Book XIV Chapter 6

One might also raise the question what the good is that things get from numbers because their composition is expressible by a number, either by one which is easily calculable or by an odd number. For in fact honey-water is no more wholesome¹ if it is mixed in the proportion of three times three, but it would do more good if it were in no particular ratio but well diluted² than if it were numerically expressible but strong. Again, the ratios of mixtures are expressed by the adding of numbers, not by mere³ numbers; e.g. it is ‘three parts to two’, not ‘three times two’. For in any multiplication⁴ the genus of the things multiplied must be the same; therefore the product 1X2X3 must be measurable by 1, and 4X5X6 by 4 and therefore all products into which the same factor enters must be measurable by that factor. The number of fire, then, cannot be 2X5X3X6 and at the same time that of water 2X3.

If all things must share in number, it must follow that many things are the same, and the same number must belong to one thing and to another. Is number the cause, then, and does the thing exist because of its number, or is this not certain? E.g. the motions of the sun have a number, and again those of the moon,-yes, and the life and prime of each animal. Why, then, should not some of these numbers be squares, some cubes, and some equal, others double? There is no reason why they should not, and indeed they must move within these limits, since all things were assumed to share in number. And it was assumed that things that differed might fall under the same number. Therefore if the same number had belonged to certain things, these would have been the same as one another, since they would have had the same form of number; e.g. sun and moon would have been the same. But why need these numbers be causes? There are seven vowels⁵, the scale consists of seven strings⁶, the Pleiades are seven, at seven animals lose their teeth (at least some do, though some do not), and the champions who fought against Thebes were seven. Is it then because the number is the kind of number it is, that the champions were seven or the Pleiad consists of seven stars? Surely the champions were seven because there were seven gates or for some other reason, and the Pleiad we count as seven, as we count the Bear as twelve, while other peoples count more stars in both. Nay⁷ they even say that X, Ps and Z are concords⁸ and that because there are three concords, the double consonants⁹ also are three. They quite neglect the fact that there might be a thousand such letters; for one symbol might be assigned to GP. But if they say that each of these three is equal to two of the other letters, and no other is so, and if the cause is that there are three parts of the mouth and one letter is in each applied¹⁰ to sigma, it is for this reason that there are only three, not because the concords are three; since as a matter of fact the concords are more than three, but of double consonants there cannot be more.

These people are like the old-fashioned Homeric scholars, who see small resemblances but neglect great ones. Some say that there are many such cases, e.g. that the middle strings are represented by nine and eight, and that the epic¹¹ verse has seventeen syllables¹², which is equal in number to the two strings, and that the scansion is, in the right half of the line nine syllables, and in the left eight. And they say that the distance in the letters from alpha to omega is equal to that from the lowest note of the flute¹³ to the highest, and that the number of this note is equal to that of the whole choir¹⁴ of heaven. It may be suspected that no one could find difficulty either in stating such analogies or in finding them in eternal things, since they can be found even in perishable¹⁵ things.

But the lauded¹⁶ characteristics of numbers, and the contraries of these, and generally the mathematical relations, as some describe them, making them causes of nature, seem, when we inspect them in this way, to vanish; for none of them is a cause in any of the senses that have been distinguished¹⁷ in reference to the first principles. In a sense, however, they make it plain that goodness belongs to numbers, and that the odd, the straight, the square, the potencies¹⁸ of certain numbers, are in the column of the beautiful. For the seasons and a particular kind of number go together; and the other agreements that they collect from the theorems of mathematics all have this meaning. Hence they are like coincidences. For they are accidents, but the things that agree are all appropriate to one another, and one by analogy. For in each category of being an analogous¹⁹ term is found-as the straight is in length, so is the level in surface, perhaps the odd in number, and the white in colour.

Again, it is not the ideal numbers that are the causes of musical phenomena²⁰ and the like (for equal ideal numbers differ from one another in form; for even the units do); so that we need not assume Ideas for this reason at least.

These, then, are the results of the theory, and yet more might be brought together. The fact that our opponnts have much trouble with the generation of numbers and can in no way make a system of them, seems to indicate that the objects of mathematics are not separable from sensible things, as some say, and that they are not the first principles.

