　______页 ______行
　　这使得证明无效。
　　
　　E.M.Landau
　　---------------------------------------------------------
　　
　　尽管有很多的稿件都退了，据说剩下的还有3米多高。
　　
　　继续讲Landau的故事和Landau讲过的故事
　　
　　13． E.Landau是比较自大的那种人，根本看不起物理化学，包括应用数学,他把任何和数学的应用有关的东西贬为“润滑油”。一次Steinhaus的博士考试需要一个天文学家的提问。Landau似乎很关心，就问Steinhaus都被问了什么问题，当他知道是有关3体问题的微分方程的时候，大声的说：“啊，如此说来，他知道这个.……”
　　
　　14． A.Rosenthal曾经和Landau住一个房间。一天，Landau回到房间向Rosenthal抱怨老年的Dedekind和他絮叨了一下午的废话，Dedekind狠狠的抱怨当年Guass对他不公平，在他的博士学位考试时，问了一些特别难的问题。
　　
　　两个间接的和Gottingen的人有关系的事情
　　Dehn是Hilbert最得意的弟子之一，曾经率先解决了一个Hilbert问题。
　　
　　15． Max Dehn离开Gottingen躲避纳粹追捕的时候，经过苏联，换火车的时候，在海参崴逗留了一阵，闲来无事去了当地的图书馆，这里的数学书仅仅占一个架子，全部都是Spring er-Verlag的黄皮书。
　　
　　16． Poincare也曾去Gottingen演讲，顺便攻击了一下Cantor的集合论，Zermelo当时恰好证明的每个集合都可以良序化，Poincare演讲的时候他恰好坐在靠近Poincare脚边的位子上，然而Poincare并不认识Zermelo，他大喊道：“Zermelo那个几乎独创的证明也应该彻底的毁掉，扔到窗外去！”Zermelo本来就性情古怪暴躁，那天更是绝望盛怒。Courant甚至认为Zermelo一定会在那天吃正餐的时候杀死Poincare。
　　
　　17. Caratheodory是希腊的一个富人子弟，后来在测度等很多方面有着重要的贡献，北大图书馆还有他的一本讲复变函数的书，非常的几何化，特别优美。他当初是一个工程师， 26岁突然放弃了这样一个有前途的职业来学习数学，众人很不理解，他说：“通过不受束缚的专心的数学研究，我的生活会变得更有意义，我无法抗拒这样的诱惑。”他选择的学校是Gottingen.
　　
　　18. W.F.Osgood是原来Havard的数学教授，来中国讲过课，我这里还有他在中国的讲稿:-)。他也是Gottingen毕业的，娶了一德国姑娘，在美国保持着德国的传统。大概是在Gottingen受的影响太大，Osgood做事都模仿F.Klein。他留着欧洲式的头发，抽烟的时候不停的用小刀戳雪茄，一直抽到发苦的烟蒂头。
　　
　　从明天开始，再也不说Gottingen了
　　
　　19. 由于纳粹对犹太人采取的政策，很多数学家都离开了Gottingen。一次纳粹的教育部长问ilbert说Gottingen 的数学现在怎么样了，Hilbert说：“Gottingen的数学，确实，这儿什么都没有了。”
　　Gottingen从那时开始一蹶不振。
　　
　　20. 这一个几乎和Gottingen没有什么关系，很多数学家都是这个样子，开始的时候自己的工作的不到承认的，譬如说S.Lie当初的李群，Cantor当初的集合论，等等。Grassmann最初是一个预科学校的教员，尽管那个时候，他就做出了反交换代数这一大堆重要的东西，但是那个时代数学家从来不曾重视他的成果。Grassmann自己不的不放弃数学这个没有前途的职业，化了不少功夫在印度的梵文，把一个叫做Rig-Veda的印度古经译成了德文。所以Grassmann在当时的语言界受到了更多的尊重。在Gottingen的图书馆里有一本Grassmann的写的维数论，标题页上面用铅笔写着Minkowski的名字，序言后的脚注是：“书付印时作者已去世。”Minkowski用几行字，清楚的表达了Grassmann的成就：“新版本将比三十多年前收到更多的尊重。”
　　开始讲述Einstein和他的广义相对论
　　作为从Gottingen的故事到其他的故事的一个过渡
　　
　　选一句永远让我心驰神往的话
　　
　　关于这个宇宙最让人难以理解的地方就是她竟然是可以被理解的。
　　——Albert Einstein
　　
　　1． Einstein构思广义相对论的时候，尽管他的数学家朋友教了他很多Riemann几何，他的数学还是不尽如人意。后来，他去过一次Gottingen,给Hilbert等很多数学家做过几次报告，他走不久，Hilbert就算出来了那个著名的场方程，Hilbert的数学当然比Einstein好很多。不久，Einstein也得出来了，有人建议Hilbert考虑这个东西的署名权问题， Hilbert很坦诚的说：“Gottingen马路上的每一个孩子，都比Einstein更懂得四维几何，但是，尽管如此，发明相对论的仍然是Einstein而不是数学家。”
　　
　　广义相对论
　　
　　据说，Einstein的场方程的第一个球对称的解，也就是Schwarzschild解，是同名的这个人，在一战的战壕里给出的。Schwarzschild是Gottingen的天文学的教授。
　　
　　Edditnton是一个伟大的天文物理学家，下面这个故事是讲他如何吹牛的
　　
　　Albert Einstein的广义相对论发表没有多久，有记者去采访Eddington,说听说世界上只有三个人懂得这套高深的理论，不知这三个人都是谁？Eddington低头沉思，很久没有回答。那个记者忍不住又问了一遍，Eddington说：“我正在想谁是第三个人……”
　　
　　似乎每一个伟大的人物都以和Einstein交谈过感到无比的光荣。杨振宁提到他当初见Einstein的时候，过于激动，以至于事后根本不知道自己说过什么Einstein又说过什么。Lev Landau，苏联最伟大的那个物理学家，就说自己当年参加某会议的时候，有幸和Einstein说过几句话，而有某个认识Landau的人说Landau纯属幻想，当时此人和Landau一起，坐在那次开会的大厅的最后几排，连听都听不清，根本不可能谈话。可见Landau对Einstein的景仰程度。
　　
　　讲几个Einstein和数学家的事情
　　
　　Einstein描述广义相对论，用的数学就是弯曲空间上的几何学，意大利的数学家 Levi-Civita在这种几何学上做出了突出的贡献。所以，有人问Einstein他最喜欢意大利的什么,他回答是意大利的细条实心面和Levi-Civita。
　　
　　Einstein是Minkowski的学生，旷了无穷多的课，至于多年以后，Minkowski知道了Einstein的理论的时候，感叹道：“噢，Einstein,总是不来上课——我真的想不到他能有这样的作为。”
　　
　　一次，P.Halmos和妻子遇到了Einstein和他的助手，Einstein很想知道“她”是谁，助手就说是Halmos的妻子，然后Einstein又问Halmos是谁……Halmos最没有面子的一次。
　　
　　
　　A.Coble是上个世纪美国的院士，做代数几何，一度很有影响。据称，他有无穷多个博士论文的题目：当你证明了一个2维的情况的时候，他叫下一个博士生去证明3维的情况，然后叫下下个博士生去做4维的。后来有个叫Gerald Huff的博士，不但做了5维的情况，而且对一般的n也解决了。这就让Coble的未来的无穷个博士无所事事了。Coble很怒。
　　
　　讲完了Einstein,继续John von Neumann (冯.诺伊曼）应该是符合道理的，这个造计算机的数学家。
　　
　　--- 当我们每次用电脑Game的时候,就应该对Neumann示以最崇高的敬意。---
　　
　　Neumann的就业态度
　　
　　von Neumann移居美国的动机，很有特别的地方。他用了一种自己认为合理的方法，发现在德国将来的3年中，教授的职位的期望值是3，而候补的人数期望为40，这是一个不理想的就业前景，所以到美国去势在必行。这就是他的根据，此时并没有涉及到政治的形势。
　　
　　------
　　阿基米德比荷马更有想象力。
　　——伏尔泰
　　------
　　
　　继续冯.诺伊曼的表演
　　
　　von Neumann曾经碰到别人问他一个估计中国小学生都很熟的问题，就是两个人相向而行，中间有一只狗跑来跑去，问两个人相遇之后，狗走了多少的这种。应该先求出相遇的时间，再乘狗的速度。如果没有什么记错的话，小时候听说过苏步青先生在德国的一个什么公共汽车上，就有人问他这个问题，他老人家当然不会感到有什么困难了。
　　
　　von Neumann也是瞬间给出了答案，提问的人很失望，说你以前一定听说过这个诀窍吧，他指的是上面的这个做法。von Neumann说：“什么诀窍？我所做的就是把狗每次跑得都算出来，然后算出那个无穷的级数。”……
　　
　　Banach在1927年参加一个数学的聚会的时候，他伙同众多数学家，一起用伏特加灌Neumann，最终Neumann不胜酒力，去了厕所，估计是呕吐。但是Bananch回忆道，当他回来继续讨论数学的时候，丝毫没有打断他的思路。
　　
　　最后两个关于冯.诺伊曼的故事
　　
　　von Nuemann的年纪比Ulam要大一些，不过两个人是最好的朋友，经常在一起谈论女人。包括他们坐船旅行，除了数学之外，就是旁边的美女，每次Nuemann就会评论道：“她们并非完美的。”他们一次在一个咖啡馆里吃东西，一个女士优雅的走过，Neumann认出她来，并和她交谈了几句，他告诉Ulam这是他的一位老朋友，刚离婚。Ulam就问：“你干吗不娶她？”后来，他们两个结了婚。
　　
　　一次Princeton举行的物理演讲，演讲者拿出一个幻灯片，上面极为分散的排列着一些实验数据，并且他试图这些数据在一条曲线上。von Neumann大概很不感兴趣，低声抱怨道：“至少它们是在同一个平面上。”
　　数学有害健康，大家过节了还是不要看书的好。下面是历史上最天才的几个数学家在这个时间轴上存在的长度： Pascal 39岁；Ramanujan 31岁；Abel 27岁；Galois 21岁；Riemann 39岁。
　　身体重要的说。
　　
　　数学家是天生的，不是造就的。
　　——H.Poincare
　　
　　de Moivre 21岁的时候，已经靠教数学为生，并且深信自己完全精通了这门学问。一个偶然的机会，他在一个公爵家里做客，且好Newton送来了自己的《原理》，他信手翻了一下，惊奇的发现，数学竟然如此精深如此美丽的一门学问。这样，他买下了这本书，尽管为了教学需要四处奔波，他还要撕下书页，以便能够带在口袋里，空闲时进行研究。
　　
　　de Moivre（棣.莫佛）有个定理好像我们中学的课本里就有，说的是一个复数n次方的事情。
　　
　　来说一个古老一点的人物
　　
　　Pascal据说14岁的时候，就已经出席了法国高级数学家的聚会，18岁发明了一台计算机，是现在计算机的始祖。尽管如此，Pascal成年之后最终致力于神学，他认为上帝对他的安排之中不包含数学，所以完全的放弃了数学。35岁的时候，Pascal牙疼，不得不思考一点数学问题来打发时间，不知不觉间，竟然疼痛全无。于是，Pascal认为这是上天的安排，所以继续开始做数学家。Pascal这次复出的时间不到一周，但是已经发现旋轮线的最基本的一些性质。尔后，他继续研究神学。
　　
　　神学也是Newton最终的选择。 :-))
　　
　　Kolmogorov(柯尔莫戈洛夫)是苏联最伟大的数学家之一，在很多很多的领域做出了开创性的工作；
　　Cauchy(柯西）就不用介绍了，从中学开始我们就认识这个法国人了。
　　
　　今天我们就来说这两个姓柯的牛人
　　
　　Kolmogorov关于数学天赋的见解。当然，很大程度上我认为他想通过这段论述来吹嘘一下。柯牛人认为，一个人作为普通人的发展阶段终止的越早，这个人的数学天赋就越高。“我们最天才的数学家，在四五岁的时候，就终止了一半才能的发展了，那正是人成长中热衷于割断昆虫的腿和翅膀的时期。”Kolmogorov认为自己13岁才终止了普通人的发展，开始成长为数学家；而Aleksandrov是16岁。
　　
　　Lagrange曾经预见了Cauchy的天才，苦心的告诫Cauchy的父亲，一定不要让Cauchy在十七岁之前接触任何数学书籍。这个巨象当年某些人不让张无忌学武功（好像有点不恰当）。:-))
　　
　　说几个数学家作为教师的生涯吧，大部分出名的人物讲课都不是太出色，或者说偶尔会很失败。譬如说 Newton 当初就经常对着空空的讲堂，他讲东西第一不是太清楚，第二太难，所以Cambridge的学生没有人喜欢他的课。
　　
　　从一些大家不是太熟悉的人讲起。
　　
　　Mondelbrolt是靠着画分形出名的，其实他的叔叔，Mandelbrojt是个更为出色的数学家，曾经是Bourbaki最早的几个成员。他做学生的时候，大老远从波兰到法国读数学，去了之后精神上受到了严重的伤害，因为他选了Goursat的分析课，然而Goursat上课永远用一种语气，讲述二三十年前就有的旧东西，听了三周左右的课，Mandelbrojt感觉和自己梦想当中的课差的太远，竟然哭了出来。不过，几年后，Bernstein来到巴黎，安慰Mandelbrojt说Goursat二十多年前就这么讲课。不过Goursat对人是很热情的。
　　
　　遥想当年Mandelbrojt那求知的感情，是多么的纯真。那种东西，似乎已经在也不属于我们这个时代。
　　
　　还是有的数学家讲课不错的。
　　Lebesgue尽管开始研究的东西很奇怪，不过他的讲课确实出奇的得受欢迎。
　　Picard则是个古怪高傲的人，他的老丈人是Hermite,两个人都是对分析很感兴趣。
　　
　　和Lebesgue一起，是一件很开心的事。据说，Lebesgue的课，总是有无穷的人去听课的，大部分人因为Lebesgue讲课不但深刻，而且很有意思。一次，一个国外的学者来法国报告自己的工作，Lebesgue说你不用报告了，我替你报告吧。:-)
　　
　　Picard总给人一种高不可攀的感觉，令人不敢接近。每次Picard上课的时候，前面有一个戴有银链子的校役引路，他高傲的踱入教室，在椅子上放有一杯水，Picard先喝一口水，然后开始讲课，大约半个小时，他再喝一口水，一个小时以后，那个银链子校役就会来请他下课。
　　
　　Lindemann，也就是证明了π的超越性的人,据说是历史上讲课最烂的的几个人之一。此处收集他的故事两则，一个是说他讲课，一个回忆了一下他在巴黎求学的两件小事，还是蛮可爱的。
　　
　　传说中Lindemann讲课课大部分时间根本就听不清，听清的话都是不可理解的听不懂的话，而少数情况下，他讲的话又清楚又听的懂，那就是错话。
　　
　　Lindemann到巴黎学习的时候，听过Bertrand和Jordan的课，当时学数学的人太少，尽管Jordan在法国算是领袖级的数学家，听他的课的人只有3个，偶尔会达到4个，其中却中一人是因为教室里暖和。
　　
　　Lindemann还曾拜访过Hermite,让他难忘的一点事，那里有一把椅子，是当年Jacobi 坐过的。：-））
　　
　　优秀的数学家在定理或理论之间看到了类似
　　卓越的数学家则从类似中间看到了类似
　　——Banach
　　
　　毋庸置疑，Lefschetz和Wiener都是这种可以从相似之间看到相似的数学家不过他们的讲课技巧实在是不能让人恭维。
　　
　　Rota曾讲了一个Lefschetz的故事，关于他的课是如何难懂得，因为他经常语无伦次。这是几何课的开场白：“一个Riemann曲面是一定形式的Hausdroff空间。你们知道Haus droff空间是什么吧？它也是紧的，好了。我猜想它也是一个流形。你们当然知道流形是什么。现在让我给你们讲一个不那么平凡的定理--Riemann-Roch定理。”要知道第一节Riemann曲面的课如果这样进行的话，恐怕Riemann复生也未必可以听懂。：-）
　　
　　Wiener尽管是个天才，却是那种不善于讲课的那种，总是以为把真正深刻的数学讲出来一定要写一大堆积分符号。有一个关于他和中文的事情，Wiener天真的认为自己懂一种汉语，一次在中国餐馆，他终于有了施展的机会，但是服务员却根本不知道他讲的是汉语。最后，Wiener不得不评论：“他必须离开这里，他不会说北京话。”……
　　
　　下一次说一些法国数学家的事情。
　　
　　数学家犹如法国人：
　　无论你对他们说什么，他们把他翻译成自己的语言，
　　于是就成了全然不同的东西。
　　—— 歌德
　　
　　法国的数学家就可想而知了。:-))
　　从最天才的人谈起
　　
　　Galois一共参加了2次Polytechnique的考试，第一次，由于口试的时候不愿意做解释，并且显得无理，结果被据了。他当时大概十七八岁，年轻气盛，大部分东西的论证都是马马虎虎，一般懒的写清楚,并且拒绝采取考官给的建议。第二次参加Polytechnique的考试，他口试的时候，逻辑上的跳跃使考官Dinet感到困惑，后来Galois感觉很不好，一怒之下，把黑板擦掷向Dinet,并且直接命中。Galios的天才是不可否认的，不过person ality是少一点了，后者在Polytechnique考试中很重要。最后和Galois决斗的那个人，是当时法国最好的枪手，Galois的勇气令人钦佩。两个人决斗的时候，相距25步， Galois被击中了腹部。
　　
　　1856年的时候，Hermite患了严重的天花，并好之后，经过Cauchy大力怂恿，竟然皈依了罗马的天主教。就在这个期间，他和德国的Fuchs一直通信联系，于是，Klein说 Hermite“在气质上不是一个领袖人物”。当然，Klein如此的评论有些个人恩怨的成分，可以参见这个系列文章的(9).
　　
　　在一次国王接见Cauchy的时候，他有五次回答国王的问题是都这样说：“我预料陛下将问我这个问题，所以我准备好了答案。”然后，他从口袋里拿出笔记本，昭本宣读。
　　
　　法语是一种恐怖的语言，Birkhoff是上个世界初美国最著名的数学家之一，一个西方人学习法语，按照常理说应当有一定的优势，不过当他老人家去了法国的时候，还是遇到了麻烦。
　　
　　Hadamard曾在法国主持讨论班，有很多人慕名而来，Birkhoff就这样子来到了法国，不过他的法语实在太差。那几天，巴黎一直下雨，一天Birkhoff见到了Mandelbrojt问：“一周......几次？”
　　大概中间的词他不会发音。Mandelbrojt说：“两次。”
　　“什么，两次？”
　　“是呀，礼拜二和礼拜五。”
　　“怎么可能呢？”
　　“下午三点半开始，五点之前就结束了。”
　　“这个绝对不肯能！！！”这个时候Birkhoff已经快疯了。
　　后来Mandelbrojt才知道原来Birkhoff问的不是讨论班的时间，而是什么时候下雨。
　　
　　所有的数学家生活在两个不同的世界里。一个是由完美的理想形式构成的晶莹剔透的世界，一座冰宫。但他们还生活在普通世界里，事物因其发展或转瞬即逝，或模糊不清。数学家们穿梭于这两个世界，在透明的世界里，他们是成人，在现实的世界里，他们则成了婴儿。
　　——S.Cappel
　　
　　说3个可爱的法国学家爷爷当年的事情,一个是Hadamard，最出色的法国数学家之一，无论在几何，分析那个方面，都是经常那种用名字来修饰“定理”这个词的人；一个是 Lebesgue,实变函数论的创始之人，其对数学的贡献不言而明；还有一个叫做Montel,相对于前两个人不是那么出名，不过在复分析当中有一个极其重要的概念，叫做Montel正规族，就是用他的名字命名的。
　　
　　这三个人都是巴黎高等师范学校毕业的（不好意思，要么Hadamard就是从Ecloe Poly- technique毕业的），Hadamard是他们那一届的第二名，一生都对那个第一名不忿，尽管那个人作为数学家来说和他严格不是一个档次；Lebesgue和Montel是同一级的学生，分别是当年的第三和第二名，两个人一生都是很好的朋友，据说那个他们同一届的第一名仍然在数学方面和他们不能相提并论。
　　
　　先说Hadamard的诡异嗜好。
　　
　　他老人家是一个狂热的蕨类植物收集者，一次他带领自己的小妹妹到阿尔卑斯山去采集这些东西，把妹妹放在一个冰河旁边，采玩了之后就自己兴冲冲的回家了；他这种马虎一直改不掉，到了40年的时候，他成功的在忘了带护照的情况下，从法国动身去了美国；当然，蕨类植物也是他一生的最爱，老年的时候，他去莫斯科访问，Kolmogorov和Aleksandrov陪同他坐船，Hadamard忽然很兴奋得让他们靠岸，自己激动得站在船头，最后终于掉到了水里，原来他发现岸上有一种罕见的蕨类植物。
　　
　　再说Lebegue和Montel,他们后来工作也是在一起厮混，所以下面的事情经常发生。
　　
　　一次，Lebesgue打电话（那个时候有电话，大概很富有了）给Montel讨论一个事情，两个人各持己见，吵了一个小时（那个时候的电话怎么收费？）也没有结果；第二天早上，Lebesgue有给Montel打了一个电话，说我开始同意你的说法了，然而Montel说我也同意你的了，于是又开始争吵。
　　
　　-----------
　　穿过Plato学院的拱形门楼，首先映入眼帘的是：
　　“不懂几何者请勿入内。”
　　-----------
　　
　　昨天Science版聚，讲到了一个和倍立方有关的小故事，也就是如何用直尺圆规做一个正方体它的体积是给定的正方体的2倍。当然这个问题用一点域扩张的知识，就可以证明是做不到的，和三等份已知角一样的。最初，在雅典流行瘟疫，人们很恐慌，就去求助于神，神谕说要使得瘟疫消失的充要条件是把一个立方形神坛重新建为一个体积是原来2倍的。按照古希腊的规矩，就是要用尺轨作图。于是大家去问Plato ,Plato说这是神的旨意，用来警告大家要对几何学有着足够的敬意。
　　
　　回过头来说法国。
　　
　　法国的数学家大都对抽象的东西情有独钟。Lagrange写出了他著名的分析力学的书的时候，就骄傲的宣称书中“没有一个图”；A.Weil在教师资格考试时，理论力学交了白卷，他认为那根本不算数学。A.Weil就这样子，曾经Pierre Carier问他Gottingen的事情，提到量子力学的时候，Weil根本不知所云，尽管当时Hilbert,Bohn,Heisenberg都在做量子论。后来，Chevally和Weil在悼念Weyl的时候，根本不提Weyl的物理学的成就，然而大家公认Weyl最有名的两本书一本关于相对论，一本关于量子力学。
　　
　　------------
　　11岁的时候，我开始学习Euclid的书，并请我的哥哥当我的老师。
　　这是我生活中的一件大事，犹如初恋般的迷人。
　　——B.Russell
　　------------
　　
　　第39篇，写伟大的却不到40岁的Riemann。在100多年后的今天，他的思想还是能够让人们感到最强烈的震撼。在此表示深深的敬意。
　　
　　Riemann的父亲是个牧师，家里特别的穷，从小体弱多病，也打算做牧师。有一个人（据说是Rieamnn的中学校长）发现他在数学上比在神学上更有潜力，送给他一部Legendre的数论书。Legendre是一个伟大的法国数学家，他的书十分的晦涩难懂。六天之后，Riemann就找到那个人把这本859页的名著还了，说：“这本书的确十分的精彩，我已经看懂了。”这个时候Riemann只有14岁。
　　
　　Riemann19岁的时候去Gottingen读神学，平时也会听一些数学的课程。他比较喜欢泡在图书馆里。一次，他在那里找到了Cauchy的分析的著作，如获至宝，读完之后，便坦然的决定放弃神学，从此开始读数学了。
　　
　　-----------
　　天行健
　　君子以自强不息
　　-----------
　　
　　今天举两个牛人，Siegal(西格尔)是那种很聪明又很努力的，而Kodaira(小平邦彦)自己经常说自己天资不好，但是他从中学开始就是那种做事情一丝不苟全身心投入的人，他回忆自己第一次学习van de Wearden的《代数学》，几乎学不懂，然后就开始抄书，一直到抄懂为止，可见的Feilds奖的人的学习方法也不见的先进，唯手熟尔。
　　
　　Siegal曾经说过，他可以从早上9点起，研究数学，一直到深夜12点，不吃不喝，最后把一天的食物一并吃掉，弄得胃很不舒服。Siegal被Kodaira称为“非常勤奋”，被Kodaira称为勤奋，可见其勤奋成都是何等的可怕。
　　
　　Kodaira一天的生活（1949年4月19日）：
　　8:00起床，剃须，穿西服，外出早餐（玉米片，牛奶，咖啡）；
　　散步到研究所，大约9:30；
　　9:40--10:40 Siegal的关于3体问题的课；
　　11:15--12:00 Weyl的讨论班；到食堂吃午饭；坐车去Priceton，
　　1:20--2:20在自己的讨论班上讲论文；回家继续写论文；
　　5：30到街上的餐馆吃饭；回家继续工作到深夜。
　　
　　开始说说波兰的数学家，从Banach开始, 最最伟大的波兰数学家。
　　Banach在数学界的登场是一段美丽的传说// :"-))
　　
　　1916年的一个夏夜，Steinhaus在一个公园里散步，突然听到了一阵阵的谈话声，更确切的是有几个词让他感到十分的惊讶，当听到“Lebesgue积分”这个词的时候，他就毫不犹豫的走向了谈话者的长椅，原来是Banach和Nikodym在讨论数学。Steinhuas就这样子发现了Banach,并把他带到了学术界。他说：“Banach是我一生最美的发现。”
　　
　　波兰学派的人似乎喜欢在咖啡馆里讨论数学，Kuratowski和Steinhaus是有钱人，他们一般在高档的罗马咖啡馆里谈论数学；Banach,Ulam和Mazur穷一些，整天呆在一个苏格兰咖啡馆里，那里的老板挺不错，即使过了营业时间，也不会赶他们。这样子很多年轻的数学家都来到这里，每次有什么重大的发现，就纪录在一个大的笔记本来，并保存在店里，这就是著名的苏格兰手册。当然，老板对他们好的一个原因就是他们每次都可以消耗大量的啤酒，据说有一次聚会长达17小时，其间，Banach不停的饮酒，Ulam说Banach是难以超越的,英文的原文是difficult to overlast and to overdrink Banach。德国人在二战的时候，需要大量的寄生虫繁殖疫苗，于是就雇佣了很多波兰人，把装有寄生虫的盒子戴在他们的手腕上，一人体作为寄主。Banach曾经就拥有这么一个盒子，其报酬是不会像Saks一样被杀死。一半以上的波兰数学家死于战争。
　　
　　一个故事说M.Stone的父亲可爱的语言；另外讲了一个Harvard的数学教授，这个人到底做过什么出色的工作，我也不知道，只是其中提到了30年代的教学情况，特别好玩。
　　
　　1. M.Stone写了一本关于Hilbert空间的书，他的父亲谈到自己的儿子时，总是自豪的说：“我困惑又很高兴，我的儿子写了一本我完全不理解的书。”
　　
　　2. 1932年J.J.Gergen不的不在一门讲授Fourier级数课程时，不使用一直收敛的概念，原因是Havard大学的数学系一致的认为一致收敛这个概念对本科生来说太难了。
　　
　　----------------
　　我不知道世人怎样看我;可我自己认为，我好像只是一个在海边玩耍的孩子，不时的为拾到更光滑些的石子
　　或更美丽的些的贝壳而欢欣，而展现在我面前的是完全未被探明的真理之海。
　　——Issac Newton
　　----------------
　　
　　这段话不同于他说的那段“站在巨人的肩上”，因为“肩上”那句话是他出来吹捧一下Hooke(胡克),或者说讽刺一下，那个时代总是为着各种东西的发明权而喋喋不休。
　　
　　Newton的一生落落寡合，没有结婚，也没有知心的朋友，人们结交他都是因为他很高的地位和渊博的学识。一个同事回忆说他只见过Newton笑过一次，当时，有一个人问Newton说Euclid的几何原本如此的老朽，不知道有什么价值。对此，Newton放声大笑。:-))
　　
　　对很多人来说，牛顿的贝壳尽管光滑尽管美丽，确实不如一块肥皂有用。数学家做的事情的确是这个样子，一种孩子般的游戏，纯粹的追求快感。Newton之后的几百年，Cambribge另一个大名鼎鼎的数学家Hardy也说过这种话： “从实用的观点来判断，我的数学生涯的价值等于零。”
　　
　　既然扯到的Hardy就说说他的轶事吧。他这个人有着各种怪癖，譬如永远不会希望见到镜子之类的，每次到一个旅馆，总是用毛巾把各个地方的镜子都遮将起来。不说这些乱七八糟的，说一下子他用“数学”解决的恐船症。
　　
　　Hardy每次做船的时候，总是怕沉了。克服这个东西的一个方法是，每次不得不坐船航行的时候，他会给同事发个电报或者明信片什么的，说已经搞定了Riemann猜想回来之后会给出细节的。他的逻辑是，上帝不会允许他被淹死，否则这又将是第二个类似于Fermat大定理的事情。
　　
　　前天闲极无聊，去下载一个叫做百年大讲堂（凤凰中文台的节目)的东东看，其中是王诗宬老师的讲座，讲的是纽结。这个以前看过若干遍了，但是看完之后依然就有一种冲动。本来再已经写好Hero系列中有王老师的，不过不打算来post，现在还是忍不住。这两次就说两三个很小很小的事情，有历史上的人物，有王老师。平行的叙述。：-））
　　
　　比做学问更重要的是做人。Erdos的Wolf奖金由5万美元之多，他却只留下了720美元，其余的都捐给了以色列作为奖学金。他说：“我记得有人告诉我说720美元在我已经很多了。”Baire是个公认的大好人，由于数学上的贡献，得到了瑞士颁发的一份奖金，有1000法郎之多，结果最后拿到了1500法郎。Baire就问他的朋友Montel说：“竟然多了500法郎呀。我该怎么办，是应该给一位学生发奖学金，还是自己买一件外套？”Montel建议买外套。
　　
　　王老师90年代初，得到了一份3万元的奖金，他全部捐给了希望工程，90年代初3万块钱的概念大家是清楚的。
　　
