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Non-Platonic geometry definitions

Nill is what is negligible, but not nonexistent.

A volume is an entity’s extent in 3 dimensions—length, breadth, and depth.

A surface is a volume of Nill depth.

A line is a surface of Nill breadth.

A point is a line of Nill length.

A "Randian" Approach to the Foundations of Mathematics

Reality is the standard, not what is “intellectually satisfying” or “elegant.”
Mathematics has to live up to reality, not the other way ‘round.

I couldn’t disagree more with such a naive, limited view of mathematics. A very simple definition would be that it is the study of patterns. Some of those patterns describe physical entities, many more do not (at this moment in time).

I'll add mathematics to the pile of things Ayn Rand is wrong about.

Please don't attribute to her what some nutjob on the net just made up. She was wrong about a lot of things, but to the best of my knowledge never turned her hand to maths. Probably for the better.

I was going to say the same thing, but unfortunately, it appears that she did in fact make numerous statements about math. As for whether she managed to mess it up as hard as the OP did, I have no idea.

Getting back to the topic at hand, it has been a while since we treated geometry as the basis of mathematics. The Indian and Islamic golden ages had seen the creation of algebra (in fact, the term "algebra" comes from Arabic), and algebra can serve as foundation of geometry. Especially the works of Muḥammad ibn Mūsā al-Khwārizmī married the two concepts, and he died in 850. Then there are the works of Peano, Zermelo, and Fraenkel, putting everything on axiomatic feet in the late 19th, early 20th century. and since then maths is based on set theory. And finally, of course, there are presently efforts to define set theory in terms of category theory, putting even more abstraction in the way.

If the OP wants to create a set of axioms that is without contradiction in which every true statement can be proved, then Kurt Gödel proved that that's impossible once the set of axioms is powerful enough to support the Peano axioms. And if they aren't, you can't even do math on natural numbers.

And finally, no, maths does not have to live up to reality. Maths is not limited to reality because mathematic concepts can be used widely outside any notion of reality for some other application. Solving an 11-variable optimization problem involves using 11-dimensional geometry, which has nothing to do with the physical world. Also it involves algebra more than geometry, because it is really hard to picture stuff like that.

The question of how reality can be modeled mathematically is called physics. And ever since Einstein we know that reality is not a Euclidean 3D space, so I don't know what he's trying to prove here.

Be careful about declaring what's known. The universe is compatible with Euclidean 3D geometry with the speed of light reducing in gravity wells in line with √(1 - 2GM/r). Spacetime is just an ideology in which light is imagined to continue moving at c in gravity wells by travelling through extra space instead of slowing down: it's a mad mathematical abstraction, and I call it mad because it's broken beyond all possible repair. All spacetime models invalidate themselves by generating event-meshing failures like this one: [url]magicschoolbook.com/science/Event-Meshing-Failures.html[/url]. Don't be so trusting of majorities who are suffering from theory-induced blindness - there are a dozen disproofs of relativity which are simply being ignored.

No offense, David, but between you and Einstein, one of you has a Nobel prize and is internationally recognized as a great theoretical physicist, and the other has a weird hobby OS. I have heard the "the counter-evidence is being ignored!" rhetoric before, and it just doesn't pan out. That's not how science works. When Einstein had his spat with Planck, the latter won out eventually because he could show his stuff actually conforms to reality. So if you had evidence that disproved relativity, there's a Nobel prize and international recognition in it for you if you can get it published.

Meanwhile, I am a mere computer science plebeian and have to go on authorities, because I have not devoted my life to divining the mysteries of the cosmos. Can't be expert at everything. I have no idea if what you're saying is true or even plausible, but the established experts are saying what I parroted above. So I am deciding questions like this on popularity: If you were right, you (or someone saying the same things) would be the internationally adored icon. You are not, therefore I assume you are wrong.

There are no event-meshing failures because general relativity includes adjustments for the speed of time - which you yourself include in your "pseudo-GTR" simulation. These adjustments are calculated relative to an observer, and they can be calculated relative to any observer, so there is no need for absolute time.


