Science Forums 2

[Doctordick]

Hi Buffy,

Sorry for the length of my posts. It is no more than an attempt to be clear. I can see so many ways my comments can be misinterpreted I try to cover all the bases. In the end, the readers usually misinterpret me anyway. I guess I am just not a decent writer. But I try!

Originally Posted by CraigD

My personal intuition is that traditional, philosophical approaches to understanding the whole phenomena of “knowing” the nature of objective reality – which is what I take to be of the focus of you search – have consumed lifetimes of minds more capable than mine, so are not likely to be fruitful paths for me.

You shouldn't sell yourself short. When I was young, my mother told me that one learns more by listening than by talking and I took her quite seriously. I listened for a long time. Now I am old and not in a position to learn much more. Maybe it is my turn to talk. I know a few things that I think are worth talking about. But I just can't find anyone who wants to listen.

In my life, I have never met anyone who's mind I would condescend to rank superior to my own. I was always told that intelligence was a measure of one's ability to solve problems: i.e., if two people know exactly the same things, the more intelligent one can do more with it. Think about that. Considering what the top people know, why is it that most of the breakthroughs are accomplished by youngsters? Now is that controversial enough for you Buffy? If you have a good answer for that one I would like to hear it. I have one; a very specific answer.

Originally Posted by Buffy

Well, one piece of advice: even smart people have short attention spans...

Yeah, I have noticed that. It's probably due to the ignorance of the people one has to deal with (notice I said "ignorance", not "intelligence"; in my opinion, the average man is far more intelligent than he is given credit for, his problem is that he doesn't know very much). If one listened to everyone, they wouldn't have any time left. I know I don't listen very much anymore myself. If you don't have a decent attention span, you might as well ignore me because what I have to say requires understanding a number of rather diverse facts ordinarily never brought to bear on one another.

Originally Posted by Buffy

To a great extent too, now that I've read it, it seems to be a bit on the "obvious" side, ...

Well, I would certainly think of it as obvious but you nonetheless may have missed the central issue I was trying to convey. You appear to have viewed the thing from the point of view of "usage" of the knowledge, not from the intended perspective of "development" of that knowledge. When looked at from the development side, the basis (or foundation) of both is rather obvious. The foundation of "squirrel" (or intuitive) knowledge is experience and the foundation of "logical" (or deduced) knowledge is presumed axioms. The fact that those axioms are arrived at via intuitive (or squirrel) processes and the fact that deduced knowledge is part and parcel of your experiences provides the connection between the two. They are inexorably bound in any concept conceived by man (or woman ). Nonetheless, they are very different processes and the differences are fundamental to answering the question, Exactly what can be deduced from first principals?

Originally Posted by Buffy

In general I like formalism, but a lot of people can't be bothered.

If you like it, perhaps I could interest you in my thoughts. For those who "can't be bothered", I really don't want to bother them. The issue I want to talk about takes a decent attention span to make sure one is performing a rational examination of that subject (particularly when most people believe the correct answer is "nothing at all". ) Anyone here who feels uninterested in the subject can drop out here; I won't feel rejected at all.

Mathematics as fundamental foundation principal

Meanwhile, for anyone who might be interested, I need to establish some fundamentals. Exactly what are the "first principals" I think should be used as the foundation of such a study? Since all logic is itself based on intuitive concepts, logic itself is a "squirrel" concept. That is, logic is constructed from concepts taken to be "self evident"; but "self evident", when examined objectively, is essentially no more than the fact that one can not conceive of them being wrong. I bring this issue up only to confront the oft raised philosophical position that logic itself is a presumptive structure and, as such, cannot be asserted to be an unquestioned requirement. (Yes, I have had that issue raised against my thoughts.) I counter their position with the assertion that "truth" by definition is the only absolute truth available to us. The issue of truth by definition rests on two very straight forward points: (1.) we either agree on our definitions or communication is impossible and (2.) only the existence of internal contradictions can invalidate a definition. Formal logic is no more than extension of the concept of definition: i.e., the definition of absolute truth. As Feynman once said, "mathematics is the distilled essence of logic". Thus it is that I take mathematics as a given foundation element but not quite as it is seen by most others. I see it as a language which has been stripped of inconsistencies through thousands of years of hard work performed by professional mathematicians. The important point being, when I give instructions in mathematics, I can be fairly confident that the listener will obtain the same results I obtained: i.e., communicantions can be much clearer than they are in English.