The End

1 wholesome   

adj.适合；卫生的；有益健康的；显示身心健康的

参考例句：

• In actual fact the things I like doing are mostly wholesome.实际上我喜欢做的事大都是有助于增进身体健康的。
• It is not wholesome to eat without washing your hands.不洗手吃饭是不卫生的。

2 diluted   

无力的，冲淡的

参考例句：

• The paint can be diluted with water to make a lighter shade. 这颜料可用水稀释以使色度淡一些。
• This pesticide is diluted with water and applied directly to the fields. 这种杀虫剂用水稀释后直接施用在田里。

3 mere   

adj.纯粹的；仅仅，只不过

参考例句：

• That is a mere repetition of what you said before.那不过是重复了你以前讲的话。
• It's a mere waste of time waiting any longer.再等下去纯粹是浪费时间。

4 multiplication   

n.增加，增多，倍增；增殖，繁殖；乘法

参考例句：

• Our teacher used to drum our multiplication tables into us.我们老师过去老是让我们反覆背诵乘法表。
• The multiplication of numbers has made our club building too small.会员的增加使得我们的俱乐部拥挤不堪。

5 vowels   

n.元音，元音字母( vowel的名词复数 )

参考例句：

• Vowels possess greater sonority than consonants. 元音比辅音响亮。 来自《现代英汉综合大词典》
• Note the various sounds of vowels followed by r. 注意r跟随的各种元音的发音。 来自超越目标英语 第3册

6 strings   

n.弦

参考例句：

• He sat on the bed,idly plucking the strings of his guitar.他坐在床上，随意地拨着吉他的弦。
• She swept her fingers over the strings of the harp.她用手指划过竖琴的琴弦。

7 nay   

adv.不；n.反对票，投反对票者

参考例句：

• He was grateful for and proud of his son's remarkable,nay,unique performance.他为儿子出色的，不，应该是独一无二的表演心怀感激和骄傲。
• Long essays,nay,whole books have been written on this.许多长篇大论的文章，不，应该说是整部整部的书都是关于这件事的。

8 concords   

n.和谐，一致，和睦( concord的名词复数 )

参考例句：

9 consonants   

n.辅音，子音( consonant的名词复数 )；辅音字母

参考例句：

• Consonants are frequently assimilated to neighboring consonants. 辅音往往被其邻近的辅音同化。 来自《简明英汉词典》
• Vowels possess greater sonority than consonants. 元音比辅音响亮。 来自《现代英汉综合大词典》

10 applied   

adj.应用的；v.应用，适用

参考例句：

• She plans to take a course in applied linguistics.她打算学习应用语言学课程。
• This cream is best applied to the face at night.这种乳霜最好晚上擦脸用。

11 epic   

n.史诗，叙事诗；adj.史诗般的，壮丽的

参考例句：

• I gave up my epic and wrote this little tale instead.我放弃了写叙事诗，而写了这个小故事。
• They held a banquet of epic proportions.他们举行了盛大的宴会。

12 syllables   

n.音节( syllable的名词复数 )

参考例句：

• a word with two syllables 双音节单词
• 'No. But I'll swear it was a name of two syllables.' “想不起。不过我可以发誓，它有两个音节。” 来自英汉文学 - 双城记

13 flute   

n.长笛；v.吹笛

参考例句：

• He took out his flute, and blew at it.他拿出笛子吹了起来。
• There is an extensive repertoire of music written for the flute.有很多供长笛演奏的曲目。

14 choir   

n.唱诗班，唱诗班的席位，合唱团，舞蹈团；v.合唱

参考例句：

• The choir sang the words out with great vigor.合唱团以极大的热情唱出了歌词。
• The church choir is singing tonight.今晚教堂歌唱队要唱诗。

15 perishable   

adj.（尤指食物）易腐的，易坏的

参考例句：

• Many fresh foods are highly perishable.许多新鲜食物都极易腐败。
• Fruits are perishable in transit.水果在运送时容易腐烂。

16 lauded   

v.称赞，赞美( laud的过去式和过去分词 )

参考例句：

• They lauded the former president as a hero. 他们颂扬前总统为英雄。 来自辞典例句
• The nervy feats of the mountaineers were lauded. 登山者有勇气的壮举受到赞美。 来自辞典例句

17 distinguished   

adj.卓越的，杰出的，著名的

参考例句：

• Elephants are distinguished from other animals by their long noses.大象以其长长的鼻子显示出与其他动物的不同。
• A banquet was given in honor of the distinguished guests.宴会是为了向贵宾们致敬而举行的。

18 potencies   

n.威力( potency的名词复数 )；权力；效力；（男人的）性交能力

参考例句：

• The soft gelatin liquid filled capsule manufacturing process is the same for all proposed potencies. 软明胶液体填注胶囊的生产工艺对所有提出的效用是一样的。 来自互联网

19 analogous   

adj.相似的；类似的

参考例句：

• The two situations are roughly analogous.两种情況大致相似。
• The company is in a position closely analogous to that of its main rival.该公司与主要竞争对手的处境极为相似。

20 phenomena   

n.现象

参考例句：

• Ade couldn't relate the phenomena with any theory he knew.艾德无法用他所知道的任何理论来解释这种现象。
• The object of these experiments was to find the connection,if any,between the two phenomena.这些实验的目的就是探索这两种现象之间的联系，如果存在着任何联系的话。