You can't disprove general relativity by arguing that it doesn't make sense because it's not supposed to make sense. It's a mathematical model. The only way to disprove it is by showing that it's mathematically inaccurate. Anything else will be rightfully ignored.

There isn't. Einstein didn't get a Nobel prize for it and no one will get one for disproving it. But you're also falling into a trap of worshiping status rather than actually looking at the argument and trusting your own mind as to who is breaking fundamental rules of mathematics and who is following them. Einstein breaks them and I simply show people where he does so. If two objects travel from spacetime location 1 to spacetime location 2 in different amounts of time, they cannot leave the first location simultaneously and arrive simultaneously at the second location. One will not get there soon enough. The only way for them to meet up successfully is if one of them is running slow relative to absolute time.

I commented on this here simply to point out that it's an error to assume that the universe is not 3D Euclidean in nature on the basis of a cult belief which ought to be thrown out of science. Now, you my not be able to see that it's broken, but you should be able to see that the 3D Euclidean model has not been ruled out at all; everything is compatible with light slowing in gravity wells in line with √(1 - 2GM/r). This has the speed of light fall to zero at the event horizon of a black hole, which means nothing falls into them, but instead piles up at the event horizon, as happens with the fuzzballs of string theory, and by magic happens with QM for information. This also eliminates the impossible singularities which bedevil GTR.


You don't. You can look at the realities of mathematics and see the impossibility of the two objects leaving point 1 simultaneously and then arriving together at point 2 while taking different amounts of time to get there.


And what do you imagine happens when everyone follows that approach? How can science ever self-correct when it's stuffed full of people who worship authority like in a religion and who refuse to see the faults? They are systematically brainwashed in universities by having half the facts hidden from them. Every aspect of relativity covered by STR, for example, can be recreated in 100% classical systems like sound in air, right through to length contraction and apparent length contraction, but this is deliberately not taught. Let me show you some of that, and it really shouldn't be beyond the ability of anyone here to follow this.

If you set up a system of standing waves of sound on open-to-air apparatus and then move the apparatus through the air at 86.6% the speed of sound, the nodes contract closer together to half their rest separation distance in the direction of travel of the apparatus, so long as you govern the sound frequency with a perpendicular open-to-air sound clock. The equivalent apparatus for the light in space case is to set up standing waves of light on apparatus which when moved at 86.6% the speed of light will contract the nodes to half their rest separation distance through the same mechanism. Both of these experiments can be done for real, though for the light in space case we have to use much lower speeds with less contraction due to cost restraints.

Next, if you are travelling at 86.6% the speed of sound and use sonar to view a stationary object while using a perpendicular open-to-air sound clock as the sonar system's clock, what happens to the measurements of the length of a stationary object being viewed by it? It is seen contracted to half its actual length. The same thing happens when a moving observer looks at a stationary object while travelling at 86.6% the speed of light. The two cases are directly equivalent and have the same mechanism.

Take a close look at relativistic velocity addition too. What happens if we put three sound clocks in a wind tunnel with clock B at rest and clocks A and C moving in opposite directions at 86.6% the speed of sound? If each of these sound clocks is aligned vertically, clocks A and C will tick half as fast as clock B while there's no wind blowing through the tunnel. Let's have the clocks put out sound beeps for every tick which can be heard from the other clocks. If we have an observer travelling with clock A who assumes himself to be at rest in air (even though he isn't), the arrival of beeps from clock C will lead to that observer calculating that the relative speed between clocks A and C is 99% the speed of sound, but the actual relative speed is 173.2% the speed of sound. This happens if he uses clock A as his clock rather than cheating by using a clock running on a mechanism governed by the speed of light. If we take all the measurements from clocks A, B and C and pass them to physicists, they won't be able to tell us what the wind speed in the tunnel was. It's only if you work through all of this stuff that you can see how relativity actually works and how it is merely apparent relativity rather than actual relativity. The whole of relativity is built on incorrect assumptions.

