4th dimension

sol1

What Dimension Means?

John,

Then how would you explain "continuity," in terms of what geometry can do?

You have consistently held to points, but this cannot happen at supersymmetrical levels because of the energy recognized.

I have created a link for those who wish to expand there minds in terms of dimension (What is dimension?) , and this follows strict lines. If one is to expand to understand how such points become smeared at high energies then you have to undertand how GR and QM come together gives insight into dynamical movements. How would you do that in points in regards to spherical and hyprbolic undertandings, as dynamical movement? Reinmann lead us to spherical considerations, yet there is a negative expression, if we understood the triangle and its degrees of, how would we know which way to measure this value?

The Friedmann equation and curvature help greatly here.

I see your sincerity and drive, and recognize it in myself... yet there is information that we must become aware that might have limited our vision of things. I mean this in a polite and respectful way. I am open to corrections as well.

Sol
 
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The thing that is confusing physicist/mathematicians is that some things, which appear to be a certain way, are really only expressions of what they are. Continuity is the best example.

If you have four “points in space” they can look like this:

Point…………Point……………………….Point………………………………..Point

A particle, like a photon is always going to travel from point to point in the same amount of time. So if we measure distance by time, such as light years, those four points will be seen as having the same distance between them. We would measure a light year in our vicinity of the universe, and assume a light year is the same length everywhere.

Yet, if we measured the photon by physical distance going between those four points, we would know the photon has clearly sped up.

Electrons orbiting a nucleus can speed up on one side of the atom if the points of space are farther apart on that side of the atom. If the electrons are going faster on one side of the atom, their centrifugal force will pull the atom to the side the electrons are orbiting faster.

So if you imagine an orbit where the electron is following points of space, and the points are farther apart on one side due to space being warped by a large mass, the atom will accelerate into the large mass.

This works because there are two mathematical systems interacting. In one system, the points are considered a continuum. We consider there is no distance between the points. In the other system, which is string theory, we consider the distance between points and consider what the particles are actually doing as they travel from point to point.
 
Forgive my clear and utter ignorance (newness can often equal naivety), but I was taught that the speed of light is constant.

Or is that constant in different fundamental situations/environments?

Photons are particles travelling at a constant speed - so how can they effectively appear to 'speed up' (gain a velocity) and 'slow' back down at will? According to the basic principles I can recall about General Relativity the alterations in mass alone caused by the added velocity would be astronomical!

I understand the concept about the photons being 'pulled' from one point to another - but that would mean that the greater the apparent 'gap' breached between two points the greater the acting 'pull' - which is the same as saying the greater the force acting upon the photon. Which force is this? Because if this 'force' can increase the speed of light then surely it is one to be reckoned with, even on a fundamental scale!

Please illuminate . . .
 

selfAdjoint

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You are right. John is mistaken. Seen from any inertial frame of reference, the photon takes twice as long to travel twice the distance. John may be thinking of the fact (also true) that the photon experiences no proper time in doing either trip. These two facts do not contradict each other in relativity.
 
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The speed of light is not completely constant. There is gravitational lensing, which happens due to gravitational warping of space. The amazing thing about gravitational lensing is that light must go faster to bend around the sun. It is impossible to set up a model for gravitational lensing where light does not increase slightly beyond the speed of light.

In regular lensing light slows down, and that makes it bend.

We also now know that we can supercool space and make light nearly stop. Why? Because there must be an energy in space itself that is pulling light along. Supercooling space takes that energy away and brings light nearly to a halt, amazingly, preserving all the wavelengths and characteristics of a particular light so that when you unfreeze it, it returns to its original self!
 
Fair comment.

However, I'm not entirely convinced about the gravitational lensing effect increasing the speed of light. All it means is that the streams of photons are deflected around the gravity well. Although they follow a slightly diverted course they are still moving at the same speed. If you are riding a motorbike at 40 mph and swerve around a rabbit in the road, your speed remains the same, it is only the distance travelled which is slightly longer. Localized gravitational lensing of incoming light around a star appears to 'bend' the photon stream but does not affect the actual speed. Due to the pretty fast movement of the photons it would be extremley difficult to detect any kind of velocity alteration on a localized level. The whole ethos of General Relativity relies upon the 'fact' that the speed of light is constant. Even increasing the speed of a single photon beyond this 'barrier' would cause dramatic effects - where the photon itself could very possible 'fall' out of the known universe!

