Zero is at the center of mathematics

Its status as a number though, is ambiguous.

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.... Numbers follow certain rules -- take any two numbers, excluding 0, and multiply them. .After changing one, multiply again. .You get a different answer. .This is a basic principle -- change one of the numbers being multiplied, and you'll change the answer. .However all numbers -- by common understanding -- when multiplied by 0, equal 0. .No other number works this way.

.... Consider the statement 4 = 7, which is false. .Since algebraic laws are designed to preserve truth, (and it's true that that statement is false), there should be no way we can make that statement into a true one, (turn lead into gold, so to speak). .Now multiply both sides by 0. .The result: 0 = 0, (by standard math again), is true. .But it's a singular kind of truth. .Zero has gobbled up the values and there's no way of getting back to the original statement. .The information is lost. .(Which has dark implications for quantum mechanics.)

.... It's clear that in the ordinary sense, 0 isn't a number. .It's sort of a black hole at the center of everything. .Numbers multiplied by it fall in and disappear. .This, at least is manageable. .But when you divide by zero the opposite happens, the result goes sailing into the ether, (the white hole effect, how many times would 0 go into 2?). .This is not manageable, so division by 0 is prohibited -- it causes math to crash. .A sort of compromise is struck: .The nature of zero, whatever it would be, is put aside and it is treated as a common number with uncommon properties. .A simplification -- and it works -- results are very accurate, and it's certainly easy to use.....

.... Here mathematics points towards a different understanding. .And when math points it's best to look. .Consider the graph above. Reading from left to right, the curve comes in from the West, when x values are negative and large, (-8), and y values are negative and small (-1/8). .Centering on -1,-1 it turns to the South and leaves -- temporarily -- at (-1/8, -8), the opposite of what we saw coming in. Then suddenly it appears from the North, does the same thing -- and leaves to the East. .It's all one function, so how did it move from South to North -- in the space of 1/4 -- without leaving a trace?

.... If the X/Y plane is flat, as standard math assumes, the curve journeyed south to negative infinity, (when x was equal to negative one over infinity), then something mysterious happened at the zero line -- because we're not allowed to divide by 0, we can't know what -- but when it was done, the function had crossed the entire plane, to positive infinity, (when x equals positive one over infinity). .Ahem...

.... There's another way of looking at it. .The Co-ordinate plane is not flat, but a globe with zero at one pole and infinity at the other. What we are watching is a function make its circuit of the world. .It left heading south and returned from the north, like an explorer, and now it will leave facing east and return from the west.

.... There are many implications of this: positive infinity and negative infinity are the same place but in different directions. .In fact no matter what bearing you take, infinity -- the same infinity -- is half a globe away. .If infinity is immeasurably large, then the globe will be too -- and would appear flat for most purposes. .But even if it's not, there is a relationship between its value and zero.

Zero equals one divided by infinity. ..This is implied in the function's leaving to the East and returning from the West. .When x equals infinity, y will be 0.
Infinity equals one divided by zero. ..This is implied in the function's leaving to the South and returning from the North. .When x equals zero, y will be infinity.
Zero times infinity equals one. ..This can be derived from either of the previous two equations.
.... Now let's return to those earlier examples...Take two numbers, 7 and our new zero, multiply them together and you get 7 divided by infinity. Let's change 7 to 8, now it's 8 divided by infinity. .Different inputs: different results, that's what we wanted.
And the preservation of falsehood? (quite a statement in itself)
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.... Not that this completely eliminates the nettlesome problem at the origin, in fact by quantizing mathematics, we've said that there really is a hole in the center of things. .Between -1/infinity and +1/infinity, there's a void! ..Not only that, but if infinity is brought down to earth and assigned a value of 10, say, so that 0 would be 1/10 -- any number that didn't divide by 1/10, 1/9, 1/8, 1/7, 1/6, 1/5, 1/4, 1/3 or1/2 would not be applicable. "Quantum-sphere mathematics" -- clearly this is a form of math for special situations. .And infinity is usually immeaurably large, making one divided by infinity immeasurably small, making the problem moot.

.... But there is one application where bringing infinity down -- all the way down -- may answer a fine question. .I'm not a physicist -- so I can't say how much application it has to this reality -- but I can hope. .Nature follows the path sensible to it.

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A Creation Myth

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Imagine a void, and that the principles of math will apply there, once they have something to apply to.

The question might be asked: "In a perfect void, is there anything to prevent a possibility from expressing itself?"

Or, to put it another way: "If everything equals nothing, nothing equals everything".

At some place in the void there emerges quantum sphere where infinity is equal to zero.

Really it's more a location than an object -- there's nothing actually there but potential. .Let's work the equations:

This is not a falsehood -- in this context.

By defining zero in terms of infinity, we are freeing it from a fixed value.

Still, it is strange to see zero exceed the value we just gave infinity...

At positive or negative one, zero's value points outside the sphere -- in other words the sphere doesn't exist yet.

Let's check back on infinity.

Wow, that was fast -- expansion is instantaneous.

The quantum sphere assigned infinity 0, now has an infinity of positive or negative one -- (the same thing, here).

Those are zero's values too. .As the system begins they share a dual identity -- interesting...

A Quiet Moment

Let's use one for infinity, go back and solve for zero.

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We could have used the negative square root -- and gotten -1. .Really it's just a matter of right and left.

Now, at this point our universe is an empty shell. .Nothing between plus and minus zero can exist -- and zero is the same as infinity.

In fact one might say that it is the universe at this time -- but that will soon change.

The first step was for the value of infinity to jump from 0 to 1 -- that was automatic.

The universe is actually stable here -- it needn't grow any further, but that's a very small creation.

Let's assume it keeps going.

Any steps between 1 and 2 would involve fractions -- and by the rules of the game, as I understand them -

- fractions don't exist before 2. .So infinity proceeds there.

Solving for 0:

Conceptually, we're out of the woods -- at least in this respect.

The value of infinity is 2, distinct from and larger than the value of zero, which is now our first fraction: 1/2.

When infinity becomes 3, zero will be 1/3; .4 begets 1/4, and so on...

Also emerging within the universe is space. .Real, fillable space in which particles may emerge as quantum spheres themselves.

Only now they won't be alone -- they'll be packed together, and that'll make things exponentially more complex.

But of course, we're here aren't we?

I take it as a point of faith -- that when mathematics says it's possible for something to happen, in one or more realities it does.

Most possibilities are caused and limited by external events.

So it's interesting to think of a place where there's nothing at first but "if" and "then".

Please see more of my work at www.nolongermichael-workbymichaelyoung.com