阿那克萨戈拉Anaxagoras

阿那克萨戈拉曾被普罗克洛描述过，后者是最后一位重要的希腊哲学家，生活于约公元450年（例如见[4]）：-

在[毕达哥拉斯]之后，阿那克萨戈拉处理了几何学中的许多问题……

阿那克萨戈拉是伊奥尼亚人，出生在士麦那的塞翁附近，即今天的土耳其境内。我们对他的早年生活所知甚少，但可以肯定的是，他生命的前一段是在伊奥尼亚度过的，在那里他了解到当地正在进行的哲学新研究，以及对世界进行科学研究的新近热情。他出身富裕家庭，却放弃了自己的财富。正如托马斯·利特尔·希思在[4]中所写：-

他忽视了自己相当可观的财产，以便献身于科学。

尽管伊奥尼亚产生了诸如毕达哥拉斯这样的哲学家，但直到阿那克萨戈拉的时代，这种对知识的新研究还没有传播到雅典。阿那克萨戈拉因在大约公元前480年移居雅典时第一个把哲学引入雅典而闻名。在阿那克萨戈拉逗留雅典期间，伯里克利掌了权。伯里克利比阿那克萨戈拉大约年轻五岁，是一位军事和政治领袖，他既成功地发展了民主，又建立了一个帝国，使雅典成为希腊的政治和文化中心。阿那克萨戈拉和伯里克利成了朋友，但这种友谊也有其不利之处，因为伯里克利的政敌也把矛头对准了阿那克萨戈拉。

大约在公元前450年，阿那克萨戈拉因声称太阳不是神、月亮反射太阳光而被监禁。这似乎是由伯里克利的反对者煽动的。伯特兰·罗素在[6]中写道：-

雅典公民……通过了一项法律，允许弹劾那些不践行宗教并教授关于“天上事物”理论的人。根据这项法律，他们迫害了阿那克萨戈拉，他被指控教授太阳是一块炽热的石头，月亮是泥土。

我们应该更仔细地考察阿那克萨戈拉关于太阳的这一教导，因为尽管它被用作将他投入监狱的理由，但它是一个极其非凡的教导。它基于他的“nous”学说，该词被翻译为“心灵”或“理性”。最初“万物在一起”，物质是某种均匀的混合物。nous在这种混合物中建立了一个漩涡。旋转[4]：-

……从中心开始，然后逐渐扩展，卷入越来越宽的圆圈。第一个效果是分离出两大团块，一个由稀薄、热、干燥的物质组成，称为“aether”，另一个由相反类别的物质组成，称为“air”。aether占据外部，air占据内部位置。从air中接下来分离出云、水、土和石头。稠密、潮湿、黑暗和寒冷以及所有最重的东西，由于圆周运动而聚集在中心，正是从这些元素凝结后形成了地球；但此后，由于旋转运动的猛烈，周围炽热的aether从地球上撕下石头并将它们点燃成星星。

这段描述中有非凡的见解。物质分化的思想在现代太阳系创世理论中扮演重要角色，这一思想已经存在。阿那克萨戈拉还表现出对离心力的理解，这再次显示了他所拥有的重大科学见解。

阿那克萨戈拉提出月亮通过来自“炽热石头”即太阳的反射光而发光，这是第一个这样的记录声明。展现出极大的天才，他随后也能够迈出下一步，成为第一个正确解释太阳和月亮食原因的人。他对太阳食的解释完全正确，但他确实破坏了他对月亮食的解释，因为他提出除了由地球阴影引起外，还有地球和月亮之间的其他暗天体也导致月亮食。他为什么觉得有必要假设这些天体的存在有点不清楚，但这并不减损数学天文学中的这一重大突破。还有其他证据表明阿那克萨戈拉将几何学应用于天文学研究。

