Software Musings

Hardly Right

Posted on: 10/03/2007

Earlier this week, a colleague devised a clever algorithm for a particular problem but it relied on the following theorem. I would love to include it inline as they manage to do on the n-Category Café but, due to my incompetence, I will have to include as a picture:

equation.gif

He sketched this quickly on my whiteboard late one afternoon, it seemed intuitively correct and I promised to spend a few minutes on it at home that night. OK, I know now that I should have simply asked Messrs Prouhet, Tarry and Escott but I bet they didn’t know about Schubert’s Winterreise or how to fly an ILS approach to minimums.

I spent some time on it and found a remarkable number of “proofs” followed by subtleties that exploded them. Finally, after an hour or so, I found a proof that seemed to work, wrote it up in a short memorandum (from which the above picture comes) and went to bed satisfied. In the shower the next morning, while thinking of something else entirely, the flaw in my “proof” came to me. And, on arriving at work, my colleague mentioned that I should just have turned to my copy of Hardy and Wright (bought, according to the flyleaf, in September 1980 and waiting for such a moment as this) and turned to page 328.

So that resolved that, but I am still overwhelmingly impressed by the unconscious brain. I assume that I was really somewhat uncomfortable about my “proof” and, although my conscious mind was happy with it, my unconscious one kept working on it to uncover the cause of concern. With a lot of analytic philosophy turning to neuro-science, I wonder whether there’s a neuro-scientific explanation of these parallel brain activities. How many parallel activities can a brain handle? Is this number what distinguishes me from a genius?

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4 Responses to "Hardly Right"

I also had some thoughts on this issue.

My opinion is that this number – or, more generally, mind capacity – is roughly the same for every human. I justify this opinion mainly by observation that all people dream, and in dreams many things are happening parallely, many more actually than one’s cosciousness “could handle”.

Often it happens that I don’t sleep well (I often burn the midnight oil, it has terrible consequences for good sleep (I use this expression for a first time in my life, I hope it means what my dictionary says it means :-)). It happens sometimes (every once in, say, 2 weeks) that I dream but I’m totally aware of it.

One of the most frightening things for me is when in such a “dream” I happen to talk to somebody, because then I know that “this something” which talks to me is some other part of my brain which I cannot control. Which lives its own life, in a way.

I believe that what distinguishes geniuses is rather that they unconsciousness is “closer” to their consciousness – the frequency of illuminations (messages from un- to consciousness) you described being higher.

Jacques Hadamard (_this_ Jacques Hadamard) wrote analysing his process of discovery (including illuminations) – you might want to read it, if you haven’t already.

All this is very interesting.

Sorry for messed up link.

The link to his own blog which, for some reason didn’t work in sirix’s comments is:

http://sirix.wordpress.com/2007/01/04/my-notes-from-reading-the-road-to-reality/#comment-20

I hope that it will work from here.

The other experience I sometimes seem to have when I’m problem solving is the “complete problem at one time” phenomenon.

I find that for days I think about different parts of the problem without being able to grasp the whole thing at once. And then, for an instant, typically when I’m not trying, I seem to have the whole problem in my head at one time, And it often cracks.

Thanks, by the way, for the reference to Hadamard. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hadamard.html indicates that he was the one to prove the prime number theorem. I had always thought that that was Gauss but, checking up, I find that Legendre and Gauss only postulated it and Hadamard proved it.

I particularly like the quotation from him that “Logic merely sanctions the conquests of the intuition.”

[…] compulsory for us: a new performance of Schubert’s Winterreise, which he and I have now been studying privately at home for the last four or five years! In this case the singer was Alexander Dobson, and his […]

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Disclaimer

The author of this blog used to be an employee of Nortel. Even when he worked for Nortel the views expressed in the blog did not represent the views of Nortel. Now that he has left, the chances are even smaller that his views match those of Nortel.
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