The limits of mathematics

Dear Ian,

No I am not affended. You are as nice a person as I have met here. It just that the question had to do with discovering when math no longer is representing reality. I have studied and used theoretical physics. I am not a physicist, but I think there is something important to be pointed out about what physics theory really represents. The difficulty to overcome is that most theory is believed to be reality. I was suggesting that none of theory represents reality. When I mentioned that the definition of mass could be chosen differently, I think it should be clear that the original choice made was a guess. No one could possibly know that mass deserves to be an indefinable property. When I mention that we learn everything via photons and that their information is limited to observing patterns in changes of velocity, I don't think that that is a theoretical statement. Photons begin with changes of velocity and end by causing changes of velocity. We can theorize about what photons hold or contain that allows them to cause changes of velocity; but, we cannot know that. It is theoretical.

My point from beginning to end is difficult to make clear against the common belief in theory. This is my point: The best 'theory' is the one that removes all theory. Theory helps us to keep our thoughts straight, but it does the opposite in terms of learning about reality. I do not mean that it is not useful. I only mean that it is invented as a means to proceed with analyzing physics knowledge without needing to understand the nature of cause. We do not know what cause is. Everything that is attributed as being a cause is invented. This practice of theorizing may be useful, but in terms of understanding the nature of the universe, it is misleading and at times misguided. If we wish to allow math to truly serve us in learning about the nature of the universe, then we must let it take its own course and not steer it this way and that way by interjecting theoretical ideas.

The difficulty with suggesting this kind of approach is that theory clearly stands in the way. It is believed to be true. How can one say that everything could be changed when it is believed that everything is known to be true? Anyway I work for the change. That is why I work alone. That is why I put my work on the Internet. There is no other way to let it out. There are no other books or sources to point to. I am not insisting that others should quickly recognize that I am correct. I may not be correct. However, I think it should be possible to challenge theory without having some theory put forward as evidence of the correctness of other theory. I think that theory can never prove theory. The mathematics will work out properly, but the mathematics has long since become the tool of the theorist and the servant of theory.

James

James

Ian,

There are plenty of technical primary and secondary sources available; however, I think the most comprehensive view and most fun to read, though philosophical and not technical, is Chaitin's collection of essays:

Thinking About Godel and Turing: essays on complexity, 1970-2007.

Tom

Ian,

I did not get the impression you are hating yourself as admitted Teller Ede.

Names can indeed be misleading. For instance, James Putnam's attitude seems to be more appealing at least to me if I compare him with Hilary Putnam who is said to have a reputation for frequently changing his position. Quine is also suspect to me for some reasons. In particular he justified some transfinite set theory that does definitely not have any bearing in physics. Isn't blind trust in "our (currently) best scientific theories" rather subservient?

In your essay PEP seems to play a role. I am not sure whether PEPing up quantum mechanics will resolve many problems. When I wrote an unpublished manuscript "A still valid argument by Ritz", I offered a guess that explains the PEP in a quite simple manner. Somewhere in the discussion to my essays I provided a link.

Regards,

Eckard

Dear Ian,

It is difficult for any of us to say those things that we think are important in a compact form. I will give it a try:

I think that the point at which math starts to diverge is when we introduce indefinable units. However, let me say this in a different way. Returning to f=ma (I purposefully do not begin with f=dP/dT), the only part of this equation that can be explained is acceleration. That is because it consists of measurements of distance and time. The rest of the equation is unexplained. Force is the unexplained cause for acceleration. Mass is the unexplained cause for the variations of that acceleration. Symbols and names of convenience are used to to form this equation. This practice is helpful without causing problems.

The properties involved are all empirical properties. Two of them are distance and time. These are real directly known indefinable properties. The other two properties are force and resistance to force. These two are indirect empirical properties. Both force and resistance to force have unobservable natures. We know from empirical evidence that they exist; however, all of that data consists of measurements of distance and time. Measurements of distance and time are the extent of direct empirical evidence.

All higher level theory will consist of combinations of these four properties. Everything else added on changing this simple perspective is theoretical. The distortional effects of theory are first introduced by chosing to define mass as an indefinable property requiring its own indefinable units. From this point on all theory using this definition of mass is no more correct than is that first definition. It is important then to get the definition of mass correct right from the start.

I have described mass as the cause of resistance to force. We do not know the nature of any cause. Cause is hidden from us except through its effects. I think that the best approach to reconsidering the definition of mass is to add nothing on to the equation and rely only upon our use of empirical evidence in the form of distance and time and their units only. That is the concept that I used in my earlier message where I showed one possible new way to interpret mass. I have gone a long way by trying out this approach. Perhaps I may have gone astray myself; however, what I can say for certain is that: This idea does not quickly fall apart, it just keeps on going and going.

I will stop and see what you think.

