Limits of mathematics in cosmology

Lev,

As I indicated in my remarks, there are those who think complex math is the answer and those who think the answer has nothing to do with complex math. I am of the latter persuasion. I realize that the schools have overproduced physicists and assorted types, that must keep busy with esoterica, and math offers the best playground for these games.

It is way beyond me to conceive of how one could believe that a formalism, any formalism, can exhibit 'constructive' power (of the type exhibited by the universe), but that was what I referred to when I spoke of the religious aspects of these pursuits. Since you seem to be enjoying your pursuit, I wish you well. It will clearly carry you to retirement, with no fear of actually solving the problem.

Edwin Eugene Klingman

Edwin,

Since you are of the persuasion that "the answer has nothing to do with complex math", and you also don't believe in radically changing the basic math. language (as I'm advocating), what do you think the "answer" is about?

You must, then, believe in miracles. ;-)

Cheers,

--Lev

Lev,

Some fqxi players believe that the problem lies in math (as you seem to); others believe that the problem is in the basic concepts of physics (as I do). Few look to miracles as the answer.

I spent a little more time looking through your paper and it appears that most of the diagrams in your paper could be reformulated as diagrams in my Automatic Theory, and hence have some level of equivalence. Much of my approach was based on pattern recognition and how this can be used to 'automatically' derive theories of physics from (numerical) observational data. Although this was my 1979 dissertation, I decided to publish it when a 3 April 2009 Science paper, Vol 324, "Distilling Free-Form Natural Laws from Experimental Data" presented essentially the same approach as novel.

Having spent over four years on Albert's Molecular Biology of the Cell, 4th and 5th editions, Robert's Embryology, Epigenesis, and Evolution, and about a dozen similar texts, including Immunology texts, I understand why you are frustrated with math and would like to be able to build a 'Bubble Man' of bubble legs, bubble limbs, bubble torso, etc., but I find it difficult to take such an approach seriously. I mention these studies because it appears we have been focussed on solving essentially similar problems: of life, growth, and consciousness. While I have been very interested in biological problems, including protein folding, my real goal has been consciousness. My guess is that you exclude consciousness from the problems you deal with, since a search of your paper did not find the word.

My belief, after four decades of effort, is that consciousness is fundamental and not an artifact. This means that consciousness does not pop into existence when all of the bubbles are in place, but has a more essential existence as a field phenomenon that interacts with the physical world at all levels, from QM entanglement to biological growth and development. The mathematics necessary to describe the interaction of this field with matter are not complicated. The "internal" aspects of the field, awareness and free will, are not susceptible to mathematical analysis. Instead of positing the essential unpredictability of Nature in mysterious quantum fields, I place it in a mysterious consciousness field. You might be surprised how much physics falls out of this approach.

Edwin Eugene Klingman

Edwin,

If numbers map 1 to 1 with time intervals, as you say, there is absolutely no difference between the number sequence and the time sequence. They are identical. Particularly, as you claim that "physical logic underlies math." Things that are not differentiable are identical in physics; e.g., the vacuum and the ether.

In fact, quantum mechanics _does_ violate classical logic. That's no secret.

And while my own research does aim at an organic continuation of mathematical models with the physical world, it requires no metaphysical assumptions. (I've been through this with LeBel, BTW). Metaphysical realism is constructed bottom up, not top down. That's not Platonism. And personal belief has nothing to do with it.

Physics absolutely does support contradictions -- all the time. The most fundamental contradiction is between quantum theory and general relativity. One has to be careful of specifying domain and range. Sure, I agree that mathematics is a game. So is life.

Tom

Lev,

I don't think you mean to say that syntax and semantics are the same. "Congruence," the term you use elsewhere, does not imply "same." The technical difference is critical, because congruence implies recognition of characteristics between this object (or event) and that -- not sameness.

An "... interconnected net of structured events ..." where congruence of syntax (meaning) and semantics (language) has a temporal ordering effect and faithfully emulates physical reality results in zero difference between the emulation and the reality.

Because we know that not all syntactically correct sentences are meaningful, however, reducing the noise-to-communication ratio does require a richer -- and time-dependent -- representation of the "something somewhere" because classical computation does not capture it. Why, however, would not quantum computation do the job, with its richer structure of Hilbert space and superpositions?

Still trying to rule out mathematical models, on a sounder theoretical basis than I have yet seen.

Tom

Edwin,

By the way, I am a firm believer that "consciousness" is a convenient cop-out (practically in the category of miracles), since what we need is *one* formalism that explicates both physical reality and biological information processing: the latter could have emerged only if its fundamental principles were embedded in the former.

Tom,

1. I don't think you mean to say that syntax and semantics are the same. "Congruence," the term you use elsewhere, does not imply "same." The technical difference is critical, because congruence implies recognition of characteristics between this object (or event) and that -- not sameness.

Yes, of course.

2. An "... interconnected net of structured events ..." where congruence of syntax (meaning) and semantics (language) has a temporal ordering effect and faithfully emulates physical reality results in zero difference between the emulation and the reality.

Yes. By the way, this is *exactly* what Helmholtz was saying.

3. Why, however, would not quantum computation do the job, with its richer structure of Hilbert space and superpositions?

I guess the shortest answer is this. We need qualitatively different structured events (e.g. QED) and we need irreversibility, i.e. to retain formative history.

For another short answer, may I recommend Milic Capek's "The Philosophical Impact of Contemporary Physics", 1961 (actually it should be called "fundamental inadequacy/incompleteness of contemporary physics"), esp. pp. 135-140, 231-240, 361-374. Here is the most profound paragraph which starts at the very bottom of p.373 (just before that paragraph he was discussing auditory, esp. musical, perception):

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"Two successive "specious presents" are not separated by imaginary durationless instants, but *by their qualitative differences*. The term "separation" is misleading; it suggests separation in a spatial sense. We need to realize that the qualitative differences of successive moments of duration are untranslatable into spatial imagery. To differ qualitatively and to be distinct in space are two different notions." (his emphasis)

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(The inadequacy of the conventional physical concept of time, chronon, "separation" of temporal segments, etc. is discussed throughout the book.)

To me this paragraph also suggests that since such successive qualitatively different events cannot originate in 'space' they must originate elsewhere!!!

Lev,

Your reply is unsurprising. And the fact that you are a "firm believer" is confirmation of the essential religious aspects of our theories. Everyone I've dealt with on fqxi is a firm believer in their own theories. Not surprising when the theories typically represent a decade or more of pursuing a unique approach to understanding a personally pressing problem. To the casual observer a specific theory may seem full of holes, but the believer has long ago filled most of these holes satisfactorily, and the whole makes sense to him. Clearly mental models have been learned. It probably requires inventing a few new categories along the way, but the final result hangs together in the mind of the believer. And who knows, one of us might just be right.

You say "what we need is *one* formalism that explicates both physical reality and biological information processing: the latter could have emerged only if its fundamental principles were embedded in the former."

We are almost in agreement here, except that I believe we need *one* physical substance (real) as opposed to one formalism (abstract). Reality proceeds from something real, not something abstract. But that is the major dividing line I mentioned earlier. Roughly speaking, it separates the Unitarists from the Dualists. The Unitarists seem to recognize the primacy of consciousness and of physical reality, while the Dualists envision some Platonic world of relations that somehow plays the role of God in designing and governing our world. I have my theories of the types of mind that gravitate to each, but it's probably nonsense. Anyway, it's a fun game, and keeps many of us busy. As you mentioned, we (probably) only get one life.

Edwin Eugene Klingman

"We are almost in agreement here, except that I believe we need *one* physical substance (real) as opposed to one formalism (abstract). Reality proceeds from something real, not something abstract."