　　再说一段王老师的评论，记得看过Atiyah的一个小册子，他评论道Thurston能够自如的看到高维的复杂图形，Thompson可以“看”到一个群。Thurston和Thompson都是得过Feilds奖的人。王老师给我们上课的时候，也做过这样的评论，说只要听懂了Thurston的一句话就可以写一篇论文，E.Witten就是一个神。呵呵..不过他说得更有意义的是紧接着的评论，说数学家有很多种，一种是像Thurston这个样子的，很聪明，所以做的工作很出色；另外一种是尽管天资不是很出众，但是自己能够耐得住寂寞，非常的刻苦，所以后来也是很出色的。
　　
　　今天再讲一个王老师的故事，也是他上课时候随口说的。他说的主持讨论班这个人就是那种工作特别刻苦，又有不错的机遇，最后做出了很大的成就。好像是Freedman吧，记不得了。
　　
　　Mandelbrojt一次在Levi-Civita家里做客，恰好E.Landau去玩。Landau在当时也算是成了名的前辈，于是Levi-Civita举行了一个小小的聚会。其间，一个老先生对Levi-Civita讲，最近有一个荷兰的年轻人Mondebroht做的工作很出色，Landau问到那是谁呀？ Mandelbrojt不得不跳出来解释说，那个人不是荷兰人，是波兰人；那个人也不叫Mondebroht，叫Mandelbrojt；那个人其实就是我……
　　
　　王老师也有类似的经历。当年在Berkeley的一个讨论班上，一个牛人主持，讲解一篇论文，王老师在期间提了一些很不错的想法。课下，那个牛人问阁下贵姓？ “姓王。” 牛人说，太巧了，我们今天讲的论文也是一个姓王的中国人写的。“那就是我……”
　　
　　
　　开始说一下mm数学家 ...... :-))
　　
　　她们做出的成就的的确确比不上男数学家的成就，但是我们依然能够发现她们的事迹中有很多的伟大，很多的美丽。
　　
　　从古希腊说起吧。那个时候，的确是一个很民主的时代，对于女性的歧视要远好于后来，譬如说很多伟大的数学家哲学家对女性参与数学的态度还是很好的，譬如说Pythagrass（毕达哥拉斯）学派当中就有女的信徒。Pythagoras本人就很鼓励女性学者，当年有个兄弟会之类的东西，里面就有28个女孩,其中有一个叫做西诺的，后来就被Pythagrass骗去做老婆了。这个女孩在当时是个比较有影响的数学家。Socrates(苏格拉底）和 Plato（柏拉图）也曾经邀请过女性去他们的学院讲学。
　　
　　从他们往后，女性在很多的行业中受到了歧视，在哲学数学自然科学这些领域更是如此了。
　　
　　有一个令人心痛的故事，讲的是Hypatia (西帕蒂娅) ，她处的时代就是Plato他们往后那么一点的时
　　候。Hypatia本身是个很优秀的数学家了（在那个时代），她的演讲很出名，而且解题也是高手，其父亲是亚历山大的一位数学教授。经常有一些数学家找他询问一些题目的做法，她也很少让大家失望。一个小故事说有人问她为什么不结婚，她回答说她已经和真理定了婚。不过Hypatia后来极为悲惨，有个叫做Cyril的什么教长之类的人，声称数学家哲学家这帮人为异端，对他们大加残害，手段令人发指。在一个封斋的日子里，Hypatia被从马车上拖到教堂，剥光衣服，身上的肉被一群狂暴的人用牡蛎的壳刮了下来。
　　
　　mm数学家之二
　　
　　话说时光飞逝，转眼间从古希腊来到了18世纪的意大利。尽管从物质生活到文化的各个方面，比起
　　希腊，已经大大的发展了，但是女性的地位相对来说还是一如既往的得不到重视。
　　
　　有一位被认为是当时欧洲最出色的数学家的女数学家，叫做Maria Agnesi(玛丽亚.阿涅西）像她
　　这样出色数学家，在欧洲还是没有研究机构愿意提供给她职位，尤其是法国这样的国家，更是对她
　　不屑一顾。
　　
　　她有一篇关于曲线的切线的文章尤为出名。但是意大利语中曲线一词叫做versiera，好像在拉丁文
　　还是什么文字当中是avversiera的缩写，后面这个词意思是魔王的妻子。于是Agnesi研究过的一段
　　曲线(versiera Agnesi)翻译成英文的时候，就被叫做Agnesi的女巫，后来，有一段时间，大家都这
　　么称呼女数学家。
　　
　　在关于女数学家的记载当中，很少有关于她们容貌的描述的，不过要说的是还是有ppmm做了数学家，上个世纪在偏微分方程方面，Sonja Kowalewski(柯瓦列夫斯卡娅.索菲娅）无疑是最优秀的数学家之一。她本人绝对是个一流的美女，据说当初Weiestrass也被她的美貌深深的吸引。
　　
　　mm数学家之三
　　
　　每每读到她为什么选择了数学，总让我心驰荡漾........
　　
　　在所有的欧洲国家中，法国对女性的歧视(学术上的)尤为严重。Sophie Germain(索菲 .热尔曼)就
　　出生在这个国家。Germain当初读过一本讲Archimedes的书，说当初他老人家专心的研究一堆沙子
　　组成的几何图形，以至于一个罗马士兵问他话他充耳不闻。那个士兵一怒之下把Archimedes杀死了。Germain认为，一个人可以如此的痴迷于一个东西以至于置生死于不顾，那么这个东西一定时是世界上最美的最迷人的。于是她选择了数学。
　　
　　开始Germain的父母强烈反对，没收了她的墨水蜡烛之类的东西，然而，Germain痴心不改，终于
　　感动了父母，一生父亲都支持她的数学工作。1794年，Polytechnique在巴黎建校，尽管这里盛产
　　数学家，但是却只接受男性，于是Germain化名为Le Blanc偷偷的混进去旁听，当然，当时确实有
　　一个人叫做Le Blanc，估计这个人比较喜欢旷课，反正他一直不到，Germain得以在那里好好的读
　　书，几个月之后，她的任课老师Lagrange发现了一个很牛的学生，Germain不得不说她其实是女儿
　　身。Lagrange毕竟不同于一般的人，他很高兴有这样的一位朋友，并乐于做Germain的导师。
　　
　　Germain不久对数论尤为倾心，可能受Lagrange的影响吧，他年轻的时候靠变分法出名，年长之后
　　在数论方面贡献卓越。Germain选择的题目是Fermat大定理，她把自己的结果寄给Gauss，令Gauss
　　特别的欣赏，她当年才刚刚20岁，而她做出的成果是当时最好的。当然，她还是怕Gauss对女性有
　　偏见，于是仍然选择了Le Blanc这个名字。后来，Napolean的军队攻入德国，Germain怕Gauss重蹈
　　Archimedes之覆辙，于是给自己的朋友，也就是当时通领三军的一位将军写信，这位将军果然对
　　Gauss很为关照。
　　
　　Germain后来又在物理上面做了很多东西，尤其是在弹性理论上面。由于她在数学物理上的突出贡献，她最终荣获了法国科学院的金质奖章，并成为第一位不是一某位成员的夫人出席科学院讲座的女性。在生命的最后几年，Gauss说服了Gottingen大学，授予Germain名誉博士学位。在那个时代，这是极大的荣誉。可惜在她的有生之年，未能亲自带上那令人骄傲的帽子。
　　
　　mm数学家之四
　　
　　这是欧说的最后一位mm数学家，也是最最伟大的一位，Emmy Noether(埃米.诺特).
　　
　　她对20世纪的数学的影响无以伦比，提到抽象代数就不得不提一下Noether.最最著名的一本抽象代数的书van de Wearden的<代数学>就是采取的Noether的讲义。E.Artin,van de Wearden等人都是她的学生。
　　
　　尽管这样子，Noether在Gottingen的同事Edmund Landau还是据决给她讲师的职位，并说“...当我们的士兵发现他们在一个女人脚下学习的时候，他们会怎么想?”不得不说 Landau令人不招人喜欢。最让人不能容忍的是有人问她Noethor是否是一个伟大的女数学家的时候，他说：“我可以作证她是一个伟大的数学家，但是对她是一个女人这点，我不能发誓."
　　
　　不过，伟大如Einstein和Hilbert的这样的人都对Noether推崇备至。Einstein曾经说Noether是“自妇
　　女开始受到高等教育以来最杰出的最富有创造性的数学天才”，Hilbert则支持Noether去争取一个讲师的职位，并反驳Landau说：“我不认为候选人的性别是反对她成为讲师的理由，评议会毕竟不是澡堂。”看来Hilbert当时有点怒了。
　　
　　----------
　　四年终究有些遗憾.
　　----- mashimaro
　　----------
　　
　　从Hadamard说起，原来讲过他是个和蔼的老头，数学好的不得了，人也是这个样子，上个世纪初还来过清华讲过课。
　　
　　每每谈及往事，Hadamard总是很惋惜的说道一辈子有两件事情特别的后悔。
　　
　　第一个在数学方面，他很早就找到了Jensen公式，由于没有发现很精辟的应用，一直就没有发表，结果Jensen抢先了一步。
　　第二个是物理方面，关于狭义相对论，他也是很早就有了这样的想法，只不过没有时间深入下去，后来Einstein就发表了。
　　
　　其实Hadamard最不能忘怀的事情，决不是上面两件，而是关于自己当初考试的。以至于年纪大的时候，仍然耿耿于怀，甚至到俄国和Kolmogorov都提这件事。就是Hadamard做学生的时候，参加数学的会考（相当于数学竞赛吧），得了第二名，第一名后来也是一个数学家，Hadamard对Kolmogorov说：“事实证明后来他做得没有我好，其实他一直没有我好。”
　　
　　当初Fermat证明不了东西时候，就写下了这句话
　　Cuius rei demonstrationem mirabilem sabe detex marginis exiguitas non caparet.
　　翻译成中文就是我有一个对这个命题的十分美妙的证明，这里的空白太小，写不下。
　　
　　后来，Hilbert也会了类似的技巧，有人问Hilbert为什么不去证明Fermat大定理，他说为什么要杀死
　　一只下金蛋的母鹅，因为这样的一个对整个数学发展有着如此深远推动的问题太少了。不过个人认为他没有能力杀死这只鹅。
　　
　　还有另外一个和金蛋有关的事情，不过和数学家没有关系。当初欧洲的反法联军快攻到巴黎的时候，Ecole Polytechnique的学生要求上战场，保卫国家，拿破仑说：“这怎么可能呢，我不能为了打赢一场战争，杀死一只会下金蛋的母鸡吧。”
　　
　　H.Whitney是很著名的美国数学家，做了很多很重要的工作，譬如说向量丛的Stiefel- Whitney类是
　　用他的名字命名的，还有一个著名的定理，说每一个n维的流形都浸入一个 2n-1维的欧氏空间嵌入一个2n维的欧氏空间，也是他的结果。欧们的图书馆里还有他的论文集的。
　　
　　很难想象,他本人一开始竟然不是学理科的.
　　
　　Whitney的本科时候读的却不是数学，话说他学业完成，到欧洲大陆去玩，大概是到了Gottingen还是什么地方了，反正是个很有名的地方，当时有一个很牛的物理学家（不是海森堡就是薛定谔）正在做一个关于量子力学的讲座.
　　
　　等得讲座结束之后，Whitney什也么没听懂，感觉及其不爽，于是找到了那个主讲的人，说，先生，我觉得你做的讲座很不成功.
　　主讲的教授很纳闷，就问他说为什么.
　　Whitney回答说，我可是Yale大学的优等的毕业生，你讲的东西我竟然听不懂，这难道不是你讲的有问题么。
　　
　　那个教授继续问,你是读什么专业的。
　　
　　Whitney回答说,我是读小提琴的.....
　　
　　教授大大的分特了，说这个我也没有办法，你要想懂的这些东西的话你应该学一点基础的课，于是告诉他这个世界上还有数学分析和线性代数等等...
　　
　　Whitney回美国之后就开始发奋学习数学，据说半年之后就可以参加很高级的讨论班了.
　　
　　当然他是非常刻苦的, 数学的历史上还是有很多这种大器晚成的例子的.
　　
　　-----------
　　上帝之所以存在
　　是因为数学是相容的
　　而魔鬼之所以存在
　　是因为我们不能证明数学是相容的。
　　——Andre Weil
　　-----------
　　
　　一个很有意思的事情，很多很多的数学家和物理学家都特别的喜欢音乐，一个很出名的例子就是爱因斯坦。数学家当中也是这个样子，大家在做完了数学之后，也会醉心于此。譬如说E.Artin,一个上个世纪影响最大的代数学家之一，据说钢琴的弹奏水平极高，尤其是特别的严格，好像他做的代数一样；譬如Courant，和Artin比起来路子要野蛮一些，水平也要低些，不过热情毫不逊色，还经常邀请Artin到家里演奏一番；再譬如说J.Nash,这个人大家比较熟悉，刚刚演的A Beautiful Mind说得就是他，他原来就喜欢绕着Princeton的Fine Hall游荡，并且嘴里吹着口哨，后来一个得了Feilds奖也得了Wolf讲的人数学家J.Milnor还说，他第一次听巴赫的音乐就是通过当时Nash的口哨声。
　　
　　更有甚者，譬如Dieudonne,这个法国Bourbaki的人，不但喜欢弹琴，更是能记住很多很多的乐谱，据说上千页的乐谱他也能背诵。曾经一次，Dieudonne和P.Cartier去音乐会，他指着手里的节目单说：“乐队的演奏漏了一个字符.……”
　　
　　再譬如说，Fox,一个美国的拓扑学家，在60年代的时候，提到这个名字，就相当于提到了低维拓扑这个方向，他本人的小提琴的演奏水平也相当专业。这个人比较喜欢故弄玄虚，据说，在一次音乐会上，Kodaira和他一起，不料这次的演奏时不时的停顿，而且有声音的时间要少于没有声音的。Kodaira感到特别不好听，Fox叹息道：“这是受了禅影响之后的音乐，我正在试图从无声之中听出有声。”
　　
　　
　　上一次说到了很多数学家都喜欢音乐。不过我的看法是似乎比较“古老”一点数学家的业余爱好要少一些，当然有可能是关于他们的记载要少一些，不过我觉得他们更能够集中精力，全身心的投入。从阿基米德，牛顿到高斯，黎曼，似乎出了研究之外。很少关心别的事情。
　　
　　譬如说Gauss(高斯)。听说过一件极其变态的事情，但是从另一个侧面我们也可以知道他不仅仅是天分出众，更重要的是努力。Gauss中年的时候妻子就死去了，那个时候，Gauss就很有名望，家里有保姆。妻子病的一塌糊涂，不过他还是专心自己的研究。这个当然不是一个值得称道的品质。就是妻子的弥留之际，他还是没有去她的身旁，保姆实在看不下去，就去Gauss做研究的地方去找他说让他赶快过去，Gauss随口答应了，但是依然做自己的东西。保姆又来了一次，痛斥了他一番，岂知Gauss告诉她说：“我马上就过去，你让她再等一会……”
　　
　　在譬如说J.Nash, 大家只是知道他的天才，却很少提到他的努力。钟开莱(Kai Lai Chung)在Princeton的时候，遇到了这么一件事情。说一下，这个姓钟的人是一个很重要的华人数学家，在概率方面很有作为。他去一个很有名的休息厅，适时恰是秋季的清晨，休息厅里空空荡荡，寂静异常，就像教堂的感觉一样。大厅中间的巨大的桌子上面，乱七八糟，全都是草稿纸，一个人躺在上面，正愣愣的思考。这正是Nash，很显然这又是一个不眠之夜，他一直在考虑数学.
　　
　　说几个和监狱有关系的事情，做数学这个东西的确不同于很多学科，只要有一个场所可以供以静坐，有纸笔可以演算，这个世界的一切都无所谓。
　　
　　最最著名的故事就是关于Leray的事情，他是法国Bourbaki学派的创始人之一。最初的时候，他做的是分析，在流体力学和力学方面卓有贡献。后来二战爆发，Leray作为法国的军官参战，40年的时候，被德国人抓到了集中营里。德国人在战争方面对于科技的重视使得他们对每一个数学家和物理学家都是很关注的，而Leray做的是分析，很有可能被德国人关起来去做各种各样的用来杀人的弹。为了避免这件事情的发生，他就以代数学家自居，在狱中的时候依然努力的做研究，出狱的时候，发表他的那套对后世影响至深的层论（Sheaf Theory）。
　　
　　还有一个关于S.Lie的传说，这个人就是李群的那个Lie.S.Lie当年普法战争的时候呆在法国，由于普鲁士口音太重，被法国当局投入监狱，后来法国战败，大概恼羞成怒，准备杀掉这帮人，幸亏Darboux想方设法把Lie从那里救了出来。一个传说时，Darboux到达牢房的时候，发现他这位朋友竟然静静的坐着研究数学，而他在研究的东西正是著名Lie群。
　　
　　--------------------
　　弄清π是无理数这件事可能是根本没有实际用处的
　　但是如果我们能弄清楚
　　那么肯定就不能容忍不去设法把它弄清楚
　　——E.C.Titchmarsh
　　--------------------
　　
　　昨天提到了2个在监狱里做出了大手笔的数学家，还有一个和监狱有关的趣事，这个发生在Gottingen,主角是E.Landau,这个人在前面提到了多次，解析数论大家，巨富无比，人高傲自大，也蛮可爱的，除了当初对我们尊敬的Noether姐姐不恭之外。
　　
　　Landau讲过Fourier级数的课，其中会涉及到一个叫做Gibbs现象的东西，当他讲到这里的时候，振振有词的评论道：“这个现象是Jail的英国数学家Jibbs发现的。”
　　
　　Landau是典型的德国人，从这句话我们可以看到他的英文水平。因为这个时候，不得不有人跳出来指出他的错误：“第一他是个美国数学家；第二他叫Gibbs不是Jibbs；第三，也是最为重要的一点时，他更不在Jail（监狱）里面，而在Yale大学。”:-))
　　
　　顺便说说这个"Jibbs"碰到的事情，Yale曾经连续7次拒绝向著名的物理学家Gibbs发薪水，理由是认为他的研究没有意义。
　　
　　
　　中国有句古话说名师出高徒，说的是你如果和高手一起切磋，整日耳濡目染，会不知不觉学到很多很多东西。大多数数学家的老师都是很牛的数学家的，可能Gauss和Newton这样的人除外，他们不需要老师的。
　　
　　有一个故事说有一个人试图画出Lefschetz的数学后代家族树，几个月后，他就不得不放弃，因为根本找不到一张足够大的纸，这是一个指数增长的典型例子。越是这种大数学家，他的学生一般来说越多，受到他影响的人也就越多。
　　
　　再譬如说在Berkeley的一次逻辑学的会议上，Tarski请Sierpinski的学生举一下手，大部分人都举了手，然后Tarski请Sierpinski的学生和学生的学生举手，所有人都举了手。这两个人都是波兰的最最著名的数学家。
　　
　　最后我列举一下一些数学家的师承，这个不完全，其实是很不完全，希望大家补充的说：
　　
　　Dirichlet是Riemann的老师
　　Wierestrass是Cantor, Killing 和 Frobenius的老师
　　Noether 是van de Wearden， Alexandroff的老师。
　　Hardy是Wiener的高等数学的老师,
　　Hermite是Dini的老师
　　Hadamard是Frechet的老师
　　Kronecker是Kummer的老师
　　Sylow是S.Lie的老师
　　Hodge是Atiyah的老师
　　Gauss的小学老师是Lobachevsky的大学老师
　　Hilbert是无穷多个人的老师
　　Kummer的妻子是Dirichlet的表妹。
　　Laurent Schwartz是Paul Levy的女婿
　　
　　
　　
　　据中国的古话说职业一共有365种，反正是很多了，应该说作为数学家，从收入上来说是相对比较少的，这个相对的意思是从付出的努力到最后真正得到的钱的比值的倒数。
　　
　　这里给一个1959--1960年度 Chicago大学数学系教授的工资情况，这里的每一个数学家都是大名鼎鼎的：
　　
　　Stone 20000 $
　　Albert 16000 $
　　S.S.Chern 16000 $
　　Maclane 16000 $
　　Zygmund 16000 $
　　Kaplansky 13000 $
　　P.R.Halmos 13000 $
　　
　　其实好像也不少了，那个时候是50年代末，有这么多钱肯定衣食无忧了，这也是为什么美国的数学家能够专心研究吧。
　　
　　从现在来看，好像学数学收入更少了，很多人出国读数学没几年就转行了，毕竟计算机经济之类的专业转化为生产力的速度更快。
　　
　　说到了转行的事情，想到了一个“内部周转”的事情，Spencer在离开英国去Princeton 的时候，
　　Littlewood去火车站送他，叮嘱：“不要改行。”于是，Spencer研究了10年的Bieberbach的系数
　　问题，后来终于受不了了，改做复流形，没有多少功夫就和Kodaira 一起发表了他们著名的工作。
　　
　　
　　说一说数学家之间的恩怨，由于门派喜好乃至政治上的分别，他们之间也往往有些小小的过节。
　　
　　法国曾经有一个很著名的Dreyfus事件，这是对法国的政局甚至日常生活影响很深的一个政治的风波（至于具体是什么，我也不知道，不过上面的信息对理解后面数学家们的行为已经足够了）。
　　
　　Hadamard个人算是一个Dreyfus派的人，不过他个人当然是对政治事件很淡的那种人了。适值那年的元旦，按照巴黎高等师范学校的传统，年轻的老师要给年长的老师拜年。 Hadamard于是跑到Hermite那里去拜谒一下子，Hermite本身是个反Dreyfus的人，看到 Hadamard来拜年，第一句话就说：“你是个叛徒！”Hadamard很难理解这句话：“为什么？”Hermite本身做分析，而且个人固执的看不起几何等分支，那时候Hadamard有一项关于负曲率曲面的文章很是著名，Hermite就对Hadamard说：“你为几何而背叛了分析。”
　　
　　Picard也曾为了这个政治的原因对Hadamard说：“由于你是数学家，我很尊重你。”言下之意，已经
　　很明显了。不过Picard这个人一向目中无人，无论对谁都是贬多褒少，一个有意思的事情说，Picard在法国科学院收到了一份Bourbaki的报告，看到了Nicolas Bourbaki的名字，说：“呃，这些外国人。”
　　
　　继续说数学家们之间的过节。整体而言，做学问的人总是让人尊敬，很少有令人讨厌的。要说几个人，他们的学问的确是一流的，但是在同行里的口碑却不是很好。
　　
　　第一个要说的人是Koebe,此人作为数学家还是很出色的但是从做人的方面来说，极为自负（其实对于数学家而言，这一点很可爱）而令人讨厌，偶尔还剽窃年轻人的想法。
　　
　　Courant（柯朗）当初就很受他的排挤。一次在Gottingen, Courant要报告一个题目，当时Koebe恰好也要报告，但是，Courant是年轻人，按照不成文的规矩，他是初学者，而且刚刚完成了博士论文，有特权先报告。当Klein问大家谁先报告的时候，Koebe迫不及待的说：“我先讲。”
　　
　　后来Courant的朋友很愤怒，在Koebe的课上，把一个藏有警报器的便壶藏在讲台下面， Koebe最终找出了这个发声的东西，引起哄堂大笑。不久，他的朋友在当地的报纸上公开了这个恶作剧。
　　
　　数学史上还有两个大师级的人物，同样的是学术很好，但是名声不济，和很多人有这样那样的误会和矛盾。
　　
　　第一个是Kronceker,大家用的很多的Kronecker符号就是用的他的名字。此人身体瘦小无比只有5尺高，当初经商和务农很牛，赚了一大笔钱，30岁之后致力于数学。他在德国算是很权威的人，但是特别烦的是，很专断，根本不相信无理数的存在。当初Linderman和他讨论π的问题的时候，他竟然说这个东西根本不存在; Cantor后来疯了，很大程度上是因为Kronecker的废话太多；据说Weiestrass都差点被他弄哭了，就是因为他对无理数抱有一种病态的看法。
　　
　　第二个人就是Brouwer,直觉学派的领头人，感觉上特别想当年的Kronecker，对于和自己不用的意见不能容忍。他称Hilbert等人为敌人，认为无穷这个东西是不存在的，不仅如此，凡是有人不同意的话，他总是想方设法刁难。他原来是某一著名杂志的主编，别人寄来的文章通常都是高置于案头，没有一年半年他决不会给人家发表。一次，他和van de Wearden的一起在朋友家里做客，后者讲到了Hilbert和Courant，并且以朋友相称。这时候，Brouwer竟然一怒之下，拂袖而去。
　　
　　
　　三个做作业的故事,他们的作业很难得说
　　
　　第一个是被大家称为线性规划之父的Dantzig(丹齐克)，据说，一次上课，Dantzig迟到了，仰头看去，黑板上留了几个题目，他就抄了一下，回家后埋头苦做。几个星期之后，疲惫的去找老师说，这件事情真的对不起，作业好像太难了，我所以现在才交，言下很是惭愧。几天之后，他的老师就把他召了过去，兴奋的告诉他说他太兴奋了。Dantzig很ft, 后来才知道原来黑板上的题目根本就不是什么家庭作业，而是老师说的本领域的未解决的问题，他给出的那个解法也就是单纯形法。据说，这个方法是上个世纪前十位的算法。
　　
　　第二个和上面的类似，Milnor（米尔诺，得过Feilds奖和Wolf奖，特别有影响的一个数学家，现在还
　　健在，但是听说因为年纪大了，没有人给他研究基金，让这个老人很痛苦）在Princeton大一的时候，上课得知Borsuk的一个和全曲率有关的东西，误以为是家庭作业，几天之后搞定了，后来就发表在年鉴上面。
　　
　　第三个讲的是Arnold, 先说一下背景，有一个很著名的问题叫做“三体问题”，粗略的说就是研究一下像太阳月亮地球这样的三个行星在万有引力的作用下，最终会不会相撞。伟大如Poincare之类的人，都只是部分解决了这个问题。再介绍一下Arnold的老师Kolmogorov, 一个苏联的大师，可以说是活在20世纪的前三位的数学家（如果可以排名的话），过几次说说他的故事。Kolmogorov对个题有了兴趣之后，着实花了些功夫，后来他觉得离着解决差不多的时候，干脆就把这个问题留成了一道课外作业，Arnold他们就奉命去写作业，若干时日之后，终于成功的解答了这个东西，当然他的贡献是特别大的，很多关键的想法都是自己创的，所以最后这个问题的解答所形成的定理叫做”KAM”，KA就是他们师徒俩人，M则是一个美国数学家Moser,也曾对这个问题做了很多的工作。
　　
　　提一个波兰的数学家，学过Fourier分析人应该对他很熟悉，他就是Fejer。关于他的数学水平可以用Poincare的评论来证实，Fejer关于Fourier级数的Cesaro和的工作是大四做的，1905年的时候，
　　H.Poincare到匈牙利去领取Bolyai奖，很多政界的人都去接见，Poincare见面就问：“Fejer在哪里？”
　　众人面面相觑：“Fejer是谁？”Poincare说：“Fejer是匈牙利最伟大的数学家，也是世界上最伟大
　　的数学家之一。”
　　
　　其实政界的人去接见Poincare并不是因为他是那种最最伟大的数学家，而是因为Poincare的的哥哥原来是法国的总理什么的，一般来说，政界的人对于谁是数学家并不关心，要不也就不至于不知道
　　Fejer了。
　　
　　据说，Fejer比较喜欢到处乱说话，有两件事情来证明。Fejer和Riesz的关系很好，但是他比Riesz晚生了两个星期，于是，就到处声称他其实比Riesz要大，因为Riesz早产了；Fejer和Kerekjarto不和，后者是一个拓扑学家，Fejer说Kerekjarto说的话和真理只不过是拓扑等价。
　　
　　Kolmogorov
　　
　　这是苏联最伟大的数学家之一，也是20世纪最伟大的数学家之一，在实分析，泛函分析，概率论，
　　动力系统等很多领域都有着开创性的贡献，而且培养出了一大批优秀的数学家。特别的用两次的时间来介绍他，因为Kolmogorov不仅作为数学家很传奇，更是有着丰富多彩经历。
　　
　　Kolmogorov一开始并不是数学系的，据说他17岁左右的时候写了一片和牛顿力学有关的文章，于
　　是到了Moscow State University去读书。入学的时候，Kolmogorov对历史颇为倾心，一次，他写了一片很出色的历史学的文章，他的老师看罢，告诉他说在历史学里，要想证实自己的观点需要几个甚至几十个正确证明才行，Kolmogorov就问什么地方需要一个证明就行了，他的老师说是数学，于是Kolmogorov开始了他数学的一生。
　　
　　二十年代的莫斯科大学，一个学生被要求在十四个不同的数学分支参加十四门考试；但是考试可以用相应领域的一项独立研究代替。所以，Kolmogorov从来没有参加一门考试，他写了十四个不同方向的有新意的文章。Kolmogorov后来说，竟然有一篇文章是错的，不过那时考试已经通过了。
　　
　　不说他老人家在数学上的成就了，因为实在太多，譬如说上同调环这个东西他也是独立发现的。
　　专心的说一下他的轶事。
　　
　　Kolmogorov总是以感激的口气提到斯大林：“首先，他在战争年代为每一位院士提供了一床毛毯；
　　第二，原谅了我在科学院的那次打架。”Kolmogorov一次在选举会上打了Luzin一个耳光，他说：
　　“（打架）那是我们常用的方式。”Luzin在实变函数方面有着很重要的贡献，但是以打架而论，远非Kolmogorov的对手，因为Kolmogorov经常自豪的回忆他在Yaroslovl车站和民兵打架的经历。
　　
　　一个人如果打架很牛的话，经验告诉我们他必然身体强壮，而Kolmogorov的确很擅长运动，并
　　经常以此自诩。譬如说，他经常提到一件事情，并且深以为撼，三十年代的一个冬天，Kolmogorov身穿游泳裤雪橇，在得意的飞速下滑，碰到两个戴相机的年轻人请他停下来，他原以为他们仰慕他的滑雪技术会为他拍照，结果他们请他为他们拍照。再譬如说，39年的时候，他突然决定在冰水中游泳以表达对自己健康体魄的高度信任，结果以住院告终，医生一致认为他差点死掉；但是，70岁的时候，突然决定到莫斯科河里游泳，仍然是冰水，这一次却没有事情。
　　
　　--------------------
　　有一条小路，穿过田野，通向新南盖特，我经常独自一人到那里去看落日，并想到自杀。然而，
　　我终于不曾自杀，因为我想更多的了解数学。
　　——B.Russell
　　--------------------
　　
　　就用下面的一篇作为这个系列的结束吧，R.Thom是法国人，35岁得的Fields奖。
　　
　　在一次采访当中，作为数学家的Thom同两位古人类学家讨论问题。谈到远古的人们为什么要保存火种时，一个人类学家说，因为保存火种可以取暖御寒；另外一个人类学家说，因为保存火种可以烧出鲜美的肉食。而Thom说，因为夜幕来临之际，火光摇曳妩媚，灿烂多姿，是最美最美的。
　　
　　美丽是我们得数学家英雄们永恒的追求。

