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Math assumes non-dimensional points on a number line are separated.

But assumes the points have no distance between them.

If a point has 0 length on a number line and it is 0 distance from the point beside it, they are the same point. You cannot create a number line with points that have no length and no distance between them.

But string theory assumes points have a length on a number line, or that the centers of the points are separated by a distance. A distance on a number line is 1 / divided by a number.

Math assumes non-dimensional points on a number line are directly beside each other, with no distance between them. The only time that is true is when their size and the distance between them is 1/infinity. Infinities don’t exist in math, so while math incorrectly assumes points with no size can sit directly next to each other, math doesn’t include an exact idea of infinity. And so math has no real input about the exact size and shape of points.

1/9,000,000,000,000,000, or however many zeroes you want to add is included in math, so the closest that math can get to dividing down to zero distance and a zero-sized point on a number line is a very small distance and a very short point, in other words, a string.

That is what string theory could be.

Given that concept for string theory, it’s possible to answer a few interesting questions.

If points are small distances, then the distances can vary, which gives us a space that can stretch, warp, and curve. Now, using that concept of string theory, we can describe a continuum, and it can change shape.

Einstein began to think, in 1936, there cannot be a continuum, maybe because he realized points cannot have 0 size and 0 distance between them, and create the continuum. By 1956, he privately concluded and said to a friend that a continuum is impossible, and said that all of his ideas about gravity are invalid.

But using the definition of string theory that I have just stated, which shows that non-dimensional points have to be strings, a continuum can exist.

So in 1956, when he realized points that are 0 in size and 0 distance apart can’t create any space, therefore, space is just an empty nothing and can’t change shape: therefore there can’t be a continuum. String theory in the 1980's suggests that all points have length. And in math it turns out to be impossible for points not to have length, since 1/infinity does not exist as an actual value.

So let’s create a string theory plane. You take points that have length and connect them together.

It doesn’t matter how long or short the points are as long as they have a length, so let’s use Q-Tips to represent string points and connect them to make a plane.

(Sorry my IMG code is off. I guess I am considered a crazy moron.)

The plane in the photo has two dimensions. You can locate any point (any Q-Tip) with an x and y axis. But to get from any point, to any point on this plane you have to zigzag through an underlying three dimensions because, this plane only contains three directions! That is the strange thing that happens when you use string points, instead of non-dimensional points sitting directly next to each other. But you can’t create any space when you use non-dimensional points with no distance between them. You can only create space when you use string points. But then, you find you are limited to only three directions! These three directions become three dimensions.

If you were to build the plane into a 3D space, you arrange the Q-Tips like this.

Now you have six underlying directions through 3D space. You have the 3 classic dimensions, and you have the dimension of time, for 10 dimensions, exactly how many dimensions string theory predicts.

-John Cauthen