Null Physics anyone?

[sol invictus]

Since this keeps coming up, here's my attempt at a concise description for how to define sizes of infinity.

Consider two sets (a set is a collection of objects, or numbers, or anything else). We want to determine which set is bigger - meaning which contains more elements. So we do the following - we find a rule that identifies the elements of one set with the elements of the other. We try to find a rule so that each and every element in set 1 identified with a different element of set 2. If we succeed, we know set 1 is smaller than or equal to set 2. If we fail to find any such rule, it means there were more elements in set 1 than in set 2.

For example, X = {1,2}, and Y = {a, b, c}. If my rule is 1->a, 2->b, I've shown |X| <= |Y| (<= is "less than or equal to", |X| means the size of X). If I can prove that there is no rule going from Y->X which satisfies the above (which I could, but won't bother), it shows that |X| < |Y|. That's correct, since in this case |X|=2 and |Y|=3.

Now we try to do exactly the same, only starting from set 2. If we succeed in finding such a rule in both directions, we know the two sets have exactly the same number of elements.

For example, if Z={j,k}, I can take the first rule to be 1->k, 2->j, and the second to be k->2, j->1, which shows |X| = |Z|.

This definition is overkill for finite sets where we can just count how many elements there are. But it's very useful when applied to infinite sets. It immediately tells us, for example, that there are the same number of integers as there are rational numbers (ratios of integers), but there are (infinitely) more real numbers between 0 and 1 than there are integers or rationals.

 

[Skwinty]

Hi Sol
did you read this article http://www.sciam.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes.
I understand this to mean that real infinity was larger than natural infinity and that the idea of > (larger than) was a break through mathematically.
So, were Cantor's ideas also fallacious.

It doesn't make sense from a layman's point of view, to then say that the 2 infinities are the same, as one is larger than the other hence there must be a difference.

Indeed a slippery slope.

 

[Skwinty]

Hi Sol
Okay, I posted my last post before I saw your last post.
So, what Cantor is saying is, If your filled an infinite space with footballs and compared it to an infinite space filled with golf balls, there would be infinitely more golf balls than footballs

 

[sol invictus]

So, what Cantor is saying is, If your filled an infinite space with footballs and compared it to an infinite space filled with golf balls, there would be infinitely more golf balls than footballs

Not necessarily - you have to define the question more carefully, and then we could apply "my" rule and check. There might be exactly the same number.

Infinities are very counter intuitive - for example there are the same number of rational numbers as integers even though there are an infinite number of rationals between 0 and 1 (or in any other finite interval).

Witt's central mistake - and that of most crackpots like him - is thinking that because he doesn't understand these facts they must be wrong. On the contrary, they are the only rules that make sense, at least that have been found by centuries of very, very smart mathematicians.

 

[Skwinty]

Not necessarily - you have to define the question more carefully, and then we could apply "my" rule and check. There might be exactly the same number.

Now I am really confused.

Lets for arguments sake let 1 cubic metre hold 10 footballs and 1 cubic metre hold 1000 golf balls.
now lets take an infinite number of 1 cubic metre containers. how could there be the same amount of golf balls as footballs.

I apologise if I seem obtuse, I am not one of those very clever mathematicians.

 

[sol invictus]

I apologise if I seem obtuse, I am not one of those very clever mathematicians.

Don't worry - it is very counter-intuitive.

Lets for arguments sake let 1 cubic metre hold 10 footballs and 1 cubic metre hold 1000 golf balls.
now lets take an infinite number of 1 cubic metre containers. how could there be the same amount of golf balls as footballs.

Because infinity is infinite.

Suppose we start with these two infinite collections of 1 cubic meter containers. I take 1 golf ball container and put it off to the left, and then I take 100 football containers and put them off to the right. I repeat that 10 times, and now I have 10,000 footballs in the collection to the right and 10,000 golfballs in the other. But I can keep doing that infinitely many times. In the end it sure sounds like I'll have two infinite collections, each with exactly the same number of balls.

The moral is, you must be more careful than that. Given an infinity you can re-arrange it to get anything you want, unless you're careful to follow the correct rules. Here's another example:

0 = 0+0+0+0+... = (1-1)+(1-1)+(1-1)+... = 1-1+1-1+1-1+... = 1+ (-1+1)+(-1+1)+(-1+1)+... = 1+(0)+(0)+... = 1. Oops!!

