Math Is Fun Forum

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

The Importance of Mathematics

Link

All around one of the best defenses of mathematics I've heard as of yet.  It has 8 parts.

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"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..."

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: The Importance of Mathematics

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.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: The Importance of Mathematics

An application of abstract algebra (group theory) to music theory:

http://www.thescienceforum.com/viewtopic.php?t=11485

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: The Importance of Mathematics

Saw Tim Gower's speech before, it is good isn't it

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: The Importance of Mathematics

@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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