What is the definition of mathematics

"First Principles of Mathematics" is an extremely esoteric subject. I have not made a careful study of it but I have managed to pull out enough to convince me of an overall viewpoint which makes sense of their approach and their results (to me at least). I have come to define mathematics as the invention and study of internally consistent systems (systems being any collection of "things" together with set of rules involving those "things"). That definition is a statement of what I mean when I refer to mathematics. I only make that comment because I have rarely found it possible to achieve agreement on that definition. Everyone else seems to think that is not the definition of mathematics but no one has ever told me what they think mathematics is so I am left holding the bag. They apparently know it when they see it and presume everyone else does too. Personally I don't care for that position; I need to know what I am talking about so I can see what my presumptions are.

When it comes to first principals of mathematics, I think most everyone misses a very significant point (particularly people ignorant of mathematics). That is the fact that numbers are mere symbols and that the operations (addition, multiplication, integration, ...) are no more than a set of rules which have been shown to establish internally consistent systems.

Application of mathematics to science

Science is an attempt to explain our examinable experiences (it is our ability to examine it which makes that experience "physical" ). The issue here is that an internally inconsistent explanation is a pretty worthless thing. By definition, an internally inconsistent explanation is one which gives different answers depending on the specific path taken through the logic (that would be the supposed rules presumed by the explanation). It should be obvious to all that, in that case, it doesn't provide an answer so its original purpose is defeated. Thus it is that inconsistency is used by everyone as the primary sign of error in an explanation.

However, it is often very difficult to prove an explanation is internally consistent (particularly if the explanation is presented in a language other than mathematics). Just as an aside, you should note that, if you can prove an explanation actually is an internally consistent structure, mathematicians will accept it as a branch of mathematics! That is the central reason Newton is credited with the invention of calculus. One of the problems with modern science is that a lot of it is compartmentalized. The individual fields may be internally consistent within the field of interest but it is often very difficult to make those different fields consistent with one another. The prime example of that difficulty is the current conflict between quantum and general relativity.

The conflict between quantum and general relativity rears its ugly head in tachyons, collapse of the wave function, the Bell inequalities and the fundamental inability of the physics community to set off a correct general relativistic version of quantum mechanics. What I am trying to point out to you is the fact that there are still a lot of internally inconsistent explanations in physics (and physics is usually put forward as a model of internal consistency): i.e., it is still not possible to reduce the whole of physics to mathematics (an internally self consistent system).

The issue I am trying to get attention to is the fact that any internally self consistent explanation of anything can be seen as mathematics. It is that primary requirement that all explanations must be internally self consistent which I felt needed examination. I have done that examination and found some very interesting consequences which are apparently of little interest to anyone. None of it has ever been published as the professional physicists contend my work is philosophy and simply refuse to look at it (they assert it has no application to their field). The professional philosophers contend my work is mathematics and it should be turned over to mathematicians as it is outside their field of expertise. The mathematicians contend there is no new mathematics in my work and the only issue is one of physics which is outside their field of expertise.

So it is my position that the question, Exactly what can be deduced from first principals? is a question which can only be answered after establishing an exact definition of an explanation. (Another of those concepts they apparently know when they see it and presume everyone else does too). Again, I need to define it if I want to know what I am talking about.

I will begin by pointing out that all "explanations" require something which is to be explained. Whatever it is that is to be explained, it can be thought of as information. It thus follows that "explanation" is something which is done to (or for) information. The question then is, if we are to define "an explanation" in general, we must lay down exactly what an explanation does to (or for) information? First, I think it is pretty clear that one cannot "explain" anything they do not understand.

It seems to me that if all the information is known, then any questions about the information can be answered (in fact, that circumstance could be regarded as the definition of "knowing"). On the other hand, if the information is understood, then questions about the information can be answered given only limited or incomplete knowledge of the underlying information: i.e., limited subsets of the information. What I am saying is that understanding implies it is possible to predict expectations for information not known. The explanation itself constitutes a method which provides one with those rational expectations for unknown information consistent with what is known.

Thus I come to define "An explanation", from the abstract perspective, to be a method of obtaining expectations from given known information. If you have any arguments with that definition, it seems to me that you need to show me either a method of obtaining those expectations which can not be conceived to be an explanation or an explanation which provides no method of obtaining expectations. If you cannot show one of those circumstance, than you should agree that it is a usable definition of an explanation consistent with the common meaning of the term.

Looking to hear your complaints.

Have fun -- Dick

Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity