Just be Glad You Aren’t Pythagoras’s Student…

Raffaello Sanzio - Pythagoras photo

If anyone who reads this is part of academia and is frustrated by how conservative his chosen field is (“Science advances one funeral at a time”), this story should make you appreciate more the current scientific climate.

From Fermat’s Last Theorem by Simon Singh:

One story claims that a young student by the name of Hippasus was idly toying with the number √2, attempting to find the equivalent fraction. Eventually he came to realize that no such fraction existed, i.e. that √2 is an irrational number. Hippasus must have been overjoyed by his discovery, but his master was not. Pythagoras had defined the universe in terms of rational numbers, and the existence of irrational numbers brought his ideal into question. The consequence of Hippasus’ insight should have been a period of discussion and contemplation during which Pythagoras ought to have come to terms with this new source of numbers. However, Pythagoras was unwilling to accept that he was wrong, but at the same time he was unable to destroy Hippasus’ argument by the power of logic. To his eternal shame he sentenced Hippasus to death by drowning.

The ability to change our minds when presented with evidence that disproves our beliefs – even our most entrenched ones – is a hard habit to acquire, but it is extremely valuable. When you start doubting, don’t turn away. Look into the light until your eyes adjust, and see if there is something there.

As P. C. Hodgell said: “That which can be destroyed by the truth should be.” See the Twelve Virtues of Rationality by Eliezer Yudkowsky.

Update: Apparently this story is apocryphal. There’s a discussion about it on Reddit (which, btw, linked this page here — welcome to all Reddit readers!).

See also: Untangling the Search for Social Status from the Search for Truth

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30 Responses to “Just be Glad You Aren’t Pythagoras’s Student…”

  1. grammar-nazi Says:

    Hmm, I didn’t know “Pythagoras” was plural.

    • Charles Says:

      Isn’t it Pythagoras’ Student? Or commonly Pythagoras’s student?

      The apostrophe being that of a possessive one…

  2. Pythagoras's Says:

    Rule #1 of Strunk and White: always form the possessive of singular nouns with ‘s. The only exception, which should be avoided, is ancient names that end in -is or -es (which Pythagoras does not).

    http://www.bartleby.com/141/strunk.html#1

    Some people have no appreciation for the classics…

  3. Michael Graham Richard Says:

    Hey, thanks guys. English is my second language and I still make these kinds of mistakes from time to time. Fixed it.

  4. Keri Says:

    Not being a grammar nazi, I was focusing on the crux of your story. I had never heard this about Pythagoras, but I found it to be an extremely timely story to read. I have been trying to understand the nature of people’s hatred of change. This is an excellent allegory to use when entering a debate about change.

    By the way, I am also thankful for the quote you put at the end of your article. I’ve been looking for something along that lines to counter an email signature quote of a colleague. I didn’t want to be brutal about it, and this has the subtlety I needed.

    Interesting. Thanks!

  5. Well Played Says:

    In case you missed it, MGR’s reaction to the first two responses is a small example of the virtue described in his post. Hodgell would be proud.

    Also, I’m impressed with how quickly Godwin’s Law played out…. ;-)

  6. David Says:

    Thanks for the quote Richard – found you via reddit.com. Very insightful. Have you read Kuhn’s “Structure of Scientific Revolutions”? It follows along the same lines.

    Don’t worry about the above comments – the truth is, MOST native speakers don’t know how to do that particular proper punctuation. Your English is fine :)

  7. Hugh O'Malley Says:

    Off with his head!!! have him drowned for dodgy punctuation…

  8. wow Says:

    Incorrect grammar nazis are the most pathetic creatures on God’s green Earth.

  9. thedaythatidie Says:

    i guess i’m lucky. i never knew that story before. interesting. no student deserves to be “pythagorassed”.

  10. hefty Says:

    wrong.

    rule #1: im #1

  11. artemisinin Says:

    Good lord… focus on the content of the article. Minor grammar mistakes are irrelevant. Pointing them out makes you look, well, like an obnoxious tubesteak.

    Awesome post. I just wonder how Pythagoras was able to sentence Hippasus to death? Was Hippasus his slave? Or was Pythagoras able to sentence his students to death? Would love to know more…

  12. Patty Says:

    http://scienceworld.wolfram.com/biography/Hippasus.html

    Different story here.

  13. Pythagorophile Says:

    From Wikipedia:

    But there are two other stories about Hippasus. The first says that Hippasus was expelled from the Pythagorean school because he published doctrines of Pythagoras, while the second says that he was drowned at sea for revealing the construction of the dodecahedron in the sphere and claiming it as his own. But since the Pythagoreans’ supposed pledge to secrecy was most likely false, the authenticity of these stories is questioned

  14. arwansp Says:

    dont know what to say…

  15. Richmond Says:

    That’s what happens to know-it-all students… hehe.

  16. Anton Olsen.com » Blog Archive » Bookmarks for November 16th Says:

    [...] Just be Glad You Aren’t Pythagoras’ Student…“That which can be destroyed by the truth should be.” – P. C. Hodgell [...]

