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Re: Everyone Should Understand Math

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Posted by Harvey on September 15, 2003 16:53:50 UTC

Hi Dick,

Unfortunately I cannot respond to your post directly since of the results of the 'hidden' function, but I'll respond here.

First, this whole forum is dedicated to Astronomy and, as I remember the division of fields in most universities, Astronomy is usually a specialty of physics: i.e., back when I was a student an astronomy degree required a rather significant physics background.

This is perhaps true, however my speculation is that God debates overtook the more specific astronomy issues, hence the webmaster probably created this forum as a means by which to talk specifically about God and science. I don't think this means that calculators are necessarily relevant to this sub-forum.

Second, Science in the absence of mathematics usually requires an adjective to separate it from what are commonly called the "hard" sciences: i.e., such as the social sciences etc. And even in these "special" sciences, an advanced degree usually requires enough math to understand statistics at least. So, science in the absence of mathematics seems to me to be a concept reserved for grade school level science.

I imagine that science could be conducted without mathematics if we were smart enough to manage such a feat. The problem is that our intellects are rather limited, so mathematics is a nifty tool to conduct scientific research. The tool is not needed in every facet of science, so it should not be looked upon as a replacement for thinking in general - only as a tool to accomplish the necessary abstract thinking that most 'hard' science requires.

Finally, as far as I am aware, most serious religionists would take it as an insult to suggest that logic is not required in a discussion of god. Thus I find the idea that a "God and Science" forum should be constrained to disallow the use of mathematics or logic is equivalent to reducing it to grade school level of correspondence.

Saying that the forum should not be constrained to allow the discussion involving mathematics and saying that everyone should understand mathematics is two quite different positions. If mathematics is relevant to a God and science topic, then why not introduce it? If it is not generally relevant, then why say that everyone should understand (some level of) mathematics?

To quote Richard Feynman, mathematics is the distilled essence of logic. Why would you expect understanding things not to require logic. My work uses numerical representations of undefined things mainly so I can deal with massive numbers of undefined concepts to discover a rational self consistent interpretation of all of them. Only mathematics provides an internally consistent structure large enough to bring so many diverse things into alignment with one another.

Feynman was perhaps fond of the (quantum) school of thought that said "shut up and calculate!". In other words, mathematics has a place in science and no one disputes this notion. However, when one starts philosophizing about their mathematical notions, then this can sometimes lead into philosophical paradoxes, and the best position to take at those times is the "shut up and calculate!" position with regard to philosophy. Your physics career might have been immensely benefited by this school of thought...

You speak of a thought crossing your mind. How can a thought cross your mind without being defined? How did you achieve that meaning? How do you know that your interpretations of those words you use are consistent with your experiences of their uses? Does another interpretation of the meanings of things exist which will bring all your experiences in alignment? How do you know such a reinterpretation does not exist?

This is philosophy, and philosophy generally does not make require mathematics in the way that science requires it. Part of the reason, I think, is that science has the "shutup and calculate!" mindset, whereas this is not a philosophical justification or explanation of what is actually happening. To talk about meaning requires encroaching theories of meaning, and mathematics isn't very helpful in these situations since mathematics doesn't give us meaning of the world. Rather, we tell ourselves what the mathematics means with regard to the world.

Words are all defined in terms of other words. Any description of anything is eventually circular if taken far enough! The only thing which might be meaningful is the collection of consistent paths through those definitions. You take a short romp down one of those paths and you get an emotional feeling that you "know what you are talking about". So long as the paths are sufficiently long that the fact that they are eventually circular is not obvious, you can maintain that emotional conviction that you are saying something of value. Take the big picture for once. For the last 2300 years, great thinkers have been trotting around in that great garden of conceptual paths, constructing mental models of pieces here, there and everywhere. It is their fond hope to eventually learn enough to put all this together and achieve the reward of understanding it all. The problem is, the whole thing is circular; there is no starting point!

There is a difference between something being circular and something being holistic. With regard to philosophy, many of the problems are holistic in that one field requires another field which requires another field, etc.

So what do I propose to do about it? Well, I will start from exactly where everyone else starts: I will presume I know what I am talking about! However, I will ignore all the poorly modeled paths and rely only on the ones which seem well modeled: "logic" and "mathematics". I will use these well modeled concepts to create a model of my own design.

