mathphile

Sometimes I wonder why I contacted that ambulance.

So, before I begin something fucking awesome:


Yes, he did play his own baseline.


Ok, now that that is out of the way time for my newest obsession: number factorization. ( Dividing. )

So, last night I had a realization. I was over a David’s house and I got to speak with his father. Now, his dad is what you’d call a sage. Whatever do I mean?

He can show you certain truths.

So, I got angry at Havana and then I realized that the person who was making me angry was me. Sure, what she did might have been wrong, but it was me who decided that it was something worth loosing my temper and arguing about.

Then I realized it, this entire world is one of suffering, bad things happen all the time. But, it is up to us to decide if that these things are really as life altering and tragic as we think they are. All of the demons that plague our society are ones of our making. Is that homeless man a determent to society and a leech or is he someone who life has been a little less than fortunate? Is a guy who robs a liquor store a hell bent anarchist who won’t get a job or he someone who has finally been crushed under the weight of the realization that no matter how hard he tries, nothing he does in life will every bring him or anyone he loves above the poverty line.

Things that hurt us the most are our emotions. The people who hurt us the most are the most in need of our love. That’s what that wise sage taught me. The thing all of the 'bad people' had been trying to show me all along was that the real bad guys aren’t the ones who are attacking us. We are our own bad guys.

What I realized was that using my intelligence to bring greater good to humanity won’t come from thinking up with some new theorem, discovering some new aspect of nature or inventing some novel device or method. It will come from spreading my love for humanity as far and as wide as I can.

Mono no aware.


In other news, I'm finally and truly free from RGIS, I got a job at Border's Books and mad crazy hours to go with it. Yes, Yay, yay, yeah.

I've also got a cool experiment in the works that if I can figure out how to do it right will produce Hawking Radiation without a black hole. I just don't now how to control the decoherence phenomena to keep the stray virtual particles. That and I think the distribution of the primes is fractal and I might be able to prove it, not by looking at the primes but by looking at the composites, specifically highly composite numbers and products of perfect squares, cubes, etc.

Time to go analogue baby!

I need a new job, arrrrg!!!!
( 80 Questions behind the cut. )

Entropy is a measure of the uncertainty of the outcome of a series of events. Plain and simple, that and nothing more. Keep in mind the bit string example, 01010101 has very little entropy and 1111111 has none. However, 010111001100000111 has a great deal of entropy as the out come of each event is a good deal less certain. Consider an collection of particles in a box and the location of each particle as the event under consideration. Now, say you have a given region of space and you can predict that a particular particle will exist within that region of space 80% if the time. Next, say that you can say about same thing for all particles in the box for a given region of space. If so, you can then say that that box has low entropy. You are fairly certain about the outcome of each event. Now, say that you can only predict the location of a particular particle only 20% of the time and about the same thing for every particle in the box. You would then say that this box has a very high entropy. There is a rather strong degree of uncertainty about the outcome of events.

Consider the fact that entropy for physical systems is defined in a statistical manner via the average velocity of individual particles to counter the fact that you cannot easily view the individual particles. For objects like crystals or sheets of metal the average velocity is very low and as such the constituent particles are very well ordered in the sense that the have well defined repeating patterns, you'd need only a small sample of the crystal and information about the external conditions to predict every physical property about said crystal. Now consider a large volume of gas that's average particle velocity is very high. As such, no matter how large the sample is you would still to take large samples to reduce the uncertainty of the volume of gas. Low velocities ensure that there will be very little deviance in terms of the particles arrangements, high velocities do just the opposite. Then universe started out as a highly ordered, low entropy, low information (entropy = information) state. It then exploded, but very soon the fundamental forces reduced the entropy of the universe by introducing order. But due simply to the fact that energy or average particle velocity exists (check out Nernst Theorem aka the third law of thermodynamics) the 'state' of any region of space will head in the direction of increased uncertainty. Why? As the particles move there location gets harder to predict, there are more possibilities for them to exist and as such any attempt to make a prediction becomes more and more uncertain. Entropy must always increase, it's just one of the properties of the universe. In fact, the larger the pool of outcomes the greater the entropy, the more 'random' a random collection can be.

I hope the clears things up, Heath. This is why I for the most part have ignoring the problem of time asymmetry in the B-theory of time. Order isn't arbitrarily defined, it is done in a general way dependent on the weighting of the outcome of a collection of events in a given probability space, their probabilities. This way entropy can be defined not in terms of the events but in terms of their probability distributions.