  17. drblsharma Says:

    The story you have narrated here is very interesting and tells about the ancient time when human values were concentrated around the power.
    Hyppasus and Pythagoras were the heroes of that time. The teacher or the masters were the over all omnipotent of the situation. Therefore, the time was different from the present .We should not compere that one.
    However, to accept and reject the version whatever it may be, is the time factor. It is the teachers`view that what he holds in his mind. This situtation can be noticed even today where research student has to follow his teacher or otherwise he has to suffer. That, does not mean that everywhere it happens. In higher education, mostly in Universities, you can find as such situation where good as well as bad masters are there. A good teacher always supports and accepts his students version.
    Therefore, on the basis of the biased attitude of the teacher one should not be dejected and leave the study. It is a human nature, that you can find every where.Thanks.

  18. Matt Says:

    This “property” of science has always been. Interesting that you pointed out such an early (ancient, even) example of it.

    The inability to accept change and challenges to theorems is a barrier not only to the introduction and propagation of new ideas, it even keeps individuals from growing and learning themselves. It’s a symptom of comfort: if an idea or a state is comfortable and then is challenged, it shakes things up and makes then not so comfortable.

  19. Savvas Dalkitsis Says:

    The story is not very accurate… Actually it IS accurate in the sense that it accurately perpetuates an urban myth about Pythagoras and this event. The truth is as follows (at least the accepted truth by the scientific community):

    The Pythagoreans were a science “cult” that followed the teachings of Pythagoras who described everything as rational quantities. They were a group that believed that science was meant only for the chosen few and that commoners should have nothing to do with it.

    When one of their students (could be Hippasus but no one is sure) discovered that the square root of two was not rational they decided that no one was to know of this since their world view would be incomplete. It remains as a question whether the one who made the discovery was killed or not.

    To say “However, Pythagoras was unwilling to accept that he was wrong”, i think undermines the genius that was Pythagoras because the truth of the proof that the student found was SO obvious no one would dare to deny its validity. The proof is so elementary that even school children can understand it.
    Wikipedia proof

  20. John Colquhoun Says:

    Irrational thoughts produce irrational outcomes … and your point is?

  21. Michael Graham Richard Says:

    “Irrational thoughts produce irrational outcomes … and your point is?”

    The point is that it’s not always so easy to know when our thoughts are irrational, and it can happen even to brilliant people. It requires some effort and vigilance to avoid that trap.

  22. Ugh Says:

    Your possessive rules are off. You add an apostrophe+”s” in every case, except when the word already ends in -s. It has absolutely nothing to do with “ancient names” or anything. A good example is “women” and “women’s”. “Womens'” is wrong, because it doesn’t already end in an -s.

  23. ooopinionsss Says:

    How you think when the economic crisis will end? I wish to make statistics of independent opinions!

  24. roy Says:

    holy crap, the first couple of comments makes me lose faith in humanity, you people are disgusting excuses for human beings that the world would be better off without. That’s my opinion anyways

  25. Ira Says:

    I knew that there was a reason I didn’t like math teachers.

  26. ZACH Says:

    It reminds me of being a child at home, a child who was his father’s son in every way even to the point of becoming an EE, and while at home as a child of even 7 OR 8 to figure out how many things work around the house OR in life that might be unexplainable at first blush wasn’t to be tolerated by my mother whenever her child would come up with an explanation separate and alone from hers that happened to be correct, at the expense of her explanation. I soon learned that it paid for me to allow her to believe just whatever she wanted to rather than to provide her with a better answer OR solution to the particular dilemma of the moment, even if it cost her money. So, there is distance in our relationship even today over this, and I am soon to be 49. So, for those of you half my age OR younger who are reading this for the first time, and for those of you who believe change will come for a parent OR loved one as you yourself change and get older, I offer you this previously explained example of change… You Are most welcome. For those of you who like to hope, well then you should hope, and for those who like to prayer I suggest you try that as well… As for me, I will scratch my head with befuddlement.

  27. Tres J Says:

    My guess is that poor old Hipparsus like all his other fellow students/initiates were sworn to secrecy about speaking to outsiders of what their work was until he and his fellow Imperators were ready to spread this wisdom.
    Pythagoras was an initiate or many mystery schools and in those one was sworn to secrecy under the IMPLICIT threat of death.
    As enlightened as these men and women were they were under constant threat from tyrants, pirates, priests etc; and nothing or nobody was above the Oath to preserve their vast knowledge of physics, healing, math, astronomy, etc.
    To judge a man who lived 2500 years ago in a rural ancient culture with the mores of a modern man is a tricky judgement to work around without running into some perplexing dichotomies.
    Without a doubt Pythagoras had to be somewhat a control freak since he started several communities through out the Med., always with the idea of a community based on his principles. Conversely his principles were light years ahead of those around him. Tolerance, equality, and a love of Nature and Knowledge were the cornerstones of their goals.

  28. captainblack Says:

    Since the probable dates for Pythagoras and Hippasus do not overlap it is unlikely that Hippasus was a direct student of Pythagoras, and even less likely that Pythagoras sentenced him to death or took part in his execution.

    As far as I can tell the current urban legent originates with Simon Singh.

  29. m,m,m, Says:

    I really, really, really doubt the veracity of this anecdote.

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