Math of Speech

  To make a sound for speech you move how open your mouth is, where your tongue is in your mouth, how rounded your lips are, whether your vocal cords are vibrating, and if so what tone in your vocal range they are producing. Every syllable has a beginning, middle and end time period where you move from one combination of all those variables to another, and then to a final state.
   So going through these let's call how open your mouth is M(m) where m can be a number from 0 to 6, with 0 closed and 6 fully open. The tongue can be at a position T(f, u) where f is how forward the tongue is and u is how far up in the mouth it is. A good range is f can be from -2 to 2 for all the way back to all the way forward and u from 0 to 2 for bottom middle and top of the mouth. Lips could be L(l) with l from 0 to 1, for not at all rounded to fully rounded. And vocal cords could be V(o, t) with o being binary 0 or 1 off or on, and t from 0 to 1 for the lowest to highest pitched tone you can make. And B(b) is whether your breathing out or not.
   So a part of a syllable looks like:
M(m), T(f, u), L(l), V(o,t)
  And a whole syllable looks like:
M(m1)    -> M(m2)    -> M(m3)
T(f1,u1) -> T(f2,u2) -> T(f3,u3)
L(l1)    -> L(l2)    -> L(l3)
V(o1,t1) -> V(o2,t2) -> V(o3,t3) 
B(b1)    -> B(b2)   -> B(b3)
For instance the syllable "boy?" where the question mark means the tone rises as you go through the word...
M(0)     -> M(3)     -> M(3)
T(2, 0)  -> T(1, 0)  -> T(1, 0)
L(1)     -> L(.5)    -> L(0)
V(1, .5) -> V(1,.75) -> V(1, 1)
B(1)     -> B(1)     -> B(1)
This basically means the mouth is going from closed to half open, the tongue goes from all the way forward on the bottom of the mouth to just a bit back still on the bottom, the lips go from rounded to not-rounded, and the voice is on and goes up in tone. 

A different example might be "swipe"
M(3)     -> M(1)     -> M(0)
T(1, 2)  -> T(1, 1)  -> T(1, 1)
L(0)     -> L(0)     -> L(0)
V(1, .5) -> V(1,.75) -> V(0, 0)
B(1)               ->    B(1)               ->    B(1)

So really a syllable is pretty complicated...  

The perfect Display

I imagine this display might be possible someday. There are three main things you do with LCD screens, viewing content abstractly related to looking at a piece of paper, tasks related to producing those or using other programs and watching movies. Here are the relevant aspect ratios:

So you see on the top left is the typical U.S. paper size 11x8.5, but I left enough space around it to handle the standard the rest of the world uses A4... But in some bizarre mathematical coincidence A4 is the perfect size to fit a U.S. standard size into and have room for all the toolbars and scroll bars and everything.
   The HDTV's now are 1.77:1 aspect ratio. But the movies you see in the theater are 2.39:1, A4 is 1.414:1 so two longways is 2.8:1.  So the idea is you would have two screens the A4 size, that you could put side by side so you can work on two different things full size but then you rotate both of them and put them side by side to go into movie mode. Unfortunately there are still black bars around the movie but this is the best I could do. And Hollywood historically has always gone to wider and wider screen 2.39:1 is the current that I used above.
  The big technical hurdle is making an lcd without a bezel, I found one 40 inch HDTV that the bezel was only four pixels wide (which would still be annoying going down the middle of the display) but that TV was 5000 dollars so right now it is expensive to do but hopefully this will be possible someday...
   I call the screens "Foils" so someone can say "Lock Foils into Movie position!"

***UPDATE***
A friend of mine, Blair Updike, suggested using projectors instead. The image projected doesn't have the limitation of the bezel around the lcd and I believe that makes it possible a lot sooner than what I had in mind. The projector would basically be two projectors built in one case that can rotate and move what they are projecting from one mode to the other.

gclamps

These are supposed to lock tight like the mechanism on the gas pump.

a natural number size kite

consider the type of number 3^(1/4)*2*y = x for natural number y.
When you plug x in for all 3 sides of Heron's formula you get:

and then fill in for x:

So this type of number makes an equilateral triangle have a natural number area. 

Interestingly because of the 3 in 3y^2, that means:

This shape I believe is called a kite, because it is 1/3 of the triangle's area it will have an area of y^2. So it has the same area as a perfect square but a different shape. 

