All around one of the best defenses of mathematics I've heard as of yet. It has 8 parts.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Very cool. He used a lot of examples that pushed his overall speech along.
The one negative thing I'd have to say is that all the examples given were only touched on, never fully explored, and it left me feeling unfulfilled. But I guess ultimately the subject was the importance of mathematics, and not to explore the individual examples. I think it's unfortunate he wasn't able to really expand on his examples, but then the overall message would have been lost. So I guess I'm retracting my original criticism, and saying that it's good that he didn't go into depth, but I'm still not happy about it (I'm not sure if that makes sense).
The coolest thing was the illustration from the children's book at the end. I really think that that speaks to our subconscious mathematician and it really shows how out thirst for mathematics is in a sense hardwired into our psyche. Even if we don't immediately know why, we can say with certainty that that picture is a bad one, to me that speaks volumes.
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
An application of abstract algebra (group theory) to music theory:
Saw Tim Gower's speech before, it is good isn't it
@Jane, I loved the chromatic scale
cyclic group shown mathematically.
This is awesome because it
demonstrates to dummies like me
how the language of math works!
OffSubj:It's weird that many harmonics
come very close to the equal temperament,
and some are not, so the trumpet player
doesn't play that note...
More stuff I made up once: trumpet lip-tightening harmonics n=1,2,3,4,5,6... chromatic steps upward from lowest note=12* (log n / log 2) number of half steps up the chromatic scale Bb trumpet notes in right column (open tones, played with no valves) 0.0 unplayable by humans, as far as I know, double low C on the trumpet. 12.0 lowest open tone on the trumpet, low C, maybe call it C1 19.01955 middle G below middle C on trumpet, probably should call it G1 24.0 middle C on the trumpet, call it C2 27.8631371 middle E on the trumpet, call it E2 31.01955 high G on the trumpet, call it G2 33.6882591 high Bb, too flat to use (see .688, not close enough to 34.0) 36.0 high C, call it C3 38.0391 high D, call it D3 39.8631371 high E, call it E3 41.5131794 halfway between double high F and F#, see the .513, means about half. 43.01955 double high G, G3 44.4052766 see the .4, this is 40% of the way between two notes. G#3 + 40 cents 45.6882591 Between Bb3 and A3, about 70 cents to high or 30 cents to low. 46.8826871 B3, only 12 cents flat, not bad at all. 12 cents because of .88 48.0 C4, double high C 49.0495541 C#4 50.0391 D4 50.9751302 Eb4 51.8631371 E4, still probably acceptable, because E2 is played on trumpet. 52.7078091 30 cents too flat 53.5131794 51 cents off, in between two chromatic notes. 54.2827435 28 cents too sharp. 55.01955 G4, close enough to 55 even, so G4. 55.7262743 30 cents too flat 56.4052766 40 cents too sharp 57.05865 5 cents, so a pretty nice 57, which circular chart says is an A4. 57.6882591 See the .6882591, well 1.0 - .688 is about .31, so 31 cents flat. 58.2957719 Bb4, 29 cents too sharp 58.8826871 B4, close enough, perhaps. 59.4503557 60.0 C5, notice 5 times 12 is 60, so C5 is a nice name.
The above stuff is all relatively speaking frequencies,
since some trumpets are different sizes and have
different "root" or "bottom" notes with certain
fingerings or no fingerings (called "open").
The harmonics can go higher and higher forever and they
get closer together as viewed from a chromatic scale,
so if the trumpet were hundreds of feet long, then you
could play really high notes for almost any pitch you
wanted just by changing your lip, and if the trumpet
was really long, then the notes might still be audible.
Last edited by John E. Franklin (2008-05-03 05:04:16)
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