Nature Has No Faithful Mathematical Representation by Roger Schlafly

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

Roger/Tom

The whole point of this particular exchange is that whatever representational device is being deployed, it must correspond with phenomemena and their relationships, 'as is' if it is to be a valid representational model. Mathematics is inherently more accurate than language, so it is a better tool for this job. But that does not mean it will be accurate, because that depends on actual correspondence between the model and the actuality being modelled. The model, of itself, cannot create accuracy, just by virtue of being intrinsically valid.

Paul

Peter

This is a specific example of the generic point I have just made above (and have made many times before). It is not the intrinsic validity of the model which ultimately counts (though it is a good start to create one which works in accord with the rules!), but its extrinsic validity vis a vis that which is being modelled.

Paul

You misunderstand me, Roger. Language is the formalized representation of physical phenomena. That it can be manipulated to produce novel forms doesn't imply meaning, however. Hence my anecdote about Einstein and the symphony.

That language is independent of meaning is what allows us to deduce meaning objectively without capriciously assigning meaning to a phenomenon -- by matching elements of theory one for one to elements of experience. If this were not so, and the world presented itself as no more than "what you see is what you get" -- without, as you say, a faithful formal representation -- all of our knowledge would be based on experience alone, and all our conclusions made inductively without an attempt at objective meaning. As it is, though, nearly all of our scientific/technical knowledge is counterintuitive, deduced from theoretical language and validated in experiment.

Tom

Roger

Are we perhaps too kind to and trusting of maths? A novel view here; http://9gag.com/gag/4689183

Peter

Thomas, you say that mathematics and music are languages, and you say that language is independent of meaning. That says that mathematics and music are independent of meaning. I disagree. They have meaning.

That isn't at all what I said. See my anecdote re Einstein and the symphony. Meaning is abstracted in the correspondence of theory to physical result.

If that isn't a "faithful representation" of reality, how could anything be shown to have (objective) meaning?

Tom

Tom

"Meaning is abstracted in the correspondence of theory to physical result"

This not so. As Roger wrote, 'what applies to one applies to the others'. They are all devices which can be used to represent something. The meaning stems from what you decide it will represent. Maths is just less open to interpretation, it is not inherently correct. But for any device to be used properly, ie scientifically, then that meaning will also be that which corresponds with the physical result. The fact that 1+1=2 in the maths system, is irrelevant if it does not in what is being modelled using that system.

Paul

What this has to do with physics? It has to do with your claim that "nature has no faithful mathematical representation." I asked if you think, by extension, that nature has no representation in ANY formal language, and you didn't disagree. These formal languages include mathematics and music. Perhaps you mean to say that nature has no COMPLETE representation in a formal language -- in which case you would have to prove that science is not progressive, because language is demonstrably progressive with science. But since you agree that science is progressive, and you obviate any role for formal language in scientific discovery. This is contradictory.

In any case, we seem to talking past one another at this point, so further replies by me may amount to a disruption. So I won't continue. Good luck in the contest.

Tom