Dear Edwin,

Do you realize that practically every post by you contains *fundamental* contradictions, which you don't seem to notice. So as *the very last thing* I point out the latest one:

On the one hand, you believe "that consciousness is fundamental" (Aug. 28) and on the other hand, you just claimed "that I [you] believe we need *one* physical substance (real)". So how do you 'put' your 'reality' in the mind: you can't put trees, stars, and clouds in the mind, can you? Or, Is you 'reality' is not really real? Moreover, do you really believe that automata, which you like so much, are 'real'?

Thank you for you comments!

My best wishes to you,

--Lev

Lev,

A consciousness field, as I propose it is a *physical field* and physical fields distribute energy over space. According to the field equations I have proposed this field can essentially *condense* under big bang conditions into particles-- neutrinos, electrons and quarks. The theory produces both the fine structure constant, massive neutrinos (with approximately correct mass), neutrons with negative cores, and an explanation for the recent finding that the proton radius for muonic hydrogen is 4% smaller than QED has computed it to be (so much for the vaunted 15 place accuracy of QED). All of these explanations are currently missing from the Standard Model.

You opinions simply reflect your undeveloped understanding of consciousness, and have no relevance to my theory. This is the problem with most religious opinions, incomprehension leading to intolerance.

Your consensus understanding of consciousness as something occurring in the mind is conventional, but I'm surprised that you haven't at least heard of or considered alternative conceptions. I would suggest that you think of the ability of the gravity field to 'pull' on mass, but you probably believe that the gravity field is simply geometry.

Try not to take new ideas personally.

Edwin Eugene Klingman

For any reading the above thread, who are unaware that there is an alternate conception of consciousness, (alternative to the consensus of consciousness as artifact) the following fqxi is a blitzkrieg introduction to the topic:

http://www.fqxi.org/community/forum/topic/561

"Fundamental Physics of Consciousness" -- essay and extensive comments

Other more detailed info available here and at Amazon:

http://www.geneman.com/books/klingman_book_list.htm

Edwin Eugene Klingman

Tom,

I think we are getting to the heart of the problem. You make two statements that I find incredible:

1) "If numbers map 1 to 1 with time intervals, as you say, there is absolutely no difference between the number sequence and the time sequence. They are identical. Particularly, as you claim that "physical logic underlies math." Things that are not differentiable are identical in physics; e.g., the vacuum and the ether."

and

2) "Physics absolutely does support contradictions -- all the time. The most fundamental contradiction is between quantum theory and general relativity."

Perhaps I have been careless and said "physics" when I meant "physical reality". I try to maintain the distinction. I don't care that "physics" is contradictory, since it is clear from the state of today's physics that all of the current models, from the Standard Model to General Relativity are in big trouble. Lev thinks it's because of problems in math, I think it's because of problems with physical concepts.

I've remarked in several comments that the dividing line as I see it is between Unitarists and Dualists, loosely defined as those who believe in one physical substance from which the world self-evolves, and those who believe in some Platonic world of math that replaces God in governing the physical world.

Those who believe in the Platonic world of math can make statements such as yours, that if two entities map into each other, 1-to-1, they are identical. Mathematically perhaps true, physically false.

I have come to believe that those who live in the 'mental' world of math and logic have, to a serious degree, actually lost touch with the physical world. Drastic, I know, but it's the only thing that I can comprehend that explains the general view which I think you are expressing.

So when you say "Physics absolutely does support contradictions -- all the time" you should notice that I said: "the most basic property of the physical universe is logic, in the sense that physical contradictions do not exist." Either you are not paying attention to the words, or else you do not distinguish between "physics" and "physical reality". Contradictions do not exist in *physical reality*. The fact that they may exist in physics should simply be considered as proof that physics is off the mark.

I don't know whether we have a language problem or, as I suspect, a more serious perceptual problem, which I believe is reflected in both these fqxi discussions, and in the wider world of politics, where there appears to be a large percentage of humans who cannot (or do not) distinguish between abstractions and reality. Math is abstraction, physical reality is not.

I do appreciate your comments,

Edwin Eugene Klingman

Edwin,

How can one do science, while making a distinction between "physics" and "physical reality?" Reality is superfluous -- as Laplace said of a certain supernatural character, "I have no need of that hypothesis."

All scientific explanations are rendered by theory alone. There is thus no operational difference between abstraction and "reality." If there does exist some underlying reality beyond that which we can explain objectively, science won't find it.

Tom

Tom,

If you don't understand, there's no way I can explain it to you. Korzybski pointed out that sanity was knowing the essential difference between the map and the territory. "Physics" is the map, "physical reality" is the territory. Apparently many mathematical physicists have wandered away from the territory and see only abstract maps.

It's as if some drive across country and see the marvelous reality, and others drive with their heads buried in maps. It seems beyond words to get this across. I suspect it's deeply psychological, since it has nothing to do with the actual territory.

Edwin Eugene Klingman

Tom,

One last try:

What do physicists say is reality?

Some say there is dark matter and energy. Some say there is a God Particle (Higgs boson) to create mass. Some say there are universes without number. Some say nothing changes in Einstein's 'block universe' of General Relativity. Some say the world is made of mathematics. Some say axions exist. Some say gravitons and gravity waves exist. Some say there is SuperSymmetry. Some say inflatons exist. Some say QCD 'color' exists. Some say the world 'splits' with every quantum decision. Some say 9 to 26 dimensions exist. Some say 'strings' and 'branes' exist. And on and on. What do *all* of these have in common? The have *never* been seen! They are inferred from various theories (guesses!) about the world.

These are the maps. What actually exists is the reality. I don't know how to make it more clear than that.

Edwin Eugene Klingman

Let me start a new thread, closer to physics.

I have noticed that one of the FQXi essays written by Don Limuti (his website), discusses motion of a particle as [math]$"\lambda-hopping".$[/math]Now, if this kind of hopping, or pulsation, can be modified to mean that the particle is being instantiated on the basis of the events in the corresponding struct, that might be a way to proceed.

Does anyone knows any other work on a similar view of particle motion? (Don talks of the original (1925?) Heisenberg paper.)

Lev,

What is physics?

Some say there is dark matter and energy. Some say there is a God Particle (Higgs boson) to create mass. Some say there are universes without number. Some say nothing changes in Einstein's 'block universe' of General Relativity. Some say the world is made of mathematics. Some say axions exist. Some say E8. Some say gravitons and gravity waves exist. Some say there is SuperSymmetry. Some say inflatons exist. Some say QCD 'color' exists. Some say the world 'splits' with every quantum decision. Some say 9 to 26 dimensions exist. Some say 'strings' and 'branes' exist. Some say lambda hopping. Some say bubble men made of bubble limbs. Some say information and time are identical. Some say syntax and semantics are the same. And on and on. What do *all* of these have in common? The have *never* been seen! They are inferred from various theories (guesses!) about the world.

These are the maps. What actually exists is the reality. And that includes consciousness.

It's been fun. Don't take it too seriously.

Edwin Eugene Klingman

Edwin,

Your analogy suffers a fatal error. If you think that one's experience of the territory is more real than the map, you neglect that the vast majority of things that we objectively know about our world are counterintuitive.

The experience, therefore, is apparently not the "reality."

Once again, the science of physics does not assume reality; reality is what theory describes as tested against its own self consistency and experimental particle and system behavior.

Tom

Tom,

I'm sure you believe that. Daniel Dennett believes that consciousness is an illusion. The name for this belief is the 'Zombie' theory.

That you believe that experience in not the best indicator of reality simply proves the point I have been making.

I wish you well in your endeavor, and will continue to see you on these blogs. Thanks for your patient comments. You help me to both understand your thinking and clarify my own.

Your fqxi friend,

Edwin Eugene Klingman