This is naive since mathematics is a tool of how to think (i.e., mathematically) and you are treating the tool as if it defines reality. That's 'okay' if your model of reality as a mathematical model is compared to reality for predictions and observations to see if your mathematical model 'matches up' with reality, but this is not what you are doing. Rather, you model reality using your mathematical tool, and then you stop short of coming up with new predictions. All of your predictions are ones made using other mathematical models (i.e., scientific theories), but the meaning of your terms do not correlate with meaning of terms used in those previous mathematical models. Your equations match previous model successes, but the terms in your equations do not match with the terms in the ones that were created by other models. In short, you have not met the criteria of model building 101, you have not substantiated that you have a model that matches with reality (i.e., our observations of reality).

The only constraint I place on my model is that it must provide an explanation of an enormous volume of totally undefined things (they are undefined if I really don't know what I am talking about). Think of my model as a designed procedure for keeping track of those undefined things (those numerical labels). It is entirely arbitrary just as the Dewey Decimal system is arbitrary. However, if you use my system, certain well defined collections of labels are guaranteed to obey some rather unusual rules. Those rules just happen to be what are ordinarily called the laws of physics. What this means is that any internally self consistent explanation of anything may be mapped into the rules of basic physics.

As we discussed in our last round of discussions, because you do not define your terms in terms of observational notions, these terms could mean anything. Add the term 'spiritual', or 'psychodelic', or 'magical', etc, in front of your key terms (e.g., unknown magical data), and right away we see the sillyness of what you are trying to do. The mathematical model no longer fits reality since the application is ridiculous. This begs the question. What is the 'right' application of your mathematical model? Well, coincidentally, it is the same one which physics attacks and the only one that you would like us to consider (instead of spiritual, psychodelic, magical, etc, etc other problem solving applications). All of this is by your design since your mathematical model was created to match the results of physics, but with the caveat that nothing new in physics is produced. Like the Bible Code it only predicts after the fact.

As we know now, you are not the one who should be credited with this use of the Fisher sampling methodology (credit goes to B. Roy Frieden), and despite your strange metaphysics involved, the issue as to why a substantial portion of the laws of physics can be modeled using this technique is a not solved issue.

So, getting back to your explanation of god. I have proved that if you can provide me with a complete coherent internally consistent explanation of god (answering every question I ask on every subject available until you are convinced I understand everything you have said), then there exists an interpretation of the vocabulary you used which is 100% consistent with your every usage of those words and which is also 100% consistent with a foundation identical to classical physics: i.e., in that alternate interpretation, god will be some physical concept obeying all the laws of physics. That result flows directly from the fact that I can take the entire conversation I had with you, apply arbitrary numerical labels to every word used in the exchange and end up generating an explanation which will be totally consistent with what has happened and will yield exactly the same exchanges achieved in the original conversation (including that part of the conversation which convinced you that I understood what you were telling me). Now, does the explanation of god have anything to do with mathematics or not? How much math does one need to understand the arbitrary construct I have created? One needs matrix algebra and calculus up through partial differential equations. What do you need to understand philosophical issues? I don't know as I do not understand the philosophical issues. But I would suggest that the ability to understand all the subjects you mention should be required. In fact, since philosophy seems (at this time) to be somewhat short of serious answers to serious questions, I would suggest that all philosophers should be well versed in all mathematics concepts so that the possible existence of a concept important to their thoughts will not be overlooked.

Here's where you make the mistake that Frieden was smart enough to avoid. You place the model in context of how we view a problem, whereas he puts it in terms of measurements. Both of these are observer based, however your approach goes overboard by demanding that anything that any real or non-real problem will conform to your model (without even a hint of how to confirm this prediction), whereas Frieden stays within the confides of physics by saying that only physical measurements will stay within the scope of his model of physics.

I have not claimed to have solved all questions. I only claim to have set up a very valuable and dependable foundation entirely through deduction with absolutely no use of induction. The things yet left to be thought about are far more extensive than those conceived of in your view of the universe.

Okay, you solved Hume's problem of induction, good for you. Unfortunately you have only introduced a problem of deduction. You have not shown that all problems solved by induction (e.g., unification of the electroweak force) can be solved by your model. Of course, if you read Frieden, you would quickly see how to do that (since this is a claim of Frieden, I think). However, he has tried to solve the unification of fermions and bosons (supersymmetry problems) and unification of gravity with the other 3 forces, and has been unsuccessful. Back to the drawing board.

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