Do you see which equality is false? (Hint: there are actually two.)

 

[Skwinty]

uppose we start with these two infinite collections of 1 cubic meter containers. I take 1 golf ball container and put it off to the left, and then I take 100 football containers and put them off to the right. I repeat that 10 times, and now I have 10,000 footballs in the collection to the right and 10,000 golfballs in the other. But I can keep doing that infinitely many times. In the end it sure sounds like I'll have two infinite collections, each with exactly the same number of balls.

Okay, I'll go with that, except that the golf ball set will always be spatially smaller than the football set and so will be infinitely smaller as we progress towards infinity.
My reasoning here is we start with one cube on the one hand compared to ten cubes on the other. The golf ball set lags by a factor of ten.

 

[sol invictus]

Okay, I'll go with that, except that the golf ball set will always be spatially smaller than the football set and so will be infinitely smaller as we progress towards infinity.

How do you know? They'll both be infinitely big, and comparing infinities is very tricky, as I've been trying to get across to you.

My reasoning here is we start with one cube on the one hand compared to ten cubes on the other. The golf ball set lags by a factor of ten.

By the same logic there are many more rational numbers than integers. After all, for every pair of sequential integers there are more than 10 (actually, an infinite number) rationals in between. And yet (using the perfectly reasonable - and correct - definition I gave above) I can prove that there are exactly as many rationals as integers.

 

[Skwinty]

Thanks Sol,
Will have to continue at a later stage.
My guests are arriving now so will have to cut our discussion short.

 

[ben m]

Skwinty, there are two online resource with good descriptions of "infinity" and its mathmatical properties. One is Wikipedia; the other is "Mathworld" at mathworld.wolfram.com. You can read about various infinities there; look for "Hilbert hotel" for a situation exactly parallel to your basketballs/golf balls paradox.

 

[Vorpal]

Minor note: Sol's method of comparing sets implicitly assumes the axiom of choice. Without AC, we cannot guarantee things like the trichotomy property of set sizes (cardinalities). There's an even nicer axiom, the generalized continuum hypothesis, which makes cardinal arithmetic even nicer (and also implies AC). The comments below about cardinalities also assume AC.

If there are varying sizes of infinity, then surely one infinity plus some value returns another infinity. This implies then that the one infinity is greater than the other.
ie infinity(1) + x > infinity(1) or infinity(1) + x = infinity(2).

Thing is, if you have two infinite cardinalities κ<λ, then κ+α = λ is true if, and only if, α = λ. In other words, to get the higher infinity by addition, you need to add as much as the next infinity is in the first place. We also have κ² = κ and κλ = λ, so the same is true for multiplication as well.

That's not to say that we cannot make sense of "infinity + 1 > infinity" or "infinity² > infinity", just that those kinds of things no longer talk about cardinalities, but something else. For example, cardinal numbers answer "how many?" (one, two, three, ...); ordinal numbers answer "which place?" (first, second, third, ...). And for transfinite ordinals, we do have true inequalities in those forms, and for other exotic number systems, we can even have "1/κ > 0" (for transfinite κ) and so on.

However, it's very hard to see how such things--either ordinal numbers or surreal numbers or whatnot--have any direct applications to physics. If Mr. Witt is talking about sizes of things, then he's simply wrong; if he's talking about something else, then he needs to (1) define a consistent system of arithmetic, and (2) explicitly connect it to something physical and show how it mirrors his system. I haven't read his book, so I've no idea if he even tries to do that, but I have the inductive hypothesis based on his webpage that the answer is "no" to both.

 

[Reality Check]

To give you a taste of Wiit's logic:

The first thing any investigation of space requires is a consistent mathematical framework for handling infinities. Since the universe is the only infinite reference we have, its extent will be used to define infinity.
The universe's diameter is the invariant width of nonexistence. It constitutes a fixed, exact level of linear largeness, and is therefore the absolute metric of unboundedness.
THEOREM 2.1 - INFINITY
INFINITY IS THE UNIVERSE'S INVARIANT DIAMETER

The universe is the source of all data and all knowledge. The only meaningful generalization within this context are not human creations; they are direct reflections of reality's underlying structure. The most accurate definition of infinity is therefore a property of the universe, no an assertion of our mathematics.