数学家们的逸闻趣事

2008-01-07T13:54:00.000-08:00

20 Super Brain Foods

2008-01-07T12:40:00.001-08:00

Great article on foods that enhance neuron firing and cross-linking in the brain. The foods mentioned in the article help you increase memory, concentrate, speed up reaction times, and even control stress.

read more | digg story

Physicists test Einstein theory in Stanford's 'mystery pit'

2008-01-07T05:59:00.001-08:00

Located in the basement of the university's Varian Physics Building, the 25-foot pit is where the team is currently testing Einstein's principle of equivalence. The pit's history is a mystery, but according to lore it was built during the 1960s for space gravity research.

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Blonde Map of Europe

2008-01-07T05:58:00.001-08:00

Interesting map of Europe, colorized by the percentage of blondes of the nation (darkest areas mean 1 - 19% percent of people are blonde). Conclusion: like blonde girls? Go North.

read more | digg story

Helene Grimaud concerto

2008-01-06T03:34:00.001-08:00

Helene Grimaud

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Scientists find missing evolutionary link using tiny fungus crystal

2008-01-06T02:43:00.000-08:00

The crystal structure of a
molecule from a primitive fungus has served as a time machine to show researchers more about the evolution of life from the simple to the complex.

By studying the three-dimensional version of the fungus protein bound to an RNA molecule, scientists from Purdue University and the University of Texas at Austin have been able to visualize how life progressed from an early self-replicating molecule that also performed chemical reactions to one in which proteins assumed some of the work.

"Now we can see how RNA progressed to share functions with proteins," said Alan Lambowitz, director of the University of Texas Institute for Cellular and Molecular Biology. "This was a critical missing step."

Results of the study were published in Thursday's (Jan. 3) issue of the journal Nature.

"It's thought that RNA, or a molecule like it, may have been among the first molecules of life, both carrying genetic code that can be transmitted from generation to generation and folding into structures so these molecules could work inside cells," said Purdue structural biologist Barbara Golden. "At some point, RNA evolved and became capable of making proteins. At that point, proteins started taking over roles that RNA played previously - acting as catalysts and building structures in cells."

Crystal image
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caption below

In order to show this and learn more about the evolution from RNA to more complex life forms, Lambowitz and Paul Paukstelis, lead author and a research scientist at the Texas institute, needed to be able to see how the fungus' protein worked. That's where Golden's team joined the effort and crystallized the molecule at Purdue's macromolecular crystallization facility.

"Obviously, we can't see the process of moving from RNA to RNA and proteins and then to DNA, without a time machine," Golden said. "But by using this fungus protein, we can see this process occurring in modern life."

Looking at the crystal, the scientists saw two things, Golden said. One was that this protein uses two completely different molecular surfaces to perform its two roles. The second is that the protein seems to perform the same job that RNA performed in other simple organisms.

"The crystal structure provides a snapshot of how, during evolution, protein molecules came to assist RNA molecules in their biological functions and ultimately assumed roles previously played by RNA," Golden said.