James

This isn't about pure math as such, but addresses the issue of whether math can fully model the physical world. I say, no. For example, note that due to its being a matter of logical necessity, math cannot produce true randomness of the sort many consider manifested by quantum behavior. What I mean by "deterministic" math is that the math process can't actually *produce* the random results. Just saying "this random variable has no specific value" etc. is "cheating" (in the sense philosophers use it), because you have to "put in the values by hand." Such math either produces "results" which are the probability distributions - not actual sequences of results - or in actual application, the user "cheats" by using some outside source of randomness or pseudo-randomness like digits of roots. (Such sequences are themselves of course, wholly determined by the process - they just have the right mix that is not predictable to anyone not knowing what they came from. In that sense, they merely appear "random.") I think most philosophers of the foundations of mathematics would agree with me. As for MWI as an doge, I still ask: why doesn't the initial beam splitter of a MZI split the wave into two worlds, thus preventing the later interference that we find?

Dear Ian,

Yes I know that distance and time are relative if we bring Relativity Theory into play. That is not a problem to me. I won't be able to say anything more than that relativity type problems and analogous forms of their respective equations can be drived without Relativity Theory. The only indication that I can put forward in a simple way is to suggest that transform equations are not safe mathematics. They can be made to fit whatever the theorists makes them fit. If the Theory of Relativity was correct, then I should think that it could be derived directly from the fundamentals without the use of transforms. That is what I suggest is both required and possible to do.

Probably something that is of more immediate interest is the fact that you mentioned electric charge. I had it in my message and then took it out. Since you astutely brought it into play, then I will say that it does receive a fate analogous to that which mass suffered. It also does not deserve indefinable status. In support of this statement, I will suggest that physics equations, from an empirical viewpoint, never include causes. Electric charge is a theoretical cause. The possibility of it being artificial is raised by the fact that it was theoretically identified as what were otherwise unknown quantities that appear in Coulomb's equation. This is not easy to say; but it was another theoretical guess.

Causes are not a part of physics equations except in the sense that they are all represented by the equal signs. I guess this is probably enough said. I have suggested before that almost everything could change. If it doesn't look right to you, I understand. It might be better to give it a rest for a while. I do appreciate your patience and thoughtfulness.

James

Can I get a scholar to do the arithmatic.

?

to get the equation for the big bang we look at a Godel universe where time is a contradiction.

And we look at the penrose equation for a black hole in a Godel universe.

And reverse it to get a non contradictory equation for a big bang in our universe.

That is without the meanningless infnities.

Dear James,

Yesterday on Feb.21 you wrote to Ian: "The only indication that I can put forward in a simple way is to suggest that transform equations are not safe mathematics."

Maybe, you did not even take into consideration the absolutely safe practice of engineers who know what they are doing. They first transform physical quantities from a real domain into an artificial, in particular a complex domain and in the end they safely return into the real domain by means of an inverse transform.

Perhaps you meant that transforms itself are safe, provided they are correctly performed, while interpretation in the artificial domain are guesswork and sometimes prone to be fallacious.

Regards,

Eckard

Dear Eckard Blumschein,

"...Perhaps you meant that transforms itself are safe, provided they are correctly performed, while interpretation in the artificial domain are guesswork and sometimes prone to be fallacious. ..."

You are of course correct. Thank you for this clarification.

James

Dear Ian,

"...Actually, special relativity can be derived without reference to the transforms. Not to beat a dead horse, but Moore does it graphically in his text. .."

I haven't seen all the sources there are to learn from; however, I would suspect that he probably went to advanced theory or end points of theory, conservation type properties, and worked his way back from them. If I am wrong than I apologize for misrepresenting what he has done. I was prompted to say this because every explanation I have seen of Relativity Theory, other than its original type derivation, usually begins with theoretically advanced properties that owe their origin to the assumed adoption of Relativity Theory. It is a practice of beginning at the end and working back toward some set of 'fundamental properties' as established by theory. .

"...Can you clarify one thing for me that seems to be hindering my full understanding of what you're saying: when you say equations in physics don't have "causes" what do you mean exactly by "cause" in this case? If it means what I think it means, I would say that most of these "causeless" equations are empirically derived, i.e. they are the way they are because that's what experiment seems to indicate. Maybe this is the point you are trying to get at but I'm not sure. ..."

Thank you for this question. I spent the weekend thinking over what I had said. It seemed clear to me; however, when I thought in terms of explaining it to someone else in detail, I had to think about it a lot. I am still thinking about it and now also writing about it. We do not know what cause is and yet it must be indicated by empirical properties, not theoretical ones, somewhere in the equations. I have already been challenging myself to support what I said. When I can say something more clear about it, or perhaps modify or rescind it, then I will respond.

I also thought that I was once again veering off into my own ideas about possible solutions. The point I really wanted to make, in answer to your original question, was that I think mathematics leaves reality behind when the theorist begins to guess about new extra givens and interjects them into the original equations by identifying unverifiable properties and even more than this, interjecting indefinable units into the otherwise empirically clean equations.

You certainly are patient with me. I acknowledge that I know less than do you about complex theoretical physics and the fullness of empirical knowledge. I do think something is fundamentally wrong; however, I know and appreciate the necessity for demonstrating it and having it challenged. Thank you for your time.

James

Ian,

Mathematics is not fundamental because they are born out of logic. Logic is more fundamental to the universe. The universe only requires logic in order to work. But the unnatural vantage point of the observer creates and requires numbers greater than one (1).

Mathematics is the extension of logic for the conscious mind. Sure, nice geometric and mathematical structures emerges in nature from the effect of logic on large numbers. But again, the appreciation of those same structures is but for the conscious mind.

Marcel,