至于物质的结构，阿那克萨戈拉假设了无限数量的元素，或基本构建块。他声称：-

每一事物中都有每一事物的一部分，即每一种基本物质的一部分……[但]每一事物最明显地就是其中含量最多的那些东西。

然而，正是nous，即心灵的力量，不仅创造了世界，而且也是世界日常过程中的驱动力。例如2：-

按照阿那克萨戈拉，生物的生长取决于生物体内心灵的力量，这种力量使它们能够从周围物质中摄取营养。

亚里士多德在阿那克萨戈拉的nous理论中都发现了许多值得称赞之处。然而，柏拉图和亚里士多德都批评了阿那克萨戈拉所提出的nous的驱动力并非伦理性的这一事实。他们希望nous始终以世界的最佳利益为行动准则。事实上，在非机械性的开端产生漩涡之后，阿那克萨戈拉的nous确实提供了一种对世界的机械解释。值得注意的是，艾萨克·牛顿的机械宇宙与阿那克萨戈拉的观点有更多共同之处，而不是与柏拉图和亚里士多德所提出的持续存在的伦理智能有更多共同之处。

我们可以获得一些关于阿那克萨戈拉所研究的数学的线索，但不幸的是，记录中留存下来的东西极少，使我们无法知道他可能证明过的确定结果。在狱中，他试图解决squaring the circle问题，即用ruler and compasses构造一个面积等于给定圆的面积的正方形。这是研究该问题的首次记录，而这个问题以及其他类似问题将在希腊数学的发展中发挥重要作用。

另一条引人入胜的信息来自维特鲁威的著作，他是一位生活在公元前一世纪的罗马建筑师、工程师和作家。他记录了在雅典上演的戏剧的舞台场景绘画的信息，并说阿那克萨戈拉写了一篇论著，论述如何绘制场景，使一些物体看起来在前景中，而另一些看起来在背景中。这条引人注目的评论必定意味着阿那克萨戈拉写了一篇关于透视法的论著，但遗憾的是没有这样的作品留存下来。

阿那克萨戈拉被伯里克利从狱中救出，但不得不离开雅典。他回到伊奥尼亚，在兰普萨库斯创办了一所学校。这座位于赫勒斯滂海峡亚洲岸边的希腊城市是崇拜普里阿普斯的地方，普里阿普斯是生育和丰产之神。阿那克萨戈拉在那里去世，他逝世的周年纪念日成为学童的假日。

关于阿那克萨戈拉的个性，我们能了解到的最好材料来自这样一个故事：有一次有人问他出生的意义是什么，他回答说[4]：-

对太阳、月亮和天空的研究。

即使这个故事是虚构的，它也很可能是基于阿那克萨戈拉的生活方式，因此向我们揭示了这位非凡科学家的某些个性，他描述了太阳系的创生，这一描述在2000年后才被改进。

Anaxagoras of Clazomenae was described by Proclus, the last major Greek philosopher, who lived around 450 AD as (see for example [4]):-

After [Pythagoras] Anaxagoras of Clazomenae dealt with many questions in geometry...

Anaxagoras was an Ionian, born in the neighbourhood of Smyrna in what today is Turkey. We know few details of his early life, but certainly he lived the first part of his life in Ionia where he learnt about the new studies that were taking place there in philosophy and the new found enthusiasm for a scientific study of the world. He came from a rich family but he gave up his wealth. As Heath writes in [4]:-

He neglected his possessions, which were considerable, in order to devote himself to science.

Although Ionia had produced philosophers such as Pythagoras, up to the time of Anaxagoras this new study of knowledge had not spread to Athens. Anaxagoras is famed as the first to introduce philosophy to the Athenians when he moved there in about 480 BC. During Anaxagoras's stay in Athens, Pericles rose to power. Pericles, who was about five years younger than Anaxagoras, was a military and political leader who was successful in both developing democracy and building an empire which made Athens the political and cultural centre of Greece. Anaxagoras and Pericles became friends but this friendship had its drawbacks since Pericles' political opponents also set themselves against Anaxagoras.

In about 450 BC Anaxagoras was imprisoned for claiming that the Sun was not a god and that the Moon reflected the Sun's light. This seems to have been instigated by opponents of Pericles. Russell in [6] writes:-

The citizens of Athens ... passed a law permitting impeachment of those who did not practise religion and taught theories about 'the things on high'. Under this law they persecuted Anaxagoras, who was accused of teaching that the sun was a red-hot stone and the moon was earth.

