Can Everything be Reduced to Pure Physics?

[Les Sleeth]

And considering your attitude, I wouldn't want to!

What attitude is that, the failure to kiss your condenscending rear?

. . . I have no compunction to throw pearls before the thoughtless.

The onlyl pearls you've been throwing are pearls of self-aggrandizement.

Essentially what I said was, if hard analytical science cannot explain it, then no valid explanation exists. Now the proof is not trivial and it requires a patient and exacting mind to follow it.

Do you really think everyone around here is going to agree ". . . if hard analytical science cannot explain it, then no valid explanation exists"? If you start off with that a priori assumption, you are going to have a fight on your hands every step of the way from some of us.

If you really are interested, I suggest you take a look at the "What is Evidence" thread starting with my post at:https://www.physicsforums.com/showthread.php?p=441146#post441146 . . . "This is a finite mechanical problem which we all know is solvable (we have all solved it via intuition); so why is no one interested in solving it via logic? Most tell me that's because it can't be solved and I am a crackpot for thinking it can be."

Maybe you should listen. It can't be done and still be called "scientific." It might be called philosophy, but who knows since all we've seen from you are attempts to get readers to commit to buying your approach wholesale, and calling them idiots for refusing of course, before you even have put out one substantial idea.

Some "hard analytical explanations" yield the existence of undecidable questions; i.e., the existence of undecidable questions does not violate my proof at all.

That is not the standard even for a good scientific theory, much less a proof.

The material below is a taken from a link provided by Tom (another supermentor...btw, Nereid is a woman) to a theorist hopeful. It's notes taken from a lecture (which explains the choppy writing) on Popper's falsification concept that is now accepted as the standard for a scientific theory. Nothing I've read of yours (or what you claim you want to do) approximates it:

What makes a theory scientific? Or, what distinguishes science from non-science? (The demarcation problem.) Initial proposals:

(1) Science offers explanations.
(2) Science is objective.
(3) Science is descriptive.
(4) Science makes predictions.
(5) Science proceeds from observation.

The trouble with the initial proposals: they don’t do any distinguishing.


Popper

The following is the wrong answer to the demarcation problem: science is inductive; it proceeds by observation and experiment. Why is that the wrong answer? Non-scientific theories can be based on observation and experiment, e.g., "…astrology with its stupendous mass of empirical evidence based on observation—on horoscopes and biographies.”

Popper’s 4 candidate theories:
(1) Einstein’s theory of relativity.
(2) Marx’s theory of history
(3) Freud’s psychoanalysis
(4) Adler’s individual psychology

Popper’s intuition: (1) is scientific, (2)-(4) not. Truth is not the issue. At the time, Popper didn’t believe that Einstein’s theory was true. Exactness also was not the issue. The appeal of (2)-(4): Their apparent explanatory power. Exposure brought about an “intellectual conversion” and confirming instances of the theory were seen everywhere. Indeed, nothing seemed to count as disconfirmation, as evidence against the theory. Every observation could be interpreted in light of the theory.

The difference with respect to (1)— Einstein’s theory: The theory makes risky predictions, predictions which, if false, sink the theory. Einstein’s theory has the result that light, like material bodies, is attracted by heavy bodies such as the sun. This led to the prediction that the light from certain stars—those which appear in the night sky as close to the sun—would appear, if observed in daylight, as slightly shifted away from their normal position, slightly further away from the sun.

This prediction can’t be tested in ordinary circumstances because of the sun’s brightness. But during an eclipse one can take a photograph of a star’s apparent position in the daytime sky. And then photos of the star taken in the day and in the night can be compared and its apparent distance from the sun can be measured. This is just what Eddington did. And the prediction of Einstein’s theory was shown to be correct. The significance of this, acc. to Popper: Einstein’s theory, unlike (3)-(4), is incompatible with certain possible results of observation.

In other words, Einstein’s theory is refutable or falsifiable (the term that has stuck). It is possibly false. If our observations had been different, it would have been shown to be false (though they weren’t and it wasn’t). This, then, is Popper’s solution to the demarcation problem: A theory is scientific just in case it is falsifiable.

Truth is not the issue for Popper. Accordingly, his solution to the demarcation problem doesn’t make being true a criterion for being science. Theories that are true may be falsifiable. But, equally, theories that are false may be falsifiable as well. Some consequences and corollaries of Popper’s solution to the demarcation problem:

Theories not falsifiable by any conceivable event are not scientific. (Thus, the naïve view that science strives for irrefutability gets things exactly the wrong way around.) Every good scientific theory is a prohibition--it denies that certain things may happen. A test of a theory is an attempt to falsify it. “Confirming evidence” is too easy to come by and should only count towards the acceptability of a theory if it is the result of an attempt at falsification.

Some genuinely falsifiable theories, when falsified, are maintained by their admirers either by re-casting the theory or adding auxilliary assumptions. Such a procedure is always possible, but it rescues the theory only by destroying or reducing the theory’s claim to scientific status. (Popper calls such rescue operations conventionalist twists.)

Who passes the falsification test?
(1)—Einstein’s theory of relativity—passes. It makes risky predictions (re: the apparent positions of stars, e.g.) Astrology fails. Vagueness of its predictions makes it unfalsifiable.
(2)—the Marxist theory of history—fails. It once passed, but it was given various conventionalist twists.
(3) and (4)—the psychoanalytic theories—fail. No conceivable bit of human behavior could refute them. Non-science but not unimportant. Analogy with primitive myths. These myths often shape later science (the ancient Greek examples).

 

[saviourmachine]

Only explanations by hard analytical science count

Essentially what I said was, if hard analytical science cannot explain it, then no valid explanation exists.

What is valid, what is valuable? Everything hard analytical science can explain nowadays? Everything hard analytical science can explain somewhere in the future? How do you know what will be explainable sometime?

I read through your linked post. What did catch my attention was:

• "A correct analysis should include all possible answers." If that is possible. That's a belief in mental (or even linguistic) reductionism (the physical plane can be mapped to the mental plane).
• "Work out logical consequences." with which logic system? S5?
• "When we find a difference [in a theory], all we have to do is look at reality and see which consequence actually occurs." If there is sufficient and obtainable data.
• "Existence of meaningless questions." If it is possible to decide what is meaningfull and what not. If the subjective viewpoint of mankind (or the individual) doesn't influence what is meaningfull.
• The frequent use of 'possible'. That falls in the realm of potentiality, not of reality.

And I've a few questions.

1. Do you think that the ambiguity in language doesn't have a function?
2. Do you think that it's impossible to have ambiguity in physics itself? That never different valid answers can be found in nature?

What is valid?

 

[Seafang]

You've missed the point. I wouldn't expect you to cite peer-reviewed academic journals, I just expect you to make your case. Often that does require a bit of evidence, but at the very minimum it requires a poster to demonstrate there are sound reasons for a stated opinion.

Just stating "The universe absent humans has no morality or ethics or religion or philosophy or anything abstract," or "MAN created GOD; not the other way around!" is saying nothing. Why should anyone care about what you think, and even if we did, how are we supposed to answer you? All someone can say is "Oh yeah, well God created man, naaaaaaaaaaaaaahhhhhh , so there!"