This hexagon has area 6*y^2. 

which is the same as the surface area of this cube:

If you imagine this tiling of hexagons made to look like cubes:

You can see layers of hexagonal tiling would be able to map the surfaces of a volume of cubes in a way that preserves area. Though not shape. 

theory behind "Air Conditioning #2"

The chord progression in this song:
IV, I, ii, vi
which is:
F major, C major, D minor, A minor
which Google doesn't show any results for the way it does many other progressions
   I tried to use one that hadn't been explored before (it may have been but I didn't see any results for it)
I put the major pentatonic over this progression, which the rule of thumb is that it matches with major triads but not really minor ones,
but I found that if I was careful I was able to avoid any sour sounding combinations. In my mind anyway :)
   The bass line stays completely within the notes of each chord for two measures at a time. I really spend a lot of time on the bass line, actually there was some kind of glitch in the program that moved everything around and I had to redo it.Actually that's how I ended up with this particular chord progression, this is basically what it randomly rearranged the notes to, and then I smoothed it out. So I guess the glitch worked out for the best because I like this progression a lot.  The fourth part of the base line is what took the longest, the first three came pretty naturally and then the fourth took a long time for me to get happy with. 
   The synth I used was "Warm Strings" and it plays the middle note of each chord throughout, I think usually it would be the root note but I decided to try it this way.
   The approach to matching the main melody with the base lins was to play basically the same pattern of moving up and down in tone but sort of improvising a pentatonic version. Well, that is, I think that's what I was doing subconsciously, it didn't really occur to me until after I played it.
   I don't know much about the theory as far as rhythm goes, I used a drum sample called "Bar Band" on the IPad.
   The whole song was done completely within the one program Garage Band on the IPad. (Best 5 dollars for a program I ever spent!)
   All in all I think it took about 8 or 9 hours to make, pretty much in one session with a couple of cigarette breaks in there. But not many and not very long ones.  A couple times I had to stop and look up some things on the internet, I just learned the Roman numeral chord notation last night.
   As far as the overall structure goes, I think it might be unique, as many different genres have all the songs in them following the same basic structures, and I try to make up a new one for each song. I'm not too sure  about this because I don't know all the different terminologies for structure. I think this one might be considered to have two bridges, but maybe that would only have been if I had changed the drum pattern when the electric guitar comes in. As it is maybe that counts as a chorus.  And for instance it might be unusual to introduce a new instrument in the last couple measures. I don't really know much about it.  I'm going off the fact that I made it up as I went along without following a set pattern and most music follows a certain set of basic patterns, so I think the chances it's been used before might be slim.
   I'm pretty happy with it, I like listening to it. My Grandma thinks it's really pretty, that makes me happy. A couple of people said each song is better than the last. I like to think I'm improving. Long ways to go yet, though.  The stressful part is thinking that someone might hate it, but I think even the greatest masterpieces have their people that can't stand them. Probably a much higher percentage of people won't like this one, haha.

System of Measurements

Ok, start with A=1x10^10 a nice enough round number

Time:
T = A cycles of radiation corresponding to the transition between two energy levels of the caesium-133 atom.
Length:
L = length of a side of a cube that holds A molecules of pure water at sea level at the melting point temperature


**All below are derived from these 2 measurements and the number A**
Volume:
V = L^3 the volume of a cube of sides L.
Mass:
M = the mass of V of said water.
Charge:
Q = A electrons
Force:
F = the amount of force needed to accelerate M mass at L length per T squared
Work:
W = A force of F acting over a distance L in the direction of L
Current:
I = Q charge flows in T time
Voltage:
P = one W per Q
Electrical Resistance:
R = the resistance needed to allow I current to flow at P voltage
Temperature:
C = the heat emitted by a resistance R under P voltage for T time.

...
many more but you see how everything is based off the nice round number 1x10^10 and two easily verified physical measurements. I believe most everything could follow.

Rational function interpolation

My first thought was this was kind of obvious but apparently when people want to find what this finds the answer to they use something called http://en.wikipedia.org/wiki/Pad%C3%A9_approximation. This is a much simpler way that I thought of.

Say you have your unknown function:

The four fractions at the bottom are what the function equals at x=1,2,3,4, you'll notice if you use regular interpolation with these numbers it won't even be close to the unknown function above.

But what you can try is to interpolate the top half of each fraction and bottom half separately, like so (Make sure they are in lowest terms or this won't work):

There that matches the unknown function very well...