As for supercooling space in such a manner as to bring photons to a halt ...

The abundance of space has a temperature a little above zero Kelvin - which is pretty supercool by anyone's standards! Photons appear to traverse these regions without difficulty. In fact, electrons move easier through a supercooled medium! There is less general resistance and an actual increase in conductivity. The idea of completely removing energy from a region of space in order to completely stop the photon flow seems bizarre to me considering that the universe itself (according to string theory) is very probably constructed by energy alone. Even at the above mentioned regions where the temperatures hover just above zero K, the energy structure of the space-time must remain intact and viable in order for that region to continue existing.

A matter for further ponderance, perhaps.
 

selfAdjoint

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You are right and John's post about slowing light is incorrect. Light rays in gravitational lensing do not slow down, and it's dangerous to use earthly dynamics to try to understand them. What happens in gravitational lensing is that the light folows the best curved path it has available - since there are no straight paths in the curved spacetime near a gravitational source. These paths are called null geodesics and only things moving at the speed of light can use them. And light continues to move at the speed c as it follows them.

As light interacts with a gravitation field it may gain or lose energy and momentum, but the physics of light is such that that can happen without affecting its speed.
 
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I thought about the coldness of space when I read about the experiment too. There are experiments that slow light to very slow speeds, in order to preserve the information in the light beam.

We know that light bends in water because the beam is slowing down in sections. The first "ray" hits the surface and slows down, then the second "ray" hits the surface a little later. Since the surface of the water is at an angle, the second ray slowed down later, and now the two rays continuing on parallel paths are going in a different direction. The first ray traveled a little farther before it slowed down.

It’s easy to say light curves around a star because the space is curved. The same thing can be said about a satellite. But if it goes at a different velocity, it follows a different curve, so it must have something to do with a force, not with the simple idea of the curve of space. The curve of space is expressing a force, maybe the same force that propels light through space.

When a glass lens, or water slows a ray of light to curve it, how does the light regain its speed after it leaves the lens? Light loses momentum, then regains it. That has to be due to a force pulling it along. In the experiment that freezes light, how does light regain its momentum after it slows down?

Through a high gravity field, light that is not originally on a path toward earth would be accelerated into the sun, curving it. Then, as it passes the sun it would be pulled perpendicularly into the sun, curving it, then as it leaves it would be decelerated, curving it. Now it is heading straight for the earth. Light has curved and temporarily altered its velocity because it has gone through a space warped by gravity. At Indianapolis Motor Speedway or any race track, the cars slow down going through turns even of their power is always full on. At first you just attribute this fact to friction, but then you realize it is mathematical. It takes more energy to go around a curve than to go straight. If light keeps a consistent velocity while bending, energy has to be added to it.

If something is traveling at optimum velocity and energy, you can’t even pull it perpendicularly without adding energy or taking velocity from it.

Light probably accelerates and decelerates when passing through gravity. The literal points of space are stretched or warped. But light probably always travels from point to point in the same amount of time. That makes light appear consistent; space is very consistently dispersed; yet, if space is slightly warped by high gravity, light would temporarily accelerate and decelerate to curve by the sun.
 

selfAdjoint

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I am afraid your ideas of light physics are all wrong. This is not some controversial subject, the physics of light has been understood since the early 20th century and quantum field theory has not changed the basics, although it has added a lot of fresh details and enabled some super calculations.

Planets in orbits do follow geodesics, but not null geodesics. Only massless objects can travel on null geodesics, and they travel at c in a vacuum. Even when the null geodesic curves in the neighborhood of a gravitating mass.

In your account of light refracting through glass, you destroy your own argument. You say the light first bends on entering the medium because it slows down, and then speeds up again when it leaves. Where did it get the energy to speed up? The environment of the light-in-glass was the same in the last centimeter of its travel through as in the first centimer. How could the one slow it down and the other speed it up? we're not talking gravitational slingshots here!

Really, I have to suggest you read up on physical optics, and take what you read seriously. I don't believe there is any branch of physics that is better established and more thoroughly understood than optics.
 
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I remember a long time ago studying optics, and this was the explanation for how a lens curved light, by slowing it down. Okay, so how does a lens curve light?

Whether or not a lens slows light down, I have heard it is fairly well established that light slows down. When two people disagree on a point, they think that means someone is stupid or mistaken. But if light ever does slows down, then how does it regain its speed? People assume light is going at a certain velocity forever, but anything and everything going at certain velocity under momentum alone slows down. If you are moving under pure momentum, all you can do is continue at the same speed or slow down. Why doesn't light slow down? That's a good question. Maybe light is being powered through space by a hidden force? If light does slow down, how does it regain is velocity? I have heard that light slows down.

But I didn't realize the significance of those questions until I made a model for how light moves through the 9-dimensions of physical space. In my model, light is being pulled from point to point by a force. It travels from one point to the next in the same amount of time, even if the points, due to being warped by gravity are different distances apart. This idea of space made of points having distance between the points is gleaned from the concept of string theory. If points are strings, then a space made of strings is a structure of tetrahedrons. In that structure, you can only travel back and forth in six directions, which are the six extra physical dimensions of string theory. This agrees remarkably with the string theory idea of 9 spatial dimensions. If a structure of tetrahedrons had a different number of angles than six, the idea wouldn't be that significant. Strings can stretch and warp, and they can get longer. Gravitational warping of space is the lengthing of strings in a local area. It's local, so light would speed up and then slow down and end up traveling at the same average velocity that we always see.

We have no way of measuring the physical speed of light many light years away. We can confidently believe it always travels from one end of the string to the other in the same amount of time, no matter how long the string that makes up space is stretched. And if it is traveling along strings, or from point to point, we can know that it can only travel in the direction of the string. We only assume that the strings in distant space are the same length as the strings around us.

A television screen has five dimensions. It has the two dimensions of a plane; then it has the points or pixels that make up the screen, which are arranged in a pattern that produce lines going in only three directions, for three more dimensions. If lines shown on the screen go in different directions from the pixels, the lines can be squiggly. We can all see that. Some lines have to zigzag through the three flat dimensions of the pixels.

And on a TV screen, the pixels are farther apart on a larger screen and the picture is bigger. If we look at a TV screen through a telescope from a mile away we see the same picture whether it is a 19-inch or a 36-inch screen. If our section of the universe is a 36-inch screen, we just assume every part of the universe is a 36-inch screen. It may be a 19-inch screen or a 60-inch screen.

If an actor is walking across a 27-inch screen, and the size of the pixels on a slice of the screen were warped into that of a 36-inch screen, the actor would appear to speed up and then slow down, even though we know he is moving at a consistent pace.

Spaces, which have theoretical points, might be made entirely of (open-ended) strings.
 
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I'm afraid I have to sit with selfAdjoint on this one.

As stated, the behavioural characteristics of optics are well established and can't be 'bent' towards your own theories regarding spatial points.

It's a little like saying, if the facts don't support the case then change the facts.

When a beam of light enters a denser medium (as in glass or water) the beam is refracted by the denser agglomeration of molecules. It isn't 'curved' away from its original path in the conventional sense of the word. It is refracted. This is basic stuff.

The speed of light is constant in our physical universe. Elsewhere, who knows?

I understand where you're coming from, but maybe your theories need a little more refining - perhaps by using what we do know as fact as foundation to your developing principles.

If it's any consolation, I like your ideas. Perhaps you're on to something. But I'd introduce established physical laws as rote, and not try to alter them to fit your assumptions.
 
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It's not worth getting tripped up on optics. I mentioned something I thought I learned in school a long time ago. There was a graphic that showed how light slows in a denser medium and curves because the whole light beam doesn't slow at once. I read about another experiment recently where light was slowed to a very slow speed, then restored keeping all of the information in the light beam intact.

But my original idea was this. If a photon is traveling through space, couldn't it hit some other particle and lose some of its momentum? If a photon is free falling through space at a perfectly consistent speed, how does it maintain that momentum for billions of years over unperceivable distances?

A long time ago, I began to think that maybe space is made of points, and we travel from point to point. For example, light has to always go from point to point in a certain amount of time, like a clock. Though I knew at the time how a line could be a series of points, and light could travel down the line from point to point like a clock, I could not think of how space could be a series of points. I toyed with the idea in my head: that space was a conglomeration of points, and everything travels from point to point. I didn’t start with this: but an image on a TV screen is a conglomeration of points. As the image moves across the screen the points change colors, the image doesn’t actually move. That is an example of moving from point to point. When I discovered string theory, a lot of things I had considered as possibilities were part of string theory. I realized if space was made of points then the points have to be arranged in a pattern, and if light did travel from point to point it could only travel in six (I originally thought seven, but realized it’s six) directions. My longtime mistake to think it was seven got me excited because I thought string theory had seven extra dimensions. I was very disappointed when I heard that string theory space has six extra spatial dimensions, not seven. Then I actually took unsharpened pencils and constructed a "string space" with them, and found my version of string space actually did have six directions, not seven. The pencils lined up at six different angles. Light could only travel along the directions of the “pencils”, which represented strings.

Strings have a high tension, ten tons, and I thought if strings made up all of space, photons which might have some mass would be pulled from string-to-string by the tension of the strings. String theory predicts tachyons, which are faster than light particles. I theorized photons were really a bundle of three tachyons in a closed loop, and if the tachyons followed the six directions of the strings of space, the entire loop could go in an arbitrary direction, but each of the tachyons would have to go faster than light in order to keep up, because they are on average traveling at an angle of 30 degrees away from the direction of the photon which the three tachyons make. They pull on each other to keep the loop or bundle going in a particular direction.

But the bottom line is the most elementary particles travel on strings that only go in six directions, and they are actually pulled along like little clocks, which is how they maintain such a consistent pace. Later, I figured out how electrons could do the same thing, and in effect the motion of electrons pulls things through space maintaining the precise momentum the object has. That idea would tend to explain how objects change shape if the objects are going faster. If the energy of the electrons is maintaining the concept of momentum and also maintaining the size and shape of a molecule, when the object goes faster it also changes its size and shape.
 
I'm going to give this some serious rumination and return with a complimentary rejoinder.
 
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Originally posted by John
But the bottom line is the most elementary particles travel on strings that only go in six directions, and they are actually pulled along like little clocks, which is how they maintain such a consistent pace. Later, I figured out how electrons could do the same thing, and in effect the motion of electrons pulls things through space maintaining the precise momentum the object has. That idea would tend to explain how objects change shape if the objects are going faster. If the energy of the electrons is maintaining the concept of momentum and also maintaining the size and shape of a molecule, when the object goes faster it also changes its size and shape.
One of the big problems with string theory is that it predicts strings to be so small that there would be no way to directly detect them. Thus, this makes it very difficult to produce a testable theory of strings. With quarks, there are ways to make testable predictions, even though we can't "see" the quarks in the common sense of the word. Strings, being so much smaller, are that much harder to deal with.

The reason why we like string theory is that it is mathematically elegant and helps to combine what are seemingly conflicting aspects of physics. And that's a great way to get something studied, but that doesn't make it true.

As one of the scientists on the recent Nova program on strings said, if string theory cannot be validated in the laboratory, then nobody should believe it.
 
I agree absolutely.

If I recall the Nova (BBC's 'Horizon' in the UK) program correctly, I think the commentator even asked the question 'will we ever be able to see superstrings?'

Since the only way we see things is by photons coming from an object and interacting with our retinas, it would be impossible to ever see superstrings in a conventional sense - because photons are so much bigger than superstrings, none are going to be reflected to show anything! Let's face it, we can't even 'see' a photon!

As for detecting them ... if all matter in the universe (even the tiniest exotic fundamental particles) are built from these 'alleged' superstrings how can we ever detect them - since detection involves either particles interacting with them or particles radiating from them. That would be like saying 'throw Jupiter at a grain of sand floating in space and see what reaction occurs'. Mmmmmmmm.

I think the scientists in the superstring camp are hedging their bets nicely.

Unless some neo-Einstein comes along to finish his Theory Of Everything succinctly, who's ever going to prove their theories wrong?

Well done, superstring scientists! You've played a blinder!
 

selfAdjoint

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The hope of the string theorists is that some version of stringy physics will predict the standard model. Notice there is no current physical experiment except gravity ones that the Standard Model does not account for, but the theory itself has several unexplained features. Think of these as the finger holes in a glove. Then the hope of the string theorists is to build fingers from their theory to fit into that glove, and have no fingers left over.

If they could do that, they would have a very powerfuil theory. Every existing quantum field theory has a high energy sector where its predictions blow up (just as Einstein's GR predictions blow up at the black hole singularity). But string theory doesn't do this; it is its own high energy sector and its predictions should be good down to the Planck Level and even beyond. So if there was a seamless joining of string theory to the standard model, that would be in one sense a complete quantum theory. Of course it wouldn;t do gravity, so it wouldn't be a TOE, but it would be a great achievement.
 

QuantumNet

Four coordinates

Three dimensions.

A person who only believes in relativity cannot explain anything but relativistic effects.

Matter and charge is not here because of words,

Einstein used others theories, to make an integral among other things.

E = mc2 is true and a consequence of that things happens slower in moving referencesystems than in still (refering to yourself).

If Einstein could not explain matter and charge, why do you think he could explain the creation of the universe?

Simply because there was a higher energy density before. Maybe the energy formed leptones in their turn forming homogene ethers in the universe. Let's say these particles obey gravity, but that they are everywere. That would explain why the universe can be seen to expand from every point.

You are evil if you can't accept new theories. Just like nazi bastards.

Best wishes Erik-Olof Wallman
 

selfAdjoint

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You are evil if you can't accept new theories. Just like nazi bastards.
No more of that kind of attack, please. We can discuss civilly without insults.
 
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Since lines of different lengths can’t logically have the same number of points, then that is a kind of mathematical proof that even theoretical points in space must have distance between them, which is what string theory assumes about point-particles. And string theory predicts multiple dimensions. Nobody can figure that out. What are multiple dimensions? The answer could be that strings are not only point particles, such as photons, but every point in space is a string.

If you draw points on a flat sheet of paper, and try to make the points equal distant apart, and then connect the points with straight lines, you get strings. Starting at any intersection, which is a string point, you will find that you can only go forward in three immediate directions. All travel from one point must be to a point directly next to it. You discover that you can only travel forward from where you are in three immediate directions. And when you get to the next intersection you can only travel forward in three immediate directions. You can travel in any direction if you zigzag through the strings, but at the most basic level you can only travel in three immediate directions.

And if you construct a 3D space out of strings, then you can only travel forward in six immediate directions, and string theory predicts six extra spatial dimensions. Here they are. I have found the extra dimensions! They are the limited number of immediate directions you can travel in a space constructed from points with a distance between them.

This is not about four dimensions, but this is where the discussion is. What about this new theory?

This theory I just described is THE answer to what multiple dimensions are. Not only that, but when you figure out how light travels though a space made of strings, you realize why light always travels at a constant speed, because it is pulled along from point to point. We know that strings have the energy of the strong force. One string snaps closed, pulling it's mass across the length of the string, then it triggers the next string to snap closed, pulling its mass across the length of that string. This is why light can maintain its speed for billions of miles and billions of years. This is really important knowledge, and if I could work with physicists, I could prove this is how it works.
 
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selfAdjoint

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John, you wrote

Since lines of different lengths can’t logically have the same number of points,
Visualize two line segments, a short one and a long one, horizontal and parallel a little distance apart, with the shorter one above. Draw a line through the left endpoints and project it up. Do the same at the right endpoints. These new lines will intersect in a point above the horizontal lines. For reference, call this point P

Now pick any point, say x in the short line. Draw a line from P through x and project it down to meet the long line. It will determine one and only one point on the long line where it intersects. This shows that for every point on the short line there is a unique corresponding point on the long line

Now pick a random point on the long line, call it u. Draw the line uP, it will intersect the short line in one and only one point, say v. This shows that for every point on the long line there is a unique corresponding point on the short line

These two statements together prove ]There is a one-to-one mapping between the set of all the points on the long line and the set of all the points on the short line. This is our modern definition of saying The two sets have the same cardinality, that is, number of members

Cheers,
selfAdjoint
 
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Those are imaginary points. You are saying that a number line with numbers 1/1000th apart corresponds to a number line with numbers 1/1010 apart in the other line, because for unequal lines to have the same number of points, the points must have different values, so the for the number of points to be the same, the points themselves must have different values, which is a glaring contradiction. Numbers that are the same can't have different values.
 

selfAdjoint

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John, you don't seem to understand the real number system. There are the same number of real numbers between 0 and 1 whether you put 0 and 1 a millimeter apart or a light year apart. Say you've got one lined segment from 0 to 1 and another that goes from 0 to a google (10100). Any number in the first segment can be mapped into the second one by multiplying it by a google. Any number in the second can be mapped into the first by dividing it by a google. This is just the arithmetic version of the geometric argument I gave before. These are not imaginary - neither were the points in my previous example; you're just grasping at straws. .5 corresponds to .5X10100 or 5X10100. Each number is represented by a point half way along its respective line.
 
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String theory says at the smallest levels points are strings having a particular length or value. Ironically, the real number system is not actually real. The Zeno Paradox kind of proves that.

We have to get mundane and unintellectual, and say that the numbers correspond to a certain absolute value, like, the value of one line is a hundred million strings. Half of that line has a value 500,000 strings. Two lines of different lengths can't logically have the same number of equal value points, and so you can't correspond every point in one line to every point in a line of a different length.

A point is really a string. The length of the string is its value. A point can't be just a point, even though we can imagine it. Halfway down one line does not correspond to halfway down a line of different length. Halfway to the kitchen does not correspond to halfway to Chicago.
 
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selfAdjoint

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String theory doesn't say that, and it uses the properties of the real number constantly.

What is the Zenon effect?

You keep saying your beliefs are logical, but they're not, they are just prejudices. I've given you two examples, one geometric and one arithmetic and you don't deal with them, you just keep saying it's not logically possible which it is. Logic is on my side not yours, and I can show you my demonstrations, where are yours?
 
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1/2 X 1 does not equal 1/2 X 1.1. So 1/2 on two lines of different length are not the same thing.

And the Zeno Paradox is about a turtle racing Achilles. If Achilles is in front, and they both progress half way to the finish line in each segment of their race, then Achilles never beats the turtle to the line. If Achilles starts out in the rear, then Achilles is moving twice as fast and he still never beats the turtle.

The only way to correlate that problem with reality is at some point use absolute numbers instead of fractions. Suppose the smallest segment you can have is ½. When Achilles is 1 unit from the finish line, the turtle is 2. When Achilles is ½, the turtle is 1. In the next segment Achilles is at 0, because there are no smaller segments than ½. Achilles wins, which makes sense. We must acknowledge a smallest segment possible for math to make sense. That is what string theory does.

String theory says a point is really a small line. Math says a point is non-dimensional, so how do you arrive at a point, mathematically?

A point is part of a line. If you reduce the line to a very small fraction, you begin to arrive at a non-dimensional point. But at 1 millionth of the line you still have a string. At ten millionth you still have a string. At a hundred trillionth of the line, you still have a string. The fact is you never arrive at a non-dimensional point. You can define a location as a non-dimensional point, but you can’t mathematically reduce something to infinitesimally small. A point will always be a string, except when defined as a location. But a location isn’t in a relationship with any number, it’s just a location.

So if you say 1 plus 2, you are talking about a string from 0 to 1 and a string from 0 to 2. Add them and you have a string from 0 to 3. The result, 3, is not a non-dimensional point defined by the location at 3 on the line. It is a quantity from 0 to 3. So you can’t do math with locations or points. You can only do math with strings or values. Therefore, to define a point mathematically you have to mathematically reduce its value to infinitesimally small. You can never do that. No matter how small it is, you can always make it smaller, so it always remains a string.

Realizing there are no non-dimensional points in math, when you go to construct a space out of strings you get the weird fact that you can only travel back and forth in six directions (when you arrange the strings in their most formal arrangement where all the strings are the same length). With strings of different lengths, in less formal arrangements you get fewer directions: 5, 4, or 3 directions. If the strings can alter their length randomly, you still only get 16 limited directions that you can travel back and forth in this space made of strings, and those are 16 dimensions. But it's easiest to have 6 extra dimensions when you construct a space out of equal length strings. And that is exactly how many extra dimensions string theory predicts. But Hawkins said that advancement in physics had currently come to an end, and his reason was because people couldn't agree with each other or see each other's ideas.
 
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