If this were an "opinion" forum, then you could just drop in, lay your egg, and that would be it. But it is a philosophy area in the midst of a science forum! Call-in radio talk shows, or the General Discussion area here at PF are the places for unsupported opinions, not in philosophy (I wouldn't try it in any of the science forums either). No, tell us why your statements must be true, what facts support them, etc., and then we have the basis for a discussion.

And here I thought the question was;- "Can everything be reduced to pure physics?". I don't see any mention of philosophy there.

At what point does an OPINION become a FACT? Is it when every sentient being in the universe; known or unknown, accepts it as his opinion, that makes it into a fact, or is just a plurality, or a majority, or some other quorum of opinion holders who turn opinions into facts.

The history of science is replete with examples of facts that turned out to be not facts; well in most people's opinion. I think they call it consensus or something like that. Is it a fact if the National Academy of Sciences says it is a fact, or is that just the opinions of a private club of individuals who self select their membership; which tends to be exclusive of dissenting opinions as to what the facts really are.

But to get back to one statement I made, which yes is my opinion; that MAN created GOD, there is plenty of historical evidence for that. The histories of social groups and cultures dating back to the dawn of history contain evidence of ordinary individuals essentially enslaving their fellow folks, and subjugating them to a life of fear and obeyance based on ignorance and fear of the unknown.

The manipulation of other people through fear is as old as history, and the number of 'gods' created in these endeavors, is as numerous as the different cultures of history and geography. One thing entirely missing from the concept of these 'gods' is any notion of universality. Even today, some presumably intelligent cultures have numerous gods all of which they created. And they all seem to have the purpose of enforcing compliance with preferred behavior.

Now all of that is simply my opinion based on my observations of people's behavior and my readings of their history and the behavior of their ancestors. None of that makes it a fact, because there will always be those who disagree, and disagreeing with someone else's opinion is a necessary and sufficient condition for an opinion not being a fact.

So perhaps there are NO facts, merely a consensus of opinion.

 

[Doctordick]

Do you like ambiguity?

Well "saviourmachine", my first impression on reading your post was that it was "Harv" (a pseudo intellectual from Chicago I am familiar with). When I discovered that you had only made 57 posts, I read them all (as I have no interest in responding to Harv). Actually, you sound like a very rational person and, barring my disillusionment, I think we could have an interesting conversation. My first comment is to point out that "only explanations by hard analytical science count" is not what I said though the position does receive a lot of support from my proof.

My second step is to first discuss your ending questions.

Do you think that the ambiguity in language doesn't have a function?

Yes, in the interactions of human beings, it has a very significant function. It allows them a great range of ambiguity in their dealings with one another. Without it many institutions essential to civilization might not even exist. Now, we could spend our entire lives discussing the "good" and "bad" aspects of that. Some people enjoy the freedom to quibble (it seems to me it drives most of the posts on this forum). In fact, that's why I thought you might be Harv. One very significant aspect of that ambiguity is that it prevents communication.

One of the excellent consequences of preventing communication is the fact that it is impossible to communicate beliefs from one generation to another. Misunderstandings will invariably occur and, in an attempt to make sense of what they think the previous generation is saying, new unique perspectives will arise. Without that ambiguity I suspect intellectual advancement would soon cease.

Do you think that it's impossible to have ambiguity in physics itself? That never different valid answers can be found in nature?

If you think what I said implies that, I have entirely failed to communicate my thoughts to you. In fact, my position is entirely opposite to that position. I am of the opinion that the entire scientific community has failed to take into account alternate interpretations of the "facts" they are trying to explain.

What is valid, what is valuable? Everything hard analytical science can explain nowadays? Everything hard analytical science can explain somewhere in the future? How do you know what will be explainable sometime?

Aren't these exactly the questions the scientists should be asking themselves? Shouldn't they do their best to take these issues into account in their perspective of the problem they are trying to solve? That is my position; I became a pariah in the physics community because I felt these issues were more important than "current research".

"A correct analysis should include all possible answers." If that is possible. That's a belief in mental (or even linguistic) reductionism (the physical plane can be mapped to the mental plane).

I think you are taking advantage of the ambiguity of language to misrepresent my position. How did "reductionism" get into my position that no possibilities should be omitted? Is it really your position that, in order to avoid being "reductionist" one must omit some possible answers? If so, would you clarify what answers you want to omit?

"Work out logical consequences." with which logic system? S5?

Aren't you referring the need for reducing ambiguity here? Or is this rather an attempt to use ambiguity to avoid thinking? I would suggest that, if you have an issue you want to explain to me, you come up with the logic system you would like to express yourself in and then explain it to me. Hopefully we can reduce the ambiguity to a level where I can understand you. If not, well, that's life; some things are very hard to communicate.

"When we find a difference [in a theory], all we have to do is look at reality and see which consequence actually occurs." If there is sufficient and obtainable data.

Isn't the existence of "sufficient and obtainable data" part of reality? Or are you using ambiguity to muddy the waters? Apparently the only complaint you have concerning looking at reality arises from the same source.

"Existence of meaningless questions." If it is possible to decide what is meaningfull and what not. If the subjective viewpoint of mankind (or the individual) doesn't influence what is meaningfull.

Even if it does my position is still valid! What is meaningful and what is not is very sensitive to what you know and what you don't. If the information necessary to answer a question cannot possibly exist in your view of reality, I think the question can easily be labeled "meaningless". It is little more than definition of the term. Almost all your complaints rest entirely on the existence of ambiguity. And I have no argument with that issue at all. It is a problem we have to deal with and I think I know how to deal with it. However, it still stands as a major barrier in trying to communicate my ideas: i.e., English is very ambiguous mode of communication; particularly with people whose interest is not in understanding.

The frequent use of 'possible'. That falls in the realm of potentiality, not of reality.

So, if you don't want to consider all possibilities in a hard scientific attack, explain to me how you, in your great authority, decide which possibilities should be ignored. Again, I really get the feeling you are using the ambiguity in communications to avoid thinking.

What is valid?

Which this question simply verifies! If you were really trying to be clear, you would realize that it is exactly your definition of "valid" which provides you with the mechanism to defend omitting those unrealistic possibilities you are accusing me of improperly including. Again we are talking about the ambiguity of the English language; there are many definitions in English which are not at all clear. But, as I said earlier, life is tough. At the moment we have little else to use in our communications.

You said you read the post I referenced. Again ambiguity raises its ugly head. What I said was:

If you really are interested, I suggest you take a look at the "What is Evidence" thread starting with my post at:

https://www.physicsforums.com/showth...1146#post441146

If you can follow my comments there and understand why I made them, there is a good chance you could follow the proof.

What I meant was for you to read the thread (or at least my posts), not just that single post. Of course, if that is too much for you I will accept it.

Have fun -- Dick

 

[Fliption]

But to get back to one statement I made, which yes is my opinion; that MAN created GOD, there is plenty of historical evidence for that. The histories of social groups and cultures dating back to the dawn of history contain evidence of ordinary individuals essentially enslaving their fellow folks, and subjugating them to a life of fear and obeyance based on ignorance and fear of the unknown.

I don't think this is necessarily untrue Seafang. But the fact that man has created gods doesn't say anything about whether god exists separate from the efforts of man. Your initial comments seemed to bridge the two. We obviously cannot prove or disprove the latter.

 

[saviourmachine]

Hi Doctor,

"Ambiguity prevents communication", so you say, and "without ambiguity [from one generation to another] intellectual advancement would cease". That has more nuances than I could find in the thread you linked, sorry that I couldn't find that at first sight.

