At 13:17, it seems Baez is confusing the zeta function with (I guess) the Gamma function... the zeta function only has one pole, at Re=1, Im=0. The Gamma function, in contrast, has multiple poles along the negative real axis.
Has anyone ever done a study to see if there is some correlation between someone's ability to understand math and their ability to know how to use a comb or hairbrush or to use a hot oil conditioner in their hair. I'm kind of joking BUT ITS TRUE!
Always joke around and say 5 is self centered lol 😂 it’s the only number that doesn’t have an opposite in multiplication and it’s the center number between “1-9”
Another place to find fives is Mayan math/arithmetic which uses a base 20 number system subdivided into horizontal bars of five and dots above the bars as ones. 5 fingers x 2 + 5 toes x 2 = 20 - hmmm?
An update from after this talk: the Leech Lattice is not just the densest lattice in 24 dimensions, but the densest possible packing, lattice or non-lattice, in 24 dimensions. The same statement is also true of the lattices A2, A3, and E8. In no other dimensions is the densest possible packing known.
"Mass"/ENERGY IS GRAVITY. Time DILATION proves that electromagnetism/ENERGY IS GRAVITY, AS E=mc2 IS F=ma. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. By Frank DiMeglio
It's humorous at 46:25 where he attempts to demonstrate what he calls a "5th" chord. Of course, a 5th is an interval not a chord - which requires a minimum of 3 notes. Anyway, he then goes on to arpeggiate a major scale and ends up at the octave. Which is technically an 8th interval, not a 5th (or a 6th).
The Fibonacci sequence has infinitely many patterns that repeat periodically: it is a divisibility sequence, so F_n divides F_m whenever n divides m. For instance, F_3=2, so F_6, F_9, F_12,... are all even. Similarly, F_4=3, so F_8,F_12,F_16,F_20,... are all multiples of 3, while F_5,F_10,F_15 etc. are all multiples of 5. Also, by the pigeonhole principle, the remainders when you divide the Fibonacci numbers by any positive integer n form a periodic sequence: so from this point of view, there is nothing special about 24.
Very interesting and worthwhile lecture. Regarding the stone geometric objects from Scotland mentioned early in the lecture, Michael Atiyah described them in a short book on Physics and Geometry. Sir Michael could only speculate on their significance, but his book has nice photos of the objects. Regarding the Pythagoreans, although they professed vegetarianism, they were forbidden to eat beans. A rather strange rule, and nobody is sure why they had this taboo. Excellent lecture.
The slide at 43:08 is wrong. When you start to work it out you immediately see that the denominator must be way larger, and in fact the continued fraction is equal to 103993/33102. The slide is correct if you erase the 1/292 term. In general, to get a good rational approximation from a continued fraction you want to stop right *before* hitting the big number, not after like prof Baez says.
Last Fermat theorem was proofed by elliptic curves in 2016 by Andrew Willes AW=1+23=24 so your maybe cannonballs packing and elliptic curves are some how connected.
Why is the wavelength not quantized? If the wavelength were quantized, a maximum frequency would exist for every string of finite length, and strings of different lengths would have different partition functions. A harmonic oscillator of frequency f only able to have f*(k+1/2) energy where k is a non-negative integer because the length of the amplitude is quantized. If the length of the amplitude was not quantized, every frequency could have an energy of 3/2. Quantizing space in 1 direction but not the other seems strange. Quantizing the wavelength which limits possible frequencies would mean that string theory does not need Zeta renormalization.
Amazing. So our ancestors were prescient in deciding on a 24 hour day and 360 (2*pi) as the circular measure. We seem to be approaching Jung's concept of the collective unconscious across time.
Interesting. Up in Massachusetts, a lot of the TDI Gurus remove the snowscreen altogether. I also don't see a need for it out here in California or in the SouthWest.
Also note how pi, a transcendental number, has very good rational approximations from its continued fraction. The numbers in the continued fraction of e are 2,1,2,1,1,4,1,1,6,1,1,8,1,... so you'll find very large numbers and thus very good rational approximations. Square roots on the other hand have periodic continued fractions so the numbers are bounded. Rational numbers themselves are the hardest to approximate with (other) rational numbers, so I would say that phi is actually the most *rational* irrational number.
yet another pile of rubbish assigning values to divergent series. Complete oxymoron. The fact that this nonsense goes on I'm sure is responsible for many otherwise brilliant mathematicians saying "fuck no" to joining this field of ignoramuses who don't understand the first thing about their discipline
Baez was the first of the serious math popularizers, with his "this week's finds in mathematical physics" posts in text files, not even word or LATEX, let alone youtube videos, so it's great to see this funny and erudite man present. I loved the way he repeatedly says "well i can't go into such-and-such" but then he does a bit more. When I was an undergraduate, I remember the group theorist (and juggler and unicyclist) Dave Benson telling me, in his fabulous rooms in Great Court Trinity full of Meccano clocks he had built, including a grandfather, that 24 was his favourite number, for similar reasons to what Baez describes here.
