You are sat at a computer. Behind a concrete barrier there is another person at a computer. On both of your computer screens is a dollar value that goes up 1 dollar per minute. When you click the screen, you recieve the dollar value on your screen in cash. However, if the other person clicks the screen before you, you get no cash.
When do you click it?
Wednesday, October 6, 2010
Quantitativeless Numbers
Well, what do 0 and infinity have in common? Besides being two of the oddest "numbers", they represent something other than a set quantity.
Numbers are representative of quantity. We used them to make order from chaos, to change a pile of fruit into a divisible stock of food. |----| is one. |--------| is two. All numbers follow this rule; two points segregating an infinity into a quantity.
So, are 0 and infinity numbers? They do not represent quantities, and they break many rules that all numbers follow. So, why do we include them in our ideas?
First, let's look at all 3 of the quanititaveless numbers I can imagine right now.
∞Infinity∞
Infinity is what you get when you take any quantity and repeat it infinitely. 3 repeated infinite times is equal to 1,000,000 repeated infinite times. Maybe an idea is starting to take shape in your head now; the idea that in terms of infinity, all rules of equality break down. If you had 2 infinite lines, they would be equal since they had the same length of infinity. Now, imagine that you take one of these lines and cut it in a random place. Is it now shorter than the "whole" line because the whole line continues where the previous one leaves off? No. This is the magic of infinity. You can divide it any number of times. You can make as many different sets of infinity as you like, and they will always be equal.
˝Infitesima˝
You can think of infitesima as the infinitely small. It's what you get when you take any number and divide it by infinity. The infitesima is best defined by Euclids first axiom: "A point is that which has no part". Since you have divided by infinity, and as you have seen before, any manipulation of infinity by a number results in more sets of infinity, any manipulation of the infitesima by a number does nothing. An infinitely small object will always be infinitely small no matter how many billions of infinitely small objects you add to it. A way of looking at it is like this:
_
.01. This is a decimal followed by an infinte amount of repeating zeroes, than a one. It represents an infitesima.
Here's a quick way to understand how this is applicable in the real world.
_
1/3=.3
_
(1/3)*3= .3 * 3
_
1=.9
So, what can you add to an infinte amount of 9's to make it zero? Well, you'd need an infinitely small number. You'd need infitesima. Without it, logic breaks down.
0Zero0
Zero. It's the most popular of the quantitativeless numbers. Dividing by it results in a breakdown of logic, and mulitplying it eradicates any number. It is the most easily understood of the quantitaveless numbers, for while others are a more abstract type, this is literally without quantity. It is zero. I'm sure you already understand this well enough.
--------------------------------------------------------------------------------------------------------------
Now, for the finale. Quantitaveless math axioms.
let x represent any number at all.
The Law of Self Morphism-
x*infinity=Infinity
x*infitesima=Infitesima
x*zero=Zero
The law of quantitativeless manipulation-
infinity*infitesima= X
zero*infinity=Zero
zero*infitesima=Zero
The law of inverse infinity-
x/infinity= Infitesima
x/infitesima=Infinity
These may seem utterly useless, but it's very interesting. It's how things beyond our normal comprehension work.
Everything is made of infinite infitesima, which really illustrates the different sizes of infinity.
I'll post on real world application, like dividing by zero, later.
Numbers are representative of quantity. We used them to make order from chaos, to change a pile of fruit into a divisible stock of food. |----| is one. |--------| is two. All numbers follow this rule; two points segregating an infinity into a quantity.
So, are 0 and infinity numbers? They do not represent quantities, and they break many rules that all numbers follow. So, why do we include them in our ideas?
First, let's look at all 3 of the quanititaveless numbers I can imagine right now.
∞Infinity∞
Infinity is what you get when you take any quantity and repeat it infinitely. 3 repeated infinite times is equal to 1,000,000 repeated infinite times. Maybe an idea is starting to take shape in your head now; the idea that in terms of infinity, all rules of equality break down. If you had 2 infinite lines, they would be equal since they had the same length of infinity. Now, imagine that you take one of these lines and cut it in a random place. Is it now shorter than the "whole" line because the whole line continues where the previous one leaves off? No. This is the magic of infinity. You can divide it any number of times. You can make as many different sets of infinity as you like, and they will always be equal.
˝Infitesima˝
You can think of infitesima as the infinitely small. It's what you get when you take any number and divide it by infinity. The infitesima is best defined by Euclids first axiom: "A point is that which has no part". Since you have divided by infinity, and as you have seen before, any manipulation of infinity by a number results in more sets of infinity, any manipulation of the infitesima by a number does nothing. An infinitely small object will always be infinitely small no matter how many billions of infinitely small objects you add to it. A way of looking at it is like this:
_
.01. This is a decimal followed by an infinte amount of repeating zeroes, than a one. It represents an infitesima.
Here's a quick way to understand how this is applicable in the real world.
_
1/3=.3
_
(1/3)*3= .3 * 3
_
1=.9
So, what can you add to an infinte amount of 9's to make it zero? Well, you'd need an infinitely small number. You'd need infitesima. Without it, logic breaks down.
0Zero0
Zero. It's the most popular of the quantitativeless numbers. Dividing by it results in a breakdown of logic, and mulitplying it eradicates any number. It is the most easily understood of the quantitaveless numbers, for while others are a more abstract type, this is literally without quantity. It is zero. I'm sure you already understand this well enough.
--------------------------------------------------------------------------------------------------------------
Now, for the finale. Quantitaveless math axioms.
let x represent any number at all.