Note his use of "theorem" to give his statements some credibility. All his statements are presented as "theorems". There are no axioms quoted or a reference to the axioms that his theorems are based on.

He does not know that there is an existing consistent mathematical framework for handling infinities.

The charitable interpretation of theorem 2.1 is that infinity is infinity since the diameter of the universe in infinite. But then there is the problem of assigning infinity the units of length.

 

[Skwinty]

There are no axioms quoted or a reference to the axioms that his theorems are based on.

hi RC

From my brief reading of Null Physics, there is only one axiom and all theorems are based on that axiom.

AXIOM 1 Null Axiom

Existance sums to Nonexistance

See page 28

 

[sol invictus]

AXIOM 1 Null Axiom

Existance sums to Nonexistance

Does that mean anything to you? It certainly doesn't to me (even if I correct the spelling). I don't know what any of the words in that sentence mean (in their context), particularly "sums".

If it does mean something, perhaps you can explain the proof of the theorem quoted by RC above, which must follow directly from this "axiom"?

 

[Vorpal]

That's what I would like to know as well, because right now I'm starting to feel that my comment of "simply wrong" was incorrect--this appears to go into the not even wrong territory instead.

 

[Skwinty]

Does that mean anything to you? It certainly doesn't to me (even if I correct the spelling). I don't know what any of the words in that sentence mean (in their context), particularly "sums".

If it does mean something, perhaps you can explain the proof of the theorem quoted by RC above, which must follow directly from this "axiom"?

Sure, the a should have been an e. You must admit though it goes with distance.
Is this a spelling bee competition?

I said in a previous post that I have started reading the book and that I probably will not understand most of it. I got a free copy. Did you?

Dont say you dont want to invest time in it as you have invested quite a lot of time re: Null Physics on this forum.

However, for some one to go to great length and detail in arguing against an idea as has RC, (Currently at 191 posts om Witts forum), it shows lack of attention to detail if he misses the fact that there is only one axiom.

As for me explaining the proofs of any of his theorems, that is as I have stated many times beyond me.

 

[Vorpal]

Sure, the a should have been an e. You must admit though it goes with distance.
Is this a spelling bee competition?

Well, swell. But it does indeed show a lot that although you've had the book for a while, you cannot explain what this lone axiom even means.

However, for some one to go to great length and detail in arguing against an idea as has RC, (Currently at 191 posts om Witts forum), it shows lack of attention to detail if he misses the fact that there is only one axiom.

Mind the context, please--we were discussing arithmetic regarding infinite quantities, and it follows from your own statements that whatever system Mr. Witt is using for that, if any, he has not provided any axioms for it.

As for me explaining the proofs of any of his theorems, that is as I have stated many times beyond me.

If they are of the same sort as his infinite arithmetic or fumbles with the Schwarzschild metric, then this quite understandable: nonexistent things cannot be reached.

 

[sol invictus]

I said in a previous post that I have started reading the book and that I probably will not understand most of it. I got a free copy. Did you?

No, although I wouldn't mind. I could start a collection of self-published crackpot monographs.

Dont say you dont want to invest time in it as you have invested quite a lot of time re: Null Physics on this forum.

Not really - most of the discussion even in this thread hasn't been about "null physics", whatever that is. Anyway, at least from my point of view this is purely for entertainment purposes, so I will do exactly as much as I feel like and no more.

However, for some one to go to great length and detail in arguing against an idea as has RC, (Currently at 191 posts om Witts forum), it shows lack of attention to detail if he misses the fact that there is only one axiom.

It's very difficult to argue coherently against nonsense on its own ground. When there are so many inconsistencies and "not even wrong" statements, it's hard to address one without temporarily accepting some others, and that tends to get you into trouble.

As for me explaining the proofs of any of his theorems, that is as I have stated many times beyond me.

Then answer a simpler question - do you understand what that "axiom" means?