Before the crystallization, Lambowitz, Paukstelis and their research team at The University of Texas at Austin were involved in a long-term project to study the function of the basic cellular workhorse protein and other evolutionary fossils from the fungus. In earlier work, the scientists studied a different protein that showed how biochemical processes could progress from a world with RNA and protein to DNA.

The protein, as found in the fungus, had adapted to take over some of the RNA molecule's chemical reaction jobs inside cells. The protein stabilizes the RNA molecule - called an intron - so that the RNA can cut out non-functional genetic material and splice together the ends of a functional gene, Paukstelis said.

"The RNA molecule in our study is capable of performing a specific chemical reaction on itself, but it requires a protein for this reaction to take place efficiently," he said.

This basic scientific information eventually could lead to clinical applications.

"This work has potential applications in the development of antifungal drugs to battle potentially deadly pathogens; that's one of the next steps," Lambowitz said. "Another is to produce more detailed structures so that we can understand the ancient chemical reactions."

Golden and Lambowitz are senior authors of the report. Golden is a member of the Markey Center for Structural Biology and Purdue Cancer Center. The Markey Center will be housed in the Hockmeyer Hall of Structural Biology when it's completed on the West Lafayette campus.
Other researchers involved in this study along with Paukstelis were Jui-Hui Chen, a Purdue biochemistry doctoral student, and Elaine Chase, a Purdue biochemistry research technician.

Scientists find missing evolutionary link

2008-01-06T02:41:00.001-08:00

The crystal structure of a molecule from a primitive fungus has served as a time machine to show researchers more about the evolution of life from the simple to the complex.

read more | digg story

Global Warming Myths Explained

2008-01-06T02:38:00.001-08:00

Have you ever been in a situation where you're talking with friends and the conversation turns to global warming? It's hard to be an expert. Sometimes it's hard to even show the slightest bit of concern without being met with with skepticism. Compiled here are some of the most commonly heard myths explained.

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Flunked: 14 Signs of a Deficient Intellect

2008-01-06T02:37:00.001-08:00

God help us.

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So....WTF are you?

2008-01-06T01:47:00.001-08:00

So....WTF are you?, originally uploaded by eric.genn.

Lama Slug? So funny

Flickr

2008-01-06T01:46:00.001-08:00

This is a test post from , a fancy photo sharing thing.

The New Christian Science Textbook [PIC]

2008-01-06T01:43:00.001-08:00

A fun and scholarly approach to learning! :D

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Linux Commands Line

2008-01-06T01:34:00.001-08:00

The most complete and updated list of commands on linux - over 350 commands divided into argoments!

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Nuclear Explosion On The Weather Report

2008-01-05T14:00:00.001-08:00

A practical joke played by a group of "artists" in the Czech Republic creates panic by showing a nuclear explosion on a television weather report.

read more | digg story

10 Tips for Editing a Podcast in GarageBand

2008-01-05T13:57:00.001-08:00

Learn how to organize your podcast sessions, simplify your editing and improve your audio mixes. The same concepts apply for editing music, voice-overs or audio for multimedia productions.

read more | digg story

EAC的认识误区

2006-12-09T01:11:00.000-08:00

EAC的认识误区_电脑狂

EAC的认识误区

一、EAC是无损抓轨
目前没有一种抓轨软件能对音频CD进行无损抓轨，EAC也不例外。EAC的工作原理是对指定曲目进行多次抓取进行校验以保证最小的误码率。但并不能说绝对是无误码。个人实验证明，当安全抓轨质量低于99.5%，也会产生误码。

二、EAC安全模式抓轨音色好
实验证明，EAC非安全模式，包括Nero、CDEX等专业软件绝大情况下抓轨不会产生误码，只有在碟片物理质量恶劣的情况下，如有严重痕划和污损，抓轨才会产生误码，几率接近于EAC的安全模式（原因在“对EAC批判”中说明），而且这类专业刻录软件的误码率都是符合光碟红皮书规定的万份之一左右，那这万份之一的误码率是一个什么概念呢？也就是一首四、五分钟的曲子出错的部分总共为百分之几秒。那误码会不会影响音色呢？如果问大家，EAC抓轨不设偏移会不会影响音色，我想所有对音频知识了解的都会答“不会”，因为大家都知道，不设偏移只会导致曲子开头或末尾最多几十分之一秒丢失，对音色没影响。但殊不知，用不用安全模式比起设不设偏移对音色更不会有影响，因为如上所述，受误码影响的合计最多只是百分之几秒的内容，而且这部分内容又不会象不设偏移那样完全丢失的（“完全丢失”在另一个意义上就是这部分音色的“全部劣化”），那为什么既然我们认为偏移对音色没影响却反觉得不用安全模式会影响音色呢？这完全是认识上的误区。

三、所有碟片都推荐用EAC的安全模式抓轨
上面已阐明，EAC的真正用处其实不是保证音色不劣化，那EAC的真正功效是什么呢？其实是保证抓轨不会因碟面过份划伤或腐蚀老化而产生暴音，但是，我们也要看到，EAC只能改变极少极少的暴音，因为当一张CD出现暴时的时候，其划伤程度可以看作坏块，已不是单单一个C1C2校验就能恢复的了，多次抓轨几乎没任何作用。因为另一方面，暴音与音色不同，暴音不能简单等同于音质的计量，暴音出现的次数是很重要的，就算是出现一次，我们都是不能接受的，同样EAC的二次抓轨如果“万幸”能减少一次暴音产生的机会，也是意义重大的。但相对于EAC对光驱伤害的程度，我们不推荐滥用EAC安全模式抓轨。而且抓轨时产生暴音的机会少于用CD机播放产生的机会，因为CD机在播放CD时虽然与抓轨一样是一次性读取的，但前者的纠错态度比后者弱得多，因为前者是定线速读取的，为的是保证在播放的连贯性，所以对可能出错的部位不会停下来认真纠错后再读，而是容错优先地一笔带过，这也就会增大了关键部分无法正确读取而导致暴音产生的机会，但后者则可以减速和延时读取以增大纠错力度，所以对什么碟抓轨时会产生暴音，什么碟不会，我们在脑海里就会有一个大致的认知，什么时候应该用安全模式，什么时候不必，也就会有一个清楚的轮廊了。

四、EAC的安全模式虽非有必要，但为了安全起见，还是用吧。
大家不知有没留意EAC官方帮助还有一句话，就是“对于破损严重的CD的暴发模式可能会得到更好抓轨效果””（见附图），这不是与上面所述出现了一个矛盾吗？“物理质量好的碟无需用EAC，物理质量差的碟又不能用，那EAC的生存空间在哪？”。的确是一个很大的疑问，但这矛盾也是EAC作者自己给自己制造出来的。这也难怪，EAC作者只是一位大学生，并不是学术专家，出现不严谨的地方在所难免，下面第五点关于“偏移设置”方面的误区就是一个很典型的例子。那这矛盾是如何产生的呢？对于物理质量很差的碟片，非安全模式由于碟片对光驱的抓轨要求超越规定的纠错范围，当出错部分是关键量化点，造成数据不能正确衔接，而产生暴音，那用EAC的安全模式抓轨又如何呢？会产生三种情况，一是出现同步错误抓轨无法继续，二是勉强完成抓轨，但也产生暴音，三是勉强完成没有暴音，第一、二情况是可能性最大的情况，但没有讨论的必要，那第三种情况呢，如果将会出现“暴音”的部分作为一个整体来看的话，大家别以为此时EAC的多次抓轨功能可以将误码率很好地控制在红皮书范围内，其实只有少部分能，大部分EAC还是会产生超越红皮书标准的误码率的，这是因为真正决定能否正确纠错的决定因素是光驱的纠错能力，如果对于越烂的碟片，光驱纠错能力又不变的话，安全模式即使有多次抓取和校验，也只能是不断重复读取着错误的音频信号而已。这时如果用EAC的安全模式反会适得其反，在一定程度上也是一种“纵容质量不合格产品通过质量检查”的不负责行为。

五、EAC创建的测试光驱偏移值的功能可以检测出光驱读偏移。
真正检测光驱偏移值是用指定的正版CD而不是这个经EAC创建的偏移值测试盘，这是因为刻录机在刻这张测试用的CDR的时候其实已写进了一个写偏移，在进行测试读取时又产生了一个读偏移，两者结合起来就是组合偏移。但EAC在我们点击应用的时候偏偏把它应用到了光驱的读偏移上了。当然，这个值是读偏移也不是没可能的，但前提就是创建该CDR的刻录机的写偏移为零，显而易见，这对于家用光驱来说几乎不可能，编写一个软件是不应该将这么重要的技术操作的关键部分放在“假设”前提之上的，如果可以这么假设，我们不如干脆就假设光驱的读偏移为零好了，那就根本不用创建什么测试偏移CD了。EAC在此处的不严谨，误导了无数的“顶礼膜拜者”的出错，各论坛上已屡见不鲜。

六、EAC的刻录功能对刻录音乐CD好
刻录（cloncd的raw方式除外）其实是PCM WAV——PCM的一个转换过程，因为CD的PCM格式已是一种定性的规范与标准，任何刻录软件都要遵循这一标准规范的，所以将WAV转换成PCM的工作原理、模式与方式也都是完全一样的，不同的只是哪个软件更成熟一点，对机器的兼容性更好一点罢。而抓轨（PCM——PCＭ　ＷＡＶ）虽然也是一种定性、规范化的过程，各个软件抓取原理及方式也一样，但情况有些特殊，因为CD碟片的纠错系统不完善，可能会由于碟片存在物理上的瑕疵而导致抓取的音频信号出错，这样ＥＡＣ的多次校验的安全模式才可以大行其道（虽然这种可行性如前所述值得质疑）。但刻录阶段情况大不一样，因为刻录的对象ＰＣＭ　ＷＡＶ格式纠错系统已完善，根本不存在物理瑕疵可能导致读取出错的情况，所以我们应该把眼光放在刻录软件上，事实上EAC这软件刻录的确问题多多，特别是lead out无法完成。有人做过比较，EAC刻录出来的盘片，结果发现其边缘没有其他软件刻的清楚，虽然他没将这跟lead out联系在一起，我没有做实验比较过，但我也相信他的比较结论是正确的，因为如果lead out出问题的话，出现这种情况是完全可以理解的，别以为lead out不正常，而CD勉强可以放就可以，这至少是可以影响到CD的保存寿命的；从另一方面分析，那些认为EAC刻录出来的CD音质比其它软件好也可能要大失望了。首先说明一个软件刻录出来音质是否好，就要先明白影响刻录CD音质的是什么因素，我想大家都知道吧，那就是jitter了，那影响刻录CD jitter的因素又是什么？就是在刻录过程中的不稳定因素。众所周知，EAC是出了名兼容性不好的了，先不说不兼容大部分的刻录机，就算对可以勉强兼容的那些刻录机，也是问题多多，例如最明显的就是前面所说的不能正常 lead out 了，而这些我们所说到的EAC种种存在的问题也只是我们“肉眼”能看到的，如果“肉眼”看不到的呢？几乎可以肯定，就算刻录成功，EAC刻录的稳定性来说的相比nero等较成熟的刻录软件来说是逊色的，也就是说EAC比较其他成熟的刻录软件来说都可能会产生更多的jitter，从而更容易影响刻录后CD的音质，也有人做过比较，发现EAC刻的盘，刻录痕比其他软件浅，这也从侧面反映出EAC的刻录问题。当然，EAC的刻录功能也有别的软件没有的优势，那就是支持写偏移了，但这对刻录音质是丝毫没影响的。

七、EAC是一个专业的音频软件
业界没有人认为EAC是专业的音频软件，只是我们外行的音乐发烧友对其推崇而已。经上面的分析，你还认为EAC是一个专业的音频软件吗？如果说EAC真正的“专业性”是抓轨和偏移设置的话，你又是否想过，为什么Nero，EasyCD等公认的专业刻录软件在不断改善其产品性能的同时却不象EAC这样注重安全模式或所谓的偏移设置呢？难道是他们没有EAC作者这么一个外行大学生想得周全吗？是他们不够专业吗？当然不是的，而是因为他们认为根本就没这个必要，也是因为他们太“专业”了，所以时至今天他们也无意在抓轨上下功夫，无意在偏移设置上下功夫，而真真正正在刻录的稳定性上进行改善，从整体刻录性能上下功夫，因为只有保证刻录的稳定性，才能把jitter尽可能减少到最小可能，才是在软件上提高刻录CD音质的最佳途径，这也是一个专业刻录软件真正的着眼点，其它在小小细节上纠缠不清的行为，只能算是“吹毛求疵”。
最后让我们回过头来看看EAC作者编写这个软件的目的并以此作为总结：“EAC的作者Andre Wiethoff是德国多特蒙德大学计算机专业的一名学生，经常抓取和监听各种WAV文件，所以使用了许多抓音轨的软件，但令他不满意的是，这些软件只有时基误差的校正，而CDROM在抓音轨时会产生其他的误差，所以，他就萌发了开发一个完全精确的抓音轨软件的念头，这样EAC诞生了。”如果认真阅读这段文字，就可发现，那些专业软件都注重的“时基误差”的校正，正是专业眼光下的一针见血。相反，EAC作者所谓不满意的地方，那他又改变了什么？可以说没有。EAC推出的两大“法宝”，偏移设值与安全模式抓轨为我们带来了什么？以前，大家都对EAC的偏移设置顶礼膜拜之极，今天，设置偏移的已廖廖无几，有也是多抱着可有可无的心态或是那些刚刚认识EAC的的新手们。因为大家都明白，EAC偏移设置这东东是“专业的级的设置应用在家用级设备”上，就算对那最多存在的几十分之一的误差进行偏移校正，也不能保证没误差，因为我们所用的刻录机机械性能实在是太不稳定了，用EAC指定的正版CD测试N张CD出现N个偏移的情况屡见不鲜，有些刻录机本身其实也存在着多个偏移值；那EAC的最“精华”的安全抓轨模式又如何呢，在前面“第二个误区”已分析过了，安全抓轨设置的可行性甚至小于偏移设置，而且其本身也有瑕疵和不严谨之处；最后，作为EAC并没推荐的，但我们很多人却“爱屋及乌”，爱上你没理由的刻录功能则更不用说了，受“牵连”而在论坛上叫苦连天的人大有人在，每天都在产生。

对EAC的批判：
CD抓取保存到电脑的转换过程是很复杂，但原理却是很简单的（这我也是经过一段时间的曲解并与行家们的讨论才弄懂的），因为音频CD的PCM数字格式与微软的PCM WAV在对应上完全是规范化的，在技术上也是完全公开的，任何抓轨软件都是遵循同一方式与准则，这相当于所有PC机都向IBM兼容一样。也就是说在抓轨方式上EAC跟nero、cdex，easycd没有两样，没有所谓更精确的提取过程的，这完全是误会。EAC唯一不同的是它内含一个编程人士常用的循环程式，这程式的功能就是对读取的WAV进行校验。也就是说，校验效果决定了安全模式抓轨存在的意义。但EAC作者似乎忘记了编写软件的一个基本步骤，就是要进行可行性分析了，在可行性分析这项上，EAC的安全模式其实是相当失败的。
为什么这么说呢？我再简单跟大家说说吧。我们知道，光碟红皮书规范下任一项内容都是有业界标准的，包括抓轨的纠错机制与过程也是如此，具体可详见 [url]http://article.pchome.net/2004/07/30/23234_2.htm[/url] ，在光驱纠错能力不变的前提下，一次判别与多次判别的结果几乎完全是一样的，也就是几乎不存在校验之后结果就变了的现象发生，这也是为什么安全模式与暴发模式在绝大多数情况下抓取的WAV在二进制比较上完全一致的原因了，但EAC的作者似乎忽略了这一基本原理，没有考虑他独有的那个“循环程序”到底具有多少的可行性。另外，很多人认为EAC安全抓轨慢所以精工出细活，暴发模式只求速度，不求质量的说法也是不准确的，第一，如前所述，CD抓轨是一个规范化的过程，任何抓取模式都要完成规定的所有步骤的，都要进行规定的纠错操作的，不存在“越级”的情况发生。第二，事实上，如果你不是强制将EAC的抓轨定在1速以下（这是没必要的）或定死在固定高速不允许降速（傻瓜才会这样做），EAC的安全模式抓轨速度是跟暴发模式一样的，我这么说，大家一定会反对我，说你这家伙不是在吹牛吗？一比较就知道安全模式慢得多啊。但是大家似乎也忘记了一个最基本的事实，EAC暴发模式是一次性抓轨的，而安全模式是多次性抓轨的，也就是说平均到一次抓轨的速度上，并减去无谓的校验时间，两者其实是完全一样的，而当碟片物理质量较差时，无论是安全还是暴发模式都会对读取进行减速处理的，这也视乎碟片本身因素而定。也就是我们忽略了这一基本事实，才会造成安全模式抓轨比暴发模式慢的错觉。
在偏移设置上，EAC作者也明显没做一个可行性的分析（版主您的实验也恰好证实了这一点）。这在软件编写来说，是不可原谅的行为，可以说，EAC作者在编写EAC的产生念头与编写过程，完全是基于一种想当然的不科学的态度之下的，自以为这个比那个好，这样比那样精确，而不求从实验上、从技术上认真分析这种想法是否与现实存在着偏差，是否只是认识上的误区，这导致了EAC这个软件细微之处处处显现出一个外行编程家的幼稚及不严谨，这也是nero，easycd等软件没有采纳偏移设置与安全模式设置的重要原因，因为这两项在可行性分析上都是行不通的。我香港那位从事计算机编程的胡姓网友打了一个精妙的比喻：“1+1=2，绝大部分人，包括口吃者在一两秒内都是可以回答的，某‘专家’却偏偏认为这不够安全，于是把回答的时间延至82秒，并对大家说，这样答案就准确多了，但他殊不知，他的所谓“更加准确”，只是对那几乎可以忽略的极度白痴人士而言，根本没有可行性，可笑的是他还偏偏抱怨其他出题者为什么不跟他一样从“安全大局”出发。EAC其实就是这样的一个软件，安全模式是，偏移设置是，刻录功能更是。

2006-12-09T00:12:00.000-08:00

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Francis Bacon (1607)PHENOMENA OF THE UNIVERSE

2006-12-08T05:46:00.000-08:00

NATURAL HISTORY For THE BUILDING UP OF PHILOSOPHY

Francis Bacon (1607)

bacon
PHENOMENA OF THE UNIVERSE
Or
NATURAL HISTORY
For
THE BUILDING UP OF PHILOSOPHY

Source: Natural History for the Building Up of Philosophy, 1609, 19th Century English edition; first 5 pages from the Preface.
PREFACE

Since it seems to me that people do not keep strictly to the straight and narrow when forming their opinions or putting things to the test, I have decided to use all the means at my disposal to remedy this misfortune. For in nothing else does the aspiration to deserve well show itself than it things are so arranged that people, freed both from the hobgoblins of belief and blindness of experiments, may enter into a more reliable and sound partnership with things by, as it were, a certain literate experience. For in this way the intellect is both set up in safety and in its best state, and it will besides be at the ready and then come upon harvests of useful things.

Now the beginnings of this enterprise must in general be drawn from natural history; for the whole body of Greek philosophy with its sects of all kinds, and all the other philosophy we possess seem to me to be founded on too narrow a natural-historical basis, and thus to have delivered its conclusions on the authority of fewer data than was appropriate. For having snatched certain things from experience and tradition, things sometimes not carefully examined or ideas nor securely established, they leave the rest to meditation and intellectual agitation, employing Dialectic inspire greater confidence in the matter.

But the chemists and the whole pack of mechanics and empirics, should they have the temerity to attempt contemplation and philosophy, being accustomed to meticulous subtlety in a few things, they twist by extraordinary means all the rest into conformity with them and promote opinions more odious and unnatural than those advanced by the very rationalists. For the latter take for the matter of philosophy very little out of many things, the former a great deal out of a few, but in truth those courses are weak and past cure. But the Natural History which has been accumulated hitherto may seem abundant on casual inspection, while in reality it is sketchy and useless, and not even of the kind I am seeking. For it has not been stripped of fables and ravings, and it rushes into antiquity, philology and superfluous narratives, neglectful and high-handed in matters of weight, overscrupulous and immoderate in matters of no importance. But the worst thing about this abundance is that it has embraced the inquiry into things natural but largely spurned that into things mechanical. Now the latter are far better than the former for examining nature's recesses; for nature of its own accord, free and shifting, disperses the intellect and confuses it with its variety, but in mechanical operations the judgement is concentrated, and we see nature's modes and processes, not just its effects. Yet, on the other hand, all the subtlety of mechanics stops short of what I am seeking. For the craftsman, intent on his work and its end, does not direct his mind or put his hand to other things, things which perhaps do more for the inquiry into nature.

Therefore we need more meticulous care and handpicked trials, not to mention funding and the utmost patience besides. For it has ruined everything in the experimental field that right from the beginning men have continually aimed at Experiments of Fruit not ones of Light, and have devoted their energies entirely to producing some splendid work, not to revealing nature's oracles, which is the work of works and encompasses in itself all power. It also comes about from men's misguided conceit that they have mostly applied themselves to things hidden and rare, and put their efforts and inquiry into those while spurning common experiments and observations, and this seems to have come about either because they sought admiration and fame, or because they fell for the belief that the function of philosophy lies in accommodating and reducing rarer events to those which occur familiarly, not equally to unearthing the causes of these common things themselves and deeper causes of those causes.

But the main point of the whole accusation against natural history is that men have gone astray not only in the work, but in its very plan. For the natural history which is in existence seems to have been composed either for the usefulness of the experiments themselves, or for the agreeableness of their narratives, and to have been made for their own sake, not so as to furnish the makings of philosophy and the sciences and as it were breast-feed them.

Thus, as far as it is within my power, I do not wish to fail to do my duty in this matter. For I have long since decided how much I should grant to abstract philosophies. Indeed, I believe that I hold fast to the ways of true and good induction, in which all things lie, and which can help the frail and crippled faculty of human intellect towards the sciences, as by mechanical aids or by some thread to guide it through a labyrinth. Nor am I unaware that if I had been willing to restrict that instauration of the sciences which I have in mind to any of the greater inventions, I could perhaps have harvested a greater crop of honour. But since God has given me a mind which knows how to submit itself to things and which readily rejects the specious out of a sense of what is right and from confidence that things will turn out well, I have also taken upon myself that part of the work which I think others have wanted either to avoid entirely, or to treat in a way different from my idea of it.

But there are two things which I wish to warn people about in this connection both for the future and, since I am girding myself for the very thing itself, for now especially. The first is to get rid of that idea which, though it be utterly false and harmful, easily invades and takes hold of men's minds, namely that the inquiry into particulars is something infinite and without end, when it would be truer to say that the way of opinions and disputations is the trifling one; but in fact these vain imaginings are condemned to perpetual errors and infinite disturbances, whereas particulars and the informations of the sense (which, when individuals and the gradations of things have been left out, is sufficient for the inquiry into truth) allow understanding for certain, and that, to be sure, neither forlorn nor hopeless.

The second is that I would have men never forget what is involved and, when they have come across troops of thoroughly vulgar things, things slight and to all appearances frivolous, even vile, and which (as the man says) must be brought in with an apology, they do not think I am trifling, or reducing the human mind to things beneath its dignity. For these things are neither examined nor described for their own sake, but in fact there is simply no other alternative open to the human intellect, and the grounds of the work are left insecure without them. I am then certainly undertaking the most serious business of all and most worthy of the human mind, that nature's light, pure and quite unclouded by vain imagination (that light whose name has sometimes been mentioned thus far, while people have known nothing about the thing itself), may be lit in this age of ours by a torch furnished and brought near by the Divine Will.

For I do not hide the fact that I believe that preposterous subtlety of argument and thought can by no means put things right again, though all the intellects of all ages be gathered together, when, at the proper time, the subtlety and truth of the basic information or true induction have been overlooked or incorrectly established, but that nature, like fortune, is long-haired at the front and bald at the back. It remains, therefore, for the matter to be attempted anew, and that with better help and with the zeal of opinions laid aside, so that we may enter into the kingdom of philosophy and the sciences (in which human power is situated, for nature is conquered only by obeying it) in the way that we gain access to the Kingdom of Heaven, which none may enter save in the likeness of a little child. Yet I do not wholly despise the base and indiscriminate custom of working by experiments themselves (for it may doubtless suggest very many useful things to men's knowledge and invention, according to the variety of their arts and capacities), nevertheless I think it is something very trivial in comparison with that entrance into human knowledge and power which I hope for from the Divine Mercy, which indeed I again humbly beseech to allow me to endow the human family with new alms through my efforts.

The nature of things is either free, as in species, or disturbed, as in monsters, or confined, as in experiments of the Arts; yet its deeds of whatever kind are worthy of report and history. But the History of Species currently available, as for example of plants, animals, metals and fossils, is puffed up and full of curiosities; the History of Marvels empty and based on rumour; the History of Experiments detective, attempted piecemeal, dealt with carelessly, and entirely for practical not philosophical use.

Therefore it is my resolve to curb the History of Species, to shake our and purify the History of Marvels, but to our special effort into Mechanical and Artificial Experiments where nature gives in to human intervention. For what are the sports and frivolities of nature to us? That is, the tiny differences of species as to shape, which contribute nothing to works but in which Natural History none the less abounds. Now knowledge of Marvels certainly pleases me, if it be purified and sifted; but why in the final analysis is it pleasing? Not for the fun of being astonished, but because it often reminds Art of its duty to lead nature knowingly where it has itself sometimes gone before of its own accord.

In general I assign the leading roles in shedding light on nature to artificial things, not only because they are most useful in themselves, but because they are the most trustworthy interpreters of natural things. Can it be said that anyone had just happened to explain the nature of lightning or a rainbow as clearly before the principles of each had been demonstrated by artillery or the artificial simulacra of rainbows on a wall? But if they are trustworthy interpreters of causes, they will also be sure and fertile indicators of effects and of works. However, I do not think it appropriate to divide my history in accordance with this threefold partition, so as to deal with singular instances separately, but I shall mix the three kinds, joining things natural with artificial. ordinary with extraordinary, and paying very close attention to all the most useful ones.

Now it would be more usual to begin with the phenomena of the ether. But I, sacrificing nothing of the seriousness of my undertaking, shall give priority to things which make up and answer to a nature more general, in which both globes share. I shall begin in fact with a history of bodies according to the difference which seems the simplest, that is, the abundance or paucity of the matter contained and spread out within the same space or boundaries, seeing indeed that none of the pronouncements about nature is truer than that double proposition. Nothing comes from nothing, nor is anything reduced to nothing, but the very quantum of nature, or the whole sum of matter always remains and stays the same, and is in no way increased or diminished. Moreover, it is no less certain. even though not so clearly noted or asserted (whatever stories people make up about the impartial potential of matter towards forms) that more or less of this quantity of matter is contained in the same volumes of space according to the diversity of the bodies which occupy them, bodies some of which we find to be very obviously more compact, others more extended or diffuse. For a vessel or cauldron filled with water and air does not hold an equal portion of matter, but more of the one and less of the other. Therefore if someone claimed that a given amount of water could be made from the same amount of air, it would be the same as saying that something can come from nothing. For what you deem to be lacking from the quantity of matter would have to have been made up from nothing. On the other hand, if someone claimed that a given amount of water could be turned into the same amount of air, it would be the same as saying that something can be reduced to nothing. For what you deem to be extra in the quantity of matter would likewise have to have vanished into nothingness. There is no doubt in my mind that this business is capable of being reduced to calculation, to indefinite proportions perhaps in some things, but to ones precise and certain in others, and known to nature. As, for example, if someone said that the concentration of matter in a body of gold exceeded than of a body of spirit of wine by a factor of twenty to one or thereabouts, he would nor be wrong. So as I now mean to present the history I mentioned concerning the abundance and paucity of matter, and its coming together and expansion, things from which the notions of Dense and Rare (if properly understood) take their origin, I shall so order matters that I shall draw up the relative figures for different bodies (as of gold, water, oil, air and flame) first. Then after examining these, I shall record with calculations or ratios the retreats and expatiations of each particular body. For a given body, even without anything being added to it or taken away, or at least nor in proportion to its contraction and extension, allows itself to be gathered by various impulses both external and internal into a larger or smaller sphere. Sometimes the body struggles and strives to restore itself into its old sphere, sometimes it clearly goes beyond that and does not try to revert. Here I shall first record the courses, differences and proportions of any natural body (as to its extent) compared with its openings and closings up, that is, with its powders, its calces, its virrifications, its dissolutions, its distillations, vapours and breaths, its exhalations and inflammations; then I shall set out the actions and motions themselves, the progressions and the limits of contraction and dilatation, and when bodies restore themselves and when they go beyond than in respect of their extent; but I shall especially note the efficient causes and media by means of which such contractions and dilatations of bodies come about; and meanwhile I shall in passing append the virtues and actions which bodies get and take on from such compressions and dilatations.

And since I know well how difficult a thing it is, in the present climate of opinion, to familiarise oneself with nature right from the very beginning, I shall add my own observations to gain men's attention and arouse them to contemplation. Now as far as the demonstration or revealing of the density and rarity of bodies is concerned, I have no doubt or hesitation that as to dense and palpable bodies the motion of gravity (as they call it) may be taken as the best and most ready test, for the more compact the body, the heavier it is. But when it comes to the level of airy and spiritual things, then scales will for sure be of no use to me, and I shall need another kind of industry. I shall begin, however, with Gold: which of all the things we have (for philosophy has nor grown up enough for us to say anything for certain about the bowels of the Earth) is the heaviest and contains the most matter in the smallest space, and I shall relate the ratios of the rest to the sphere of this body, with the reminder that I am not dealing here with the history of weights except in so far as it sheds light for demonstrating the space or dimensions of bodies. ...

Francis Bacon (1607)PHENOMENA OF THE UNIVERSE

2006-12-08T05:45:00.001-08:00

NATURAL HISTORY For THE BUILDING UP OF PHILOSOPHY

Francis Bacon (1607)

bacon
PHENOMENA OF THE UNIVERSE
Or
NATURAL HISTORY
For
THE BUILDING UP OF PHILOSOPHY

Source: Natural History for the Building Up of Philosophy, 1609, 19th Century English edition; first 5 pages from the Preface.
PREFACE

Since it seems to me that people do not keep strictly to the straight and narrow when forming their opinions or putting things to the test, I have decided to use all the means at my disposal to remedy this misfortune. For in nothing else does the aspiration to deserve well show itself than it things are so arranged that people, freed both from the hobgoblins of belief and blindness of experiments, may enter into a more reliable and sound partnership with things by, as it were, a certain literate experience. For in this way the intellect is both set up in safety and in its best state, and it will besides be at the ready and then come upon harvests of useful things.

Now the beginnings of this enterprise must in general be drawn from natural history; for the whole body of Greek philosophy with its sects of all kinds, and all the other philosophy we possess seem to me to be founded on too narrow a natural-historical basis, and thus to have delivered its conclusions on the authority of fewer data than was appropriate. For having snatched certain things from experience and tradition, things sometimes not carefully examined or ideas nor securely established, they leave the rest to meditation and intellectual agitation, employing Dialectic inspire greater confidence in the matter.

But the chemists and the whole pack of mechanics and empirics, should they have the temerity to attempt contemplation and philosophy, being accustomed to meticulous subtlety in a few things, they twist by extraordinary means all the rest into conformity with them and promote opinions more odious and unnatural than those advanced by the very rationalists. For the latter take for the matter of philosophy very little out of many things, the former a great deal out of a few, but in truth those courses are weak and past cure. But the Natural History which has been accumulated hitherto may seem abundant on casual inspection, while in reality it is sketchy and useless, and not even of the kind I am seeking. For it has not been stripped of fables and ravings, and it rushes into antiquity, philology and superfluous narratives, neglectful and high-handed in matters of weight, overscrupulous and immoderate in matters of no importance. But the worst thing about this abundance is that it has embraced the inquiry into things natural but largely spurned that into things mechanical. Now the latter are far better than the former for examining nature's recesses; for nature of its own accord, free and shifting, disperses the intellect and confuses it with its variety, but in mechanical operations the judgement is concentrated, and we see nature's modes and processes, not just its effects. Yet, on the other hand, all the subtlety of mechanics stops short of what I am seeking. For the craftsman, intent on his work and its end, does not direct his mind or put his hand to other things, things which perhaps do more for the inquiry into nature.

Therefore we need more meticulous care and handpicked trials, not to mention funding and the utmost patience besides. For it has ruined everything in the experimental field that right from the beginning men have continually aimed at Experiments of Fruit not ones of Light, and have devoted their energies entirely to producing some splendid work, not to revealing nature's oracles, which is the work of works and encompasses in itself all power. It also comes about from men's misguided conceit that they have mostly applied themselves to things hidden and rare, and put their efforts and inquiry into those while spurning common experiments and observations, and this seems to have come about either because they sought admiration and fame, or because they fell for the belief that the function of philosophy lies in accommodating and reducing rarer events to those which occur familiarly, not equally to unearthing the causes of these common things themselves and deeper causes of those causes.

But the main point of the whole accusation against natural history is that men have gone astray not only in the work, but in its very plan. For the natural history which is in existence seems to have been composed either for the usefulness of the experiments themselves, or for the agreeableness of their narratives, and to have been made for their own sake, not so as to furnish the makings of philosophy and the sciences and as it were breast-feed them.

Thus, as far as it is within my power, I do not wish to fail to do my duty in this matter. For I have long since decided how much I should grant to abstract philosophies. Indeed, I believe that I hold fast to the ways of true and good induction, in which all things lie, and which can help the frail and crippled faculty of human intellect towards the sciences, as by mechanical aids or by some thread to guide it through a labyrinth. Nor am I unaware that if I had been willing to restrict that instauration of the sciences which I have in mind to any of the greater inventions, I could perhaps have harvested a greater crop of honour. But since God has given me a mind which knows how to submit itself to things and which readily rejects the specious out of a sense of what is right and from confidence that things will turn out well, I have also taken upon myself that part of the work which I think others have wanted either to avoid entirely, or to treat in a way different from my idea of it.

But there are two things which I wish to warn people about in this connection both for the future and, since I am girding myself for the very thing itself, for now especially. The first is to get rid of that idea which, though it be utterly false and harmful, easily invades and takes hold of men's minds, namely that the inquiry into particulars is something infinite and without end, when it would be truer to say that the way of opinions and disputations is the trifling one; but in fact these vain imaginings are condemned to perpetual errors and infinite disturbances, whereas particulars and the informations of the sense (which, when individuals and the gradations of things have been left out, is sufficient for the inquiry into truth) allow understanding for certain, and that, to be sure, neither forlorn nor hopeless.

The second is that I would have men never forget what is involved and, when they have come across troops of thoroughly vulgar things, things slight and to all appearances frivolous, even vile, and which (as the man says) must be brought in with an apology, they do not think I am trifling, or reducing the human mind to things beneath its dignity. For these things are neither examined nor described for their own sake, but in fact there is simply no other alternative open to the human intellect, and the grounds of the work are left insecure without them. I am then certainly undertaking the most serious business of all and most worthy of the human mind, that nature's light, pure and quite unclouded by vain imagination (that light whose name has sometimes been mentioned thus far, while people have known nothing about the thing itself), may be lit in this age of ours by a torch furnished and brought near by the Divine Will.

For I do not hide the fact that I believe that preposterous subtlety of argument and thought can by no means put things right again, though all the intellects of all ages be gathered together, when, at the proper time, the subtlety and truth of the basic information or true induction have been overlooked or incorrectly established, but that nature, like fortune, is long-haired at the front and bald at the back. It remains, therefore, for the matter to be attempted anew, and that with better help and with the zeal of opinions laid aside, so that we may enter into the kingdom of philosophy and the sciences (in which human power is situated, for nature is conquered only by obeying it) in the way that we gain access to the Kingdom of Heaven, which none may enter save in the likeness of a little child. Yet I do not wholly despise the base and indiscriminate custom of working by experiments themselves (for it may doubtless suggest very many useful things to men's knowledge and invention, according to the variety of their arts and capacities), nevertheless I think it is something very trivial in comparison with that entrance into human knowledge and power which I hope for from the Divine Mercy, which indeed I again humbly beseech to allow me to endow the human family with new alms through my efforts.

The nature of things is either free, as in species, or disturbed, as in monsters, or confined, as in experiments of the Arts; yet its deeds of whatever kind are worthy of report and history. But the History of Species currently available, as for example of plants, animals, metals and fossils, is puffed up and full of curiosities; the History of Marvels empty and based on rumour; the History of Experiments detective, attempted piecemeal, dealt with carelessly, and entirely for practical not philosophical use.

Therefore it is my resolve to curb the History of Species, to shake our and purify the History of Marvels, but to our special effort into Mechanical and Artificial Experiments where nature gives in to human intervention. For what are the sports and frivolities of nature to us? That is, the tiny differences of species as to shape, which contribute nothing to works but in which Natural History none the less abounds. Now knowledge of Marvels certainly pleases me, if it be purified and sifted; but why in the final analysis is it pleasing? Not for the fun of being astonished, but because it often reminds Art of its duty to lead nature knowingly where it has itself sometimes gone before of its own accord.

In general I assign the leading roles in shedding light on nature to artificial things, not only because they are most useful in themselves, but because they are the most trustworthy interpreters of natural things. Can it be said that anyone had just happened to explain the nature of lightning or a rainbow as clearly before the principles of each had been demonstrated by artillery or the artificial simulacra of rainbows on a wall? But if they are trustworthy interpreters of causes, they will also be sure and fertile indicators of effects and of works. However, I do not think it appropriate to divide my history in accordance with this threefold partition, so as to deal with singular instances separately, but I shall mix the three kinds, joining things natural with artificial. ordinary with extraordinary, and paying very close attention to all the most useful ones.

Now it would be more usual to begin with the phenomena of the ether. But I, sacrificing nothing of the seriousness of my undertaking, shall give priority to things which make up and answer to a nature more general, in which both globes share. I shall begin in fact with a history of bodies according to the difference which seems the simplest, that is, the abundance or paucity of the matter contained and spread out within the same space or boundaries, seeing indeed that none of the pronouncements about nature is truer than that double proposition. Nothing comes from nothing, nor is anything reduced to nothing, but the very quantum of nature, or the whole sum of matter always remains and stays the same, and is in no way increased or diminished. Moreover, it is no less certain. even though not so clearly noted or asserted (whatever stories people make up about the impartial potential of matter towards forms) that more or less of this quantity of matter is contained in the same volumes of space according to the diversity of the bodies which occupy them, bodies some of which we find to be very obviously more compact, others more extended or diffuse. For a vessel or cauldron filled with water and air does not hold an equal portion of matter, but more of the one and less of the other. Therefore if someone claimed that a given amount of water could be made from the same amount of air, it would be the same as saying that something can come from nothing. For what you deem to be lacking from the quantity of matter would have to have been made up from nothing. On the other hand, if someone claimed that a given amount of water could be turned into the same amount of air, it would be the same as saying that something can be reduced to nothing. For what you deem to be extra in the quantity of matter would likewise have to have vanished into nothingness. There is no doubt in my mind that this business is capable of being reduced to calculation, to indefinite proportions perhaps in some things, but to ones precise and certain in others, and known to nature. As, for example, if someone said that the concentration of matter in a body of gold exceeded than of a body of spirit of wine by a factor of twenty to one or thereabouts, he would nor be wrong. So as I now mean to present the history I mentioned concerning the abundance and paucity of matter, and its coming together and expansion, things from which the notions of Dense and Rare (if properly understood) take their origin, I shall so order matters that I shall draw up the relative figures for different bodies (as of gold, water, oil, air and flame) first. Then after examining these, I shall record with calculations or ratios the retreats and expatiations of each particular body. For a given body, even without anything being added to it or taken away, or at least nor in proportion to its contraction and extension, allows itself to be gathered by various impulses both external and internal into a larger or smaller sphere. Sometimes the body struggles and strives to restore itself into its old sphere, sometimes it clearly goes beyond that and does not try to revert. Here I shall first record the courses, differences and proportions of any natural body (as to its extent) compared with its openings and closings up, that is, with its powders, its calces, its virrifications, its dissolutions, its distillations, vapours and breaths, its exhalations and inflammations; then I shall set out the actions and motions themselves, the progressions and the limits of contraction and dilatation, and when bodies restore themselves and when they go beyond than in respect of their extent; but I shall especially note the efficient causes and media by means of which such contractions and dilatations of bodies come about; and meanwhile I shall in passing append the virtues and actions which bodies get and take on from such compressions and dilatations.

And since I know well how difficult a thing it is, in the present climate of opinion, to familiarise oneself with nature right from the very beginning, I shall add my own observations to gain men's attention and arouse them to contemplation. Now as far as the demonstration or revealing of the density and rarity of bodies is concerned, I have no doubt or hesitation that as to dense and palpable bodies the motion of gravity (as they call it) may be taken as the best and most ready test, for the more compact the body, the heavier it is. But when it comes to the level of airy and spiritual things, then scales will for sure be of no use to me, and I shall need another kind of industry. I shall begin, however, with Gold: which of all the things we have (for philosophy has nor grown up enough for us to say anything for certain about the bowels of the Earth) is the heaviest and contains the most matter in the smallest space, and I shall relate the ratios of the rest to the sphere of this body, with the reminder that I am not dealing here with the history of weights except in so far as it sheds light for demonstrating the space or dimensions of bodies. ...

Francis Bacon (1607)PHENOMENA OF THE UNIVERSE

2006-12-08T05:45:00.000-08:00

NATURAL HISTORY For THE BUILDING UP OF PHILOSOPHY

Francis Bacon (1607)

bacon
PHENOMENA OF THE UNIVERSE
Or
NATURAL HISTORY
For
THE BUILDING UP OF PHILOSOPHY

Source: Natural History for the Building Up of Philosophy, 1609, 19th Century English edition; first 5 pages from the Preface.
PREFACE

Since it seems to me that people do not keep strictly to the straight and narrow when forming their opinions or putting things to the test, I have decided to use all the means at my disposal to remedy this misfortune. For in nothing else does the aspiration to deserve well show itself than it things are so arranged that people, freed both from the hobgoblins of belief and blindness of experiments, may enter into a more reliable and sound partnership with things by, as it were, a certain literate experience. For in this way the intellect is both set up in safety and in its best state, and it will besides be at the ready and then come upon harvests of useful things.

Now the beginnings of this enterprise must in general be drawn from natural history; for the whole body of Greek philosophy with its sects of all kinds, and all the other philosophy we possess seem to me to be founded on too narrow a natural-historical basis, and thus to have delivered its conclusions on the authority of fewer data than was appropriate. For having snatched certain things from experience and tradition, things sometimes not carefully examined or ideas nor securely established, they leave the rest to meditation and intellectual agitation, employing Dialectic inspire greater confidence in the matter.

But the chemists and the whole pack of mechanics and empirics, should they have the temerity to attempt contemplation and philosophy, being accustomed to meticulous subtlety in a few things, they twist by extraordinary means all the rest into conformity with them and promote opinions more odious and unnatural than those advanced by the very rationalists. For the latter take for the matter of philosophy very little out of many things, the former a great deal out of a few, but in truth those courses are weak and past cure. But the Natural History which has been accumulated hitherto may seem abundant on casual inspection, while in reality it is sketchy and useless, and not even of the kind I am seeking. For it has not been stripped of fables and ravings, and it rushes into antiquity, philology and superfluous narratives, neglectful and high-handed in matters of weight, overscrupulous and immoderate in matters of no importance. But the worst thing about this abundance is that it has embraced the inquiry into things natural but largely spurned that into things mechanical. Now the latter are far better than the former for examining nature's recesses; for nature of its own accord, free and shifting, disperses the intellect and confuses it with its variety, but in mechanical operations the judgement is concentrated, and we see nature's modes and processes, not just its effects. Yet, on the other hand, all the subtlety of mechanics stops short of what I am seeking. For the craftsman, intent on his work and its end, does not direct his mind or put his hand to other things, things which perhaps do more for the inquiry into nature.

Therefore we need more meticulous care and handpicked trials, not to mention funding and the utmost patience besides. For it has ruined everything in the experimental field that right from the beginning men have continually aimed at Experiments of Fruit not ones of Light, and have devoted their energies entirely to producing some splendid work, not to revealing nature's oracles, which is the work of works and encompasses in itself all power. It also comes about from men's misguided conceit that they have mostly applied themselves to things hidden and rare, and put their efforts and inquiry into those while spurning common experiments and observations, and this seems to have come about either because they sought admiration and fame, or because they fell for the belief that the function of philosophy lies in accommodating and reducing rarer events to those which occur familiarly, not equally to unearthing the causes of these common things themselves and deeper causes of those causes.

But the main point of the whole accusation against natural history is that men have gone astray not only in the work, but in its very plan. For the natural history which is in existence seems to have been composed either for the usefulness of the experiments themselves, or for the agreeableness of their narratives, and to have been made for their own sake, not so as to furnish the makings of philosophy and the sciences and as it were breast-feed them.

Thus, as far as it is within my power, I do not wish to fail to do my duty in this matter. For I have long since decided how much I should grant to abstract philosophies. Indeed, I believe that I hold fast to the ways of true and good induction, in which all things lie, and which can help the frail and crippled faculty of human intellect towards the sciences, as by mechanical aids or by some thread to guide it through a labyrinth. Nor am I unaware that if I had been willing to restrict that instauration of the sciences which I have in mind to any of the greater inventions, I could perhaps have harvested a greater crop of honour. But since God has given me a mind which knows how to submit itself to things and which readily rejects the specious out of a sense of what is right and from confidence that things will turn out well, I have also taken upon myself that part of the work which I think others have wanted either to avoid entirely, or to treat in a way different from my idea of it.

But there are two things which I wish to warn people about in this connection both for the future and, since I am girding myself for the very thing itself, for now especially. The first is to get rid of that idea which, though it be utterly false and harmful, easily invades and takes hold of men's minds, namely that the inquiry into particulars is something infinite and without end, when it would be truer to say that the way of opinions and disputations is the trifling one; but in fact these vain imaginings are condemned to perpetual errors and infinite disturbances, whereas particulars and the informations of the sense (which, when individuals and the gradations of things have been left out, is sufficient for the inquiry into truth) allow understanding for certain, and that, to be sure, neither forlorn nor hopeless.

The second is that I would have men never forget what is involved and, when they have come across troops of thoroughly vulgar things, things slight and to all appearances frivolous, even vile, and which (as the man says) must be brought in with an apology, they do not think I am trifling, or reducing the human mind to things beneath its dignity. For these things are neither examined nor described for their own sake, but in fact there is simply no other alternative open to the human intellect, and the grounds of the work are left insecure without them. I am then certainly undertaking the most serious business of all and most worthy of the human mind, that nature's light, pure and quite unclouded by vain imagination (that light whose name has sometimes been mentioned thus far, while people have known nothing about the thing itself), may be lit in this age of ours by a torch furnished and brought near by the Divine Will.

For I do not hide the fact that I believe that preposterous subtlety of argument and thought can by no means put things right again, though all the intellects of all ages be gathered together, when, at the proper time, the subtlety and truth of the basic information or true induction have been overlooked or incorrectly established, but that nature, like fortune, is long-haired at the front and bald at the back. It remains, therefore, for the matter to be attempted anew, and that with better help and with the zeal of opinions laid aside, so that we may enter into the kingdom of philosophy and the sciences (in which human power is situated, for nature is conquered only by obeying it) in the way that we gain access to the Kingdom of Heaven, which none may enter save in the likeness of a little child. Yet I do not wholly despise the base and indiscriminate custom of working by experiments themselves (for it may doubtless suggest very many useful things to men's knowledge and invention, according to the variety of their arts and capacities), nevertheless I think it is something very trivial in comparison with that entrance into human knowledge and power which I hope for from the Divine Mercy, which indeed I again humbly beseech to allow me to endow the human family with new alms through my efforts.

The nature of things is either free, as in species, or disturbed, as in monsters, or confined, as in experiments of the Arts; yet its deeds of whatever kind are worthy of report and history. But the History of Species currently available, as for example of plants, animals, metals and fossils, is puffed up and full of curiosities; the History of Marvels empty and based on rumour; the History of Experiments detective, attempted piecemeal, dealt with carelessly, and entirely for practical not philosophical use.

Therefore it is my resolve to curb the History of Species, to shake our and purify the History of Marvels, but to our special effort into Mechanical and Artificial Experiments where nature gives in to human intervention. For what are the sports and frivolities of nature to us? That is, the tiny differences of species as to shape, which contribute nothing to works but in which Natural History none the less abounds. Now knowledge of Marvels certainly pleases me, if it be purified and sifted; but why in the final analysis is it pleasing? Not for the fun of being astonished, but because it often reminds Art of its duty to lead nature knowingly where it has itself sometimes gone before of its own accord.

In general I assign the leading roles in shedding light on nature to artificial things, not only because they are most useful in themselves, but because they are the most trustworthy interpreters of natural things. Can it be said that anyone had just happened to explain the nature of lightning or a rainbow as clearly before the principles of each had been demonstrated by artillery or the artificial simulacra of rainbows on a wall? But if they are trustworthy interpreters of causes, they will also be sure and fertile indicators of effects and of works. However, I do not think it appropriate to divide my history in accordance with this threefold partition, so as to deal with singular instances separately, but I shall mix the three kinds, joining things natural with artificial. ordinary with extraordinary, and paying very close attention to all the most useful ones.

Now it would be more usual to begin with the phenomena of the ether. But I, sacrificing nothing of the seriousness of my undertaking, shall give priority to things which make up and answer to a nature more general, in which both globes share. I shall begin in fact with a history of bodies according to the difference which seems the simplest, that is, the abundance or paucity of the matter contained and spread out within the same space or boundaries, seeing indeed that none of the pronouncements about nature is truer than that double proposition. Nothing comes from nothing, nor is anything reduced to nothing, but the very quantum of nature, or the whole sum of matter always remains and stays the same, and is in no way increased or diminished. Moreover, it is no less certain. even though not so clearly noted or asserted (whatever stories people make up about the impartial potential of matter towards forms) that more or less of this quantity of matter is contained in the same volumes of space according to the diversity of the bodies which occupy them, bodies some of which we find to be very obviously more compact, others more extended or diffuse. For a vessel or cauldron filled with water and air does not hold an equal portion of matter, but more of the one and less of the other. Therefore if someone claimed that a given amount of water could be made from the same amount of air, it would be the same as saying that something can come from nothing. For what you deem to be lacking from the quantity of matter would have to have been made up from nothing. On the other hand, if someone claimed that a given amount of water could be turned into the same amount of air, it would be the same as saying that something can be reduced to nothing. For what you deem to be extra in the quantity of matter would likewise have to have vanished into nothingness. There is no doubt in my mind that this business is capable of being reduced to calculation, to indefinite proportions perhaps in some things, but to ones precise and certain in others, and known to nature. As, for example, if someone said that the concentration of matter in a body of gold exceeded than of a body of spirit of wine by a factor of twenty to one or thereabouts, he would nor be wrong. So as I now mean to present the history I mentioned concerning the abundance and paucity of matter, and its coming together and expansion, things from which the notions of Dense and Rare (if properly understood) take their origin, I shall so order matters that I shall draw up the relative figures for different bodies (as of gold, water, oil, air and flame) first. Then after examining these, I shall record with calculations or ratios the retreats and expatiations of each particular body. For a given body, even without anything being added to it or taken away, or at least nor in proportion to its contraction and extension, allows itself to be gathered by various impulses both external and internal into a larger or smaller sphere. Sometimes the body struggles and strives to restore itself into its old sphere, sometimes it clearly goes beyond that and does not try to revert. Here I shall first record the courses, differences and proportions of any natural body (as to its extent) compared with its openings and closings up, that is, with its powders, its calces, its virrifications, its dissolutions, its distillations, vapours and breaths, its exhalations and inflammations; then I shall set out the actions and motions themselves, the progressions and the limits of contraction and dilatation, and when bodies restore themselves and when they go beyond than in respect of their extent; but I shall especially note the efficient causes and media by means of which such contractions and dilatations of bodies come about; and meanwhile I shall in passing append the virtues and actions which bodies get and take on from such compressions and dilatations.

And since I know well how difficult a thing it is, in the present climate of opinion, to familiarise oneself with nature right from the very beginning, I shall add my own observations to gain men's attention and arouse them to contemplation. Now as far as the demonstration or revealing of the density and rarity of bodies is concerned, I have no doubt or hesitation that as to dense and palpable bodies the motion of gravity (as they call it) may be taken as the best and most ready test, for the more compact the body, the heavier it is. But when it comes to the level of airy and spiritual things, then scales will for sure be of no use to me, and I shall need another kind of industry. I shall begin, however, with Gold: which of all the things we have (for philosophy has nor grown up enough for us to say anything for certain about the bowels of the Earth) is the heaviest and contains the most matter in the smallest space, and I shall relate the ratios of the rest to the sphere of this body, with the reminder that I am not dealing here with the history of weights except in so far as it sheds light for demonstrating the space or dimensions of bodies. ...

Physics and Philosophy

2006-12-08T02:51:00.000-08:00

MIA Philosophy Resource from Andy Blunden

Werner Heisenberg (1958)
Physics and Philosophy

Source: Physics and Philosophy, 1958; Chapters 2 (History), 3 (Copenhagen interpretation) and 5 (HPS), reproduced here;
Published: by George Allen and Unwin Edition, 1959.
3
The Copenhagen Interpretation of Quantum Theory

THE Copenhagen interpretation of quantum theory starts from a paradox. Any experiment in physics, whether it refers to the phenomena of daily life or to atomic events, is to be described in the terms of classical physics. The concepts of classical physics form the language by which we describe the arrangements of our experiments and state the results. We cannot and should not replace these concepts by any others. Still the application of these concepts is limited by the relations of uncertainty. We must keep in mind this limited range of applicability of the classical concepts while using them, but we cannot and should not try to improve them.

For a better understanding of this paradox it is useful to compare the procedure for the theoretical interpretation of an experiment in classical physics and in quantum theory. In Newton's mechanics, for instance, we may start by measuring the position and the velocity of the planet whose motion we are going to study. The result of the observation is translated into mathematics by deriving numbers for the co-ordinates and the momenta of the planet from the observation. Then the equations of motion are used to derive from these values of the co-ordinates and momenta at a given time the values of these co-ordinates or any other properties of the system at a later time, and in this way the astronomer can predict the properties of the system at a later time. He can, for instance, predict the exact time for an eclipse of the moon.

In quantum theory the procedure is slightly different. We could for instance be interested in the motion of an electron through a cloud chamber and could determine by some kind of observation the initial position and velocity of the electron. But this determination will not be accurate- it will at least contain the inaccuracies following from the uncertainty relations and will probably contain still larger errors due to the difficulty of the experiment. It is the first of these inaccuracies which allows us to translate the result of the observation into the mathematical scheme of quantum theory. A probability function is written down which represents the experimental situation at the time of the measurement, including even the possible errors of the measurement.

This probability function represents a mixture of two things, partly a fast and partly our knowledge of a fact. It represents a fact in so far as it assigns at the initial time the probability unity (i.e., complete certainty) to the initial situation: the electron moving with the observed velocity at the observed position; 'observed' means observed within the accuracy of the experiment. It represents our knowledge in so far as another observer could perhaps know the position of the electron more accurately. The error in the experiment does - at least to some extent - not represent a property of the electron but a deficiency in our knowledge of the electron. Also this deficiency of knowledge is expressed in the probability function.

In classical physics one should in a careful investigation also consider the error of the observation. As a result one would get a probability distribution for the initial values of the co-ordinates and velocities and therefore something very similar to the probability function in quantum mechanics. Only the necessary uncertainty due to the uncertainty relations is lacking in classical physics.

When the probability function in quantum theory has been determined at the initial time from the observation, one can from the laws of quantum theory calculate the probability function at any later time and can thereby determine the probability for a measurement giving a specified value of the measured quantity. We can, for instance, predict the probability for finding the electron at a later time at a given point in the cloud chamber. It should be emphasised, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. l he probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. Only then does the probability function allow us to calculate the probable result of the new measurement. The result of the measurement again will be stated in terms of classical physics.

Therefore, the theoretical-interpretation of an experiment requires three distinct steps: (I) the translation of the initial experimental situation into a probability function; (2) the following up of this function in the course of time; (3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function. For the first step the fulfilment of the uncertainty relations is a necessary condition. The second step cannot be described in terms of the classical concepts; there is no description of what happens to the system between the initial observation and the next measurement. It is only in the third step that we change over again from the 'possible' to the 'actual'.

Let us illustrate these three steps in a simple ideal experiment. It has been said that the atom consists of a nucleus and electrons moving around the nucleus; it has also been stated that the concept of an electronic orbit is doubtful. One could argue that it should at least in principle be possible to observe the electron in its orbit. One should simply look at the atom through a microscope of a very high revolving power, then one would see the electron moving in its orbit. Such a high revolving power could to be sure not be obtained by a microscope using ordinary light, since the inaccuracy of the measurement of the position can never be smaller than the wave length of the light. But a microscope using ~~-rays with a wave length smaller than the size of the atom would do. Such a microscope has not yet been constructed but that should not prevent us from discussing the ideal experiment.

Is the first step, the translation of the result of the observation into a probability function, possible? It is possible only if the uncertainty relation is fulfilled after the observation. The position of the electron will be known with an accuracy given by the wave length of the y-ray. The electron may have been practically at rest before the observation. But in the act of observation at least one light quantum of the y-ray must have passed the microscope and must first have been deflected by the electron. Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations. Therefore, there is no difficulty with the first step.

At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus. The second step shows a wave pocket moving not around the nucleus but away from the atom, because the first light quantum will have knocked the electron out from the atom. The momentum of light quantum of the y-ray is much bigger than the original momentum of the electron if the wave length of the e-ray is much smaller than the size of the atom. Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense. The next observation - the third step - will show the electron on its path from the atom. Quite generally there is no way of describing what happens between two consecutive observations. It is of course tempting to say that the electron must have been somewhere between the two observations and that therefore the electron must have described some kind of path or orbit even if it may be impossible to know which path. This would be a reasonable argument in classical physics. But in quantum theory it would be a misuse of the language which, as we will see later, cannot be justified. We can leave it open for the moment, whether this warning is a statement about the way in which we should talk about atomic events or a statement about the events themselves, whether it refers to epistemology or to ontology. In any case we have to be very cautious about the wording of any statement concerning the behaviour of atomic particles.

Actually we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus. Such a description would directly contradict the other description if one does not pay attention to the limitations given by the uncertainty relations. Through the limitations the contradiction is avoided. The use of 'matter waves' is convenient, for example, when dealing with the radiation emitted by the atom. By means of its frequencies and intensities the radiation gives information about the oscillating charge distribution in the atom, and there the wave picture comes much nearer to the truth than the particle picture. Therefore, Bohr advocated the use of both pictures, which he called 'complementary' to each other. The two pictures are of course mutually exclusive, because a certain thing cannot at the same time be a particle (i.e., substance confined to a very small volume) and a wave (i.e., a field spread out over a large space), but the two complement each other. By playing with both pictures, by going from the one picture to the other and back again, we finally get the right impression of the strange kind of reality behind our atomic experiments. Bohr uses the concept of 'complementarity' at several places in the interpretation of quantum theory. The knowledge of the position of a particle is complementary to the knowledge of its velocity or momentum. If we know the one with high accuracy we cannot know the other with high accuracy; still we must know both for determining the behaviour of the system. The space-time description of the atomic events is complementary to their deterministic description. The probability function obeys an equation of motion as the coordinates did in Newtonian mechanics; its change in the course of time is completely determined by the quantum mechanical equation, but it does not allow a description in space and time. The observation, on the other hand, enforces the description in space and time but breaks the determined continuity of the probability function by changing our knowledge of the system.

Generally the dualism between two different descriptions of the same reality is no longer a difficulty since we know from the mathematical formulation of the theory that contradictions cannot arise. The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The formalism is normally written to resemble Newtonian mechanics, with equations of motion for the coordinates and the momenta of the particles.

But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary three-dimensional matter wave. Therefore, this possibility of playing with different complementary pictures has its analogy in the different transformations of the mathematical scheme; it does not lead to any difficulties in the Copenhagen interpretation of quantum theory.

A real difficulty in the understanding of this interpretation arises, however, when one asks the famous question: But what happens 'really' in an atomic event? It has been said before that the mechanism and the results of an observation can always be stated in terms of the classical concepts. But what one deduces from an observation is a probability function, a mathematical expression that combines statements about possibilities or tendencies with statements about our knowledge of facts So we cannot completely objectify the result of an observation, we cannot describe what 'happens' between this observation and the next. This looks as if we had introduced an element of subjectivism into the theory, as if we meant to say: what happens depends on our way of observing it or on the fast that we observe it. Before discussing this problem of subjectivism it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations.

For this purpose it is convenient to discuss the following ideal experiment: We assume that a small source of monochromatic light radiates toward a black screen with two small holes in it. The diameter of the holes may be not much bigger than the wave length of the light, but their distance will be very much bigger. At some distance behind the screen a photographic plate registers the incident light. If one describes this experiment in terms of the wave picture, one says that the primary wave penetrates through the two holes, there will be secondary spherical waves starting from the holes that interfere with one another, and the interference will produce a pattern of varying intensity on the photographic plate.

The blackening of the photographic plate is a quantum process, a chemical reaction produced by single light quanta. Therefore, it must also be possible to describe the experiment in terms of light quanta. If it would be permissible to say what happens to the single light quantum between its emission from the light source and its absorption in the photographic plate, one could argue as follows: The single light quantum can come through the first hole or through the second one. If it goes through the first hole and is scattered there, its probability for being absorbed at a certain point of the photographic plate cannot depend upon whether the second hole is closed or open. The probability distribution on the plate will be the same as if only the first hole was open. If the experiment is repeated many times and one takes together all cases in which the light quantum has gone through the first hole, the blackening of the plate due to these cases will correspond to this probability distribution. If one considers only those light quanta that go through the second hole, the blackening should correspond to a probability distribution derived from the assumption that only the second hole is open. The total blackening, therefore, should just be the sum of the blackenings in the two cases; in other words, there should be no interference pattern. But we know this is not correct, and the experiment will show the interference pattern. Therefore, the statement that any light quantum must have gone either through the first or through the second hole is problematic and leads to contradictions. This example shows clearly that the concept of the probability function does not allow a description of what happens between two observations. Any attempt to find such a description would lead to contradictions; this must mean that the term 'happens' is restricted to the observation.

Now, this is a very strange result, since it seems to indicate that the observation plays a decisive role in the event and that the reality varies, depending upon whether we observe it or not. To make this point clearer we have to analyse the process of observation more closely.

To begin with, it is important to remember that in natural science we are not interested in the universe as a whole, including ourselves, but we direct our attention to some part of the universe and make that the object of our studies. In atomic physics this part is usually a very small object, an atomic particle or a group of such particles, sometimes much larger - the size does not matter; but it is important that a large part of the universe, including ourselves, does not belong to the object.

Now, the theoretical interpretation of an experiment starts with the two steps that have been discussed. In the first step we have to describe the arrangement of the experiment, eventually combined with a first observation, in terms of classical physics and translate this description into a probability function. This probability function follows the laws of quantum theory, and its change in the course of time, which is continuous, can be calculated from the initial conditions; this is the second step. The probability function combines objective and subjective elements. It contains statements about possibilities or better tendencies ('potentia' in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer; and it contains statements about our knowledge of the system, which of course are subjective in so far as they may be different for different observers. In ideal cases the subjective element in the probability function may be practically negligible as compared with the objective one. The physicists then speak of a 'pure case'.

When we now come to 'the next observation. the result of which should be predicted from the theory, it is very important to realize that our object has to be in contact with the other part of-the world, namely, the experimental arrangement, the measuring rod, etc., before or at least at the moment of observation. This means that the equation of motion for the probability function does now contain the influence of the interaction with the measuring device. This influence introduces a new element of uncertainty, since the measuring device is necessarily described in the terms of classical physics; such a description contains all the uncertainties concerning the microscopic structure of the device which we know from thermodynamics, and since the device is connected with the rest of the world, it contains in fact the uncertainties of the microscopic structure of the whole world. These uncertainties may be called objective in so far as they are simply a consequence of the description in the terms of classical physics and do not depend on any observer. They may be called subjective in so far as they refer to our incomplete knowledge of the world.

