The limits of mathematics

James,

When I was reading your essay on time, I felt not yet immediately in position to judge whether or not your application of Bohr's model of an electron orbiting a proton might be correct. I got already confused when you did not distinguish between my and my_zero, epsilon and epsilon_zero. You finally lost me when you claimed that my_zero is not 4 pi 10^-7 Vs/Am but the relation between the velocity of light (obviously in vacuum because there is no known value for the velocity of light in copper) and the velocity of sound. This is perhaps easily falsifiable. Sorry.

Eckard

Eckard,

Thank you for your reply. An electrical signal traveling through copper moves at the speed of light. The speed of light always measures the same under any local conditions. I refer to any mu and epsilon for any material. The equation works well for solids and not so well for gases. I began with the simple bohr model because it is sufficient, within the constraint of a 10 page essay, to make my points. I also write in as simple a form as I can so that readers other than physicists can follow my work. I anticipated that physicists would not read my work or would reject it outright. I think it is quite clear that I cannot be correct unless theoretical physics is wrong about almost everything. There were results given in that essay that go beyond the points you raised. If they are not sufficient to raise the interest of others, then that will have to remain the case for now. My total work is far more extensive than that essay. I think I should return to doing it. I need next to re-interpret the fundamentals of quantum theory. Thank you for taking the time to read my essay. I really am interested in reading more of what you have to say about your ideas in discussions with professional physicists and mathematicians. I will look for future posts.

James

Dear Eckard,

I think I should say more since your interest in the audible spectrum is very high:

"...You finally lost me when you claimed that my_zero is not 4 pi 10^-7 Vs/Am but the relation between the velocity of light (obviously in vacuum because there is no known value for the velocity of light in copper) and the velocity of sound. This is perhaps easily falsifiable. Sorry."

The velocity of sound is a rate of interaction between particles of matter. Similarly to that of light, sound as we hear it, is a limited part of the sound spectrum. In other words, particles interact between one another, theoretically speeking, over any distance. It will usually be the case that most of the interaction is undetectible by the hearing sense. Even in free space there are particles and they do interact with one another in the same manner in which more dense particles create the sensation we call sound. The difference is not of kind but rather of intensity. Therefore, in the strictest sense, if the effect is called sound in its most general form, then there is an effect of sound even in free space. We do not need to hear it in order to anticipate that it must be occurring even there. What do you think? By the way, I do not recall ever saying that the magnitude of mu_zero is not 4 pi 10^-7 (appropriate units can be added here, either yours or mine. They are different).

James

Sorry everyone, I thought I was in a different forum speaking to Eckard. I do not know how I managed to cause my message to appear here. Anyway, please carry on and disregard it. Thank you.

James

Another minor interruption by me. My message is in the correct forum. Dear Genevieve Mathis I was not responding to your message. Anyway hello to you.

James

Dear Eckard,

I am repeating this message here after mistakenly posting it in another thread:

I think I should say more since your interest in the audible spectrum is very high:

"...You finally lost me when you claimed that my_zero is not 4 pi 10^-7 Vs/Am but the relation between the velocity of light (obviously in vacuum because there is no known value for the velocity of light in copper) and the velocity of sound. This is perhaps easily falsifiable. Sorry."

The velocity of sound is a rate of interaction between particles of matter. Similarly to that of light, sound as we hear it, is a limited part of the sound spectrum. In other words, particles interact between one another, theoretically speeking, over any distance. It will usually be the case that most of the interaction is undetectible by the hearing sense. Even in free space there are particles and they do interact with one another in the same manner in which more dense particles create the sensation we call sound. The difference is not of kind but rather of intensity. Therefore, in the strictest sense, if the effect is called sound in its most general form, then there is an effect of sound even in free space. We do not need to hear it in order to anticipate that it must be occurring even there. What do you think? By the way, I do not recall ever saying that the magnitude of mu_zero is not 4 pi 10^-7 (appropriate units can be added here, either yours or mine. They are different).

James

Dear Genevieve Mathis,

Since I mistakenly interrupted your thread, I read your message and am now responding to it. Your evolutionary outlook appears to accept intelligent results without intelligent causes. Also, you appear to me to analyze trhe evolution of the human brain and mathematical thought from a macroscopic approach and then decide that it is a macroscopic product. Am I correct in reading your message this way?

James

James,

You might judge yourself whether or not your ideas are correct and of what use. I am very sorry, I cannot hide my disagreeing. For instance, electric signals do not at all propagate within copper. The signal in a 50-Ohm cable propagates approximately with a velocity of 2/3 c. Do not try discussing. Try to live with the possibility of being simply wrong.

All the best,

Eckard

Florin,

you wrote:"there are so many different logics possible, and yet Nature seems to favor only one. Why is that?"