So, what do people do when they're confronted by the facts? They say, "Oh, I'm not qualified to judge this," so they just outsource their checking to an authority which is lying to them. Why is the above stuff not taught in universities? Why are students deliberately starved of essential understanding of the subject? What we have is a mad cult that dominates in physics, and if you don't conform to their faith, they throw you out: you simply don't win the status you need and you are ignored and ridiculed. That's the trap they're all in. Rational people get out and the mad ones go on to become part of the authority - they are selected for this by their irrationality, and then people like you who are overly trusting of authorities just believe them without checking the facts. Write your own simulations and anyone competent can check my claims for yourself and find that they're correct. It's better than that though, because not only have I come up with a dozen disproofs of relativity, some of the most recent ones not only show that absolute speeds must exist, but show that they can in principle be pinned down in expanding space. I'll show you that in the next post (in case the word limit kicks in here.)

Those adjustments can only be made by having some "times" slow under the governance of a superior time, so how are they comparing themselves with each other for that governance to work, and which one's the boss?


Things don't make sense when they break mathematically. If it was mathematically accurate it would make sense, but it doesn't. There's a far better theory available which makes full sense, and that's modern LET (Lorentz Ether Theory) - it has the same predictive power as STR+GTR with the same precision, but it achieves that rationally instead of through nonsense. Why would anyone favour the irrational theories over the rational one?

Let me show you that absolute speeds exist, because once you have those, you necessarily have absolute time too. Picture lots of clocks being created just after the big bang, and these can move in random directions at random speeds. What would those clocks be doing today? They'd be passing other clocks just as the cosmic microwave background radiation continually passes through every point in the universe from all directions all the time. Take a clock sitting out in space near us. What happens when another clock born just after the big bang passes it at 86.6% the speed of light? One clock says that the universe has been around for nearly 14 billion years (because that's the time on that clock), but the other clock says it's only been 7 billion years since the big bang. These timings are measures of their absolute speeds. Another clock goes past the opposite way at 0.866c and it too says the universe is 7 billion years old. Other clocks go past even faster and they give lower figures for the age of the universe. Relativity simply falls to pieces when you do the work to check it for validity. For relativity to be valid, those clocks would need to agree on their timings when they pass each other, but if they were to do that, you could use them to break the normal results of the twins paradox.

Here's another experiment taking advantage of expanding space. If you have two clocks a fixed distance apart with space expanding between them, if one is at rest in the local space fabric, the other cannot be and will tick more slowly. They could both tick at the same rate if the mid point between them is at rest in its local space fabric, but in other situations we could measure absolute speeds by the timing differences. Turning this into an actual experiment would be hard due to the tiny magnitude of the differences over a short distance, but in principle it works. Einstein's theories are a pile of old broken junk, but they're kept going by a bullying cult which simply shouts anyone down who tries to point out the faults. They're not doing science properly, but have held it back for a century.

Slow or fast. It works both ways.


Again, it's a mathematical model. It doesn't explain how time "knows" to go faster or slower. What it does is accurately model the data we have available, and accurately predict new data before we collect it.


Whichever one you want! The results are consistent regardless of observer.


Because it is simpler. There is only one difference between modern aether theory and relativity: aether theory proposes the existence of an aether that cannot be proven to exist, and relativity does not.


For your example to be valid, you would need to take into account that the clocks can only meet if they change their inertial frame of reference, and the change in inertial frame of reference causes a change in the apparent passage of time.


It doesn't work. Any measurement of timing has to be performed at some reference point, and the timing difference you observe will depend on your reference point.

The point is that the only way to avoid event-meshing failures is for some "times" to run slow (which means they are merely providing apparent time) under the governance of a superior time (absolute time). The model does not allow that though, so event-meshing failure occur when you simulate it and the model invalidates itself. It is mathematically incompetent.


It isn't simpler - if fills a gap with magic and then asserts that the magic is simpler than aether, but the magic represents a complex aether built out of an infinite number of aethers which all govern the speed of light differently from each other such that every pulse of light moves at an infinite number of speeds relative to itself at all times in order to pander to the idea of equal validity for all frames of reference rather than simply having one that represents reality correctly while all the rest misrepresent it. Also, the aether (space fabric) can be shown to exist.