I agree with you with posing many answers to a question, trying to falsify them and so on. If there is ambiguity in physics itself, and science would find a way to handle that, it would be fine. I hope science will continue to pose (non-)standard answers.

That is something I hope for, not where I believe in. I am afraid that the current scientific way to look at things is too immature, that I've been born too early. For example, I am looking at the moment to definitions as: phonetics, phonology, morphology, syntax, semantics, pragmatics, lexicon, prosody, syllable, that all are defined (in different ways ) in linguistics, but without taking in consideration sign languages or iconic* languages.

IMHO ambiguity has to be reduced generally, but not at all costs. And probably it will turn out, not to be possible either. Therefore we do have different logical systems, different physical theories, different opinions about self-arising systems and so on.
If I "use ambiguity to avoid thinking"? Maybe... I point to the plurality of opinions, theories, systems in advance, but when I've time, I try to go into depth.

* see thread on EvC forum (link), actually, I am looking for a linguistic forum

 

[quantumcarl]

How true is the claim that everything in the whole universe can be explained by Physics and Physics alone? How realistic is this claim? Does our ability to mathematically describe physical things in spacetime give us sufficient grounds to admit or hold this claim? Or is there more to physical reality than a mere ability to matheamtically describe things?

The only way to describe our physical universe is by way of our experience of the physical universe which is often termed physics.

Even biology, psychology and other disciplines rely soley on physics for their very existence. Without the intracate mechanisms that arise from a physical existence no other science or study could exist.

I will even further suggest that ethics is governed by physics. I've seen the equations and they make sense. If I must I will dig them up for you. But there are parallels in physics with ethical philosophy that leave little room for anything other than a strong suggestion of a governance of physics.

To site the numerous conjectures that claim higher powers have created and control existence in the physical universe is easy until you try to prove the contention.

The fact is that even if there are non-physical entities doing their dambedest to run the physical we cannot study them for the simple fact that we are physical and our physical nature would pollute our study results of the non-physical.

In conclusion I believe the zen approach is the best way to try to get a full understanding of whatever the universe throws at us... including spirit or non-physical realities. That approach entails studying, with great discipline, that which we have in front of us. Studying that which we can observe. Studying it until we know it like we know our own breath. Then, there will come a moment when we may have a glimpse of understanding with regard to other matters... or non-matters!

 

[loseyourname]

Even biology, psychology and other disciplines rely soley on physics for their very existence. Without the intracate mechanisms that arise from a physical existence no other science or study could exist.

Come on, that doesn't even answer his question. Do physicists really believe this? The entailment of other sciences by physical phenomena doesn't mean that an appeal to physics is enough to explain living systems. You can describe the quantum states of nucleotides, but is that really a good explanation of natural selection? Or is it better to say 'abundant population, scarce resources, leading to survival of the fittest?' Which approach gives us more useful information?

 

[quantumcarl]

Come on, that doesn't even answer his question. Do physicists really believe this? The entailment of other sciences by physical phenomena doesn't mean that an appeal to physics is enough to explain living systems. You can describe the quantum states of nucleotides, but is that really a good explanation of natural selection? Or is it better to say 'abundant population, scarce resources, leading to survival of the fittest?' Which approach gives us more useful information?

Come on yourself.

If you look at the evolution of matter it is a macroscopic blueprint that matches the evolution of the neucliotide or the evolution of anything for that matter. Philosophically speaking.<p>The study of ethics is, in effect, a study of physics. Just type into Google something like "the physics equation of ethics". Another search that turns up some rare and cool stuff is this phrase "the physics equation for Karma". It gets very spooky but I have the confidence that you will approach it with an open mind.

 

[loseyourname]

Come on yourself.

If you look at the evolution of matter it is a macroscopic blueprint that matches the evolution of the neucliotide or the evolution of anything for that matter. Philosophically speaking.<p>The study of ethics is, in effect, a study of physics. Just type into Google something like "the physics equation of ethics". Another search that turns up some rare and cool stuff is this phrase "the physics equation for Karma". It gets very spooky but I have the confidence that you will approach it with an open mind.

"Evolution of matter" hardly does the process justice, which is exactly my point. I really can't think of any way to explain why one type of gene proliferates rather than another without reference to how its phenotypic expression fits into a certain environmental niche, can you? There are certainly equations in population genetics (Hardy-Weinberg comes to mind), but they are not physics equations. Even reducing evolutionary biology entirely to molecular biology causes us to lose crucial information. There are phenomena in the world that are just emergent, and cannot be comprehended entirely by an appeal to their lower-order constituent pieces. These are discussed frequently around here, the latest being autocatalytic processes in chemistry and the non-linear dynamics of complex systems.

I'm not going to look at your example of karma and ethics, because they don't concern me for the purposes of this thread. I'm just bringing up other sciences that cannot be reduced to physics.

 

[Doctordick]

Yes, one could talk a long time on the nuances of ambiguity; but what purpose would the discussion serve since, in all probability, anything one could say would be ambiguous. The most general service ambiguity serves is that it allows idiot savants to appear rational: i.e., you can usually find an interpretation which makes some sense. I personally think there is a good approach to AI in there somewhere.

I agree with you with posing many answers to a question, trying to falsify them and so on.

I am afraid that is not what I am trying to get across here. As I said, usually finding a single answer is so difficult that coming up with one is difficult enough. All I was doing in that post was pointing out that I was no more than restating the standard scientific method to bring attention to these issues. What I am talking about is the importance of creating methods of attack which will keep one's options open. I have a method of doing that I would like to communicate; but, I can't find anyone reasonable enough to follow my thoughts.

If you read that thread, you should have looked at my post on the differences between "squirrel thought" and "logical thought". I made that post over six months ago and it hasn't generated a single response either supporting or rejecting my position that the division is significant. I can only assume that no one who read it had any comprehension of the issues I was confronting. Without understanding those issues, it is not possible to think about mechanisms to get around them.

I had thought "honestrosewater" was at least trying to understand (based on the last response to my earlier post) so I tried to make the next step in my presentation. See my post at:

https://www.physicsforums.com/showthread.php?p=447328#post447328

All of this was to get down to one very simple statement: the first thing I want to define is, "the field of mathematics".

Maybe I should have said, "put mathematics forward as a defined thing". I thought I had made the step clear!

I leave your understanding and facility in that area entirely to your personal "squirrel thought" capabilities. That is, I am essentially assuming that statements I make in mathematics are communicable; the procedures and relationships so expressed are "equivalent" in your world view and mine in spite of the fact that there might actually exist an alternate interpretation of that collective set of concepts and relationships. (And, if there are inconsistencies, people much more qualified than I am are already working hard to straighten it out.)

Apparently no one understood why I went to the trouble to put what I said the way I said it. At least no one has responded to the post.

The issue is that we don't want to throw the baby out with the bath water so to speak. If we are going to communicate we must establish a set of tokens as unambiguous as possible and this most definitely requires us to depend on squirrel constructs (meanings which are established by intuition and impossible to check). Thus I begin by officially recognizing mathematics as the most unambiguous collection of symbols, procedures and relationships available to us. Very through men have spent thousands of years trying to make sure it is internally consistent .

