Nature Has No Faithful Mathematical Representation by Roger Schlafly

Joe

Correct. For any existence to occur physically, and then alter, it can only have one physically existent state at a time. This applies to anything that has physical existence, elementary particle, light, cathedral, you, whatever. Change involves more than one, with the new one replacing the old one. There is no change within any given reality (existent state-a preent).

Paul

Dear Paul,

Change is a singularity. It might only normally be applied to the whole of the Universe. A more correct term would be changing. The Universe stays in one place because all of its integral parts are in motion. The Universe remains stable because all of its integral parts are constantly changing.

Joe Fisher

Joe

What is happening to the universe as a whole we cannot know, because we cannot externalise ourselves to it.

But staying in the reality we can know, change is indeed a singularity. Everything is a singularity. The very nature of physical existence necessitates that. But change involves more than one, because it is the identification of difference, which must involve more than one in order to effect a comparison. So, whilst change occurs one at a time, it is a characteristic concerned with alteration from one to another. It is not an attribute of any given one.

Paul

Paul,

The word we as you are fully aware is a pronoun indicating a state of plurality of you and I, therefore, I agree with you that we could never possibly understand how one Universe could eternally exist once. Perhaps what we could try to do is make a better effort to dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity. For instance, there is a singular motion to the one Universe, but there is no such a thing as speed. In order to measure speed, there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe. While one has to admire how humans have satisfactorily applied numbers to the speed of falling bodies, and motor cars and light, and practically everything else, one cannot help but notice that these numbers keep changing, whereas the one Universe continues to have only one motion. There is certainly one space and one substance distributed throughout one Universe, but space is not distance and substance is not material. Of course there is heat throughout the Universe. But heat is not temperature.

Joe

Joe

"dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity"

Yep, this is the crux of the problem. Different philosophical takes as to how reality is fundamntally constituted underpin different theories, which is why they have flaws and do not marry up.

I noticed you comment on speed before, and am not sure I agree with it, as written. So let me put it this way. There is movement, which is relative alteration in spatial position. Now, it is relative beause everything must be deemed to be moving. Therefore, in order to calibrate this, one particular example thereof must be selected as a reference (it could be any possible example), otherwise the judgement cannot be effected. Subsequently, this reference must be used consistently to ensure comparability. In simple language, this is no right or wrong answer, only a relative one. The concept of speed is just the relative rate of that movement.

I would certainly not agree with: "there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe", because there obviously must be such points, otherwise there would be no existence. The difficulty comes in identifying them.

Space is an interesting one. It is actually what is not something. There is only something which physically exists, but the 'space' between A & B is only that because of the way in which we have defined A & B. In physical reality, A &/or B may be part of C. And there is something, just not A and B between A & B, but we are not interested in it. Space is just a conceptualisation of the relative size/shape of these somethings. So they can be conceived of as occupying spatial position. So there is intrinsic space, ie the spatial 'footprint' of any given something, or there is extrinsic space, ie that which is not the somethings as defined.

Paul

You packed a lot into 9 pages, Roger! It was a good read. However. I'm curious about something that you didn't mention -- if mathematics is not a faithful language of reality, does that obviate *any* formal representation, e.g., Lev Goldfarb's ETS formalism?

If you get a chance to read it, my essay "The perfect first question" addresses issues that you raise about hidden variables and Bell's theorem.

Good luck in the competition.

Tom

The evidence, yes. When the evidence is, however, identical to one's expectation of experimental results, how can one determine that the evidence (data) is a "true" representation of reality? Without a principle of correspondence between a formalized theory and physical experience, we would -- like Mach -- never accept the reality of atoms. Now suppose that atoms are only approximate, sure -- at least, the theory gets us from the naive Bohr orbital model to something more.

Roger, do you agree that science is progressive? If so, what role does language play in that progress? If not, what's the point of doing science?

Tom

Roger

Your essay was so refreshing I've had to re-read it. A small issue on your point about last years essays. I flagged up the role of maths and took a wholly ontological approach to expose and overcome a measurement methodology problem in handling 'discrete' kinetics (2020 'Vision'). It was a top 10 finalist but I was disappointed the judges seemed to miss or avoid the important conclusion.

Indeed I strongly applaud your suggestion that relativity is "a theory about something that would be due to our methods of measurement." I'm reasonably sure I've identified a serious misunderstanding about measurement methodology which has broad and deeply fundamental implications (the essay should pop up any time now). I really look forward to your comments.

For now, can you comment on this; As motion is an invalid concept in geometry, and geometry is the basis of vector space, can we assume that motion is validly and adequately described by vector space algebra?

Peter

Roger,

Deductive science is not necessarily progressive. It starts with assumptions (axioms) which could be false. For instance, special relativity is based on the assumption that the speed of light is independent of the speed of the emitter. If that is false, not only relativity but modern physics as a whole is 100% degenerate. The following quotation hints at possible falsehood:

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Pentcho Valev pvalev@yahoo.com

Roger, the reason that I asked, is that if language is independent of meaning -- i.e., if there is direct correspondence between formal descriptions of natural phenomena and the physics as we experience it (Tarski) -- then if language is not primary to discovery, how is one to judge progress?

If the role of language is merely to describe phenomena, so that personal experience is identical to language (I realize that this is the LP view) it follows as well, that experience is substituted for meaning. That being so, it stands to be demonstrated that no meaning can be assigned to a positivist result that is not evident in physical experience.

Does this accurately describe your position? If so, how does one prove within this framework that science is progressive? After all, such a feat must first assume that language is progressive and independent of meaning, and we have arrived at a contradiction.

Tom

Roger,

Einstein was a plagiarist but this is not indeed very relevant to the progress of science. If his 1905 light postulate is true, then special relativity, plagiarized or not, is great. However if the light postulate is false, then "nothing will remain of contemporary physics":

http://www.perimeterinstitute.ca/pdf/files/975547d7-2d00-433a-b7e3-4a09145525ca.pdf

Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."

Clues:

http://arxiv.org/ftp/physics/papers/0101/0101109.pdf

"The two first articles (January and March) establish clearly a discontinuous structure of matter and light. The standard look of Einstein's SR is, on the contrary, essentially based on the continuous conception of the field."

http://www.pbs.org/wgbh/nova/einstein/genius/

"And then, in June, Einstein completes special relativity, which adds a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves."

Pentcho Valev pvalev@yahoo.com

Let me try and put it this way, then. Do you think that cell phones and the Higgs boson were discovered independent of the physical theories that incorporated and predicted them?

Most important, how likely do you think those theories would have been possible without the language that supports them, that makes comprehension possible?

There's no question -- that whatever else mathematics is -- it is a language. This is exceedingly easy to demonstrate, by the mere fact that any mathematical statement (though it is most unnecessary, tedious and impractical) can be translated into natural language.

Tom

Pentcho

Einstein's 1905 light postulate had a condition, ie in vacuo. Later this was dropped. That is, in 1905, light is existent in one condition (ie no interaction from anything else) whilst matter is being affected by something else, becasuse there is Lorentz's length contraction on matter. In simple language, not all entities are in the same world at the same time. Note the caveat between the presentation of the two postulates: "only apparently irreconcilable". In other words, 1905 does not equal SR. Indeed, in 1916 when expounding GR, he clearly stated what constituted SR.

Paul

Roger, of course music is a language -- and like mathematics and natural language itself, also an art. I am reminded that Einstein (an expert violinist) once remarked that a symphony could be described mathematically by variations in sound wave pressure, though that would not capture the meaning of the symphony.

Likewise, Einstein's mathematically complete theory of relativity does not reveal its meaning in the symbols, but in the playing.

Tom