This morning I found myself asking a question, “What is the difference between abstraction and encoding?” ( The answer )

Disclaimer: THIS IS NOT MINE!

bloodninja: Ok baby, we got to hurry, I don't know how long I can keep it ready for you.

j_gurli3: thats ok. ok i'm a japanese schoolgirl, what r u.

bloodninja: A Rhinocerus. Well, hung like one, thats for sure.

j_gurli3: haha, ok lets go.

j_gurli3: i put my hand through ur hair, and kiss u on the neck.

bloodninja: I stomp the ground, and snort, to alert you that you are in my breeding territory.

j_gurli3: haha, ok, u know that turns me on.

j_gurli3: i start unbuttoning ur shirt.

bloodninja: Rhinoceruses don't wear shirts.

j_gurli3: No, ur not really a Rhinocerus silly, it's just part of the game.

bloodninja: Rhinoceruses don't play games. They f*cking charge your ass.

j_gurli3: stop, cmon be serious.

bloodninja: It doesn't get any more serious than a Rhinocerus about to charge your ass.

bloodninja: I stomp my feet, the dust stirs around my tough skinned feet.

j_gurli3: thats it.

bloodninja: Nostrils flaring, I lower my head. My horn, like some phallic symbol of my potent virility, is the last thing you see as skulls collide and mine remains the victor. You are now a bloody red ragdoll suspended in the air on my mighty horn.

bloodninja: Goddam am I hard now.

We are strange things in a very strange place.

I always wondered how many instances of svchost.exe should be considered exceptable?

if everyone is so intent on placing the blame upon my shoulder, I'll do you all a favor and remove myself from the equation.

Christ, it's just one fucking insult after another.

P.S. Kole I really appreciated that letter. Thank you.

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303820

Yay!

I really hate having to correct almost every other answer in this text book. Why even place an answer key in the book if it is almost always wrong!?! WHY? This the most pendantic study session I've had in years, and it's all due to a shitty text.

ARRRRRRGGGGGG....!

The truest beauty of the world lies in it's symmetry.

All combinatorial roads lead to number theory.

Well, after a lot of thought and a few weird dreams I've finally found a way to the beginnings of a formal version for my theory to unite quantum mechanics and general relativity. To my great surpise it involves a great deal of combinatorics, a branch of mathematics I don't know to terriably much about. I've only used it in application to probability theory, never anything to deep. It looks as though I accidentally recreated a highly informal branch of geometric combinatorics trying to explain what I like to call gravation's riddle.

If I can place this on a rigrous basis I might be able to finish it before I get my Ph.D, what a thesis that would be!

P.S. I've got a new phone number (I actully don't know it yet, Havana does, however.) and I'm switching from bellsouth DSL to comcast. So, for the time being, I've no internet at home.

P.P.S. Also if anyone knows of a good statistical thermodynamics or statistical mechanics book, PLEASE TELL ME.

Now that the winter depression is clearing away I'm getting more and more into my private research. I'm so far behind my quest though! After Knuth's book I'm going to start studying differential and algebraic topology heavily. Same with differential geometry. I guess for a while I was just floating around and collecting facts, but now I'm going to do something unique. The funny thing is that I was motivated to this by an idea I sharply disagree with. The idea, wrong or right, of the applicability of Heath's concept of a substance to major problems in metaphysics has gotten me feeling as though I'm not thinking. Just absorbing. I need to change that.

Thanks for the pick me up Heath-kun!

Heath, as I no longer am in possession of your email address I've no choice but to post my reply to your question here.

Your idea that different, but still logically consistent variants of geometry could by juxtaposed to the idea of a fiction is logically flawed, the metaphor fails for the following reasons: axioms, unlike like the beginnings of a tale, cannot be arbitrarily chosen. In a story, one is free to allow her imagination to fly as far and as wide as she may. Anything may go, even if the informational entropy of the tale has an upper bound of what could be potentially realized within the current material universe.

To begin selecting axioms, one must first show that they be consistant and also complete. Basically, that all theorems proven by said axioms be true and that they all provable in a finite number of steps. Then, they must all be shown to be independent of each other, i.e. you shouldn't be able to prove on axiom from any other, they are the atoms of the system. Then of course, it must also be shown that no axiom is superfluous, waste not, want not. If you look over the writtings of Peano, Tarski, Hilbert, Kleen, Lobachevsky and a myriad of others, you would see the exteme difficulty in creating an axiomatic system. You would also note the universality. It is enough to suggest that things could be no other way.

Now, the variants of geometry are intriguing. For a good 2100 years, mathematicians attempted in vain to show that the fifth postulate, the parallel postulate or Playfair's axiom, was not an axiom at all, but a theorem. Logic hadn't developed very far from Aristotle and thus was of no use. The only thing mathematicians had was trial and error. But Gauss, Riemann and Lobachevsky decided to either modify the axiom or ditch it all together. The assumption was that this would lead to a contradiction or an incomplete version of geometry, it didn't. Even with the advent of mathematical logic, which did invent such consistant fictions, it was shown that all three variants of geometry satisfied the requirments for completeness and consistancy as long as elementary number theory was shown to be consistant and complete. They're all equally as valid, also they all share most of the same axioms with a minor difference here and there. They also contradict each other, if Riemann's geometry hold for a surface, Euclid's cannot.

There is a fourth variant, absolute geometry, but it is logically incomplete.

You see, Heath, due to the nature of logic and the nature of mathematics you cannot pick and choose your axioms, the theorems of your system are not like some manner of convenient fiction. In fact, even weakening the axioms from elementary number theory leads to a consistant and complete variant of number theory, it also leaves out many important theorems. It can even be made to generate a statment of it's own inadaquecy.

So these variants are not like fictions, they exists as they do because they must.

I know what the problem here is though, you've made in the incorrect assumption that mathematics is an outcropping of logic or vice versa. I know why, you've heard of axioms and the only branch of math you've been exposed to is basic algebra. From what you've been exposed to, math is nothing but symbol shuffling. Even in the calculus, you can get by by memorizing symbol shuffling rules, of course that is why many people fail calculus, there are far more rules to remember. However, in linear algebra you first experience true mathematics. The mapping of vectors and then linear operators to other coordinate systems is the first time when one is forced to divorce oneself from the concept of mathematics as symbol shuffling. Then of course, there is abstract algebra and the higher analysis (advanced calculus) which, if you tried to think of them in terms of symbol shifting you'd understand nothing.

This, I think, is where the error in your thought stems, you assume that everything is proven from axioms, not so. Axioms are devolped long after the branch of mathematics is established, in fact not all branches of mathematics have been axiomized, combinatorics for example. Axioms are tools to assure oneself that she is on the right track for devolping theorems and proofs, they aren't the be all and end all of maths.

Study some group theory and the idea of functions and relations a bit more. You'd see that math is about patterns and relations, not symbols and axioms.

Someone posted this a while ago somewhere else.

A group of people are talking at a party about the jobs they do.
"What do you do?" someone will ask someone else.
"I'm an XXX", is the reply.
"Oh, well I have a question about that .....".
A stranger walks up to the group.
"What do you do?", they ask the stranger.
"I'm a mathematician," he replies.
There is a silence, until someone says, "What about those Mets?"


A group of mathematicians are talking at a party, discussing their fields.
"What do you do?" someone will ask someone else.
"I'm a topologist", is the reply.
"Oh, well I have a question about that .....".
A stranger walks up to the group.
"What do you do?", they ask the stranger.
"I'm a mathematical logician," she replies.
There is a silence, until someone says, "What about those Mets?".


A group of people are chatting at a party. Alex walks up to the group.
"What do you do?" they ask Alex.
"Oh, I'm an astro-physicist," Alex answers.
There is a silence, until someone says, "What about those Mets?".

The next day, Alex goes to another party, and walks up to another group of people.
"What do you do?" they ask Alex.
Alex hesitates, then says, "I'm an astronomer."
"Oh wow, that's so interesting", they say. "Tell me, is there life on Mars? How big is the universe? What are Saturn's rings made of? Did NASA really land on the Moon? ..."

Everybody is free

By Rozalla featuring Aquagen.

Everybody's free to feel good
Everybody's free to feel good
Everybody's free
Brother and sister
Together we'll make it through
Some day a spirit will
Lift you and take you there
I know you've been hurting
But I've been there
Waiting to be there for you
And I'll be there just helping you out
Whenever I can
Everybody's free to feel good
Everybody's free to feel good
We are all a family
That should stand together as one
Helping each other
Instead of just wasting time
Now is the moment to
Reach out to someone
It's all up to you
When everyone's sharing their hope
Then love will win through
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good
Everybody's free to feel good