I chose that as my starting point in order to clarify the fact that, even when it comes to mathematics (a field taken by most to be the very essence of exact), the fundamental issues of "logic", "common sense", "belief" and "knowledge" arise. This arises because it is based, as is everything, on "squirrel thought": the fundamental source of our beliefs. If the subject is mathematics, humanity has a more consistent belief set than any other field. In fact, most people cannot even comprehend the idea that an alternate interpretation of the field of mathematics might exist.

You should be able to comprehend that the fact that you cannot think of a totally consistent alternate interpretation of something is no evidence that such a thing does not exist.

This is a specific, small but reasonable, example of the mechanisms I use to keep the important aspects of the situation open in spite of the fact that I have no alternate interpretation to offer.

I don't believe anyone on the forum has the slightest idea of what I am talking about. I do not know if the problem is their simple failure to pay any attention to what I say or an overwhelming desire to feed their egos by spouting ambiguous comments which hide their inability to think about it. I do note that a lot of people read the threads without posting. Perhaps one of them will eventually speak up. After all, you did. :!)

IMHO ambiguity has to be reduced generally, but not at all costs. And probably it will turn out, not to be possible either. Therefore we do have different logical systems, different physical theories, different opinions about self-arising systems and so on.

I am not arguing with you at all. All I am trying to do is lay out as unambiguous set of definition I can in order to present a very subtle argument in a very exact way.

I have looked at the forum you referred to and read a substantial number of the posts. I am afraid I found little which would interest me. I am an old man and my mental abilities are already beginning to deteriorate significantly. Many things which I found easy to think out forty years ago severely tax my attention now. I wish you luck in finding intelligent conversation. At least more luck than I have had.

In conclusion I believe the zen approach is the best way to try to get a full understanding of whatever the universe throws at us... including spirit or non-physical realities. That approach entails studying, with great discipline, that which we have in front of us. Studying that which we can observe. Studying it until we know it like we know our own breath. Then, there will come a moment when we may have a glimpse of understanding with regard to other matters... or non-matters!

The whole field of "zen" illustrates the power of what I refer to as "squirrel thought". I would have called it "zen thought" except for the fact that the conotations of "zen" include not a touch of the fact that the correctness of zen cannot be proved and that is an important point when it comes to exact science. See the following and think about zen when I talk of "squirrel decisions":

https://www.physicsforums.com/showthread.php?p=222763#post222763

Have fun -- Dick

 

[freemind]

If I understand Kurt Godel's Incompleteness Theorem correctly (which I probably don't), it states - hand-wavingly - that mathematics is not a 'closed-consistent' system, that something beyond it is required for consistency. I'm thinking this is the reason why the universe cannot be explained purely by physical laws and properties. Or am I gravely mistaken?

 

[Canute]

Not gravely, but perhaps slightly. What he showed is that no formal system of mathematics (or whatever, given the usual provisos) can be shown to be consistent unless it is incomplete (and so may in the end turn out to be inconsistent). This does have metaphysical/cosmological implications, some of which Goedel explored himself, but I don't think it quite shows that the universe (everything) cannot be explained by physical laws and properties.

Rather, it shows that the universe cannot be completely and consistently explained full stop. Perhaps it would be better to say that the universe cannot be modeled/represented completely by a consistent formal system of symbols, or modeled/represented consistently by a complete formal system of symbols. This is, for instance, what Stephen Hawking concludes. It is what many people have been saying for the last three millenia.

 

[saviourmachine]

Scientific method

I was no more than restating the standard scientific method to bring attention to these issues.

So, okay, let us use the hypothetico-deductive method. And you want it to refine it according:

My perspective puts major emphasis on existence of alternate answers and the existence of meaningless questions, two issues not seriously considered in the standard perspective.

Squirrel & Logical thought

"Logical thought" cannot solve the problem because "logical thought" is far too limited to encompass the totality of relationships involved. And "squirrel thought" cannot solve the problem because there exists no way to validate "squirrel thought". The solution can only be achieved through intimate cooperation between the two modes and that has to be done with full knowledge of the range of errors possible in each and a way of handling those errors such that the consequences are minimized (hopefully eliminated).

I am very interested in your ideas about how to address scientific problems in both these modes.

Mathematics as language

Maybe I should have said, "put mathematics forward as a defined thing". I thought I had made the step clear!

You may use mathematics as mean to formulate statements and assume I understand them as you do. Yes.

Unclear

In fact, most people cannot even comprehend the idea that an alternate interpretation of the field of mathematics might exist.

I don't really understand what you want to say by this. Do I belong to that group of people?

 

[Doctordick]

You sound very rational to me!

I don't really understand what you want to say by this. Do I belong to that group of people?

I am not surprised and you shouldn't be embarrassed. The issue is actually quite simple. Everything we know arises from accepted truths generated by our intuition, zen comprehension or, as I call it "squirrel decisions". Everyone who has thought about this seriously admits that there exists no proof that these "truths" are true; they are merely "self-evident" which really means that we cannot comprehend them being false.

Now, anyone familiar with the history of science is aware that the fact that we cannot comprehend something does not stand as a proof that it cannot be. There are lots of well understood phenomena today which our ancestors would have found incomprehensible. I can tell a number of stories on my grandmother (bless her soul). The point is that the only truth we can really stand behind is, none of us really "know" anything. Even mathematics must be included in that category. I personally cannot comprehend that the rules and relationships which constitute mathematics could be interpreted in a manner different from the way I see the field but I must (if I am to be exact) hold open the possibility that there could be such an interpretation.

Meanwhile, I will use mathematics as I understand it because I am confident that I will obtain almost universal agreement with any conclusions I can deduce consistent with that field of endeavorer.

Thus, if you agree with my definition of mathematics (that is, the symbols, operations and procedures commonly referred to as mathematics) we can consider the entire field to be, for all practical purposes, a well understood vocabulary (one must comprehend that communication is the central issue of everything). As I have said earlier (on a number of different occasions) I consider mathematics to be the invention and study of internally consistent systems. If you spend much time talking to professional mathematicians that seems to be very much the criteria they use to determine if a set of operations and/or relationships should be admitted into their field. Contrary to what a lot of people think, mathematics is not a closed and settled field; new research into new possibilities occurs every day.

Now, that paragraph is there because it clarifies something brought up by a great many scientists (including some held in great respect for their deep insights into how the universe functions). From time to time many scientists will ask why it is that mathematics, a construct purely created from the human mind, should play such an important role in exact sciences (another seemingly deep philosophical question). If one understands exactly what mathematics is all about (internal consistency if you have forgotten) then this question almost answers itself.

The single most important characteristic of any explanation of anything is that it answers some question. That is, it provides the person who understands the explanation a way of reaching an answer of some kind. If that procedure yields different answers depending on the persons path through the explanation then the explanation fails in its basic purpose: it fails to answer the question the explanation was created to answer. Now don't get confused here. The answer need not be a definitive prediction; the answer might be, "sometimes this occurs and sometimes that occurs". There is nothing inconsistent about not being able to make a specific prediction. On the other hand, if one path through the explanation yielded "'A' will definitely occur" while another approach (using the same explanation) yielded "sometimes 'A' will occur and sometimes 'B' will occur" then the explanation has failed in its purpose as it gives two different answers to the same question. What I am getting at here is the fact that "consistency" is also the central requirement of any acceptable explanation of anything.