After this interaction has taken place, the probability function contains the objective element of tendency and the subjective element of incomplete knowledge, even if it has been a 'pure case' before. It is for this reason that the result of the observation cannot generally be predicted with certainty; what can be predicted is the probability of a certain result of the observation, and this statement about the probability can be checked by repeating the experiment many times. The probability function does - unlike the common procedure in Newtonian mechanics - not describe a certain event but, at least during the process of observation, a whole ensemble of possible events.

The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place. Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation also has undergone the discontinuous change and we speak of a 'quantum jump'. When the old adage 'Natura non facit saltus' is used as a basis for criticism of quantum theory, we can reply that certainly our knowledge can change suddenly and that this fact justifies the use of the term 'quantum jump'.

Therefore, the transition from the 'possible' to the 'actual' takes place during the act of observation. If we want to describe what happens in an atomic event, we have to realize that the word 'happens' can apply only to the observation, not to the state of affairs between two observations. It applies to the physical, not the psychical act of observation, and we may say that the transition from the 'possible' to the 'actual' takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.

To what extent, then, have we finally come to an objective description of the world, especially of the atomic world? In classical physics science started from the belief - or should one say from the illusion? - that we could describe the world or at least parts of the world without any reference to ourselves. This is actually possible to a large extent. We know that the city of London exists whether we see it or not. It may be said that classical physics is just that idealisation in which we can speak about parts of the world without any reference to ourselves. Its success has led to the general ideal of an objective description of the world. Objectivity has become the first criterion for the value of any scientific result. Does the Copenhagen interpretation of quantum theory still comply with this ideal? One may perhaps say that quantum theory corresponds to this ideal as far as possible. Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event. But it starts from the division of the world into the 'object' and the rest of the world, and from the fact that at least for the rest of the world we use the classical concepts in our description. This division is arbitrary and historically a direct consequence of our scientific method; the use of the classical concepts is finally a consequence of the general human way of thinking. But this is already a reference to ourselves and in so far our description is not completely objective.

It has been stated in the beginning that the Copenhagen interpretation of quantum theory starts with a paradox. It starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately. The tension between these two starting points is the root of the statistical character of quantum theory. Therefore, it has sometimes been suggested that one should depart from the classical concepts altogether and that a radical change in the concepts used for describing the experiments might possibly lead back to a non-statical, completely objective description of nature.

This suggestion, however, rests upon a misunderstanding. The concepts of classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of all natural science. Our actual situation in science is such that we do use the classical concepts for the description of the experiments, and it was the problem of quantum theory to find theoretical interpretation of the experiments on this basis. There is no use in discussing what could be done if we were other beings than we are. At this point we have to realize, as von Weizsäcker has put it, that 'Nature is earlier than man, but man is earlier than natural science.' The first part of the sentence justifies classical physics, with its ideal of complete objectivity. The second part tells us why we cannot escape the paradox of quantum theory, namely, the necessity of using the classical concepts.

We have to add some comments on the actual procedure in the quantum-theoretical interpretation of atomic events. It has been said that we always start with a division of the world into an object, which we are going to study, and the rest of the world, and that this division is to some extent arbitrary. It should indeed not make any difference in the final result if we, e.g., add some part of the measuring device or the whole device to the object and apply the laws of quantum theory to this more complicated object. It can be shown that such an alteration of the theoretical treatment would not alter the predictions concerning a given experiment. This follows mathematically from the-fact that the laws of quantum theory are for the phenomena in which Planck's constant can be considered as a very small quantity, approximately identical with the classical laws. But it would be a mistake to believe that this application of the quantum-theoretical laws to the measuring device could help to avoid the fundamental paradox of quantum theory.

The measuring device deserves this name only if it is in close contact with the rest of the world, if there is an interaction between the device and the observer. Therefore, the uncertainty with respect to the microscopic behaviour of the world will enter into the quantum-theoretical system here just as well as in the first interpretation. If the measuring device would be isolated from the rest of the world, it would be neither a measuring device nor could it be described in the terms of classical physics at all.

With regard to this situation Bohr has emphasised that it is more realistic to state that the division into the object and the l rest of the world is not arbitrary. Our actual situation in research work in atomic physics is usually this: we wish to understand a l certain phenomenon, we wish to recognise how this phenomenon follows from the general laws of nature. Therefore that part of matter or radiation which takes part in the phenomenon is the natural 'object' in the theoretical treatment and should be separated in this respect from the tools used to study the phenomenon. This again emphasises a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning. Our scientific work in physics consists in asking questions about nature in the language that we possess and trying to get an answer from experiment by the means that are at our disposal. In this way quantum theory reminds us, as Bohr has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence we are ourselves both players and spectators. It is understandable that in our scientific relation to nature our own activity becomes very important when we have to deal with parts of nature into which we can penetrate only by using the most elaborate tools.

Galileo’s Considerations on the Copernican Opinion

2006-12-08T02:48:00.000-08:00

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MIA Philosophy Resource from Andy Blunden

Galilei Galileo (1615)
Galileo’s Considerations on the Copernican Opinion

Source: Galileo’s Considerations on the Copernican System, 1615, from The Galileo Affair, edited by Maurice Finocchiaro. Complete letter.

In order to remove (as much as the blessed God allows me) the occasion to deviate from the most correct judgment about the resolution of the pending controversy, I shall try to do away with two ideas. These are notions which I believe some are attempting to impress on the minds of those persons who are charged with the deliberations, and, if I am not mistaken, they are concepts far from the truth.

The first is that no one has any reason to fear that the outcome might be scandalous; for the earth’s stability and sun’s motion are so well demonstrated in philosophy that we can be sure and indubitably certain about them; on the other hand, the contrary position is such an immense paradox and obvious foolishness so that no one can doubt in any way that it cannot be demonstrated now or ever, or indeed that it can never find a place in the mind of sensible persons. The other idea which they try to spread is the following: although that contrary assumption has been used by Copernicus and other astronomers, they did this in a suppositional manner, and insofar as it can account more conveniently for the appearances of celestial motions and facilitate astronomical calculations and computations, and it is not the case that the same persons who assumed it believed it to be true de facto and in nature; so the conclusion is that one can safely proceed to condemn it. However, if I am not mistaken, these ideas are fallacious and far from the truth, as I can show with the following considerations. These will only be general and suitable to be understood without much effort and labor even by someone who is not well versed in the natural and astronomical sciences. For, if there were the opportunity to treat these points with those who are very experienced in these studies, or at least who have the time to do the work required by the difficulty of the subject, then I should propose nothing but the reading of Copernicus’s own book; from it and from the strength of his demonstrations one could clearly see how true or false are the two ideas we are discussing.

That it is not to be disparaged as ridiculous is, therefore, clearly shown by the quality of the men, both ancient and modern, who have held and do hold it. No one can regard it as ridiculous unless he considers ridiculous and foolish Pythagoras with all his school, Philolaus (teacher of Plato), Plato himself (as Aristotle testifies in his book On the Heavens), Heraclides of Pontus, Ecphantus, Aristarchus of Samos, Hicetas and Seleucus the mathematician. Seneca himself not only does not ridicule it, hut he makes fun of those who do, writing in his book On Comets: “It is also important to study these questions in order to learn whether the universe goes around the motionless earth, or the earth rotates but the universe does not. For some have said that we are naturally unaware of motion, that sunrise and sunset are not due to the motion of the heavens, but that it is we ourselves who rise and set. The matter deserves consideration, so that we may know the conditions of our existence, whether we stand still or move very fast, whether God drives everything around us or drives us.” Regarding the moderns, Nicolaus Copernicus first accepted it and amply confirmed it in his whole book. Then there were others: William Gilbert, a distinguished physician and philosopher, who treats it at length and confirms it in his book On the Loadstone; Johannes Kepler, a living illustrious philosopher and mathematician in the service of the former and the current Emperor, follows the same opinion; Origanus (David Tost) at the beginning of his Ephemerides supports the earth’s motion with a very long discussion; and there is no lack of other authors who have published their reasons on the matter. Furthermore, though they have not published anything, I could name very many followers of this doctrine living in Rome, Florence, Venice, Padua, Naples, Pisa, Parma, and other places. This doctrine is not, therefore, ridiculous, having been accepted by great men; and, though their number is small compared to the followers of the common position, this is an indication of its being difficult to understand, rather than of its absurdity. Moreover, that it is grounded on very powerful and effective reasons may be shown from the fact that all its followers were previously of the contrary opinion, and indeed that for a long time they laughed at it and considered it foolish. Copernicus and I, and all others who are alive, are witnesses to this. Now, who will not believe that an opinion which is considered silly and indeed foolish, which has hardly one out of a thousand philosophers following it, and which is disapproved by the Prince of the prevailing philosophy, can become acceptable through anything but very firm demonstrations, very clear experiences, and very subtle observations? Certainly no one will be dissuaded of an opinion imbibed with mother’s milk from his earliest training, accepted by almost the whole world and supported by the authority of very serious writers, unless the contrary reasons are more than effective. If we reflect carefully, we find that there is more value in the authority of a single person who follows the Copernican opinion than in that of one hundred others who hold the contrary, since those who are persuaded of the truth of the Copernican system were in the beginning all very opposed. So I argue as follows.

Either those who are to be persuaded are capable of understanding the reasons of Copernicus and others who follow him, or they are not; moreover, either these reasons are true and demonstrative, or they are fallacious. If those who are to be persuaded are incapable, then they will never be persuaded by the true or by the false reasons; those who are capable of understanding the strength of the demonstrations will likewise never be persuaded if these demonstrations are fallacious; so neither those who do nor those who do not understand will be persuaded by fallacious reasons. Therefore, given that absolutely no one can be dissuaded from the first idea by fallacious reasons, it follows as a necessary consequence that, if anyone is persuaded of the contrary of what he previously believed, the reasons arc persuasive and true. But as a matter of fact there are many who are already persuaded by Copernican reasons. Therefore, it is true both that these reasons are effective and that the opinion does not deserve the label of ridiculous but the label of worthy of being very carefully considered and pondered.

Furthermore, how futile it is to argue for the plausibility of this or that opinion simply from the large number of followers may be easily inferred from this: no one follows this opinion who did not previously believe the contrary; but instead you will not find even a single person who, after holding this opinion, will pass to the other one, regardless of any discussion he hears; consequently, one may judge, even if he does not understand the reasons for one side or for the other, that probably the demonstrations for the earth’s motion are stronger than those for the other side. But I shall say more, namely that if the probability of the two positions were something to be won by ballot, I would be willing to concede defeat when the opposite side had one more vote than I out of one hundred; not only that, but I would be willing to agree that every individual vote of the opponents was worth ten of mine, as long as the decision was made by persons who had perfectly heard, intimately penetrated, and subtly examined all the reasons and evidence of the two sides; indeed it is reasonable to expect that such would be those who cast the votes. Hence this opinion is not ridiculous and contemptible, but somewhat shaky is the position of whoever wanted to capitalise on the common opinion of the many who have not accurately studied these authors. What then should we say of the noises and the idle chatter of someone who has not understood even the first and simplest principles of these doctrines, and who is not qualified to understand them ever? What importance should we give him?

Consider now those who persist in wanting to say that as an astronomer Copernicus considered the earth’s motion and the sun’s stability only a hypothesis which is more adequate to save celestial appearances and to calculate the motions of planets, but that he did not believe it to be true in reality and in nature. With all due respect, these people show that they have been too prone to believe the word of someone who speaks more out of whim than out of experience with Copernicus’s book or understanding the nature of this business. For this reason they talk about it in a way that is not altogether right.

First, limiting ourselves to general considerations, let us see his preface to Pope Paul III, to whom he dedicates the work. We shall find, to begin with, as if to comply with what they call the astronomer’s task, that he had done and completed the work in accordance with the hypothesis of the prevailing philosophy and of Ptolemy himself, so that there was in it nothing lacking. But then, taking off the clothes of a pure astronomer and putting on those of a contemplator of nature, he undertook to examine whether this astronomical assumption already introduced, which was completely satisfactory regarding the calculations and the appearances of the motions of all planets, could also truly happen in the world and in nature. He found that in no way could such an arrangement of parts exist: although each by itself was well proportioned, when they were put together the result was a very monstrous chimera.

And so he began to investigate what the system of the world could really be in nature, no longer for the sole convenience of the pure astronomer, whose calculations he had complied with, but in order to come to an understanding of such a noble physical problem; he was confident that, if one had been able to account for mere appearances by means of hypotheses which are not true, this could be done much better by means of the true and physical constitution of the world. Having at his disposal a very large number of physically true and real observations of the motions of the stars (and without this knowledge it is wholly impossible to solve the problem), he worked tirelessly in search of such a constitution. Encouraged by the authority of so many great men, he examined the motion of the earth and the stability of the sun. Without their encouragement and authority, by himself either he would not have conceived the idea, or he would have considered it a very great absurdity and paradox, as he confesses to have considered it at first. But then, through long sense observations, favourable results, and very firm demonstrations, he found it so consonant with the harmony of the world that he became completely certain of its truth. Hence this position is not introduced to satisfy the pure astronomer, but to satisfy the necessity of nature.

Furthermore, Copernicus knew and wrote in the same place that publishing this opinion would have made him look insane to the numberless followers of current philosophy, and especially to each and every layman. Nevertheless, urged by the requests of the Cardinal of Capua and the Bishop of Kulm, he published it. Now, would he not have been truly mad if, considering this opinion physically false, he had published that he believed it to be true, with the certain consequence that he would be regarded as a fool by the whole world? And why would he not have declared that he was using it only as an astronomer, but that he denied it as a philosopher, thus escaping the universal label of foolishness, to the advantage of his common sense?

Moreover, Copernicus states in great detail the grounds and reasons why the ancients believed the earth to be motionless, and then, examining the value of each in turn, he shows them to be ineffective. Now, who ever saw a sensible author engaged in confuting the demonstrations that confirm a proposition he considers true and real? And what kind of judgment would it be to criticise and to condemn a conclusion while in reality he wanted the reader to believe that he accepted it? This sort of incoherence cannot be attributed to such a man. Furthermore, note carefully that, since we are dealing with the motion or stability of the earth or of the sun, we are in a dilemma of contradictory propositions (one of which has to be true), and we cannot in any way resort to saying that perhaps it is neither this way nor that way. Now, if the earth’s stability and sun’s motion are de facto physically true and the contrary position is absurd, how can one reasonably say that the false view agrees better than the true one with the phenomena clearly visible and sensed in the movements and arrangement of the stars? Who does not know that there is a most agreeable harmony among all truths of nature, and a most sharp dissonance between false positions and true effects? Will it happen, then, that the earth’s motion and sun’s stability agree in every way with the arrangement of all other bodies in the universe and with all the phenomena, a thousand of them, which we and our predecessors have observed in great detail, and that this position is false? And can the earth’s stability and sun’s motion be considered true and not agree in any way with the other truths? If one could say that neither this nor that position is true, it might happen that one would be more convenient than the other in accounting for the appearances. But, given two positions, one of which must be true and the other false, to say that the false one agrees better with the effects of nature is really something that surprises my imagination. I add: if Copernicus confesses to having fully satisfied astronomers by means of the hypothesis commonly accepted as true, how can one say that by means of the false and foolish one he could or would want to satisfy again the same astronomers?

However, I now go on to consider the nature of the business from an internal viewpoint, and to show with how much care one must discuss it.

Astronomers have so far made two sorts of suppositions: some are primary and pertain to the absolute truth of nature; others are secondary and are imagined in order to account for the appearances of stellar motions, which appearances seem not to agree with the primary and true assumptions. For example, before trying to account for the appearances, acting not as a pure astronomer but as a pure philosopher, Ptolemy supposes, indeed he takes from philosophers, that celestial movements are all circular and regular, namely uniform; that heaven has a spherical shape; that the earth is at the center of the celestial sphere, is spherical, motionless, etc. Turning then to the inequalities we see in planetary movements and distances, which seem to clash with the primary physical suppositions already established, he goes on to another sort of supposition; these aim to identify the reasons why, without changing the primary ones, there is such a clear and sensible inequality in the movements of planets and in their approaching and their moving away from the earth. To do this he introduces some motions that are still circular, but around centers other than the earth’s, tracing eccentric and epicyclic circles. This secondary supposition is the one of which it could be said that the astronomer supposes it to facilitate his computations, without committing himself to maintaining that it is true in reality and in nature.

Let us now see in what kind of hypothesis Copernicus places the earth’s motion and sun’s stability. There is no doubt whatever, if we reflect carefully, that he places them among the primary and necessary suppositions about nature. For, as I have already stated, it seems that he had already given satisfaction to astronomers by the other road, and that he takes this one only to try to solve the greatest problem of nature. In fact, to say that he makes this supposition to facilitate astronomical calculations is so false that instead we can see him, when he comes to these calculations, leaving this supposition and returning to the old one, the latter being more readily and easily understood and still very quick even in computations. This may be seen as follows. Intrinsically, particular calculations can be made by taking one position as well as the other, that is, by making the earth or the heavens rotate; nevertheless, many geometers and astronomers in many books have already demonstrated the properties of orthogonal and oblique displacements of parts of the zodiac in relation to the equator, the declinations of the parts of the ecliptic, the variety of angles between it and both meridians and oblique horizons, and a thousand other specific details necessary to complete astronomical science. This ensures that, when he comes to examining these details of the primary motions, Copernicus himself examines them in the old manner, namely as occurring along circles traced in the heavens and around the motionless earth, even though stillness and stability should belong to the highest heaven, called the Prime Mobile, and motion to the earth. Thus in the introduction to Book Two he concludes: “People should not be surprised if we still use the ordinary terms for the rising and setting of the Sun and stars and similar occurrences, but should recognise that we are speaking in customary language, which is acceptable to everyone, yet always bearing in mind that ‘For us who ride the Earth, the Sun and Moon are passing; patterns of stars return, and then again recede’.” We should therefore understand clearly that Copernicus takes the earth’s motion and sun’s stability for no other reason and in no other way than to establish it, in the manner of the natural philosopher, as a hypothesis of the primary sort; on the contrary, when he comes to astronomical computations, he goes back to the old hypothesis, which takes the circles of the basic motions with their details to be located in the highest heaven around the motionless earth, being easier for everyone to understand on account of ingrained habit. But what am I saving? Such is the strength of truth and the weakness of falsehood, that those who speak this way reveal themselves not completely capable of understanding these subjects and not well versed in them; this happens when they let themselves be persuaded that the secondary kind of hypothesis is considered chimerical and fictional by Ptolemy and by other serious astronomers, and that they really regard them as physically false and introduced only for the sake of astronomical computations. The only support they give for this very fanciful opinion is a passage in Ptolemy where, unable to observe more than one simple anomaly in the sun, he wrote that to account for it one could take the hypothesis of a simple eccentric as well as that of an epicycle on a concentric, and he added he preferred the first for being simpler than the second; from these words some very superficially argue that Ptolemy did not consider necessary, but rather wholly fictional, both this and that supposition, since he said they are both equally convenient, while one and only one can be attributed to the sun’s behaviour. But what kind of superficiality is this? Who can do both of the following? First, to suppose as true the primary suppositions that planetary motions are circular and regular, and to admit (as the senses themselves necessarily force us) that in running through the zodiac all planets are now slow and now fast, indeed that most of them can be not only slow but also stationary and retrograde, and that we see them now very large and very near the earth and now very small and very far; and then, having understood these former points, to deny that eccentrics and epicycles can really exist in nature? This is wholly excusable for men who are not specialists in these sciences, but for others who would claim to be experts in them it would be an indication that they do not even understand the meaning of the terms eccentric and epicycle. One might just as well first admit that there are three letters, the first of which is G, the second O, and the third D, and then at the end deny that their combination yields GOD and claim that the result is SHADOW. But if rational arguments were not sufficient to make one understand the necessity of having to place eccentrics and epicycles really in nature, at least the senses themselves would have to persuade him: for we see the four Medicean planets’ trace four small circles around Jupiter which are very far from enclosing the earth, in short, four epicycles; Venus, which is seen now full of light and now very thinly crescent, provides conclusive evidence that its revolution is around the sun and not around the earth, and consequently that its orbit is an epicycle; and the same may be argued for the case of Mercury. Moreover, the three outer planets are very near the earth when they are in opposition to the sun, and very far when in conjunction; for example, Mars at its closest appears to the senses more than fifty times larger than at its farthest, so that some have occasionally feared that it had gotten lost or had vanished, being really invisible because of its great distance; now, what else can one conclude but that their revolution is made in eccentric circles, or in epicycles, or in a combination of the two, if we take the second anomaly into consideration? So, to deny eccentrics and epicycles in the motions of planets is like denying the light of the sun, or else it is to contradict oneself. Let us apply what I am saying more directly to our purpose: some say that modern astronomers introduce the earth’s motion and sun’s stability suppositionally in order to account for the phenomena and to facilitate calculations, just as epicycles and eccentrics are assumed in the same manner, though the same astronomers consider them physically chimerical and repugnant; I answer that I shall gladly agree with all this talk, as long as they limit themselves to staying within their own conceptions, namely that the earth’s motion and sun’s stability are as false or true in nature as epicycles and eccentrics. Let them, then, make every effort to do away with the true and real existence of these circles, for if they succeed in demonstrating their non-existence in nature, I shall immediately surrender and admit the earth’s motion to be a great absurdity. But if, on the contrary, they are forced to accept them, let them also accept the earth’s motion, and let them admit to have been convinced by their own contradictions.

