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Subject: "The square root of 2 is irrational"     Previous Topic | Next Topic
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Monty
Member since Jul-27-04
May-05-09, 05:50 PM (EST)
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"The square root of 2 is irrational"
 
   The article on this subject reports a conversation between Socrates and Theaetetus on the square root of 2.

It doesn't appear to be a 'real' conversation, for in Plato's works Socrates is always asking, not answering the questions.

I have a copy of Plato's works which is beautifully indexed, but I can't find a discussion of irrational numbers. (one of the books is titled Theaetetus) There is a neat discussion of areas in the book Meno, and in it Socrates teaches a Boy that doubling the side of a square does not double its area. This is right on the edge of the irrational number subject, but Socrates does not go there.

Do you know just where in Plato's works irrational numbers are discussed?


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  Subject     Author     Message Date     ID  
  RE: The square root of 2 is irrational alexbadmin May-05-09 1
     RE: The square root of 2 is irrational Monty May-06-09 2
         RE: The square root of 2 is irrational alexbadmin May-06-09 3
             RE: The square root of 2 is irrational Monty May-06-09 4
     Socrates and irrational numbers Monty May-21-09 5
         RE: Socrates and irrational numbers alexbadmin May-21-09 6
             Greater Hippias Monty May-22-09 7
                 RE: Greater Hippias alexbadmin May-22-09 8

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alexbadmin
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2378 posts
May-05-09, 06:09 PM (EST)
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1. "RE: The square root of 2 is irrational"
In response to message #0
 
   I have a two volume Random House edition from 1937. Translated by B. Jowett, M.A. (Master of Balliol College, Regius Professor of Greek in the University of Oxford, Doctor of Theology of the University of Leyden), with an introduction by Prof. Raphael Demos.

The dialog is in the second volume, pp. 148-149. (This is pages six-seven of the dialog in my edition.)

Far as I can see, the word "rational" does not appear in the dialog at all. So it is useless to check the Index. I believe that the Greeks used the word "unspeakable" when talking of irrational number - arrhetos or something. The word "rational" came in use much later.

Does this answer your concern?


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Monty
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May-06-09, 10:57 AM (EST)
 
2. "RE: The square root of 2 is irrational"
In response to message #1
 
   My edition is in one huge volume with many translators. So a page number is of no help. Could you tell me which dialog it's in, and roughly how far through the dialog (pages 6-7 is roughly how far? 1/8, 3/4 or ....)?

My index includes the word 'irrational'. In one of the entries under 'irrational' there is this remark by Socrates (in the "Greater Hippias" dialog) He says, "Or may the same principal apply as in mathematics, when for instance the two components of even numbers may severally be odd but may also be even, and, again, when quantities which are irrational if taken singly may be either rational or irrational if taken together?"


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alexbadmin
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2378 posts
May-06-09, 11:07 AM (EST)
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3. "RE: The square root of 2 is irrational"
In response to message #2
 
   >My edition is in one huge volume with many translators. So a
>page number is of no help. Could you tell me which dialog
>it's in,

Why? Theaetetus, of course.

>and roughly how far through the dialog (pages 6-7
>is roughly how far? 1/8, 3/4 or ....)?

Starts on 6/78

(i.e., the whole dialog is 78 pages, the start of the cited part is on page 6 into the dialog.)


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Monty
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May-06-09, 12:56 PM (EST)
 
4. "RE: The square root of 2 is irrational"
In response to message #3
 
   Found it!! Thanks very much.


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Monty
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May-21-09, 06:40 PM (EST)
 
5. "Socrates and irrational numbers"
In response to message #1
 
   I've just found, in Plato's Greater Hippias 303b, Socrates talking about 'irrational numbers'. In my translation he says, 'the two components of even numbers may be severally be odd, but may also be even, and, again, when quantities which are irrational if taken singly may be either rational or irrational if taken together'.

I'm not sure I understand either of these remarks. He can't mean the two factors of even numbers may be odd. That's impossible. So what is he saying? I guess he means that 6=2+4 (2 components even) and 6=3+3 (two components odd)...?

And what does he mean by an 'irrational number'? If it's the same meaning as ours today, and 'taken together' means multiplying, then we would agree. The square root of two multiplied by itself is rational; but the square root of two multiplied by the square root of 3 is irrational.

Are those the explanations?


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alexbadmin
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May-21-09, 06:44 PM (EST)
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6. "RE: Socrates and irrational numbers"
In response to message #5
 
   >I've just found, in Plato's Greater Hippias 303b

My edition does not contain this dialog.


>Socrates
>talking about 'irrational numbers'. In my translation he
>says, 'the two components of even numbers may be severally
>be odd, but may also be even, and, again, when quantities
>which are irrational if taken singly may be either rational
>or irrational if taken together'.
>
>I'm not sure I understand either of these remarks. He can't
>mean the two factors of even numbers may be odd. That's
>impossible. So what is he saying? I guess he means that
>6=2+4 (2 components even) and 6=3+3 (two components odd)...?

I am certain of that.

>And what does he mean by an 'irrational number'? If it's the
>same meaning as ours today, and 'taken together' means
>multiplying, then we would agree.

I'd think the meaning is the same as for the even numbers: addition.

sqrt(2) + (1 - srtq(2)) = 1.


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Monty
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May-22-09, 11:29 AM (EST)
 
7. "Greater Hippias"
In response to message #6
 
   In my edition the Greater Hippias is in the Appendix, which begins with the note "The Epinomis, the Greater Hippias, and the Letters are here printed for the convenience of the reader. Their authenticity has been the subject of a long debate but all, with the exception of Letter I, have had scholarly defenders in recent times ; their contents have been included in the index."

Presumably that's why your edition doesn't contain Greater Hippias. I wonder what's the current status of the authenticity debate.


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alexbadmin
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2378 posts
May-22-09, 11:42 AM (EST)
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8. "RE: Greater Hippias"
In response to message #7
 
   Yes, probably.

Curiously, I just checked my Russian translation in three volumes I have not touched probably for some 35 years. They do have the Greater Hiipias. However, the translation uses the word "undetermined" instead of "irrational" as in "... two undetermined quantities taken together sometimes give a definite (or, probably 'well determined', AB) quantity and sometimes undetermined."


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