If mathematics is the creation and study of self consistent systems, and usable explanations must be self consistent systems it becomes self evident (i.e. very difficult to comprehend being false ) that the only reason an explanation does not use mathematics is that the required mathematics has not yet been invented. It is important that this relationship between "mathematics" and "an explanation" be kept in mind at all times.

If what I have said above is understood, there is an area of mathematics which I need to make sure you understand clearly. The area is related to the concept of symmetry; an issue not clearly understood by a lot of professional scientists in spite of the fact that it is central to the most fundamental principals of physics.

I appreciate your interest and am looking forward to further exchanges. If we agree that what I have so far said makes sense to you and is consistent with your concept of reality, I will continue this discussion with an analysis of the power of symmetry considerations. Symmetry consideration are important as they are the only arguments which can generate truths from ignorance. (In actual fact, they can appear to generate truth from ignorance, a subtlety different statement which I will attempt to make clear).

I appreciate your attention very much -- Dick :!)

 

[Philocrat]

The only way to describe our physical universe is by way of our experience of the physical universe which is often termed physics.

Most philosophers have a problem with 'Experience'. One of the standard charges against Physicalism/Materialism (especially with regards to Explanation, Meaning and Truth) is that Experiance cannot be completely trusted. Your senses can transmit into your conscious expereince false information. Equally, the products of your thinking or reason such as Propositions and beliefs are capable of being false. Hard facts: the products of experience affect all disciplines in philosophy (Epistemology, Ethics, Philosophy of Mathematics, Formal Logic, Philosophical Logic, Philosophy of language, Metaphysics, Philosophy of Science, etc)

At what point does an OPINION become a FACT? Is it when every sentient being in the universe; known or unknown, accepts it as his opinion, that makes it into a fact, or is just a plurality, or a majority, or some other quorum of opinion holders who turn opinions into facts.

The history of science is replete with examples of facts that turned out to be not facts; well in most people's opinion. I think they call it consensus or something like that. Is it a fact if the National Academy of Sciences says it is a fact, or is that just the opinions of a private club of individuals who self select their membership; which tends to be exclusive of dissenting opinions as to what the facts really are.

Yes, substantially, you do have a point here. Yet, this needs to be put in clearer context:

a) Yes, there are many truths we now rely upon that started originally as ordinary opinions. There are several instances littererd about in the human history to at least indicate this. The perfect examples are all the disciplines that started as speculatory parts of Philosophy. As Bertrand Russell observed in 1912, as soon as any aspect of philosophy found practicality of some sort in the human experience, it systematically and seminally detaches itself from philosophy to establsih itself as separate self-sustaining discipline in its own right. I had a conversation with Les or someone else about this earlier on this thread. I am not quite sue whether Russell implied that aspects of philosophy detache themselves, leaving their opinionated and speculatory status behind, as soon as they find themselves or their truth-values to be materially and adiquately verifiable and consitent with what experience throws at us the perceivers. This suggests that we do have the capacity to know, even if it means starting from the point of ordinary commonsense and opinion, up to higher level of perceptual and intellectual rigour. Yes, it is undeniable that we do know at least enough to get us by in life, even while it is not 100% so!

b) Yes, equally, we do have many opinions and theories that we were very confident of as true and unfalsifiable, which eventually turned out to be false. This is typical of many theories in the sciences, and most importantly, countless ones in other disciplines that science rigorously examined and rendered them false later on in the human intellectual development. The perfect example of this are diseases that used to be ignorantly thought to be caused by witchcrats and evil demons of which we now have clear and undisputed scientific explanations for them. Even the incurable diseases that exist today, we have at least some good explanation of their causes, even though we are still searching for their cures. Upon the same token, we now know beyond doubt that the Earth is not flat as it used to be ignorantly thought and believed earlier in the human existence.

So far, all well and good,... but we still have to find some explanation as to why the sum totality of the human ability to perceive things in the physical world, evaluate them by means of thinking and explain them not only to ourselves but to others, tend to fluctuate between possibility (a) and possibility (b). Why are some things difficult to know? Is it the things themselves that are making themselves difficult to know? Or is it us, the perceivers, that have the problem of knowing? The fundamental issue that confronts us now is not to confuse issues and pretend that human beings are so blind and perceptually disadvantaged that we are incaplabe of knowing anything. I am always filled with utter disgust and horror when people go down this road of trying to degrade the human perceptual capacity to a point where it starts to look as if though we are incapable of knowing anything. As far as I am concerned this is logically and quantitativelly impossible. I am claiming that it is impossinle to render human beings perceptually useless while such human beings are claimed to exist. Even if I were an ordinary inanimate toy, I cannot say anything about myself and not exist. Leave that problem to stones! From the human sperspective, the most intelligible thing to do now is to do stock taking of the following things:

1) Make an estimate of 'WHAT WE ALREADY KNOW'

2) Make an estimate of 'WHAT IS KNOWABLE THAT IS YET TO BE KNOWN

3) And weigh against 'WHAT IS UNKNOWABLE THAT IS YET TO BE KNOWN

Well, someone once suggested to me and argued that (3) is irrelevant because if anything is unknowable, then it is irrelevant to the human existence. Well, I leave that one to everyone's taste. What do you guys think about this one. Is this a correct line of reasoning?

 

[Philocrat]

But to get back to one statement I made, which yes is my opinion; that MAN created GOD, there is plenty of historical evidence for that. The histories of social groups and cultures dating back to the dawn of history contain evidence of ordinary individuals essentially enslaving their fellow folks, and subjugating them to a life of fear and obeyance based on ignorance and fear of the unknown.

I think Flipton's distinction between the notion of 'Man being the creator God' and a totallly independent fact that 'God may exist' (that needs to be epistemologically demonstratd) gives a clearer picture of what you were trying to do. Infact, many philosophers that I know would not lose sight of this distinction. They will always keep them seperate. When you hear people saying that philosophers do not believe in the existence of God, all that this means is that philosophers do so technically...from purely the point of view of Logic. Yet, there are many philosophers that do not rule out the possibility of God completely. Infact, depending on what type of logic you are versed in, such possibility is not logically ruled out either, just as many epistemologically problematic issues in science are not logically ruled out on the same note.

Yes, people that you accused of creating their own Gods usually have some logicaly basis for their own arguments and beliefs as well. The most famous one is the so-caled 'DESIGN ARGUMENT' which states that:

'EVERY DESIGN HAS A DESIGNER'

According to these people, just like a chair or table has a maker or a creator, so has the physical world that we purportedly experience in every moment of the human existence. From my own examination of this point of view, I think it would be ill-advised and a fatal error for anyone to playdown its logical and resolving power. Yes, logically, there may be things that have always been there without possible creators, yet it is equally not logically ruled out that there are vast majority of things that were created by whatever means...and our physical world may be one of such created things. Nor neither is it logically ruled out that an independednt creative Agency may be respossible for bringing about our present world. The issue here seems to be that of misunderstanding and confusion over what type of creation that we are referring to or talking about:

1) Were some of these things SELF-CREATED (that is, certain things that had sufficient and efficient powers to do so)?

2) Were some of them RANDOMLY CREATED by some sort of interaction of a conglomeration of things that have always been wandering about a boundless and uncreated vacuum?

Or:

3) Were some of them created by a totally INDEPENDENT CREATIVE AGENCY that is structurally and functionally sefl-sufficient and efficient?

These are all likely possibilities that I personally do not see anyone qualified enough to completey logically destroy them. The question that I asked before now resurfaces here: (a) Are these things themselves that ingeniously hid thelselves away from the human perception and explanation?; or (b) Does the problem of perception and explanation of these things rest in the human beings themselves? Well, let me now admit for the first time that these two questions are precisely what I came onto PF to find out. If there is anyone out there who knows the answers to these two questions, let him or her table them now! For, as I have argued elsewhere, any attempt to find asnwers to these questions should trigger some sort of progressive thoughts and actions in us.

The manipulation of other people through fear is as old as history, and the number of 'gods' created in these endeavors, is as numerous as the different cultures of history and geography. One thing entirely missing from the concept of these 'gods' is any notion of universality. Even today, some presumably intelligent cultures have numerous gods all of which they created. And they all seem to have the purpose of enforcing compliance with preferred behavior.

Yes, controlling ourselves is crucial for sucessfull and peaceful co-existence. But the BIGGEST question that has confronted us since the advent of man is: HOW DO WE DO THIS? Many Political philosophers of all ages, from Plato to John Lokce, have all suggested the best ways for people collecting into a society to control themselves, yet none of these suggestions turned out to be sufficient, let alone efficient. One of the key arguments in philosophy is that if these political theories were sufficient and efficient, then one way we would be able to measure and know this is if there were no more misunderstadnings and conflicts in the societies concerned. But you know as well as I do that up to this very moment this is not actually the case. As much as we have managed to coexist and get on with life, we are still as confused and conflicts-prone as ever. We are still fightting and killing each other in hundreds of thousands, from character assassination and witch-hunting to brutal wars of WMD's scale.

Now all of that is simply my opinion based on my observations of people's behavior and my readings of their history and the behavior of their ancestors. None of that makes it a fact, because there will always be those who disagree, and disagreeing with someone else's opinion is a necessary and sufficient condition for an opinion not being a fact.

So perhaps there are NO facts, merely a consensus of opinion.

Everything we know today could not all amount to opinions only without some logically and consistently deduced facts from what we perceive of the world. At least some of what we perceive of the world must be and amount to concrete facts, otherwise it would logically and quantitatively imply that we are all blindly and non-directionally erring into oblovion. Life as a whole would be a meaningless, pointless venture in spacetime

 

[saviourmachine]

If we agree that what I have so far said makes sense to you and is consistent with your concept of reality, I will continue this discussion with an analysis of the power of symmetry considerations. Symmetry consideration are important as they are the only arguments which can generate truths from ignorance. (In actual fact, they can appear to generate truth from ignorance, a subtlety different statement which I will attempt to make clear).

Hi DoctorD, yes, it does all make sense to me. Mathematics as the study of (self) consistent systems.

If our dialogue does not infer with this very thread I appreciate further efforts to tell about symmetry in a scientific analysis (or in another thread if the other readers approve of that ). I know only about symmetry in the field of group theory, although that's quite extensive field already.

 

[Canute]

Unless a mathematical system is very simple then it cannot be shown to be self-consistent. Because of this I'm not sure it's correct to say that mathemtics studies self-consistent systems. Perhaps it's better to say that it studies systems which are as consistent as it can make them.

 

[Tournesol]

Concepts could have laws that are followed implicitly - Same as you have physical laws. If conceptual geometric forms (made of nothing at all) obey what we term physical laws - Reality still looks and feels and acts the same as the physical one you adhere to.

I can conceive of things that don't exist, and I can conceive of things
that don't follow physical laws, or follow different ones. Yet only certain things exist, and only certain laws are followed. So the physical
is at least a subset of the conceptual -- and a rather stubborn subset
that doesn't change into sonething else when you decide to think differently.

In a physical reality you have a couple of choices. Either the entire panoply , including the vacuum of space is composed of physical entities by which movement seems unlikely to be even remotely possible, or we have physical entities opposed by nothing at all, by which we differentiate those physical entities?

You seem to have some problems with the way the physical world works, although I am not at all celar what they are. But if you replace physical entities with concepts that work exactly the sme way, surely the same problems will re-occur ?

 

[saviourmachine]

A consistent framework

Mathematics as the study of (self) consistent systems.

Unless a mathematical system is very simple then it cannot be shown to be self-consistent. Because of this I'm not sure it's correct to say that mathemtics studies self-consistent systems. Perhaps it's better to say that it studies systems which are as consistent as it can make them.

1.) I used 'system' in the sense of 'framework'. 2.) I don't want to say that mathematics can prove consistency or not.

Creating an useful consistent framework
You see self-consistency as something that has to be shown / proved. I see mathematics as an analysis / method that creates frameworks that are consistent out of their very nature. Methods that result in inconsistent frameworks are generally not appreciated I think.

Creating an useful inconsistent framework
I am not aware of mathematics that is used to set up frameworks that are not consistent. If you know such kind of math, I am interested. Where can it used for?

-- Edit: I think this is exactly something I like. It's using a scientific manner to account for paradoxes. I already this a google on "Inconsistent Mathematics". Interesting.

 

[Canute]

I suppose there's more than one way of looking at this. But we know that mathematical systems (if by that we mean formal axiomatic systems of a certain complexity etc) cannot be both complete and consistent. If we try to complete such a system then we find we can only do so inconsistently. In this sense mathematical systems are inevitably inconsistent or inevitably incomplete, depending on which way you want to look at it.

Stephen Hawking discusses this online somewhere, and concludes that physics must remain incomplete, preferring this conclusion to the alternative. So it seems fair to say that mathematics studies inconsistent systems, although it would be equivalent to say that it studies incomplete ones.

However this is a minefield of a topic, so I wouldn't want to get into an argument about it. It's ever so easy to misinterpret the incompleteness theorem and maybe that's what I'm doing. Still, I agree with you about 'using the scientific method to account for paradoxes', which I take to mean using formal logic and reasoning to account for them. It's a fascinating pastime, since it's formal logic and reasoning that creates them. As I understand it this was Goedel's masterstroke, to turn logic back on itself to prove its own limitations by its own methods.

 

[selfAdjoint]

A consistent framework
1.) I used 'system' in the sense of 'framework'. 2.) I don't want to say that mathematics can prove consistency or not.

Creating an useful consistent framework
You see self-consistency as something that has to be shown / proved. I see mathematics as an analysis / method that creates frameworks that are consistent out of their very nature. Methods that result in inconsistent frameworks are generally not appreciated I think.

Creating an useful inconsistent framework
I am not aware of mathematics that is used to set up frameworks that are not consistent. If you know such kind of math, I am interested. Where can it used for?

-- Edit: I think this is exactly something I like. It's using a scientific manner to account for paradoxes. I already this a google on "Inconsistent Mathematics". Interesting.

Mathematical systems that are complex enough to contain full-bore arithmetic are incomplete. That is Goedel's theorem. This means any attempt to prove them consistent will fail in principle. This is a fundamentally different condition than being consistent but not having any proof yet of that fact. The word you should google on is not inconsistent, but incomplete.

 

[saviourmachine]

Definition mathematics
I'll give this definition: "Mathematics as the creation of coherent frameworks; with as few assumptions and contradictions (or none*) as possible." [I see assumptions and contradictions both as a kind of axioma.]

