数学家传记
恩培多克勒 是一位希腊哲学家,以其认为所有物质由四种元素组成:火、空气、水和土而闻名。有些人认为他是修辞学的发明者和意大利医学科学的创始人。
恩培多克勒出生于西西里岛南海岸的阿克拉加斯。阿克拉加斯这个名字是希腊语,而该镇的拉丁语名称是阿格里真托姆。后来该镇被称为吉尔真蒂,再后来以其现在的名称阿格里真托而闻名。在公元前406年被迦太基人摧毁之前,它一直是古代世界最美丽的城市之一。在恩培多克勒时代,它是一个富有的城市,拥有最优秀的希腊文化。一些毕达哥拉斯学派成员在克罗顿的中心遭到攻击后曾来到那里。
恩培多克勒出生于一个富有的贵族家庭。他游历希腊世界,全身心投入那片土地上人们对学问与理解的非凡渴望之中。Sarton [5]对他有如下描述:-
他不仅是哲学家,还是诗人、先知、物理学家、社会改革者,热情如此之高,以至于有些人很容易把他视为江湖骗子,而在另一些人眼中则成为传奇英雄。
关于恩培多克勒的生平有许多传说。他写诗,其中450行被西里西亚的辛普利修斯、亚里士多德、Plutarch等后世作家保存下来。不难看出关于恩培多克勒的大多数传说的来源,因为这些传说建立在他自己写的诗歌之上。在这些诗中,他声称拥有神一般的力量,但这究竟只是一种诗歌风格,还是他真的相信自己拥有这样的力量,很难说。当然,他的诗很受赞赏,例如Lucretius就欣赏他的六音步诗。
如果我们要了解这个人的性格,那么它将来自保存下来的诗行:他的诗作Peri physeos(《论自然》)中的400行,以及他的诗作Katharmoi(《净化》)中的其余部分。这些[1]:-
……展现出一个想象力炽热、多才多艺、雄辩滔滔、略带戏剧性的人。
他游历的一些细节看来是准确的。他去过意大利,公元前445年后不久在卢卡尼亚的图里伊城。从那里他前往伯罗奔尼撒,公元前440年在奥林匹亚。那一年他的歌曲在奥林匹克运动会上被演唱。他有一个年轻朋友,Anchitos之子Pausanias,随他一起旅行。关于他死亡的许多传说中,最可能的是他在伯罗奔尼撒的一次宴饮后去世。Sarton写道[5]:-
恩培多克勒是一位如此伟大而罕见的人,以至于他没有留下学派;他的任何崇拜者或弟子,甚至忠实的Pausanias,都无法继续这位大师的工作。
恩培多克勒被赋予了许多“第一”。据说亚里士多德认为他是修辞学的发明者,而Galen则将他视为意大利医学科学的奠基人。然而,他最著名的是他相信所有物质都由四种元素组成:火、气、水和土。
他提出四元素理论的原因是为了论证对埃利亚学派信仰的修改,埃利亚学派是希腊哲学中领先的前苏格拉底学派之一,由巴门尼德在芝诺于意大利南部创立。这个学派的哲学,包括芝诺,主张许多看似存在的事物仅仅是一个单一永恒的现实。恩培多克勒并不赞同“一切为一”的版本,但他的“一切由四元素组成”在科学发展中极为重要,因为它被柏拉图和亚里士多德所采纳。正如Sarton所写[5]:-
尽管其任意性,这一假说却有着非凡的命运,因为它以某种形式主导了西方思想,几乎直到十八世纪。
我们还应注意该假说的一个重要特征。它像毕达哥拉斯的思想一样,试图将世界上看到的众多复杂性解释为少数简单基本属性的结果。尽管我们不再相信恩培多克勒的四元素理论,我们仍然寻找简单的数学来解释我们周围的复杂现象。
恩培多克勒的四元素假说并非基于任何实验证据。然而,他确实将其他一些科学思想建立在实验基础上,并且通过实验表明空气存在,而不是虚空。他用一个漏壶做到了这一点,那是一个底部和顶部各有一个孔的容器。将容器底部的孔置于水下,恩培多克勒观察到容器充满了水。然而,如果他用手指堵住顶部的孔,那么水就不会从底部的孔进入,但一旦他移开手指,水就会进入。恩培多克勒正确地推断出容器中的空气阻止了水的进入。
恩培多克勒相信光以有限的速度传播,当然不是通过任何实验证据,而仅仅是通过推理。亚里士多德在De sensu中写道:-
恩培多克勒说,太阳的光在到达眼睛或抵达地球之前,首先到达中间的空间。这似乎很可能是这样。因为凡是在空间中移动的东西,都是从一个地方移动到另一个地方;因此,也必定有一段相应的时间间隔,在这段时间里它从一个地方移动到另一个地方。但任何给定的时间都可分割成部分;所以我们应该假定有一个时刻,太阳的光线尚未被看见,而仍在中间的空间中行进。
值得注意的是,恩培多克勒的许多想法后来被证明是正确的。除了相信光速有限之外,他还基于适者生存发展出一种粗略的进化理论。他也有某种形式的能量守恒定律,并有一种化学反应中定比的理论。他的想法,尽管对科学的发展几乎没有影响,但以我们当前的科学知识来看,却是相当令人难以置信的。如果我们必须解释为什么如此具有预言性正确的想法会产生如此小的影响,我们就必须同意哲学家汉斯·赖兴巴赫的观点,他在1957年出版的一本书中说(见[1]):-
……一个在不够充分的理论框架内陈述的好想法会失去其解释力并被遗忘。
Empedocles was born in Acragas on the south coast of Sicily. The name Acragas is Greek, while the Latin name for the town was Agrigentum. Later the town was called Girgenti and more recently it became known by its present name of Agrigento. It was one of the most beautiful cities of the ancient world up to the time it was destroyed by the Carthaginians in 406 BC. It was, in Empedocles time, a rich city containing the finest Greek culture. Some of the Pythagoreans had come there after being attacked in their centre at Croton.