We should examine this teaching of Anaxagoras about the sun more closely for, although it was used as a reason to put him in prison, it is a most remarkable teaching. It was based on his doctrine of "nous" which is translated as "mind" or "reason". Initially "all things were together" and matter was some homogeneous mixture. The nous set up a vortex in this mixture. The rotation [4]:-

... began in the centre and then gradually spread, taking in wider and wider circles. The first effect was to separate two great masses, one consisting of the rare, hot, dry, called the "aether", the other of the opposite categories and called "air". The aether took the outer, the air the inner place. From the air were next separated clouds, water, earth and stones. The dense, the moist, the dark and cold, and all the heaviest things, collected in the centre as a result of the circular motion, and it was from these elements when consolidated that the earth was formed; but after this, in consequence of the violence of the whirling motion, the surrounding fiery aether tore stones away from the earth and kindled them into stars.

There are remarkable insights in this description. The idea of differentiation of matter which plays a large role in modern theories of creation of the solar system is present. Anaxagoras also shows an understanding of centrifugal force which again shows the major scientific insights that he possessed.

Anaxagoras proposed that the moon shines by reflected light from the "red-hot stone" which was the sun, the first such recorded claim. Showing great genius he was also then able to take the next step and become the first to explain correctly the reason for eclipses of the sun and moon. His explanation of eclipses of the sun is completely correct but he did spoil his explanation of eclipses of the moon by proposing that in addition to being caused by the shadow of the earth, there were other dark bodies between the earth and the moon which also caused eclipses of the moon. It is a little unclear why he felt it necessary to postulate the existence of these bodies but it does not detract from this major breakthrough in mathematical astronomy. There is also other evidence to suggest that Anaxagoras had applied geometry to the study of astronomy.

As to the structure of matter, Anaxagoras postulated an infinite number of elements, or basic building blocks. He claimed:-

... there is a portion of every thing, i.e. of every elemental stuff, in every thing...[but] each is and was most manifestly those things of which there is most in it.

However, it was the power of nous, or mind, that not only created the world but also was the driving force in its day to day processes. For example [2]:-

The growth of living things, according to Anaxagoras, depends on the power of mind within the organisms that enables them to extract nourishment from surrounding substances.

Aristotle both found much to praise in Anaxagoras's theory of nous. Both Plato and Aristotle, however, were critical of the fact that the driving force of the nous as proposed by Anaxagoras was not ethical. They wanted nous to always act in the best interests of the world. In fact the nous of Anaxagoras does provide a mechanical explanation of the world after the non-mechanical start when the vortex is produced. It is worth noting that Newton's mechanical universe would have more in common with Anaxagoras's views than the continuing ethical intelligence proposed by Plato and Aristotle.

We can obtain some clues to the mathematics that Anaxagoras studied but, unfortunately, very little remains in the records to allow us to know of definite results which he may have proved. While in prison he tried to solve the problem of squaring the circle, that is constructing with ruler and compasses a square with area equal to that of a given circle. This is the first record of this problem being studied and this problem, and other similar problems, were to play a major role in the development of Greek mathematics.

One other intriguing piece of information comes from the writing of Vitruvius, a Roman architect, engineer, and author who lived in the first century BC. He records information about the painting of stage scenes for the plays which were performed in Athens and says that Anaxagoras wrote a treatise on how to paint scenes so that some objects appeared to be in the foreground while other appeared in the background. This fascinating comment must mean that Anaxagoras wrote a treatise on perspective, but sadly no such work survives.

Anaxagoras was saved from prison by Pericles but had to leave Athens. He returned to Ionia where he founded a school at Lampsacus. This Greek city on the Asiatic shore of the Hellespont was the place for the worship of Priapus, a god of procreation and fertility. Anaxagoras died there and the anniversary of his death became a holiday for schoolchildren.

The best that we can hope to learn of Anaxagoras's personality is from the story that when once asked what as the point of being born he replied [4]:-

The investigation of sun. moon, and heaven.

Even if this story is fictitious, it is likely to be based on the way that Anaxagoras lived his life and so tells us something of the personality of this remarkable scientist who gave a description of the creation of the solar system that took 2000 years to improve upon.