But to narrow down to: "Mathematics as the study of (self) consistent systems" is perfectly fine for me too. For the sake of the discussion with DoctorD.

Agreement of language to be used
I know Gödel's theorema. Who doesn't? I don't want to focus only on mathematics of complete systems. Again, for the discussion I only want to make clear that I accept DoctorD's language to communicate. I think your remarks - about that this language can't address everything - are important, but premature. We/I don't know what DoctorD wants to say yet.

Completeness & inconsistency

So it seems fair to say that mathematics studies inconsistent systems, although it would be equivalent to say that it studies incomplete ones.

This isn't true. The 'inconsistent mathematics' I mentioned is complete, because it embeds inconsistencies! Completeness and inconsistency is different from each other.
I hope you don't want to say that mathematics studies only inconsistent systems.

* self-consistent frameworks

 

[Canute]

I just meant that formal systems subject to the I-theorem are, at their best, either complete and inconsistent or consistent and incomplete. There's an ambiguity here for me about whether a system can be consistent even if we cannot prove within the system that it is, as Self-Adjoint seems to suggest, but I'm a bit unclear about that. I'd say not, but I'm happy to be corrected.

 

[Philocrat]

GUIDLINES FOR MATHEMATICAL STUDIES

Mathematics must make distinction between systems and formulate formal procedures for studying each type in isolation, and then finally state the fundamental relations between those sytems.

There are fundamantally three types of system:

(1) OPEN SYSTEMS

A system is Mathematically Open if it is structurally and functionally open to change (It may be internally and externally reorganised to something completely different, or both its internal and external relations may be rendered fully dynamic.

A matheamatical study of an open system must describe:

a) How things and events are LINEARLY distributed, actioned and correlated

b) How Things and events are RANDOMLY distributed, actioned and correlated

c) How to reconcile SIMULTANEITY with SEQUENTIALISM interplaying in an open system.

d) And how structurally and functionally progressive things and events can be created from LINEARLY and RANDOMLY distributed, actioned and correlated things and events in an open sytem.

(2) SEMI-CLOSED/SEMI-OPEN SYSTEMS

A system is mathematically semi-closed or semi-open if its possesses needs that are internally fulfilable (or self-fulfilled) and needs that are externally fulfilable. (I am making this definination as wide as possible to give every intellectual discipline access to it. Every discipline should be able to derive their own tighter but relevant definition from it)

A Mathematical study of a Semi-closed or Semi-open system must describe:

a) How things and events are LINEARLY distributed, actioned and correlated in the overall internal organisation of a semi-closed system.

b) How Things and events are RANDOMLY distributed, actioned and correlated in the overall internal organisation of a semi-closed system.

c) How to reconcile SIMULTANEITY with SEQUENTIALISM interplaying in the internal organisation of things and events in a semi-closed system.

d) How INTERNAL DEPENDENCIES are quantitatively and logically interfaced with EXTERNAL DEPENDENCIES (or simply, how a semi-closed system is structurally and functionally dependent upon external systems of equivalent or different nature).

e) How to FORMALLY but SUFFICIENTLY render a semi-closed system structurally and functionally closed (call this 'THE FORMAL PROCEDURE FOR PERFECTING A SEMI-CLOSED SYSTEM' if you like, controversial though this may seem).

(3) CLOSED SYSTEMS

A system is mathematically closed if its possesses neither needs that are exteranlly fulfilable nor needs that are externally desireable. It stays structurally and functionally closed and completely disconnected from everything outside it.

A mathematical study of a Closed system must describe:

a) How to reconcile SIMULTANEITY with SEQUENTIALISM interplaying in the internal organisation of things and events. And since it is externally disconnected from everything thing else, this remains the only problem for the mathematician to tackle.

NOTE: The Formal Mathematical Procedure must respect completetly the Engineering Principle of 'THE PERFECT FIT'. The Procedure must predict PARAPLEXES precisely engineered into a PRAPLEXED SYSTEM.

 

[selfAdjoint]

A matheamatical study of an open system must describe:

a) How things and events are LINEARLY distributed, actioned and correlated

b) How Things and events are RANDOMLY distributed, actioned and correlated

c) How to reconcile SIMULTANEITY with SEQUENTIALISM interplaying in an open system.

d) And how structurally and functionally progressive things and events can be created from LINEARLY and RANDOMLY distributed, actioned and correlated things and events in an open sytem.

An open system can't be nonlinear or deterministic? Where do you get these ideas?

 

[Philocrat]

An open system can't be nonlinear or deterministic? Where do you get these ideas?

Yes, I know that. I woke up early this morning, and sat there for hours trying to define it and couldn't, so I pulled a fast one as a means of inviting people to help me define it. I am not quite sure, but I think I may have succeeded in recognising that an open system is fundamental and different except that I can't define it. Well, I leave that one to you guys in the science community to define it. I do not mind being enlightened, So, please pardon me on this one.

 

[quantumcarl]

Dr.D.

Zen thought. One way to prove it to yourself is to try it.

I get these dimwits telling me I can't prove the sky is blue because when someone expresses their impression of an experience it is not valid proof of the experience. One has to experience things for one's self. That's as far as it goes. You can write papers and poll populations til the cows come home but none of what you recover will be admissable as proof that experiences happen etc.

What I suggested was to study that which one can observe. And, of course that would mean observing the laws of physics. Beyond that there is only what you can imagine exists.

In fact, its not entirely certain that the physical world is not just a large artifact of mass hypnosis and active imagination.

 

[CronoSpark]

How true is the claim that everything in the whole universe can be explained by Physics and Physics alone? How realistic is this claim? Does our ability to mathematically describe physical things in spacetime give us sufficient grounds to admit or hold this claim? Or is there more to physical reality than a mere ability to matheamtically describe things?

I am not sure if you are referring to everything as in everything including the past of the universe. Right now there is a possibility that physics might explain it. To boldly state that it can is something that is highly questionable.

Our own perception toward things in the universe may hinder our explanations.

If it includes the past, then if physics can prove that "something" can be produced by "nothing", then I would say yes it explains everything about the universe.

 

[Doctordick]

Hi saviormachine,

Actually, you need a better handle, like a nickname or such ! I am very glad to hear you have some knowledge of symmetries. My interest concerns an aspect of symmetry very seldom brought to light. For the benefit of others, I will comment that the consequences of symmetry are fundamental to any study of mathematical physics. The relationship between symmetries and conserved quantities was laid out in detail through a theorem proved by http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Noether_Emmy.html sometime around 1915. The essence of the proof can be found on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's web site[/URL]. This is fundamental physics accepted by everyone. The problem is that very few students think about the underpinnings of the circumstance but rather just learn to use it.

You will hear many professors simply state that "symmetry arguments are the most powerful arguments which can be made" without explaining what makes them so powerful. They usually give fairly simple examples and walk the student through, displaying the result as a self evident conclusion. These examples almost always begin with the phrase, "assume we have [such and such] symmetry". Notice the opening to John Baez's proof starts exactly the same way:

John Baez[/URL]]Next, suppose the Lagrangian L has a symmetry, meaning that it doesn't change when you apply some one-parameter family of transformations sending q to some new position q(s).

At least he tells you what he means by a symmetry. Symmetry is another of these things that is "understood" on an intuitive level without much thought.