Imagine two objects moving at 0.5c relative to each other along a straight line. We introduce a pulse of light which moves along the same line at c relative to the first object. The speed of that light is 0.5c or 1.5c relative to the second object (depending on which direction along the line that object is moving in). STR denies that measurement and insists that the correct relative speed for the light and second object is c, but if the relative speed of the light to both objects is c, the two objects cannot be moving at 0.5c relative to each other: their relative speed to each other would have to be zero.

What’s going on here? Well, Einstein bans you from accepting some measurements between light and objects that travel at lower speed than c. He requires you to change frame to make the second object stationary, and only then will he accept the relative speed for the light and that object. In that new frame, the relative speed between the light and the first object is now 1.5c or 0.5c, but again he bans you from accepting that measurement. So, he mixes frames to get the two measurements which he wants to make so that they conform to his bonkers theory, and he rejects all measurements that disagree with his ideology. In the course of changing frame, he changes the speed of the light relative to both objects, or he has the light move at two different speeds relative to itself. In doing so and mixing frames, he is making an illegal mathematical move.

Let's look at another case:-

Picture an observer watching two ships in the distance which are passing each other, one moving towards him and the other moving away from him. The two ships each put out a flash of light at the moment when when they are side by side. These two flashes of light travel alongside each other all the way to the observer who sees them both arrive simultaneously. How did the two flashes of light know to travel at the same speed as each other? Did they decide to travel at c relative to one ship rather than the other ship? Did they decide to travel at c relative to the observer? They aren't going to know how the observer's moving until they reach him, so they can't do that. Also, we can have some of the light pass the first observer and be seen by a second observer further away who is moving relative to the first observer along the same line as all the rest of the action, so is the light supposed to move at c relative to that observer too?

Einstein would have you believe that the speed of the light is c relative to both observers, but that would mean the two observers couldn't be moving relative to each other. There could also be observers on the two ships who see the flashes pass them, and again Einstein wants the speed of that light to be c relative to them. He is trying to have an infinite number of contradictory things all happen at the same time. In reality, the speed of the light is c relative to the space fabric and needn't be c relative to any of the ships or observers at all. As soon as you deny the space fabric and its absolute frame, you lose the ability to govern the speed of the light from one flash to make it move at the same speed as the light from the other flash: each flash would have to travel at c relative to the ship that it was emitted from, so the light from one flash would reach the observer before the light from the other flash. Einstein's insistence that the speed of light is always c relative to any observer is nothing more than a contrived mathematical abstraction, and it breaks fundamental rules by tolerating contradictions - if he has the light move at c relative to all ships and observers, he has it moving at four speeds relative to itself.


The clocks are fully capable of passing each other and comparing their timings while they're at the same location as each other without caring which frame of reference any mad physicist is trying to apply to them. They provide direct facts with these timings, and these facts reveal their absolute speeds of travel.


We can sit half way between the two clocks and send radio/light signals in from the two clocks to show us how fast they're ticking. The trip taken by these signals is constant, so the frequency won't change in transit. If we are at rest in our local space, the expansion of space means that the two clocks aren't, so they'll both tick slow, but they'll both tick equally slow, confirming that we are at rest in the local space. However, if one of the two clocks is the one at rest in its local space fabric, we are moving thorough our local space fabric and the other clock is moving through its local space fabric twice as fast as we are, so that clock will be ticking slower than the first clock. Our slowed functionality will lead to it looking as if the first clock is ticking fast, but the other clock will look as if it's ticking slow. Again, this allows us to pin down our absolute speed. If there are no timing differences and no clocks are ticking slow, then the space the experiment is being run in cannot be expanding.

You display a profound lack of understanding of the Special Theory of Relative.

That is by the by - none of it is relevant to the OP.

This is one of the silliest threads I have seen on these forums. I expect mambo-jumbo pseudo-science from the sort of people who worship Donald Trump, not from what I have always thought be be reasonably intelligent people.

How wrong can you be.

...Under modern aether theory, it's impossible for any experiment to detect the presence of aether. Are you arguing a disproven version of aether theory?


I'll admit it's been more than a few years since I took a physics class that covered relativity, but I don't think this is related to intelligence...