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
You refer to Lev Goldfarb. As I understand his approach, it might describe observations or knowledge, but cannot be a true representation of reality.
I see Bell's theorem as just one of many arguments against hidden variables. People want to believe in these hidden variables for some reason, but I say that all the evidence is against the whole concept.
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
Yes, I agree that science is progressive. T. Kuhn is famous for saying the opposite, with his paradigm shift theory of science, but he was wrong. Not sure what you mean about language. Sometimes it is useful to have new terminology or language to describe ideas.
Vector spaces are ideal for describing motion of particles. If the moving particle is really a wave, then the situation is more complicated.
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
Pentcho, it does not make any difference whether Eintein thought of light as particles or waves. He was not accounting for the Michelson-Morley experiment, as you point out above, by quoting Norton. His axioms came from Lorentz's work. If you want to understand the progressive nature of those axioms, you have look at the work of Lorentz and Poincare.
Hoffmann is confused where he says, "Einstein resisted the temptation to account for the null result ... and introduced as his second postulate ...". Einstein was not trying to account for the null result. Einstein got the second postulate from Lorentz without explanation. For proof of that, in Einstein's own words, see my blog. So these aspects of Einstein's work are not really relevant to the progress of science.
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
Thomas, I am not sure I understand your question. When I say that science is progressive I mainly mean that modern science keeps bringing advances like cell-phones and Higgs bosons, that were just not possible with previous levels of science. I also have a positivist philosophy, so I believe that science advances just as facts and knowledge accumulate.
My trouble with the word "language" is people sometimes say that mathematics is a language. But math can prove things as well as describe things. Maybe you could give an example to explain just what you mean.
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
Thomas, I would say that physical theories were need for those advances. The language is the easy part. I would not call mathematics a language. Yes, mathematical ideas can be expressed with mathematical symbols. You call use of those symbols a language. But what's the point? Do you call music a language?
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
Okay, Thomas, call physical theories, mathematics, and music languages if you want. By your definition, something is a language if it can be represented in some other way, with loss of meaning. But then I have to disagree with your earlier premise that "language is independent of meaning".
Roger
When a photon in a medium interacts with an electron moving laterally (i.e. at the refractive plane of a moving medium), the interaction time is non zero (say 6.5x 10^-24s for c and a classic electron radius) so there must be a 'kinetic' effect from the evolution of interaction. This is consistent with recent findings at a larger scale, i.e. from astronomy (i.e. Emsellem, E., et al., Atlas 3D. MNRAS 414 2. 888-912. June, 2011) which derives a kinetic term for the interaction with halo matter which matches observation (also finding galaxy rotational velocities quite accurately).
Yet Cartesian co-ordinate systems and 'point' particles can't even 'see' any such effect mathematically. When using Propositional Dynamic Logic instead of simple maths an ontology emerges, but this would point at vector space and overlapping inertial 'wire' frames as inadequate to model reality ('time stepping' maths can also do it after a fashion). Could it possibly be so? And would that be just tooo heretical?
Peter
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