I don't - and I think that's because it's utterly meaningless. Axioms are used to define a logical structure from which one can build something interesting. They must be very precise, and there must be a consistent set of rules with which one can manipulate them. Witt's "axiom" doesn't come anywhere near that - it's just schizophrenic gibberish.

 

[Reality Check]

Sure, the a should have been an e. You must admit though it goes with distance.
Is this a spelling bee competition?

I said in a previous post that I have started reading the book and that I probably will not understand most of it. I got a free copy. Did you?

Dont say you dont want to invest time in it as you have invested quite a lot of time re: Null Physics on this forum.

However, for some one to go to great length and detail in arguing against an idea as has RC, (Currently at 191 posts om Witts forum), it shows lack of attention to detail if he misses the fact that there is only one axiom.

As for me explaining the proofs of any of his theorems, that is as I have stated many times beyond me.

You are right - there is a total of 1 axiom in the book. However it is nonsense and anything based on it is nonsense.

In fact I have ignored most of the "geometry" in his book because it is not geometry. I have instead concentrated on the Null Physics statements of fact, several of which are badly researched, e.g.

• Electrons do not have an intrinsic magnetic moment.
  But the Stern–Gerlach experiment done (and repeated many times since) in 1922 shows that electrons (and other particles) have an intrinsic angular momentum and thus an intrinsic magnetic moment.
• One NP prediction is that the Milky Way's core is a massive black hole with a radiant output of ~6(10)^31 W peaking in the infrared near ~0.06 mm.
  But there are plenty of observations in the infrared of the galactic center and no sign of the radiation (~100,000 suns). Terry Witt and his team are currently trying to hide the radiation by some sort of new? gravitational effect of the mass of 3.7 million solar masses.
• The Lyman-alpha forest allows astronomers to measure the density of neutral hydrogen between us and distants galaxies and quasars. They see that it increases as we look further back in time. This means that the universe is not static and is indirect evidence for the Big Bang.
  Null Physics relies on an infinite (conventional meaning not NP meaning) and static universe.

Oddly enough in the 30 years that Terry has been formulating Null Physics he seems to have never heard of the Stern–Gerlach experiment. Nor did he have his theory reviewed by anyone (e.g. an real physicist) who knows about the experiment.

 

[Skwinty]

Well, swell. But it does indeed show a lot that although you've had the book for a while, you cannot explain what this lone axiom even means..

If having the book for 3 days equates to quite a while, then a year must be close to infinity. I do have a real job in the real world.
Apart from the fact that you expect me to explain something to you, which once again, I have stated quite clearly that I probably do not understand.
I am however interested in learning a bit more before consigning it to the trash can.

Mind the context, please--we were discussing arithmetic regarding infinite quantities, and it follows from your own statements that whatever system Mr. Witt is using for that, if any, he has not provided any axioms for it..

This thread is called "Null Physics Anyone".
My post related to this comment of RC's

"Note his use of "theorem" to give his statements some credibility. All his statements are presented as "theorems". There are no axioms quoted or a reference to the axioms that his theorems are based on."

How is this out of context?

If they are of the same sort as his infinite arithmetic or fumbles with the Schwarzschild metric, then this quite understandable: nonexistent things cannot be reached.

From what I have gathered so far is that space, which is infinite, is an infinite set consisting of nothingness. Existence is a subset of this nothingness.

Now, my logic tells me, if you magnify any particle sufficiently, you will find a great deal of nothing. A point here and a point there, with a great deal of nothing in between.

An example would be, if a split pea on the floor of the Basilica Dome represented the nucleus of an atom, the first electron would be a speck of dust on the ceiling. A great deal of empty space would lie between them.

Now, take matter/antimatter, infinite space as a set of nothingness, why could one not think that existence sums (adds) to nonexistence.
Or "Something is a subset of Nothing"
This is why I asked for a free book, so that I could actually read it before calling anyone a crackpot. It's called "Giving the benefit of doubt"

Heres what Blaise Pascal said a few hundred years ago.

"For in fact what is man in Nature
A Nothing in comparison with the Infinite
an All in comparison with the nothing
a mean between nothing and everything"

This is also why I believe that Philosophy of Science is still valid today, even if the sole outcome of philosophical musing is just another point of view.