Empedocles was born into a rich aristocratic family. He travelled throughout the Greek world participating fully in the extraordinary desire for learning and understanding which gripped that part of the world. He is described as follows by Sarton [5]:-
He was not only a philosopher but a poet, a seer, a physicist, a social reformer, a man of so much enthusiasm that he would easily be considered a charlatan by some people, or become a legendary hero in the eyes of others.
There are many legends regarding Empedocles life. He wrote poetry and 450 lines of such had been preserved by later writers such as Simplicius, Aristotle, Plutarch and others. It is not difficult to see the source of most of the legends about Empedocles for these are built on the poems that he wrote himself. In these he claims god-like powers, but whether this was simply a poetic style or whether he really did believe that he had such powers it is hard to say. Certainly his poems were much appreciated, for example Lucretius admired his hexametric poetry.
If we are to gather anything about the character of the man then it will come from the lines of poetry which have been preserved: 400 lines from his poem Peri physeos (On Nature) and the remainder from his poem Katharmoi (Purifications). These [1]:-
... reveal a man of fervid imagination, versatility, and eloquence, with a touch of theatricality.
Some details of his travels appear accurate. He went to Italy and was in the town of Thurii, Lucania shortly after 445 BC. From there he went to the Peloponnese and he was in Olympia in 440 BC. His songs were sung at the Olympic games in that year. He had a young friend, Pausanias the son of Anchitos, who went with him on his travels. Of the many legends regarding his death, the most likely would appear to be that he died following a feast in the Peloponnese. Sarton writes [5]:-
Empedocles was so great and rare a man that he left no school; none of his admirers or disciples, not even the faithful Pausanias, was able to continue the master's work.
Certainly Empedocles was attributed with many "firsts". Aristotle is said to have considered him the inventor of rhetoric while Galen regarded him as the founder of the science of medicine in Italy. He is best known, however, for his belief that all matter was composed of four elements: fire, air, water, and earth.
The reason for his four element theory was to argue a modification of the belief of the Eleatic School, one of the leading pre-Socratic schools of Greek philosophy, which had been founded by Parmenides in Elea in southern Italy. The philosophy of this school, which included Zeno of Elea, was the claim that the many things which appear to exist are merely a single eternal reality. Empedocles did not go for the "all is one" version, but his "all is composed of the four elements" is extremely important in the development of science since it was adopted by Plato and Aristotle. As Sarton writes [5]:-
In spite of its arbitrariness, that hypothesis had a singular fortune, for it dominated Western thought in one form or another almost until the eighteenth century.
We should also note an important feature of the hypothesis. It, like the ideas of Pythagoras, tried to explain the multitude of complexity seen in the world as being the consequence of a small number of simple underlying properties. Although we no longer believe in Empedocles' four element theory, we do still look for simple mathematics which will explain the complex phenomena that surround us.
Empedocles did not base his four element hypothesis on any experimental evidence. He did base some other scientific ideas on experiment, however, and he showed by experiment that air existed and was not empty space. He did this with a clepsydra, a vessel with a hole in the bottom and one in the top. Placing the bottom hole of the vessel under water, Empedocles observed that the vessel filled up with water. If, however, he put his finger over the top hole, then the water did not enter the hole at the bottom but it did once he removed his finger. Empedocles correctly deduced that the air in the container prevented the water entering.
Empedocles believed that light travelled with a finite velocity, not through any experimental evidence, of course, but simply through reasoning. Aristotle writes in De sensu :-
Empedocles says that the light from the Sun arrives first in the intervening space before it comes to the eye, or reaches the Earth. This might plausibly seem to be the case. For whatever is moved through space, is moved from one place to another; hence, there must be a corresponding interval of time also in which it is moved from the one place to the other. But any given time is divisible into parts; so that we should assume a time when the sun's ray was not as yet seen, but was still travelling in the middle space.
It is remarkable how many of Empedocles' ideas have turned out to be correct. In addition to his belief in the finite velocity of light he also developed a crude evolutionary theory based on the survival of the fittest. He also had a form of the law of conservation of energy and had a theory of constant proportions in chemical reactions. His ideas, although they had little influence on the development of science, can be seen in the light of our current scientific knowledge to be quite incredible. If we have to explain how such prophetically correct ideas could have such little influence we have to agree with the philosopher Hans Reichenbach who, in a book published in 1957, said (see [1]):-
... a good idea stated within an insufficient theoretical frame loses its explanatory power and is forgotten.
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