I could present many other things for this same purpose. However, since I think that whoever is not persuaded by what I have said would not be persuaded by many more reasons either, I want these to suffice. I shall only add something about what could have been the motive why some have concluded with any plausibility that Copernicus himself did not really believe his own hypothesis.

There is on the reverse side of the title page of Copernicus’s book a certain preface to the reader, which is not by the author since it mentions him in the third person and is without signature. It clearly states that no one should believe in the least that Copernicus regarded his position as true, but only that he feigned and introduced it for the calculation of celestial motions; it ends its discussion by concluding that to hold it as true and real would be foolish. This conclusion is so explicit that whoever reads no further, and believes it to have been placed at least with the author’s consent, deserves to be somewhat excused for his error. But what weight to give to the opinion of those who would judge a book without reading anything but a brief preface by the printer or publisher, I let each one decide for himself. I say that this preface can only have originated from the publisher to facilitate the sale of a book which common people would have regarded as a fanciful chimera if a similar preface had not been added; for most of the time buyers are in the habit of reading such prefaces before buying the work. Not only was this preface not written by the author, but it was included without his consent, and also without his knowledge; this is shown by the errors it contains, which the author would never have committed.

This preface says no one can consider it verisimilar, unless he is completely ignorant of geometry and optics, that Venus has such a large epicycle enabling it now to precede and now to follow the sun by 40 degrees or more; for it would have to happen that when it is highest its diameter should appear only one-fourth of what it appears when it is lowest, and that in the latter location its body should be seen as sixteen times bigger than in the former; but these things, he says, are repugnant to the observations made throughout the centuries. In these assertions we see, first, that the writer does not know that Venus departs on one side and on the other of the sun by about 48 degrees, and not 40 as he says. Moreover, he asserts that its diameter should appear four times, and its body sixteen times, larger in one position than in the other. Here, first, due to a geometrical oversight he does not understand that when one globe has a diameter four times larger than another, its body is sixty-four times bigger, and not sixteen, as he stated. Hence, if he considered such an epicycle absurd and wanted to declare it to be physically impossible, if he had understood this subject, he could have made the absurdity much greater; for, according to the position he wants to refute (well known to astronomers), Venus digresses from the sun almost 48 degrees, and when farthest from the earth its distance must be six times greater than when closest, and consequently its apparent diameter in the latter position is more than six times larger than in the former (not four times), and its body more than two hundred and sixteen times greater (and not just sixteen). These errors are so gross that it is impossible to believe they were committed by Copernicus, or by anyone else but the most unqualified persons. Moreover, why label such a large epicycle most absurd, so that because of such an absurdity we would conclude that Copernicus did not regard his assumptions as true, and that neither should others so regard them? He should have remembered that in chapter 10 of the first hook Copernicus is speaking ad hominem and is attacking other astronomers who allege that it is a great absurdity to give Venus such an epicycle, which is so large as to exceed the whole lunar orbit by more than two hundred times, and which does not contain anything inside; he then removes the absurdity when he shows that inside Venus’s orbit is contained the orbit of Mercury and, placed at the centre, the body of the sun itself. What frivolity is this, then, to want to show a position mistaken and false on account of a difficulty which that position not only does not introduce in nature, but completely removes? Similarly it removes the immense epicycles which out of necessity other astronomers assumed in the other system. This only touches the writer of Copernicus’s preface; so we may argue that, if he had included something else professionally relevant, he would have committed other errors.

But finally, to remove any shadow of a doubt, if the failure to observe such great variations in the apparent sizes of the body of Venus should cast doubt on its circular revolution around the sun (from the viewpoint of the Copernican system), then let us make careful observations with a suitable instrument, namely with a good telescope, and we shall find all effects and experiences exactly agreeing; that is, we shall see Venus crescent when it is nearest to the earth, and with a diameter six times larger than when it is at its maximum distance, namely above the sun, where it is seen round and very small. I have discussed elsewhere the reasons for not detecting these variations with our simple eyesight, but just as from this failure we could reasonably deny that supposition, so now, from seeing the very exact correspondence in this and every other detail, we should abandon any doubt and consider the supposition true and real. As for the rest of this admirable system, whoever desires to ascertain the opinion of Copernicus himself should not read the fanciful preface of the printer, but the whole work of the author himself; without a doubt he will grasp first-hand that Copernicus held as very true the stability of the sun and the motion of the earth.
II

The motion of the earth and stability of the sun could never be against Faith or Holy Scripture, if this proposition were correctly proved to be physically true by philosophers, astronomers, and mathematicians, with the help of sense experiences, accurate observations, and necessary demonstrations. However, in this case, if some passages of Scripture were to sound contrary, we would have to say that this is due to the weakness of our mind, which is unable to grasp the true meaning of Scripture in this particular case. This is the common doctrine, and it is entirely right, since one truth cannot contradict another truth. On the other hand, whoever wants to condemn it judicially must first demonstrate it to be physically false by collecting the reasons against it.

Now, one wants to know where to begin in order to ascertain its falsity, that is, whether from the authority of Scripture or from the refutation of the demonstrations and observations of philosophers and astronomers. I answer that one must start from the place which is safest and least likely to bring about a scandal; this means beginning with physical and mathematical arguments. For if the reasons proving the earth’s motion arc found fallacious, and the contrary ones conclusive, then we have already become certain of the falsity of this proposition and the truth of the opposite, which we now say corresponds to the meaning of Scripture; so one would be free to condemn the false proposition and there would be no danger. But if those reasons arc found true and necessary, this will not bring any harm to the authority of Scripture; instead we shall have been cautioned that due to our ignorance we had not grasped the true sense of Scripture, and that we can learn this meaning with the help of the newly acquired physical truth. Therefore, beginning with the arguments is safe in any case. On the other hand, if we were to fix only on what seemed to us the true and certain meaning of Scripture, and we were to go on to condemn such a proposition without examining the strength of the arguments, what a scandal would follow if sense experiences and reasons were to show the opposite? And who would have brought confusion to the Holy Church ? Those who had suggested the greatest consideration of the arguments, or those who had disparaged them? One can see, then, which road is safer.

Moreover, we admit that a physical proposition which has been proved true by physical and mathematical demonstrations can never contradict Scripture, but that in such a case it is the weakness of our mind which prevents us from grasping its true meaning. On the other hand, whoever wants to use the authority of the same passages of Scripture to confute and prove false the same proposition would commit the error called “begging the question.” For, the true meaning of Scripture being in doubt in the light of the arguments, one cannot take it as clear and certain in order to refute the same proposition; instead one must cripple the arguments and find the fallacies with the help of other reasons and experiences and morc certain observations. When thc factual and physical truth has been found in this manner, then, and not before, can one be assured of the true meaning of Scripture and safely use it. Thus the safe road is to begin with the arguments, confirming the true and refuting the fallacious ones.

If the earth de facto moves, we cannot change nature and arrange for it not to move. But we can rather easily remove the opposition of Scripture with the mere admission that we do not grasp its true meaning. Therefore, the way to be sure not to err is to begin with astronomical and physical investigations, and not with scriptural ones.

I am always told that, in interpreting the passages of Scripture relevant to this point, all Fathers agree to the meaning which is simplest and corresponds to the literal meaning; hence, presumably, it is improper to give them another meaning or to change the common interpretation, because this would amount to accusing the Fathers of carelessness or negligence. I answer by admitting that the Fathers indeed deserve reasonable and proper respect, hut I add that we have an excuse for them very readily: it is that on this subject they never interpreted Scripture differently from the literal meaning, because at their time the opinion of the earth’s motion was totally buried and no one even talked about it, let alone wrote about it or maintained it. But there is no trace of negligence by the Fathers for not thinking about what was completely hidden. That they did not think about it is clear from the fact that in their writings one cannot find even a word about this opinion. And if anyone were to say that they considered it, this would make its condemnation more dangerous; for after considering it, not only did they not condemn it, but they did not express any doubt about it.

Thus the defence of the Fathers is readily available and very easy. On the contrary, it would be very difficult or impossible to excuse or exonerate from a similar charge of carelessness the Popes, Councils, and Congregations of the Index of the last eighty years, if this doctrine were erroneous and deserving of condemnation; for they have let this opinion circulate in a book which was first written on orders from a Pope, and then printed on orders from a cardinal and a bishop, dedicated to another Pope, and, most important, received by the Holy Church, so that one cannot say that it had remained unknown. If, then, the inappropriateness of charging our highest authorities with negligence is to be taken into account, as it should, Let us make sure that in trying to escape one absurdity we do not fall into a greater one.

But assume now that someone regards it as inappropriate to abandon the unanimous interpretation of the Fathers, even in the case of physical propositions not discussed by them and whose opposite they did not even consider; I then ask what one should do if necessary demonstrations showed the facts of nature to be the opposite. Which of the two decrees should be changed? The one which stipulates that no proposition can be both true and erroneous, or the other one which obliges us to regard as articles of faith physical propositions supported by the unanimous interpretation of the Fathers? It seems to me, if I am not mistaken, that it would be safer to modify this second decree than to be forced to hold as an article of faith a physical proposition which had been demonstrated with conclusive reasons to be factually false in nature. It also seems to me that one could say that the unanimous interpretation of the Fathers should have absolute authority in the case of propositions which they aired, and for which no contrary demonstrations exist and it is certain that none could ever exist. I do not bring in the fact that it is very clear that the Council requires only that one agree with the unanimous interpretation of the Fathers “in matters of faith and morals, etc.”
III

1. Copernicus uses eccentrics and epicycles, but these were not the reason for rejecting the Ptolemaic system, since they undoubtedly exist in the heavens; it was other difficulties.
2. In regard to philosophers, if they were true philosophers, namely lovers of truth, they should not get irritated, but, learning that they were wrong, they should thank whoever shows them the truth; and if their opinion were to stand up, they would have reason to take pride in it, rather than being irritated. Theologians should not get irritated because, if this opinion were found false then they could freely prohibit it, and if it were discovered true then they should rejoice that others have found the way to understand the true meaning of Scripture and have restrained them from perpetrating a serious scandal by condemning a true proposition.
In regard to falsifying Scripture, this is not and will never be the intention of Catholic astronomers such as ourselves; rather our view is that Scripture corresponds very well to truths demonstrated about nature. Moreover, certain theologians who are not astronomers should be careful about falsifying Scripture by wanting to interpret it as opposed to propositions which may be true and demonstrable.
3. It might happen that we could have difficulties in interpreting Scripture, but this would occur because of our ignorance and not be cause there really are or can be insuperable difficulties in reconciling Scripture with demonstrated truths.
4. The Council speaks “about matters of faith and morals, etc.” So there is an answer to the claim that such a proposition is “an article of faith by reason of the speaker,” though not “by reason of the topic,” and that therefore it is among those covered by the Council. The answer is that everything in Scripture is “an article of faith by reason of the speaker,” so that in this regard it should be included in the rule of the Council; but this clearly has not been done because in that case it would have said that “the interpretation of the Fathers is to be followed for every word of Scripture, etc.,” and not “for matters of faith and morals”; having thus said “for matters of faith,” we see that its intention was to mean “for matters of faith by reason of the topic.”
Then consider that it is much more a matter of faith to hold that Abraham had some children and that Tobias had a dog, because Scripture says it, than it would be to hold that the earth moves, even if this were found in the same Scripture, and further that to deny the former is a heresy, but not to deny the latter. It seems to me that this depends on the following reason. There have always been in the world men who had two, four, six children, etc., or none, and similarly people who have dogs and who do not, so that it is equally credible that some have children or dogs and others do not; hence there appears to be no reason why in such propositions the Holy Spirit should speak differently from the truth, the negative and the affirmative sides being equally credible to all men. But it is not so with the motion of the earth and the stability of the sun; these propositions are very far removed from the understanding of the masses, for on these matters not relevant to their eternal life the Holy Spirit chose to conform its pronouncements with their abilities, even when facts are otherwise from the point of view of the thing in itself.
5. In regard to placing the sun in heaven and the earth outside it, as Scripture seems to affirm, etc., this truly seems to me to be a simple perception of ours and a manner of speaking only for our convenience. For, in reality all that is surrounded by heaven is in heaven, just as all that is surrounded by the city walls is in the city; indeed, if one were to express a preference, what is in the middle is more in heaven and in the city, being, as it were, at the heart of the city and of heaven. That difference exists because one takes the elemental region surrounding the earth as being very different from the celestial region. But such a difference will always exist regardless of where these elements are placed; and it will always be true that from the viewpoint of our convenience the earth is below us and heaven above, since all the inhabitants of the earth have heaven above our heads, which is our upwards, and the center of the earth under our feet, which is our downwards; so, in relation to us the center of the earth and the surface of heaven are the farthest places, that is, the endpoints of our up and down, which are diametrically opposite points.
6. Not to believe that there is a demonstration of the earth’s mobility until it is shown is very prudent, nor do we ask that anyone believe such a thing without a demonstration. On the contrary, we only seek that, for the advantage of the Holy Church, one examine with the utmost severity what the followers of this doctrine know and can advance, and that nothing be granted them unless the strength of their arguments greatly exceeds that of the reasons for the opposite side. Now, if they are not more than ninety percent right, they may be dismissed; but if all that is produced by philosophers and astronomers on the opposite side is shown to be mostly false and wholly inconsequential, then the other side should not he disparaged, nor deemed paradoxical, so as to think that it could never he clearly proved. It is proper to make such a generous offer since it is clear that those who hold the false side cannot have in their favour any valid reason or experiment, whereas it is necessary that all things agree and correspond with the true side.
7. It is true that it is not the same to show that one can save the appearances with the earth’s motion and the sun’s stability, and to demonstrate that these hypotheses are really true in nature. But it is equally true, or even more so, that one cannot account for such appearances with the other commonly accepted system. The latter is undoubtedly false, while it is clear that the former, which can account for them, may be true. Nor can one or should one seek any greater truth in a position than that it corresponds with all particular appearances.
8. One is not asking that in case of doubt the interpretation of the Fathers should be abandoned, but only that an attempt be made to gain certainty regarding what is in doubt, and that therefore no one disparage what attracts and has attracted very great philosophers and astronomers. Then, after all necessary care has been taken, the decision may be made.
9. We believe that Solomon, Moses, and all other sacred writers knew perfectly the constitution of the world, as they also knew that God has no hands, no feet, and no experience of anger, forgetfulness, or regret; nor will we ever doubt this. But we say what the Holy Fathers and in particular St. Augustine say about these matters, namely that the Holy Spirit inspired them to write what they wrote for various reasons, etc.
10. The error of the apparent movement of the shore and stability of the ship is known by us after having many times observed the motion of boats from the shore, and many other times observed the shore from a boat; and so, if we could now stay on earth and now go to the sun or other star, perhaps we would acquire sensible and certain knowledge of which one of them moves. To be sure, if we looked only at these two bodies, it would always seem to us that the one we were on was standing still, just as looking only at the water and the boat always gives the appearance that the water is flowing and the boat is standing still. Moreover, the two situations are very different: there is great disparity between a small boat, separable from its environment, and the immense shore, known by us through thousands of experiences to be motionless, that is, motionless in relation to the water and the boat; but the other comparison is between two bodies both of which are substantial and equally inclined toward motion and toward rest. Thus it would be more relevant to compare between themselves two boats, in which case it is absolutely certain that the one we were on would always appear to us as motionless, as long as we could not consider any other relationship but that which holds between these two ships.
There is, therefore, a very great need to correct the error about observing whether the earth or else the sun moves, for it is clear that to someone on the moon or any other planet it would always appear that it was standing still and the other stars were moving. But these and many other more plausible reasons of the followers of the common opinion are the ones that must be untied very openly, before one can pretend even to be heard, let alone approved; unfortunately we have not done a very detailed examination of what is produced against us. Moreover, neither Copernicus nor his followers will ever use this phenomenon of the shore and the boat to prove that the earth is in motion and the sun at rest. They only adduce it as an example that serves to show, not the truth of their position, but the absence of contradiction between the appearance of a stable earth and moving sun to our simple sense experience, and the reality of the contrary. For if this were one of Copernicus’s demonstrations, or if his others did not argue more effectively, I really think that no one would agree with him.

百度搜索引擎存在重大缺陷漏洞 - 月光博客

2006-12-06T10:07:00.000-08:00

[Enter your comment here]so it is

有關于今天晚上音樂會：莫扎特250誕辰紀念

2006-12-01T11:16:00.000-08:00

比我大228歲的wolfgang生日是1月27日，卒于1791年12月5日。

　　關于wolfgang我沒有太多介紹的，所以借著這個機會，我多聊聊西安的音樂文化狀況。

　　

　　錯過了開場的Figaro婚禮的序曲，我用20￥買了一張黃牛票進場，沒有想到噩夢開始了：偉大的卞組善調教并指揮陜西樂團配合著師大音樂老
師調戲著或者說褻瀆著D小調協奏曲，NO.20,這部被高傲的貝多芬最為推崇的鋼琴協奏曲。暫且不談音色控制、演奏者對樂曲的獨特詮釋，連基礎的音準都不
嫩保證，鋼琴演奏者的錯誤幾乎不是藝術性的，更恐怖的莫過于第二樂章的第二主題，我隱約看到指揮頭上的烏鴉。號稱錯音之王的Rubinstein，更多的
是一種激情的揮發，錯的一蹴而就，錯的水到渠成；而這位老師似乎完全出於態度的不認真以及對觀眾的不尊重。除卻這些恐怖元素，我想最值得表揚的還是演奏者
的心理素質，除了那么大的錯誤還嫩全身而退可謂是及其出色的演員，而非音樂家。意料之中，觀眾的熱情在每個樂章結束時體現了出來，甚至在第三樂章開始時還
沒有得到控制。第三樂章則更像一座搖搖欲墜的大樓，大家各自為政，嘩啦啦樹倒猢猻散，卞指揮出於憤怒，放任自流，趕緊結束了要緊，似乎觀眾的注意力都已經
放在了鮮花的mm身上，畢竟愛美之心人皆有之。

　　

　　如果說鬧劇的開場往往嫩夠起到活躍輕松氣氛的作用，放松了的我們開始緊繃神經傾聽Wolfgang的另一個偉大成就：歌劇。美麗的
Cherubino選擇的是著名唱段Voi che sapete che cosa amor(你們可知道）和Non so pi cosa son
cosa
facio（不知道自己幹了些什么）。很多中國演唱者的問題就是咬字不清，更多的在意自己聲音而忽視了唱的內容以及如何與觀眾交流。這點問題在這位美女也
有所體現，但是她良好的臺風拉近了與觀眾之間的距離。都說mezzo
soprano不好唱，此話不假，聽了那么多大師級的演繹，我得出的結論是能找到開與閉之間最佳平衡的，就是大師。我看出這位美女的努力，但是天賦似乎更
加起到決定性。

　　

　　逐漸進入狀態的音樂會迎來了本場最高水平的soprano。分別詮釋Don
Giovanni的zerlina和Figaro的公爵夫人，選段Dove sono ibei
momenti的絕對體現了她的實力。把怨婦對美好婚姻生活的懷念和對新生活的追求之情體現的淋漓盡致，無論是咬字，音準還是音色都屬上乘。美麗的花腔之
后，場上的氣氛到達了高潮，觀眾似乎也來了興趣，可惜無奈的是：居然就這么完了。PS，她的顫音還不是很成熟，這是小小的敗筆。

　　

　　難道真的是拋物線嗎？選擇憂鬱的G小調40交響曲就要正確的演奏，這是我一貫的認知：不是什么東西都可以拿來惡搞的。第一樂章采取Bohm的
慢速，壓抑的處理方法，雖然我個人更加傾向Bruno
Walter的風格。但是對第一主題的再現似乎應該用中強以體現情緒的變化，可是不知乜原因，也許是樂隊的能力有限，這一點無法體現出來。令人欣慰的是第
二主題非常的正常，沒有出現管樂的失誤，小提琴也沒有錯音，恩。

　　第二樂章的錯誤非常多，灰常灰常的多，以至于連我旁邊的大爺都笑場了。令人擔心的小提琴再次出現了紕漏，然而表現一直不錯的管樂居然也瘋了似的吹出騷擾美女的音符，好在最強悍的低音部保證了曲子嫩夠繼續下去，再次挺他們的低音部，尤其是首席大提琴。

　　最正經的還是第三樂章，弦樂總算爭氣了一回，合奏的非常漂亮，尤其是第一小提琴，冷峻、干脆和直接可以形容他們的表現。莊嚴的小步舞曲，大調
與小調的對比，憂鬱而沉重的第一主題和明亮而純凈的第二主題之間體現了現實的殘酷與理想的美好。典型的莫扎特，典型的水瓶座左撇子，我都不敢再類比了（有
些飄飄然不好意思）。

　　可惡的第四樂章難度太大了，又回到了協奏曲的第三樂章水平，混亂，混亂還是混亂。奔放的賦格難道還要出現在本聲部里嗎？向上的音節充滿了希望，弦樂和管樂的交融簡直水乳，美感就在這里體現。

　　

　　居然還有bonous，我暈。選擇的是第一交響曲的第三樂章，僅僅是為了紀念這個音樂prodigy而已。能夠想象8歲的孩子，就能寫出像樣的交響曲嗎，沒有他老豆的早期音樂教育，也就沒有他的成功。

　　

　　最后總結一下：這個樂隊的脊柱還是很硬的，灰常有前途。觀眾的素質還是需要慢慢培養的，比如開始前現做個培訓什么的。

　　

　　雖然這個樂隊水平很一般，但是醜兒子都有母親愛的，何況這個樂隊是我們這里的一片綠洲呢。我批判，我關心，我喜歡。

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2006-12-01T11:07:00.000-08:00

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