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Posted by Harvey on March 28, 2002 00:43:10 UTC

Dick,

The whole point of my scenario is to understand how you arrive at your 'problem'. Whether you do the math in your head or write in on paper is irrelevant.

***H: (11) You notice that the inductive conclusions (which you labelled 'laws of physics') are deductively concluded from your efforts in (10). D: No, what I notice is that it is impossible to set up a self consistent closed system of concepts which do not obey those particular laws. A rather surprising result.***

Try to understand your flow of thought:

(1) Accept all mathematics and classical logic

(2) Reject the results that our sense impressions lead us to believe

(3) Define reality as numbers

(4) Divide the numbers into subsets. One subset is our alternative reality and the other is reality.

(5) Define all observations as undefined data

(6) Define certain terms (e.g., time) and construct mathematical equations that make use of these terms in a well-defined mathematical manner.

(7) Do the equations

(8) Obtain most well-known laws of physics

(C) Most of physics is tautological.

Now, let me list a few of the reasons what is wrong with the above reasoning.


a) Accepting (1) presents significant problems:

i) By accepting (1) wholeheartedly you have done so for inductive reasons based on your sense impressions. However, this is in contradiction to the whole point of your paper. Your paper is a skepicism about our sense impressions, but you need sense impressions to establish the conclusions of your paper!

ii) By accepting (1) you might unwittingly have introduced (8) simply because of the causative role (1) plays on (8). That is, (1) might require (8) and may have nothing to do with (6). The universe may simply be mathematical which requires (8). That is something that many physicists believe.

iii) The limitations imposed by mathematics on our observations as well as on the kind of physics we discover is not clearly understood. It may be that something is 'mathematical' means that we can reason that way, and not the other way around. You cannot say that something (in the real world) is required because of mathematics. This is beyond what mathematics can say. Mathematics is only concerned with what is possible in mathematics - it is not about what is possible or not possible in the world. This is what science tries to establish with experiment and what philosophy tries to establish through logical analysis.

iv) Mathematics may represent a limitation of our creativity of patterns. There may be ET's out there that that have an entirely different and contradictory collection of (1). For example, there are logic's which contradict other logic's (e.g., classical logic uses a bivalence principle whereas other logic's reject it).

v) The axioms of mathematics are selected for non-mathematical reasons (e.g., intuitively attractive, matches intuitive experiences, theorems are consistent with the mathematics developed so far, etc). This fact undercuts your need to treat all observations as undefined patterns that may be in error. You want to avoid the blind acceptance of our sense impressions, but by accepting (1) you are accepting whatever blind acceptance that comes from accepting each and every axiom of mathematics.

b) Your (2) is faulty. I agree that there is no guarantee that our sense impressions are correct (there is the possibility of error), but you need sense impressions to have any coherent knowledge of the world. If you treat your sense impressions as undefined, then you must treat all of your knowledge as undefined. The problem in doing so is that even the questions (and problems) you are considering as valid are based on a lifetime of having sense impressions. For example, if we lived in a Chess World where everything was about the play of chess, to treat our observations as undefined would still require that our reasoning be limited to what occurs in Chess World since that is the only world we experience. Our models would be necessarily limited to Chess World since this is where our experience was limited. Any model that we used to decipher the nature of our observations would necessarily come up 'Chess World'-oriented. Hence, it makes absolutely no sense in abstracting ourselves from our sense impressions. Rather, we should try to communicate our sense impressions and form a collective experience so that we can conduct experiments that are as universally accepted as possible (aka, science).

c) I'm sorry to say that (3) is faulty since it is trying to redefine a term that already means 'all that is out there'. We discussed this issue already some time ago. In addition, there is no indication that 'all that is out there' must succumb to being represented by a number. It is conceivable that a theoretical holistic entity that resists reduction to numbers might have 'kickable' observables that can be tested by experiment. That is, the observables might be representable by numbers, but the entity itself is not. According to your (3), it cannot exist even if it actually does exist.

d) Your (4) is simplistic at best. We cannot say that there is one alternative reality since the instrument of interpretation of reality is the brain, yet the brain divides our sense impressions into different areas. There is no conclusive evidence that we have one mental image of the world. There may be a visual mental image, a auditory mental image, etc. This approach strikes me as psychologist and without any basis in fact (I'm being tough on you because this is what would occur if your work was ever published in a scholarly journal - and by those standards I am being exceedingly kind).

e) Your (5) is problematical. What does it mean to treat an observation (i.e., an observable) as undefined? In mathematics it simply means that a value (or position, or certain area between two points, etc) has no specific mathematical representation. However, in terms of observation this does not make any sense. The world we experience is not a formal system. We don't encounter mathematically undefined things in the world. We may simply lack knowledge of something that is observed (e.g., exosolar planets), but this is not the same as saying it is undefined. To say something is undefined means that there exists a formal system that an observation remains undefined within. You can, I believe, have undefined entities in a theoretical model (e.g., quantum spin is undefined in terms of their physical meaning), but these features are believed to be unobservable.

At one time we even discussed (5) in terms of what counts as an observable. You were of the opinion, if I remember, that scientific observables are not part of (5). The reason if I recall is that scientific observables are only known to exist based on theory-laden predictions and validations. However, that would mean that your model is not even dealing with scientific observables.

f) Your (6) is not based on fact but based on human interpretation (specifically your interpretation of physical terms). You are defining terms based on physical concepts in terms of a mathematical formulation as you understand them. There is no indication that these terms are a 'correct' interpretation to our experience with these terms, nor is there indication that you have correctly identified the mathematical relationships between these terms.

Another problem is that the terms of (6) do not correspond exactly with the physics terms of (8). You said they are isomorphic, but this is not exactly true. For example, your terms of (6) require an observer for the term to have any meaning, but the terms of physics are often stated in observation-free terms (e.g., non-observables of quantum physics). In addition, there are differences in terms from different fields of physics. This is a source of friction between GR and QM since certain terms are treated differently (e.g., time).

The fact that you force an exact formal definition on terms when in fact there is no exact formal definition of terms is very troubling, if not fully in error.

g) From what I can tell, you are making symmetry assumptions in your (7). This would indicate that you are obtaining correct physics equations simply because you are assuming symmetry. Emmy Noether became famous because she was able to show how physics is really about basic symmetries that hold in the world. You may simply have rediscovered her work (et al.) by playing with basic symmetries of nature. By the way, this might indicate why you didn't come upon other laws of physics since late 1940's since these involve other symmetries (i.e., local symmetries).

h) As just mentioned, since (8) is so limited to the laws of physics as they were known in the 1940's, the fundamental character of your work is in doubt. The reason is that fundamental work produces other fundamental results. If you are producing work that is not so fundamental, then it usually indicates that you were not familiar enough with the more modern/fundamental work in order to 'curve fit' your results to that fundamental work-in-progress. In addition, it might mean that you didn't include in your assumptions other basic symmetries that would have yielded more fundamental results.

i) Your (C) is an ill-founded conclusion based on the above. I'm sure there are many more holes (even more damaging) to your paper, but this is what occurs to me as I sit here and give you my impressions.

I guess I've been rather negative on your paper. I'm not sure if that's right or not. You seem tough-skinned and wanting to have honest accessments (you seem to write off negative opinions anyway). At the same time I see so many people 'fall' for these ideas and I don't know why.

Like I said, I'm willing to quit this discussion with you if it bothers you. I can only give you what I really think is the case. I know you don't take my criticisms as applicable to your paper, so I guess it doesn't matter.

Warm regards, Harv

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