posted
See, the thing about emacs is that it does this kind of thing for you! Who could resist a text editor that's also a calculator, and indeed psychologist, email reader, syntax highlighter, and Tetris game? Don't listen to the carping critics who say that emacs has everything but a kitchen sink; they're wrong, emacs does have a kitchen sink. And a battery of las-blasters to destroy all opposition! Death to vi!
Posts: 10645 | Registered: Jul 2004
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OK, weird-not-in-pi sequences aside, I have a thing to say about numbers: in Rouen we had a chemistry teacher who when he had to make multiplications between large numbers would take the log of those, add them up and then calculate 10 to the power of the result... in his head! o_O That's one weird feat, I tell you!
Posts: 4519 | Registered: Sep 2003
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Well, don't get me wrong, I love chemistry... Especially physical chemistry... When it's more like physics... Oh well, I love physics, who am I trying to kid anyway? Posts: 4519 | Registered: Sep 2003
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I liked Bio-Chemistry best of all. I was hopeless at Physics and standard Chemistry. I did better in Organic Chemistry. But then I discovered the nexus between chemistry and behavior and finally started understanding it. I LOVED my upper-division class on the chemistry of hormones and neurotransmitters.
It also helped that the class sizes were smaller and the prof was able to take a closer interest in each student.
I like Newtonian physics. I can't wrap my mind around anything like Relativity or Quantum Mechanics. I'm too directly empirical.
Posts: 22497 | Registered: Sep 2000
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quote:I can't wrap my mind around anything like Relativity or Quantum Mechanics.
Uh, I've been to Physics contests for which I had to learn those, and while I was able to solve problems, I can't say I actually *understood* those theories... And my father, who's a Physics teacher, and quite a good one too, also had problems with Quantum theory throughout University. So you're in good company, Bob, if I'm allowed to say so... Posts: 4519 | Registered: Sep 2003
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Sometimes I wish I knew more bio-chemistry though... I'm reading "Darwin's Radio" by Greg Bear right now and parts of it read "blablablablabla" to me... Posts: 4519 | Registered: Sep 2003
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The best way I know to get a feel for relativity and quantum mechanics is to play with them in real life. Everyone should build their own home accelerator, you know?
No but seriously, I read tons of descriptive books first, relativity for laymen, einstein explained, etc. My favorite for quantum mechanics is "QED (Quantum Electrodynamics) The Strange Theory of Light and Matter" by Richard P. Feynman. Then took the problem solving courses later. It helped a whole lot in understanding what we were actually doing when we solved the problems.
quote:Originally posted by Bob_Scopatz: That's Greg Bear's fault, not yours...
You're most probably right. I've read Gregory Benford's Timescape and Frank Herbert's White plague and didn't feel the need of a physics/chemistry book to better understand them. I guess Greg Bear just didn't know when to stop with the details...
And Tatiana, yeah, it's probably better to first read some descriptive books, but when those things are in your high-school Physics class you might not have the time for that... As for the contests, there were lots of other things to learn, so I kinda had to go to problem solving directly. I loved them, don't get me wrong - otherwise I wouldn't have cared enough to want to go to those contests, right? - but they are quite difficult theories to "feel"...
Posts: 4519 | Registered: Sep 2003
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You know, there's an easy way to test the randomness of pi.
Every sequence of n digits should be equally probable. I propose taking a sample of sequences at various lengths and then plotting the distribution of the number of times each appears in the first 200 million digits of pi.
Basically, there shouldn't be wild fluctuations in frequency of the various n-length sequences. But...what fluctuation is there should obey some fairly straightforward rules of probability.
I suspect at the very least we would get a bell-shape on the frequency distribution centering on the mean frequency for sequences of length = n. I can't think of a good reason for it to follow any other distribution.
posted
There's no reason a transcendental number like pi needs to use the number 9, much less have a uniform distribution of it.
Posts: 15770 | Registered: Dec 2001
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I'd bet frequency of each digit would be roughly equal, but I'm not sure if that's enough to be random. Wouldn't the order count, too? 123456789009876543211122334455667788990000998877665544332211... will have roughly equal frequencies over the long term. I could make it even more so by moving the starting digits in a methodical fashion and rotating through. But it's not random, is it?
I am so far out of my depth here.
Posts: 26071 | Registered: Oct 2003
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fugu, I thought the question was whether or not pi's sequence of digits is random. Maybe Dag was the one who asked that.
Anyway, we used to have to test our "random number generators" in the early days of using personal computers to run experimental apparatus. To do that, we could check frequencies of digits or look at runs of particular digits.
Basically, the logic goes that a run of five zeroes in a row should be equally likely as the sequence 12345 or the sequence 43211 or any other sequence of five digits.
I see no reason to suspect that pi is composed of a random sequence of digits, to be honest. It is a number that expresses the stable relationship between the circumference and the diameter of a circle, no? So, it's based in a physical reality that is an inviolate law of geometry. Why would that have any randomness to it at all?
But the question has come up about whether the sequence that IS pi is indeed random or not.
I don't know, but I know how to test it.
Posts: 22497 | Registered: Sep 2000
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You can just evaluate the sequence to see if its 95% likely pi is the result of a generator choosing among ten possibilities, using a sample size of whatever length you desire.
Posts: 15770 | Registered: Dec 2001
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Can you fill that in for me? I come at this stuff from a brute-force empirical background, so I'm not sure I'm understanding your method or the statistical (probability) metric you'd use to guage 95% confidence limit...
Posts: 22497 | Registered: Sep 2000
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[aside] You gotta love our ability to derail threads! I mean, here's a thread about 0.17*37 (?!?) and it goes through chemistry, learning Relativity and Quantum theories, hard SF books, and randomness of Pi! Way to go, Hatrack! [/aside]
Posts: 4519 | Registered: Sep 2003
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posted
All we'd have to do would be to come up with a random variable that reflects the various outcomes and had a normal distribution, then see if the distribution over a lengthy sequence from pi was in the 95% confidence interval for the rv.
Posts: 15770 | Registered: Dec 2001
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