Do not blame nature for being wrong. Theory is patient, nonsense has no limits, and it provides honor as well as money. Mutually contradicting theories cannot likewise fit simultaneously to the same object. That's why I vote for ultimate realism.

The Greeks established the logical connections among their results, deducing the theorems from starting assumptions (axioms). For Aristotle, the axioms are truth, and hence the theorems are also truth. Leibniz conceived the idea of symbolic logic, a universal language in which all rational thinking could be expressed. Intuitionists can, and do, deny that, for any mathematical statement p, it is a logical truth that 'either p or not p'. Equideductive logic is offered instead of set theory. I fear, it does not solve the problems. Sound common sense is still necessary.

Anyway, your question seems to be worth a very radical consideration.

Eckard

Ok no more discussion.

James

Dear Ian,

Thank you for your previous messages and time. Due to your lack of participation here, I am leaving your forums. Congratulations to you for winning a prize for your essay. I wish you well as a new member of fqxi.

James

Dear Ian,

Sorry about that message. I became impatient. I did not wish to get into any conversations about my own work, but it happened anyway. I believe in the work I am doing, I do not expect others to feel the same way. My intent here is simply to give my perspective on speculative mathematical analysis. I have pointed out that I think that speculation became a part of physics theory as early as the interpretation of mass in f=ma. In fact I am certain that mass was interpreted incorrectly. However, my only point that is appropriate here is: Can physicists justify introducing indefinable properties into their equations? There are others besides mass. I say they cannot.

James

Eckard,

I do not "blame" nature for anything. I was just restating Wheeler's question: "why those equations?" into "why this logic?"

Ian,

In my last message I said:

"...Can physicists justify introducing indefinable properties into their equations? There are others besides mass. I say they cannot."

Looking at it now, I did not state my case correctly. I am restating it as:

'Can physicists justify introducing indefinable units into their equations?'

I am simply adding my opinion to the record here. I do not expect and certainly do not insist that others must see things my way. I will let the totality of my work determine that in the long run. So, it is fine with me if it goes undebated here. Either way is ok. I am satisfied to continue developing my own theoretical work and look forward to the next essay contest.

I would like to read opinions about your question from members. I hope they decide to participate. Their opinion is more relevant to the physics community than is mine.

Best wishes,

James

James

Florin,

Yes, I read your essay and wonder about your references 3-6 to a bit too Platonic ideas. Let me refer to an undergraduate text by Anglin who compares in detail Platonists like Goedel with Formalists like Hilbert and intuitionists like Brouwer. You repeatedly mentioned "the Platonic world of abstract mathematics".

I found an utterance by von Neumann:

"As a mathematical discipline travels far from its empirical source, or still more, if it is a second or third generation only indirectly inspired by ideas coming from 'reality,' it is beset with very grave dangers. It becomes more and more purely aestheticizing , more and more purely l'art pour le'art. ... In other words, at a great distance from its empirical source, or after much 'abstract' inbreeding, a mathematical subject is in danger of degeneration." [The Mathematician, in R.B. Heywood, ed. The Works of the Mind, Univ. of Chicago Press. References to Collected Works, Vol.I: Logic, theory of sets, and quantum mechanics, ed. A. H. Taub, Oxford, Pergamon.]

Do you know Weyl's diagram?

Weyl Russell Zermelo

Brouwer Hilbert

More constructive tendencies are located to the left, more axiomatic ones to the right, more evident and deeper founded on the bottom, more customary on top.

more

Eckard

Ian,

I stated in an earlier message that cause is included in theoretical physics equations only by representation as symbolized by the equals sign. I think that is correct to say. In a later message I wrote:

"...I am still working to support what I said about cause and the equal sign. I have made that statement before, but, this time it struck me as representing something more fundamental than I had previously realized. If cause is unknown and yet it makes its presence known, then in what ways does that occur in theoretically clean empirical equations. ..."

Here is what I think: In general - The left side of an equation shows initial conditions. The right side of an equation shows final conditions. The equal sign symbolically represents the cause of transforming initial conditions into final conditions. There is representation of the cause on the right side of an equation, but not by its fundamental identity. In other words, a force is not represented directly as the property force. The force is represented by its potential change of distance with respect to time. So an equation, in simplest form would look like this:

(velocity_1) plus (potential-change-of-velocity) = (velocity_2)

All units are in the form of distance and time only. In other words: An initial value of distance with respect to time is to be added to the potential change in the distance with respect to time resulting in a new single value of distance with respect to time. The means by which this addition occurs is represented by the equal sign. We never know the nature of the means. We only know the patterns we observe in its effects on velocity. The effects are always changes of velocity. The potential change in velocity is derived by observing the patterns in empirical evidence and using them to project a specific change.

There is no need to respond to this unless you think it is of interest and worth your time. It represents my view and it is worth my time to state it here. I like it, but I do not insist that others should agree with me.

James