The Law of Self Morphism-
x*infinity=Infinity
x*infitesima=Infitesima
x*zero=Zero
The law of quantitativeless manipulation-
infinity*infitesima= X
zero*infinity=Zero
zero*infitesima=Zero
The law of inverse infinity-
x/infinity= Infitesima
x/infitesima=Infinity
These may seem utterly useless, but it's very interesting. It's how things beyond our normal comprehension work.
Everything is made of infinite infitesima, which really illustrates the different sizes of infinity.
I'll post on real world application, like dividing by zero, later.
Sunday, October 3, 2010
Creating Black Holes
Planck's Length is 1.6*10^-35 meters. That's .000000000000000000000000000000000016 meters. Very small. The significance of Planck's Length is the borderline between classical physics and physics of a more quantum flavor. Essentially, it is likely that any object that was that small would turn into a black hole.
Now, you can't just chop something into a particle that size, because there is no part of it that small; you cannot divide it into a smaller piece than its base piece.
You cannot compress it into being that small, as any thing you tried to use to compress anything to this length would need a completely whole surface; the small imperfections would allow anything being compressed to shelter and be compressed only to the size of these molecular crevasses.
So, how can you turn something into a planck's length, creating a manafactured black hole?
Speed.
Special Relativity tells us that an accelerated object compresses along the axis of motion. There's even a simple equation for it;
Length of object at given velocity=(Length of object when resting)*√(1-v^2-c^2)
or
L'=L*√(1-V^2/C^2)
So, if you were too plug in Planck's Length as the resultant Length, you could find the speed necessary to compress any object to Planck's length; effectively you could find the speed you need to accelerate anything too to turn anything into a black hole. Let ℓP=Planck's Length
ℓP=L*√(1-V^2/C^2)
ℓP^2=L^2*(1-V^2/C^2)
ℓP^2=L^2-(V^2*L^2)/(C^2*L^2)
ℓP^2+(V^2*L^2)/(C^2*L^2)=L^2
(V^2*L^2)/(C^2*L^2)=L^2-ℓP^2
V^2*L^2=(L^2-ℓP^2)(C^2*L^2)
V^2=((L^2-ℓP^2)(C^2*L^2))/L^2
Just plug the length into that last equation, and you know how fast you need to accelerate that length into a black hole!
Now, you can't just chop something into a particle that size, because there is no part of it that small; you cannot divide it into a smaller piece than its base piece.
You cannot compress it into being that small, as any thing you tried to use to compress anything to this length would need a completely whole surface; the small imperfections would allow anything being compressed to shelter and be compressed only to the size of these molecular crevasses.
So, how can you turn something into a planck's length, creating a manafactured black hole?
Speed.
Special Relativity tells us that an accelerated object compresses along the axis of motion. There's even a simple equation for it;
Length of object at given velocity=(Length of object when resting)*√(1-v^2-c^2)
or
L'=L*√(1-V^2/C^2)
So, if you were too plug in Planck's Length as the resultant Length, you could find the speed necessary to compress any object to Planck's length; effectively you could find the speed you need to accelerate anything too to turn anything into a black hole. Let ℓP=Planck's Length
ℓP=L*√(1-V^2/C^2)
ℓP^2=L^2*(1-V^2/C^2)
ℓP^2=L^2-(V^2*L^2)/(C^2*L^2)
ℓP^2+(V^2*L^2)/(C^2*L^2)=L^2
(V^2*L^2)/(C^2*L^2)=L^2-ℓP^2
V^2*L^2=(L^2-ℓP^2)(C^2*L^2)
V^2=((L^2-ℓP^2)(C^2*L^2))/L^2
Just plug the length into that last equation, and you know how fast you need to accelerate that length into a black hole!
Saturday, October 2, 2010
Subatomic Structures
So; There are two basic ways that the tiniest particles can be composed. This is disregarding String Theory, which holds that electrons and whatnot are composed of one dimensional objects.
Theory One: The Base Particle
The smallest parts of matter can be composed of pieces of made of no more pieces; perfectly, infitesimally small objects. These would be true atoms, since the word atom comes from a greek word meaning "indivisible". However, such a thing would be rigid; since there were no bits composing it, matter would trael through the object immediately, and reach the other side of the object instantly. This would be faster than light speed, which violates Einstein's Theory of Special Relativity, which has plenty of trippy effects.
Theory Two: Infinite Parts
Every particles is composed of more particles, composed of more particles, etc. The problem with this idea is once again energy transferrence; one object would hit another, would hit another inside that, forever. Energy would constantly be pushing the other parts of the bits making up electrons, collidin and traversing an infinite amount of messengers carrying it. The problem is the infinity; the infinity cannot be traversed.
Obviously both of these are impossible.
Theory One: The Base Particle
The smallest parts of matter can be composed of pieces of made of no more pieces; perfectly, infitesimally small objects. These would be true atoms, since the word atom comes from a greek word meaning "indivisible". However, such a thing would be rigid; since there were no bits composing it, matter would trael through the object immediately, and reach the other side of the object instantly. This would be faster than light speed, which violates Einstein's Theory of Special Relativity, which has plenty of trippy effects.
Theory Two: Infinite Parts
Every particles is composed of more particles, composed of more particles, etc. The problem with this idea is once again energy transferrence; one object would hit another, would hit another inside that, forever. Energy would constantly be pushing the other parts of the bits making up electrons, collidin and traversing an infinite amount of messengers carrying it. The problem is the infinity; the infinity cannot be traversed.
Obviously both of these are impossible.
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