What I would like to point out is that any symmetry is essentially an expression of a specific ignorance. For example, mirror symmetry means that there is no way to tell the difference between a given view of a problem and its mirror image: in effect you are in a state of enforced ignorance as to which view is being presented. Shift symmetry, the symmetry which yields conservation of momentum via Noether's theorem, arises if shifting the origin of your coordinate system has no impact on the nature of the problem: i.e., the information as to where the origin must be is unavailable to you. In a careful examination, every conceivable symmetry can be seen as a statement of some specific instance of ignorance.

The fundamental issue behind the power of symmetry arguments is the fact that information which is not available can not be produced by any algebraic procedure. It is a characteristic of mathematics that everything is deduced from a set of axioms; a proof amounts to a specific procedure which demonstrates that some piece of information is contained in a particular set of axioms. That being the case, how were we able to solve the problem above for specific expressions of q when changing q has no impact on the problem? The answer lies in Noether's theorem. There must be another relationship which relates the range of possibilities for q (the transformations Baez refers to) to the various specific solutions. In shift symmetry, this required relationship is conservation of momentum; in rotational symmetry, the required relationship is angular momentum.

The above can be seen as a means of obtaining information from ignorance. This is why it is called the most powerful argument which can be made. But let's think about that for a moment. Noether's theorem is a mathematical result and, as such, cannot produce anything which is not contained in the axioms. Ignorance cannot be the true source of our result; it must be arising from some other source. I will get into the real source of that result at a later date. For the moment, I want to get across the idea that symmetry is a form of ignorance. In many respects, Noether's theorem may be seen as a subtle result of conservation of ignorance.

There are about a half a dozen other fundamental observations (axioms ?) which I would like to get across before I step off into my proof.

Have fun -- Dick

 

[selfAdjoint]

Hi saviormachine,

Actually, you need a better handle, like a nickname or such ! I am very glad to hear you have some knowledge of symmetries. My interest concerns an aspect of symmetry very seldom brought to light. For the benefit of others, I will comment that the consequences of symmetry are fundamental to any study of mathematical physics. The relationship between symmetries and conserved quantities was laid out in detail through a theorem proved by http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Noether_Emmy.html sometime around 1915. The essence of the proof can be found on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's web site[/URL]. This is fundamental physics accepted by everyone. The problem is that very few students think about the underpinnings of the circumstance but rather just learn to use it.

You will hear many professors simply state that "symmetry arguments are the most powerful arguments which can be made" without explaining what makes them so powerful. They usually give fairly simple examples and walk the student through, displaying the result as a self evident conclusion. These examples almost always begin with the phrase, "assume we have [such and such] symmetry". Notice the opening to John Baez's proof starts exactly the same way:
At least he tells you what he means by a symmetry. Symmetry is another of these things that is "understood" on an intuitive level without much thought.

What I would like to point out is that any symmetry is essentially an expression of a specific ignorance. For example, mirror symmetry means that there is no way to tell the difference between a given view of a problem and its mirror image: in effect you are in a state of enforced ignorance as to which view is being presented. Shift symmetry, the symmetry which yields conservation of momentum via Noether's theorem, arises if shifting the origin of your coordinate system has no impact on the nature of the problem: i.e., the information as to where the origin must be is unavailable to you. In a careful examination, every conceivable symmetry can be seen as a statement of some specific instance of ignorance.

The fundamental issue behind the power of symmetry arguments is the fact that information which is not available can not be produced by any algebraic procedure. It is a characteristic of mathematics that everything is deduced from a set of axioms; a proof amounts to a specific procedure which demonstrates that some piece of information is contained in a particular set of axioms. That being the case, how were we able to solve the problem above for specific expressions of q when changing q has no impact on the problem? The answer lies in Noether's theorem. There must be another relationship which relates the range of possibilities for q (the transformations Baez refers to) to the various specific solutions. In shift symmetry, this required relationship is conservation of momentum; in rotational symmetry, the required relationship is angular momentum.

The above can be seen as a means of obtaining information from ignorance. This is why it is called the most powerful argument which can be made. But let's think about that for a moment. Noether's theorem is a mathematical result and, as such, cannot produce anything which is not contained in the axioms. Ignorance cannot be the true source of our result; it must be arising from some other source. I will get into the real source of that result at a later date. For the moment, I want to get across the idea that symmetry is a form of ignorance. In many respects, Noether's theorem may be seen as a subtle result of conservation of ignorance.

There are about a half a dozen other fundamental observations (axioms ?) which I would like to get across before I step off into my proof.

Have fun -- Dick

Good post. I have two comments.

1. What you have called ignorance could also be called indifference. In shift symmetry for example, there is no preferred place for the origin of our coordinate system. It is not the case that there is an origin around here somewhere but we don't know where it is; rather we can put the origin wherever we like and it won't make any difference to the physics.

2. There is an invisible elephant of assumed information in the whole Noether argument. That is that the Lagrangean works. This assumes that the "stationary action principle" describes the world, and that is not an obvious statement at all, and the original arguments for its ancestor the least action principle were theistic in nature.

 

[quantumcarl]

"Evolution of matter" hardly does the process justice, which is exactly my point. I really can't think of any way to explain why one type of gene proliferates rather than another without reference to how its phenotypic expression fits into a certain environmental niche, can you? There are certainly equations in population genetics (Hardy-Weinberg comes to mind), but they are not physics equations. Even reducing evolutionary biology entirely to molecular biology causes us to lose crucial information. There are phenomena in the world that are just emergent, and cannot be comprehended entirely by an appeal to their lower-order constituent pieces. These are discussed frequently around here, the latest being autocatalytic processes in chemistry and the non-linear dynamics of complex systems.

I'm not going to look at your example of karma and ethics, because they don't concern me for the purposes of this thread. I'm just bringing up other sciences that cannot be reduced to physics.

The subjects of all the physical sciences are physical. All things physical are governed by the laws of physics. Two of the most basic princibles involved in all the physical subjects of scientific inquiry are efficiency and conservation. These two princibles apply to natural selection, evolution and all other observable phenomena. Correct me if I'm off here!

 

[loseyourname]

The subjects of all the physical sciences are physical. All things physical are governed by the laws of physics. Two of the most basic princibles involved in all the physical subjects of scientific inquiry are efficiency and conservation. These two princibles apply to natural selection, evolution and all other observable phenomena. Correct me if I'm off here!

No, you're not off, but those two principles do not explain evolution. "Genes that result in phenotypes making an organism a better fit for whatever environmental niche it inhabits at any given time are selected for through differential reproductive success" better explains it.

There is also the problem of downward causation, a case of strong emergence, in which the parts of a system are constrained by the nature of the system, rather than the other way around.

 

[quantumcarl]

No, you're not off, but those two principles do not explain evolution. "Genes that result in phenotypes making an organism a better fit for whatever environmental niche it inhabits at any given time are selected for through differential reproductive success" better explains it.

There is also the problem of downward causation, a case of strong emergence, in which the parts of a system are constrained by the nature of the system, rather than the other way around.

A gene is modified by the trials and errors that are inherent in its interaction with the environment. The modifications take place during the sequence of the gene's production, reproduction and subsequent resulting generations. The outcome is that only those modifications will survive in the gene that produce a survival trait or have a benign influence on an organism. Any other modifications will result in the supression or elimination of the gene.

This reminds me of the way wind can wear away at sand leaving a natural sculpture of slightly compressed sand.