Can Everything be Reduced to Pure Physics?

**Les Sleeth** · May11-05, 06:12 PM

Originally Posted by Faust

It's interesting how the original question (Can Everything be Reduced to Pure Physics?) ended up as a debate on communication.

In my opinion, anytime you see a discussion about something as real as physics turn into a communication debate, then you know rationalistic philosophy has been dominating the dialogue.

Originally Posted by Faust

Perhaps it's only natural, since the meaning of the question itself is too obscure to have, in my opinion, any relevance. . . . Let's start with "can" . . . I won't even get into the mess of what "everything" is supposed to mean . . . Or what "reduced" means . . . Or what "pure physics" means . . . All in all, it's as the old Arab proverb says: "foolish questions beget foolish answers". Something like that.

I'm going to disagree with you a bit here. I know this is a long thread, but I think early on we established what the question was. It might have degenerated into a semantics battle, but up front I think most everyone was clear that:

"Can" meant is it provable.

"Everything" meant all that exists.

"Reduced" meant, can all that exists be accounted for at this time . . .

"Pure physics" meant physical principles only.

My analysis of the debate is that committed physicalists believe all existence can be explained/accounted for with physical principles alone, but the most honest of the physicalists admit that at this time they can't do it. Those more inclined to exaggerate what physics can explain tried to convince we skeptics physicalism is pretty much a done deal.

My mother didn't raise a dummy, so I ain't buyin' physicalist propaganda. I know, beyond any possible doubt, that physical principles at this time cannot be proven to explain all existence. Further, I doubt that they will EVER account for reality (with proof) in the future, but that's just my personal, unproven opinion. If it's done, then I'd have no choice but to accept the ugly truth

of physicalism.

May11-05, 08:38 PM

Originally Posted by Les Sleeth

In my opinion, anytime you see a discussion about something as real as physics turn into a communication debate, then you know rationalistic philosophy has been dominating the dialogue.

Wouldn't that be analytic philosophy?

I'm going to disagree with you a bit here. I know this is a long thread, but I think early on we established what the question was.

That may be the case, but it doesn't change the fact that the discussion did degenerate into a debate on communication.

My analysis of the debate is that committed physicalists believe all existence can be explained/accounted for with physical principles alone, but the most honest of the physicalists admit that at this time they can't do it.

It couldn't be different, given that you just stated what defines "physicalists" and "honest physicalists". Sorry for the little digression into semantics

I see a more important aspect to the debate though. The point is, over time physicalists have consistently triumphed over their opponents. If physicalists get a little arrogant sometimes, we must understand them, after all history is on their side.

Can you recall a single case where a physicalist account for a real phenomenon has been proven false? I wish I could remember one, but I can't.

Those more inclined to exaggerate what physics can explain tried to convince we skeptics physicalism is pretty much a done deal.

It probably is for them. And even though I'm not an enthusiast of physicalism, I do envy the fantastic success of their doctrine. I certainly wish we could have even a fraction of that success using different approaches; it would make for a far more interesting world but alas, hasn't happened so far.

I know, beyond any possible doubt, that physical principles at this time cannot be proven to explain all existence.

You are probably right, but I fail to see what the relevant consequences of that are. Besides the brawls between people in different philosophical camps, what can a neutral observer expect from the physicalist/anti-physicalist debate?

In other words, think of a person who's not into philosophy but is eagerly awaiting for the experts in their fields to find out truths about the universe: what would the failure of physicalism entail to that person? The possibility of miracles? Eternal life? Peace on earth?

I honestly fail to see what the fuss is all about. I would certainly be happy if everything could be reduced to pure physics if pure physics could give me happiness and eternal life in one way or another. Who cares if it's angels or subatomic particles? The ends justify the means.

If it's done, then I'd have no choice but to accept the ugly truth of physicalism.

What is that ugly truth? It's an honest question.

I believe in many things whose existence is denied by physicalists, but I don't see how those things are at odds with physicalism per se. Whereas some (not all) physicalists say "miracles can't possibly happen", I see physicalism as saying "if miracles do happen, then they can be explained". I find that a rather sensible position and, why not, even beautiful.

Of couse, I may be missing the point of physicalism for not being a physicalist

**Les Sleeth** · May11-05, 11:25 PM

Originally Posted by Faust

Wouldn't that be analytic philosophy?

No. Rationalism would be thinking without sufficient reference to observed facts. It assumes truth can be had by reason alone. Empiricism changed all that by requiring that what one supposes to be true has to be confirmed by experience/observation. So my point was that since rationalists feel little need to actually look at what they are philosophizing about, they tend to over-emphasize the language used in a debate.

Originally Posted by Faust

That may be the case, but it doesn't change the fact that the discussion did degenerate into a debate on communication.

A thread isn't just the end . . . it is all of it. You can pick some spot in almost any thread and point out how it's off topic. I was trying to suggest what most of the participants recognized as the issue here.

Originally Posted by Faust

The point is, over time physicalists have consistently triumphed over their opponents. If physicalists get a little arrogant sometimes, we must understand them, after all history is on their side.

Can you recall a single case where a physicalist account for a real phenomenon has been proven false? I wish I could remember one, but I can't.

That seems like a rather one sided view. Physicalists have not triumphed over anything outside their realm. What they have triumphed over is ignorant beliefs about the physical nature of the universe. They have not understood anything I know of about the meaning of life, how to be happy, how to realize the deeper things. Your admiration is like giving a golf pro all the credit for explaining a great athelete because he understands the principles of proper form. Physics explains mechanics, it explains form, it explains processes. Physics doesn't make one wise, loving, compassionate. . . but I suppose it all boils down to what one values most doesn't it.

Originally Posted by Faust

It probably is for them. And even though I'm not an enthusiast of physicalism, I do envy the fantastic success of their doctrine. I certainly wish we could have even a fraction of that success using different approaches; it would make for a far more interesting world but alas, hasn't happened so far.

I don't get your "envy." I have absolutely no hesitation acknowledging science as the best avenue for studying physical things. Where I balk is when those studying physicalness start to proclaim that's all there is. Well, is it really is a mystery when you look only at physicalness and then wonder why that's all you ever see?

Personally, I've had lots of success meditating. It doesn't stop me from being physical, but I do value the inner me more than anything I've ever done physically. I think it is more lasting, and far more satisfying. I can't see a single reason to envy anyone, but if someone has achieved deeper and more constant happiness than I have, then I hope he/she teaches me how to do it for myself. However, I don't see physicalists as instructive in this respect.

Originally Posted by Faust

You are probably right, but I fail to see what the relevant consequences of that are. Besides the brawls between people in different philosophical camps, what can a neutral observer expect from the physicalist/anti-physicalist debate?

Sincerity?

Originally Posted by Faust

In other words, think of a person who's not into philosophy but is eagerly awaiting for the experts in their fields to find out truths about the universe: what would the failure of physicalism entail to that person? The possibility of miracles? Eternal life? Peace on earth?

Personally? I am interested in how I can be fulfilled realistically and NOW. I couldn't possibly care less about miracles or eternal life.

Originally Posted by Faust

I honestly fail to see what the fuss is all about. I would certainly be happy if everything could be reduced to pure physics if pure physics could give me happiness and eternal life in one way or another. Who cares if it's angels or subatomic particles? The ends justify the means.

I don't think it's about what turns out to be true. The truth is the truth, I have no problem with that. But imagine you find yourself in a world run by accountants, and who insist all philosophy be accountant philosophy. Everything has to add up, everything has to balance, everything has to be fiscally sound . . . Is that an accurate, full representation of reality? Or is the accountants' worldview limited and molded by their particular focus and priorities?

Originally Posted by Faust

What is that ugly truth? It's an honest question.

The ugly truth is -- a life without feeling, or at least enough of it. Just the mechanics, er facts, ma'am.

Originally Posted by Faust

I believe in many things whose existence is denied by physicalists, but I don't see how those things are at odds with physicalism per se. Whereas some (not all) physicalists say "miracles can't possibly happen", I see physicalism as saying "if miracles do happen, then they can be explained". I find that a rather sensible position and, why not, even beautiful.

It seems to me you are confusing science and physicalism. They are not the same.

But let's see if we can agree. I love science, totally. I can't get enough of it. I am only disputing the claim that physicalness is all there is to reality. If there weren't reasons to doubt that claim, then I'd be fine with it. But I believe there are glaring exceptions which those committed to physicalism tend to ignore, dismiss, gloss over and generally pretend are just little glitches in their theory when really they are major problems. I say, that a priori commitment to their belief system so biases their view they can't debate objectively.

And me? I am free to accept whatever is true since I'm not committed to anything except discovering the secrets to wisdom and a happy existence.

**Daminc** · May12-05, 03:30 AM

As far as I can see, the problem of understanding one another is precisely the problem of understanding anything. And, I would be very pleased to find anyone willing to think about it. I personally have spent a lot of time thinking about it.

I've been seriously thinking about it since 1991 (when I was 20

)

Lets take this statement to be true for a moment "Everything CAN be explained by pure physics".

Without the ability to communicate and/or understand the the answer (I've been reliably informed that the answer is 42

) then the answer is meaningless.

Also, I believe it is impossible to accurately communicate between 2 humans due to the subjective nature of how we perceive things. We could get really close, but every single person has a unique perception of the world around them and a unique background, combined with a unique genetic makeup, to interperate that perception.

Any answer that has a chance of being correct would have to be calculated by objective reasoning and observation which, I think, would have to be done by computers. Then we can use our subjective reasoning to interperate the answer by a common source of reference (the objective answer).

That way, we can go through the process of communication and attempt to reach understanding.

May12-05, 10:05 AM

Originally Posted by Les Sleeth

Rationalism would be thinking without sufficient reference to observed facts. It assumes truth can be had by reason alone. Empiricism changed all that by requiring that what one supposes to be true has to be confirmed by experience/observation. So my point was that since rationalists feel little need to actually look at what they are philosophizing about, they tend to over-emphasize the language used in a debate.

The problem is that empiricism cannot be applied to most philosophical questions, certainly not to metaphysics. So when you look at philosophical claims, what else do you have to go by other than the words themselves? Sure, there are the ideas behind the words, but perhaps we haven't been paying enough attention to the words themselves. I don't agree that everything is about language, but I do think there's more to language than we are willing to acknowledge. It's a fact that many of our utterances, when looked at from an analytic perspective, turn out to be no more than tautologies. Not enough attention has been paid to that fact, in my opinion, but then again one can pay too much attention to it.

Physicalists have not triumphed over anything outside their realm. What they have triumphed over is ignorant beliefs about the physical nature of the universe.

That is what I meant anyway. The problem is that those ignorant beliefs were often not recognized as such. And that was my point; I didn't suggest physicalism was closer to the truth, I only pointed out the fact that physicalist arguments are quite powerful. I will give you an example further down.

They have not understood anything I know of about the meaning of life, how to be happy, how to realize the deeper things.

I'm not really sure about this. Clearly our existence has many purposes, but the two most obvious are survival and reproduction. As a result of that, we in the West came to understand that sex is not a sin. I consider that a major triumph over non-physicalist views, and it has everything to do with being happy, the realization of deeper things, etc.

I think it's wrong to portray physicalists as heartless monsters bent on destroying feeling and emotion. I really don't get that from them.

Your admiration is like giving a golf pro all the credit for explaining a great athelete because he understands the principles of proper form.

I do not admire physicalists, I'm just trying to look at all the different philosophical currents from a neutral perspective. I don't really root for one camp or another, I have grown out of the whole debate. I reached a perspective from which it all appears as irrelevant, although I still enjoy talking about it, like someone who likes a sport but is not attached to any particular team.

Physics explains mechanics, it explains form, it explains processes. Physics doesn't make one wise, loving, compassionate. . .

Certainly not, but what does?

I don't get your "envy."

It was just a figure of speech.

Personally, I've had lots of success meditating.

I'm sure you've had. As for me, meditation doesn't seem to offer the things I want. (by the way, neither does physicalism or any brand of philosophy)

It doesn't stop me from being physical, but I do value the inner me more than anything I've ever done physically. I think it is more lasting, and far more satisfying. I can't see a single reason to envy anyone, but if someone has achieved deeper and more constant happiness than I have, then I hope he/she teaches me how to do it for myself.

Well, I don't see my life as a pursuit for happiness, so knowing that a specific doctrine has made someone happy doesn't entice my curiosity.

I don't think it's about what turns out to be true. The truth is the truth, I have no problem with that. But imagine you find yourself in a world run by accountants, and who insist all philosophy be accountant philosophy. Everything has to add up, everything has to balance, everything has to be fiscally sound . . . Is that an accurate, full representation of reality? Or is the accountants' worldview limited and molded by their particular focus and priorities?

Well, nobody likes accountants, but I think it's mostly because what they say cannot be disputed. It has nothing to do with the accountants' worldview itself, but more to do with the fact that you have to agree with what an accountant says even if you're not an accountant yourself.

Same with physicalism. You may not like it, you may think physicalists are heartless nerds, but the fact remains that they're pretty hard to beat at any game, not only their own.

The ugly truth is -- a life without feeling, or at least enough of it. Just the mechanics

You mean physicalists don't have feelings, or enough of them? They don't enjoy nature, appreciate the arts, fall in love, have ideals? That sounds preposterous to me, I'm sure I misunderstood you.

It seems to me you are confusing science and physicalism. They are not the same.

Of course not, but physicalism is the basis of science. You can't have the latter without the former. Three milennia of meditation may have revealed truths about the mind, but only physicalist science is capable of treating epilepsy, schizophrenia, impotence. That is not to say physicalism is a true account of the mind, but it does ring more true than the alternatives.

But let's see if we can agree. I love science, totally. I can't get enough of it. I am only disputing the claim that physicalness is all there is to reality. If there weren't reasons to doubt that claim, then I'd be fine with it. But I believe there are glaring exceptions which those committed to physicalism tend to ignore, dismiss, gloss over and generally pretend are just little glitches in their theory when really they are major problems. I say, that a priori commitment to their belief system so biases their view they can't debate objectively.

I don't think we disagree at all, I just think you're battling a windmill. Nothing is being endangered, nothing is being profaned, the world is not becoming a worse place. There's nothing wrong with the world, nothing wrong with the people in it that can be fixed by changing our philosophies. That is how I see it anyway, and apparently it's the only point of contention between us: you think the world can be a better place if only we thought about it differently, I think that doesn't matter at all.

I am free to accept whatever is true since I'm not committed to anything except discovering the secrets to wisdom and a happy existence.

Well, you do seem committed to a certain worldview which implies some truths about meditation. I am of the opinion that meditation is useless - europeans didn't know about it for centuries, and their lives were not the worse for it. But that's my commitment. No one is free to accept whatever is true, we all have commitments.

**Les Sleeth** · May12-05, 11:03 AM

Originally Posted by Faust

You mean physicalists don't have feelings, or enough of them? They don't enjoy nature, appreciate the arts, fall in love, have ideals? That sounds preposterous to me, I'm sure I misunderstood you.

I meant as a philosophy, it tends to describe humans heartlessly.

Originally Posted by Faust

Of course not, but physicalism is the basis of science. You can't have the latter without the former.

We have to disagree on this. Physicalism is the belief that all existence is physical or the result of physicalness. Science is the study of the physical universe. One doesn't have to believe all existence is physical in order to study and appreciate the physical aspects of existence.

Originally Posted by Faust

Three milennia of meditation may have revealed truths about the mind, but only physicalist science is capable of treating epilepsy, schizophrenia, impotence. That is not to say physicalism is a true account of the mind, but it does ring more true than the alternatives.

To not confuse things, it would be better if you'd said "three millennia of contemplation" rather than meditation, which is something different.

In any case, it isn't physicalism that has been successful, it is scientists. The physical account of the mind is the physical part. Just because there is physicalness there doesn't mean that's all there is. Again, I have to say that I see the problem as one of researchers not really knowing themselves. I don't see how one can understand consciousness if one never stops, sits down, and experiences its nature within one's own realm.

If all you do is look at processes, and in looking at processes all you do is be a processing device yourself, then you are not going to find or experience anything but processes. That is exactly why physicalists believe we are nothing but a bunch of physical processes.

Originally Posted by Faust

. . . I just think you're battling a windmill. Nothing is being endangered, nothing is being profaned, the world is not becoming a worse place. There's nothing wrong with the world, nothing wrong with the people in it that can be fixed by changing our philosophies. That is how I see it anyway, and apparently it's the only point of contention between us: you think the world can be a better place if only we thought about it differently, I think that doesn't matter at all.

Do you really believe it makes no different what people think? I can't remember the name of the tribe I studied years ago in an anthropology class, but in this tribe the main goal of life was to kill people in other tribes. Children were taught this way of thinking and were generally ignored until they were old enough to participate in killing. It was not a nice place to live.

Right now in this world there are some pretty destructive philosophies. That spot in New York where the World Trade Center used to be is the result of someone's philosophy. Obviously physicalism isn't in that league of evil, but I see it as an evil nonetheless. Why? Because it portrays us as "things," and that philosophy is a step toward heartlessness when, IMO, what humanity needs is to step toward the heart.

Yes we are embodied in a thing, which evolved out of a universe of things . . . but is consciousness a thing? That belief, I say, is counterproductive to the further evolution of consciousness because it prioritizes the various aspects of a human incorrectly. The more we accept we are first and foremost a thing, the more we are going to do little more than study things.

Originally Posted by Faust

Well, you do seem committed to a certain worldview which implies some truths about meditation.

There's no worldview needed for meditation, not for me anyway. I've done it daily for over thirty years because I love how it stills my consciousness, allows me to think better when I decide to think, and because I like the heightened awareness that results. If there is any effect on my "view" it is simple clarity.

Originally Posted by Faust

I am of the opinion that meditation is useless - europeans didn't know about it for centuries, and their lives were not the worse for it. But that's my commitment. No one is free to accept whatever is true, we all have commitments.

It doesn't sound like you know anything about it, so I'm not sure why you have such an opinion. If you think Europeans haven't known about it, you are quite uninformed. They've practiced it, mostly in monasteries, for nearly 2000 years. I suggest you read Evelyn Underhill's classic "Mysticism" to see just how extensively turning inward has been practiced. Or try the Greek Orthodox collection of writings known as the "Philokalia."

**saviourmachine** · May12-05, 05:02 PM

Understanding

Originally Posted by Doctordick

On reason I presumed you were backing away is that the last post from me, which you failed to respond to contained a lot of important relationships. I doubt you understood it all and proceeding without understanding is pretty well a waste of time.

You got me! Sorry!

I've printed your last two posts addressing me.

Concreet example
I find the concepts of the sets still a bit difficult. Can you give some concrete examples? Can I take 'warmth' - with all kind of properties - as set A? Excuse me for the layman approach. The discovery of the concept "temperature" would than belong to category B. The discovery of the concept "noise temperature" would again change our knowledge, it's B_j. Both would me members of C. No, I'm at a loss. What's x_i exactly in this context? I definitely need a concreet example. This is too abstract for me.

$LaTeX Code: B \\subset A$ or $LaTeX Code: B \\equiv \\{A_{some}, A_{other}, ..., A_{another}\\}$
$LaTeX Code: C \\subset A$ and $LaTeX Code: C \\equiv \\{\\{B_{some}\\}, \\{B_{other}\\}, ..., \\{B_{another}\\}\\}$
C is finite, but not "stable".

Message vs label
The elements of C are messages. What would be a message in a concreet example? The elements of B are labels. What is a label in a concreet example? Maybe using some standard mathematical notation - like above - can clear things up too.

Numeric example

Try and follow a thought experiment regarding the following problem: I have some set "A" in my head and I am going to take arbitrary collections of elements of "A" (sets "B") and give them to you. Based on "C" (the entire collection you have so far received) you are to come up with a method of establishing your expectations: i.e., your estimate as to the probability of getting any conceivable specific "B". On a small scale this is a problem given to students all the time: if I gave you a "one" and then gave you a "two" and then a "three", you would probably put a high probability on getting a four.

So a set "B" is in this case "one number" and represents a change in my knowledge of A... So, "B" can be seen as an "sensorial vector", an observation. Based on "C" - that formed my pattern recognition system - I am able to use the new information "B" to adjust my predictions. The labels are assigned to the observed elements of A: numbers.
With B₁ = {3, 7}, B₂ = {5, 9}, B₃ = {7, 11} the difference between the messages (sets B_j) and the labels {3, 7, 9, 11} is clear. Did I got that right? Is the focus on the relationship between the elements of the message, or the relationship between a message and previous messages?

Layman example
I sort of understand the numeric example, but when considering something like 'gravity' or 'temperature' I don't know what A, B and C mean in that context. Can you help me with that? Or does the nature of the problem forbid you to fill on some details?

Predicting an element in a set "B"

Suppose, for the fun of it, someone gave you all the elements but one from some "B" and asked you what element could be added to make that list a valid example of one of the sets you were given. Your table is very close to answering that question. Can anyone out there think of a way to make that result possible in every case?

The next message can be as predicted or it can be a surprise.

Extrapolation
If the first message is from Newton, and the second is from Einstein, I don't know what the third will be. I'm at a loss what you're exactly extrapolating.

I hope you don't mind to explain it a bit more. Thanks for your time!

~~Doctordick~~ · May15-05, 06:55 PM

Originally Posted by saviourmachine

Concreet example
I find the concepts of the sets still a bit difficult. Can you give some concrete examples?

Sure, anytime you catagoize something, give it a name, you are thinking of a "set". The elements of the set constitutes the entire collection of things which you have decided are included under that name. Lastly, coming up with a name for the set is not required; at least not in the abstract. I like the following comment on the issue of "abstract" from Robert M. Hutchins and Mortimer J. Adler in the "Gateway to the Great Books": "If you have learned to add two and five without asking "Two and five what?" you already have both feet off the ground--higher than you think. You are now air-born. The rest is just a matter of gaining altitude."

Originally Posted by saviourmachine

Can I take 'warmth' - with all kind of properties - as set A?

Sure; however, if you do then membership in the set would be anything which you would consider satisfying what you mean by 'warmth' – with all kind of properties. I am not at all sure what you would wish to call 'warmth' – with all kind of properties. A coat??? A smoldering fire??? A friendly girl??? Since I defined B to be a finite collection of elements of A, "the discovery of the concept "temperature" would not belong to B unless you would include "the discovery of the concept 'temperature'" as an example of 'warmth' – with all kind of properties. Why would you include this particular discovery as an example of 'warmth' - with all kind of properties?

Originally Posted by saviormachine

The discovery of the concept "noise temperature" would again change our knowledge, it's B_j.

Not with any meaning of 'warmth' – with all kind of properties I would consider reasonable. Under your example B_j would be a change in the specifc set of things you catagorize as 'warmth' – with all kind of properties. Your mother bought you some warm cloths or some hot (if 'warmth' – with all kind of properties included "hot") girls walked in the room. That is, the collection of things which you regarded to be in that set 'warmth' – with all kind of properties would change. C is the end result of all changes to date and would be everything you currently regard to be 'warmth' – with all kind of properties.

B is not a subset of A, B is a finite collection of elements taken from A. The significant difference is that it is possible for an element which appears only once in A could appear multiple times in B. A subtly which has profound consequences which I won't get into for a while. Likewise, C also being a finite collection of sets B need not be a subset of A.

Originally Posted by saviormachine

Message vs label
The elements of C are messages. What would be a message in a concreet example? The elements of B are labels. What is a label in a concreet example? Maybe using some standard mathematical notation - like above - can clear things up too.

C is the collection of information available to you (knowledge of the things you consider to be 'warmth' – with all kind of properties as presented above). The elements of C are changes in that information (knowledge of the things you consider to be 'warmth' – with all kind of properties as presented above) which arrive via the addition of new elements to that set C which are labeled B_j. Message just seemed to be a good reference label to put on "change in information". I have no idea what you meant by 'warmth' – with all kind of properties. You could have meant "putting a coat on" as an example of an element of A. B was a collection of elements: perhaps putting a coat on together with three warm girls named susie, joan and kate in front of a low fire in a fireplace. Call it an experience if you wish.

The real problem here is that the moment you begin to put meaningfull labels on these elements, you are proposing a solution (i.e., you know what you are talking about) and not examing the problem (trying to understand what you are talking about). Read my post to Les on the "Are Qualia Real" thread.

Originally Posted by saviormachine

Numeric example
...
Did I got that right? Is the focus on the relationship between the elements of the message, or the relationship between a message and previous messages?

I really didn't understand what you were getting at. I don't think you understand why I am talking about sets. Given any problem concievable, C constitutes the information available to you to solve the problem. C is not A because we can not know for sure that all the information is available to us even though it is assumed that A is what we are trying to understand. And the set Bis required to provide for the possibility of change. That's really all there is to it.

Originally Posted by saviormachine

Layman example
I sort of understand the numeric example, but when considering something like 'gravity' or 'temperature' I don't know what A, B and C mean in that context. Can you help me with that? Or does the nature of the problem forbid you to fill on some details?

"Gravity" and "temperature" are meaningfull labels of concepts essential to the modern solution to all those environmental problems ordinararly referred to as "physics". Their very existence means that one is working with a solution, not with the problem. One could ask, what was the problem which lead to that solution? That would be the history of physics or maybe the history of science or perhaps the history of man. At any rate, the path to that solution is far beyond what I could write. What I am trying to do is to look at the fundamental nature of all problems themselves.

Originally Posted by saviormachine

The next message can be as predicted or it can be a surprise.

I think you misunderstood what I was asking. First, I was talking about a representation of C (that upon which your solution is to be based). What I had pointed out to you was that, since C was a finite collection of sets B (which I had labeled as B_j) and every B constituted a finite collection of elements of A (by definition) I could put arbitary numerical labels on each element of every B and then have a specific list of all B in C. Possessing this list I could answer the question, "is this specific B (specific in the sense that I have a set of numerical labels which specify the B I am talking about) in the complete set C?"

I should comment about this circumstance. Essentially I have not given those numeric labels any meaning at all and yet I can answer a very specific question; however, my ability to answer that question depends on those numerical labels I have assigned. Again, you need to recognize that meaningfull labels are part of a solution and not a mere formality. As soon as I give two elements somewhere in this set the same label (numerical or otherwise), I am fundamentally asserting they are the same element. How in the world did I know they were the same? For the moment, let us just say I guessed and maybe I guessed right and maybe I guessed wrong. Later I will point out some interesting aspects of having the freedom to label things anyway I wish. At the moment, in order to avoid making presumptions, I must assure that, whenever I make an assertion about C, that the assertion must be true no matter what labeling proceedure was used.

But meanwhile, you have a list of every B you have ever seen (in the problem so far) and, having labeled them, can refer to any specific one via the list of labels assigned to it. Against that backdrop I asked, "suppose, for the fun of it, someone gave you the labels of all the elements but one from some B and asked you what element could be added to make that list a valid example of one of the sets you were given." Your answer, "the next message can be as predicted or it can be a surprise", presumes we are talking about a new message. We are not, we are talking about answering questions about the C which is available to you.

There is a very simple proceedure which will create a set of lists from the lists you have prepared where this second list will asnswer the above question. First, take each list you had to start with and, for any two lists which are identical, add a label which does not exist on any list (since we are using numerical labels and the number of elements already labeled is finite, there exist a plentyful quantity of unused labels). Now, for each of these altered lists, make every list possible which is identical to that list except for the absense of one element. Now repeat the first step above, eliminating any duplicate lists created in step two, Finally, replace the labels which were removed in step two.

The result has a very curious property. That is the fact that no matter what list you choose of the finished collection, you can remove any element and there will be no list in the remainder of the lists which have the same set of numbers you are looking at. This property is achieved no matter what the original label assignment was. Given this new set of lists, if someone gives you the labels of all the elements but one, there is only one possible missing element so the question asked above may be answered.

I suspect you are questioning what value lies in the above performance. The value arrises when you realize that the collection of lists you have constructed can be seen as a mathematical function. The numerical result (the missing label) is given by the table of all lists missing one element (it is not a continuous function as it is only defined for the arguments in the table). It is a function of many variables (the list of B labels missing one element) which results in the label which is missing. Mathematically this can be written:

$LaTeX Code: x_n=f(x_1,x_2, \\cdots, x_{n-1})$

If that is true, then it implies there exists a function F, defined by

$LaTeX Code: F(x_1, x_2 , \\cdots, x_n)=f(x_1,x_2, \\cdots, x_{n-1})-x_n$

where the rule which tells you whether a particular list is valid is given by F=0, a very simple rule. This result was achieved by imagining the existence of some elements which were not part of A: i.e., they were totally made up in order to achieve that simple rule. What I have shown is that the existance or non-existence of any finite collection of elements can be constrained to exactly what has been seen (no matter what that collection is) by the simple rule F=0 and the introduction of imaginary or make believe elements.

Now what does this have to do with reality? Throughout history, scientific hypothicies have consisted of invented entities and invented rules. The rules are supposedly invented to explain what we see and the invented entities are then invented to correct for the problems in what we see. Every time we are able to prove that what we see is consistent with the entities and the rules (we think are true) we consider it proof that that they both exist. If you are going to give me the freedom to invent any entities I want and the freedom to propose any rules I want, you have given me more freedom than I need to explain everything which is known (since "everything which is known" is finite). I can construct a very simple universe based on that simple rule F=0 which is quite interesting. That is, if one is interested in thinking.

Have fun -- Dick

**Daminc** · May16-05, 09:53 AM

Originally Posted by DoctorDick

which is quite interesting. That is, if one is interested in thinking.

I'm sorry, but this highlights why I'm not interested in what you have to write. You imply that if I don't find it interesting then I don't think

I think all the time. Sometimes it becomes bad for my health because I cannot turn my mind of even though my body is crying out for sleep. You have to be one of the most self-centered, egocentric individuals I have come across on the Web.

If your intention was to be listened to then the smart thing to do would be not to alienate your target audience which is something you obviously haven't figured out yet.

I'll read your stuff when you learn a bit of modesty

**saviourmachine** · May16-05, 11:06 AM

Labels

Originally Posted by Doctordick

The real problem here is that the moment you begin to put meaningfull labels on these elements, you are proposing a solution (i.e., you know what you are talking about) and not examing the problem (trying to understand what you are talking about). Read my post to Les on the "Are Qualia Real" thread.

Yes, I understand. A message can be a composition/mixture of e.g. {3, red} or {2309.23 €, "bkkkpoi", banana-taste}. To label the elements '3' and 'red' is unwanted and unjustified 'labelism'.

The nature of a 'message'

Originally Posted by DoctorDick

I don't think you understand why I am talking about sets. Given any problem concievable, C constitutes the information available to you to solve the problem.

Does a message / obervation embed it's whole context {time, place, etcetera}? However, I think your representation is still that abstract that it can account for problem solving in general. I was confused because I'm thinking of neural nets, in which e.g. the order in which messages are received can be important. The elements of the message are unordered, but the messages itself are ordered, are they?

Question: 1 missing label

"suppose, for the fun of it, someone gave you the labels of all the elements but one from some B and asked you what element could be added to make that list a valid example of one of the sets you were given."
...
we are talking about answering questions about the C which is available to you.

That is very simple indeed. I was confused by your use of the word list. That denotes one message in this case.

Look for all B in C, compare every B_j with the B_asked and if there is only one that does match, than it's the one.

B_asked = {red}

B₀ = {5, 2}
B₁ = {red, 2}
B₂ = {apple, red}
B₃ = {apple, 5}
B₄ = {red, 2}

Here it is nr. 1, nr. 2 and nr. 4.

Simple procedure

There is a very simple proceedure which will create a set of lists from the lists you have prepared where this second list will answer the above question. 1. First, take each list you had to start with and, for any two lists which are identical. 2. Add a label which does not exist on any list (since we are using numerical labels and the number of elements already labeled is finite, there exist a plentyful quantity of unused labels). 3. Now, for each of these altered lists, make every list possible which is identical to that list except for the absense of one element. 4. Now repeat the first step above, eliminating any duplicate lists created in step two. 5. Finally, replace the labels which were removed in step two.

Odd way. It's amazing how you can obscure a very simple procedure.

Can you write some programming code please? "5 ... removed in step two?"
It's just providing every entree in the table with an unique keyword / identifier isn't it?

Removing element

The result has a very curious property. That is the fact that no matter what list you choose of the finished collection, you can remove any element and there will be no list in the remainder of the lists which have the same set of numbers you are looking at. This property is achieved no matter what the original label assignment was.

Of course. Even removing the identifier does not lead to another entree (with - still - its own identifier).

The messages are coded

Given this new set of lists, if someone gives you the labels of all the elements but one, there is only one possible missing element so the question asked above may be answered.

Of course, if the messages are coded (and received) that way.

Valid lists

Mathematically this can be written:

$LaTeX Code: x_n=f(x_1,x_2, \\cdots, x_{n-1})$

If that is true, then it implies there exists a function F, defined by

$LaTeX Code: F(x_1, x_2 , \\cdots, x_n)=f(x_1,x_2, \\cdots, x_{n-1})-x_n$

where the rule which tells you whether a particular list is valid is given by F=0, a very simple rule.

Okay, assigning x_i numeric value.

Universe

I can construct a very simple universe based on that simple rule F=0 which is quite interesting. That is, if one is interested in thinking.

I'm curious.

~~Doctordick~~ · May17-05, 09:56 AM

Hi "saviormachine", it's nice to hear from you.

Originally Posted by saviourmachine

Yes, I understand. A message can be a composition/mixture of e.g. {3, red} or {2309.23 €, "bkkkpoi", banana-taste}. To label the elements '3' and 'red' is unwanted and unjustified 'labelism'.

I am not entirely sure what you have in mind when you use the phrase "unjustified 'labelism'". I suspect you are commenting about my statement, "At the moment, in order to avoid making presumptions, I must assure that, whenever I make an assertion about C, that the assertion must be true no matter what labeling procedure was used." I don't know that I would use the word "unjustified"; what I want you to be aware of is the fact that the very act of labeling introduces a constraint on the interpretations which are possible. The act is essentially the creation of a language and the language itself implies constraints. Constraints are essentially the elimination of possibilities and I have no desire to do that. At the same time, in the final analysis, a real solution requires that we find a set of labels consistent with the information embedded in those "messages", "experiences", "tokens of change" or whatever one wants to call them. For the moment they are no more than the members of the sets B_j which make up C (that which we wish to understand).

Originally Posted by saviourmachine

However, I think your representation is still that abstract that it can account for problem solving in general.

That is exactly my contention. If you notice any reason at all that my presentation is not totally general, please point it out to me as, if such a difficulty exists, it constitutes a serious flaw in my work.

Originally Posted by saviourmachine

I was confused because I'm thinking of neural nets, in which e.g. the order in which messages are received can be important. The elements of the message are unordered, but the messages itself are ordered, are they?

Not really; and that is another serious issue with far reaching consequences. The sets B were created to make it possible to represent change in the set C and were created for that reason only. The concept of time is seriously embedded in our understanding of anything (particularly in our understanding of anything involving change). In my general representation the fact that B represents a change in C can not be taken to imply there is any order in that change. C constitutes all the information you have to work with. In a general problem you cannot assume you and another were given the information in the same order even if, at the moment you compare your solutions, you have exactly the same C available to you.

What I am getting at here is that the "j" label attached to that B_j is just another label attached by you. There are some subtle consequences of that fact that won't be evident for quite a while so let's lay the issue of order aside for the moment as any individual certainly has a specific order in mind: the order with which he became aware of the new information. That order is certainly important to him and can have a serious impact on his expectations.

Originally Posted by saviourmachine

Look for all B in C, compare every B_j with the B_asked and if there is only one that does match, than it's the one.

Exactly correct and your example is excellent except for two issues. First, I specified we were going to use numerical labels and you have decided to use "red" and "apple". That is not a serious issue at all as we are only talking about arbitrary labels but it might somewhat confuse the issue of "mathematical functions of those labels". I am presuming you are sufficiently intelligent as to understand that there is no real problem here. Some people might find the concept of something being a functions of words too abstract to comprehend.

The other issue is a little more serious. It has to do with determining the equality of sets B. In your example, you assume the asked set {red} is equal to the observed sets {red, 2}, {apple, red} and {red, 2} ( j = 1, 2, and 4). Under my definitions (as I intended them), you never received the set {red} (that would be "red" in the absence of any other elements). Also, as order is of no significance, your example might be better if you either included {2, red} or explicitly stated that order in your defined sets was not significant (a small issue but it might be confusing to some; the central issue is to avoid any misinterpretation of the instructions). Both these issues are quite trivial and I strongly suspect you have an excellent grasp of what I am talking about.

Originally Posted by saviormachine

It's amazing how you can obscure a very simple procedure. :blush: Can you write some programming code please? "5 ... removed in step two?"

Sorry about that, in my head the steps you list as 1. and 2. were a single step. That makes your step 3. correspond to my step two (the step where elements were removed which created the possibility of duplicate lists). I apologize sincerely for not expressing the steps clearly. From your further comments I get the impression you understood what I was describing. Thank you for your indulgence.

Originally Posted by saviourmachine

It's just providing every entry in the table with an unique keyword / identifier isn't it?

That is exactly what it is. The only important issue is that these "invented" elements need to be seen as utterly no different from any other element in B when it comes to solving our problem. They essentially stand as "hypothetical" elements; if we find a usable solution, then we can certainly hold that these "invented" elements need to be there (at least with regard to that solution we found). That is the reason I described it the way I did: that is, I didn't want to use the words "keyword" or "identifier" as that implies a specific status to the entry. I want you to simply regard it as an imagined entry. (What I have called "unknowable data" elsewhere.) The fundamental issue is that there must be no way of differentiating between these imagined entries and the entries derived from "A". Once you include them, they are presumed elements of the B_j in any of your analysis. (Again, any assertion I make about C must be true for any possible "keyword", "identifier" or "unknowable" whatever you want to call this entry.)

I am very sorry that I obscured a very simple procedure. I could write some programming code but it would be pretty worthless as, although the number of elements to be included in any reasonable problem are finite, their number can be expected to be astronomical and there are other much more important issues to be discussed first. Actually, with the memory and speed of modern computers, I think it might be very valuable to write such a program. (Another project for another day.)

Originally Posted by saviourmachine

Of course. Even removing the identifier does not lead to another entry (with - still - its own identifier).

I think you understand. There is only one point I might make: when you are looking for the B_j (which corresponds to the B_asked with an element missing) you must look through the entire list of all B's you have created from the original B's with every possible omission. This expands the problem considerably (though it is still a finite problem).

What I want you to keep in mind is the fact that I have just proved that, so long as the number of elements in C are finite, it is always possible to add "unknowable data" (imaginary information) which will allow a rule F=0 to constrain the elements to exactly what was observed no matter what was observed (by "observed", I mean the specific elements in the B's which make up C).

To continue, we need a universal abstract way of expressing an explanation in order to describe the universe I am going to create. So, the first step is to define an abstract definition of an explanation. I tried to express this definition to Canute a while ago but I don't think he has much interest in exact science. I define "an explanation", from the abstract perspective, to be a method of obtaining expectations from given known information. It should be clear to you that the "known information" is the collection of B_js which go to make up C. If we use numerical labels for the elements of B, then every B can be seen as a collection of numbers. From these numbers (the numbers which define what B we are looking at) we are to supposed to express our expectations. What else are our expectations if they are not the probability that we expect to see that particular B just referred to? It follows that "our explanation" constitutes knowing that probability as a function of those arguments.

If follows that we can express our explanation with the notation:

$LaTeX Code: P(x_1, x_2 , \\cdots, x_n)$

If we can discover that function, we know our expectations and thus have an explanation of C. The first thing of interest to us is that our explanation should be consistent with all the $LaTeX Code: B_j (x_1, x_2, \\cdots, x_n)$ that go to make up C (it doesn't explain C otherwise). Notice that we are actually talking about the collection of all those

and the probability of seeing a particular one can not be a function of our labeling procedure as we were free to label things anyway we please (our labels are fundamentally meaningless). It should be obvious that, in most cases, any change in the labeling procedure will most likely confuse us as to which B's we were talking about before and after the relabeling (the form of that function is very dependent upon the labeling). None the less, there do exist relabeling procedures which will not confuse that identification. Any relabeling procedure which does not confuse the identification of

must yield exactly the same expectations after the relabeling as it did before. If it doesn't, the explanation is inconsistent with C.

It is the expectations for the B's which interest us; not the arbitrary labels we happen to put to those B's. Those labels exist for the sole purpose of allowing us to refer to the elements of B. (That is exactly what language is all about.)

I will leave it there for the moment because I want to be sure you understand exactly what I have said. Meanwhile, when I was looking up that post to Canute above, I ran across a post by you which I had apparently missed.

Originally Posted by saviourmachine

<off-topic>
By the way, it's interesting to see the difference between the texts of DoctorDick and Philocrat. Both of you I find difficult to follow. DoctorDick, because your texts have such a small "definition density". With common words you tackle difficult concepts, without using many terms that are in use in contemporary science and philosophy. It's like you're writing assembly code. Philocrat, because your texts have such a big "definition density". You use many new definitions that nobody before, ever thought of creating words for. I guess you've immediately a word for the problem I've with understanding you both. It's like you're writing a high-level programming language that nobody knows.

I am very impressed with the fact that you picked up on that. I would say that my "definition density" is as close to minimal as one can get and your use of the metaphor "assembly code" is very apt. I would also comment that there are other similarities. The problem with the high-level language is that you can only express things which have already been prepared for in the design of the language while, in assembly code, you can express anything. However, expressing simple things in "assembly code" can easily get quite long compared to the same thing in a high-level language. I think I tend to exceed most peoples attention span very quickly. I hope you have the patience to follow my arguments through; the arguments themselves are actually quite simple.

Looking for your response -- Dick

**saviourmachine** · May18-05, 03:33 AM

That is exactly my contention. If you notice any reason at all that my presentation is not totally general, please point it out to me as, if such a difficulty exists, it constitutes a serious flaw in my work.

As problem solving your presentation is general enough. However, like somebody pointed out in another thread, considering the problem of the origin of the apparatus that receives and distinguish as such the messages B_j, and that can contain memory (set C), I don't see how it can account for that. How evolution works is sending indirect messages by destroying the 'owners' of a set C less adapted to their environment. The idea of mutations in combination with natural selection doesn't fall into this scope. Or, if you have any idea how it does fall into this scope, I appreciate to hear that.

Coded messages

The other issue is a little more serious. It has to do with determining the equality of sets B. In your example, you assume the asked set {red} is equal to the observed sets {red, 2}, {apple, red} and {red, 2} ( j = 1, 2, and 4). Under my definitions (as I intended them), you never received the set {red} (that would be "red" in the absence of any other elements).

But how can you make sure that your messages are in the form you need? If you assign an arbitrary label, you can 'calculate' as if every message is coded like that, but 'at the end' it's possible to 'calculate' without this proposed construction, isn't it?

Order & numbers

Also, as order is of no significance, your example might be better if you either included {2, red}

Therefore I added B₂ = {apple, red}. I agree with using only numbers, so B₂ = {8088, 3945} is fine for me too.

Word 'identifier'

That is exactly what it is. The only important issue is that these "invented" elements need to be seen as utterly no different from any other element in B when it comes to solving our problem.

Yes, you're right. That went also through my mind when I wrote 'identifier', because the way your tabel is coded, every label [column] can be called 'identifier' (whatever element is deleted, the entry [row] is still unique). It's like adding an 'error bit' to make sure the amount of 'ones' in a binary message is even and subsequently not having to know which bit the error bit exactly is.

Hypothetical

They essentially stand as "hypothetical" elements; if we find a usable solution, then we can certainly hold that these "invented" elements need to be there (at least with regard to that solution we found). That is the reason I described it the way I did: that is, I didn't want to use the words "keyword" or "identifier" as that implies a specific status to the entry. I want you to simply regard it as an imagined entry. (What I have called "unknowable data" elsewhere.)

Yes, this is the clue, exactly the doubt I uttered in 'Coded messages'. I'm curious how handy these hypothetical elements will turn out to be. I agree that if there is 'unknowable data', that there is no point to dismiss beforehand the possibility that these hypothetical elements exist.

Expectation

If follows that we can express our explanation with the notation:

$LaTeX Code: P(x_1, x_2 , \\cdots, x_n)$

Agreed.

It should be obvious that, in most cases, any change in the labeling procedure will most likely confuse us as to which B's we were talking about before and after the relabeling (the form of that function is very dependent upon the labeling).

Aha! The message are received in code, or there is a 'relabeling' procedure. I thought the label was artificial, but inherently bounded to each message. So, there wouldn't be a 'behore' and 'after'.

It is the expectations for the B's which interest us; not the arbitrary labels we happen to put to those B's. Those labels exist for the sole purpose of allowing us to refer to the elements of B. (That is exactly what language is all about.)

Agreed.

Looking forward for more.

~~Doctordick~~ · May18-05, 09:39 PM

Originally Posted by saviourmachine

As problem solving your presentation is general enough. However, like somebody pointed out in another thread, considering the problem of the origin of the apparatus that receives and distinguish as such the messages B_j, and that can contain memory (set C), I don't see how it can account for that.

I don't account for that. I think you have a very slight misunderstanding of what I am doing. The issue is that we have come from nothing except the universe itself. Somehow, having begun with totally undefined information (what we have come to call the universe or reality) which was delivered to us via a totally undefined mechanism (what we have come to call our senses) we have constructed a very sophisticated mental model of reality which seems to be quite valid (our expectations are pretty much in line with what happens). I take that as evidence that the problem (creating a valid model of a collection of totally undefined information transformed by a totally undefined mechanism) is a solvable problem.

That is the problem I have attacked. I am not claiming that I know how "we" (human beings) did it, I am simply claiming it can be done. That is, it is a problem which can be solved. I analytically solved it over twenty years ago. And I find my solution both very reasonable and very interesting. In fact, my single greatest interest is in talking to someone about the implied consequences of that solution. You are one of the very few people who has had the patience to get this far and I am actually astounded by how well you have managed to comprehend what I am saying. Most everyone else fails to even comprehend there is a problem here. How can one explain a solution to a problem which they refuse to admit exists?

Originally Posted by saviourmachine

How evolution works is sending indirect messages by destroying the 'owners' of a set C less adapted to their environment. The idea of mutations in combination with natural selection doesn't fall into this scope. Or, if you have any idea how it does fall into this scope, I appreciate to hear that.

I wouldn't say evolution destroys 'owners' of a set C less adapted to their environment. The set C possessed by a rock is probably quite minimal if it exists at all and the rock isn't "destroyed"; it just lays there. What was C again anyway? All the information about the universe it has to work with wasn't it? Or at least that which "it" can "remember". I guess for a rock that would be the collection of interactions it has had with the rest of the universe and it's memory would be in the vibrations and/or make up of the chemicals which are part of it. Really, I think this aspect of the problem is better left to later, after you understand the solution I have discovered.

Originally Posted by saviourmachine

But how can you make sure that your messages are in the form you need?

I can't. Again this is a simple consequence of your slight misinterpretation of what I am doing. I am solving a very specific problem, not theorizing about how we do it. The problem is to start with totally undefined information and develop a model (or an explanation if you will) which will yield expectations in perfect alignment with the information you have. (I tried to interest the military in this problem about fifteen years ago but got the "quack" response. I actually have a letter from the pentagon signed by a "Captain Nasty" if you can believe that!) The problem is actually a very complex decoding problem.

Originally Posted by saviourmachine

If you assign an arbitrary label, you can 'calculate' as if every message is coded like that, but 'at the end' it's possible to 'calculate' without this proposed construction, isn't it?

At the end, everything that is possible will be possible; but, for the moment, being able to use mathematics is very valuable tool. As Feynman once said, "mathematics is the distilled essence of logic". My solution is analytic and not at all intuitive. Everything I say could be put into pure logic terms but you have already complained that following me is like following assembly code. I would like a little higher level language. Mathematics is actually little more than a language which has been constrained to internally consistent constructs which have achieved a high degree of acceptance. When I tell you to perform a procedure in mathematics I can be pretty confident you will understand exactly what that procedure is. Actually, in metaphor, it's a little like going from machine language to assembly language.

Originally Posted by saviourmachine

It's like adding an 'error bit' to make sure the amount of 'ones' in a binary message is even and subsequently not having to know which bit the error bit exactly is.

I think you understand the phenomena exactly. I only comment because I want you to know that I am again impressed with your ability to see the essence of these steps.

Originally Posted by saviourmachine

I'm curious how handy these hypothetical elements will turn out to be.

They are the essence of understanding itself. Think about the proof that any arbitrary collection can be made the only possibility by requiring F=0. The hypothetical elements were central in bring about that result. I think it will be a lot clearer later.

Originally Posted by saviourmachine

Aha! The message are received in code, or there is a 'relabeling' procedure. I thought the label was artificial, but inherently bounded to each message. So, there wouldn't be a 'behore' and 'after'.

I am not exactly sure I understand this comment. The labeling procedure is the first step to creating a language capable of expressing the relationships between the elements. I would also comment that "reductionism" is the process of reducing the number of "fundamental" things (labels) required: i.e., once you get to the minimum number of labels required, other important concepts can be explained in terms of those fundamental labels. But you shouldn't worry about that now; it is an issue which arises after the analytical solution is obtained. My process does not require reductionism as it implicitly sets up the minimum number of labels required and we will set up those labels as we proceed.

As I said in my previous post, "any relabeling procedure which does not confuse the identification of

must yield exactly the same expectations after the relabeling as it did before". There are two very simple relabeling procedures with very significant consequences: since I am using numerical labels, I can either add some given number to every label in any given B or multiply every given label by an arbitrary number. If the label sets were unique before the labeling they will be unique afterwards. This means that I can write the following equations:

$LaTeX Code: P(x_1, x_2, \\cdots, x_n) = P(x_1+a, x_2+a,\\cdots, x_n+a) = P(x_1+b, x_2+b,\\cdots, x_n+b)$

$LaTeX Code: P(x_1, x_2, \\cdots, x_n) = P(a*x_1, a*x_2,\\cdots, a*x_n) = P(b*x_1, b*x_2,\\cdots, b*x_n)$

The consequences of the second will arise later in the presentation. The consequences of the first are important now. Look at what it says if I set $LaTeX Code: b=a+\\Delta a$ . Since the labels refer to exactly the same

in all three expressions we know that the correct solution to the original problem (that function $LaTeX Code: P(x_1, x_2 , \\cdots, x_n)$ ) must yield the same probability(we haven't changed the

, we have only changed the labeling). Thus we know,

$LaTeX Code: \\frac{d}{da} P(x_1+a, x_2+a, \\cdots, x_n+a) =$

$LaTeX Code: \\lim_{\\Delta a \\rightarrow 0} <BR>\\frac {P(x_1+a+\\Delta a, x_2+a+\\Delta a,\\cdots, x_n+a+\\Delta a) - P(x_1+a, x_2+a,\\cdots, x_n+a)}{\\Delta a}=0.$

Note that the equation is true even when $LaTeX Code: \\Delta a$ is far from zero; the limit is only there to satisfy the definition of a differential. This is a pure consequence of the arbitrariness of the labeling and places utterly no constraint on the actual solution. It can be thought of as the consequence of the fact that the solution can be expressed in different languages; this is just a very specific and very subtle change in language (specific labels) not easily expressed in term of the ordinary concepts used in the translation between human languages I am aware of (other than secret codes that is).

At any rate, we can use that fact to create another very valuable expression. Since what we have above is a well defined mathematical expression, we can also see the addition of a as a simple change of variables

. Then we take the well known method of extracting a differential of a function with regard to a variable embedded in the arguments of that function. That is, replace $LaTeX Code: P(x_1+a, x_2+a , \\cdots, x_n+a)$ with $LaTeX Code: P(z_1, z_2 , \\cdots, z_n)$ . We can then write

$LaTeX Code: \\frac{d}{da}P(z_1,z_2, \\cdots, z_n)=\\sum_i \\frac {dz_i}<BR>{da}\\frac{\\partial}{\\partial z_i}P(z_1,z_2,\\cdots,z_n)$

But $LaTeX Code: \\frac{dz_i}{da} = 1$ for all values of i. It follows as the night the day that

$LaTeX Code: \\sum_i \\frac{\\partial}{\\partial z_i}P(z_1,z_2,\\cdots,z_n)=0.$

We cannot change that fact by changing the variable from z to x (they are just numerical labels) so it follows that we may write

$LaTeX Code: \\sum_i \\frac{\\partial}{\\partial x_i}P(x_1,x_2,\\cdots,x_n)=0.$

The only reason I changed the variable back to x was to be consistent with my earlier notation. What is above is nothing more than a consequence of the Noether theorem. That is why I brought up her theorem earlier and emphasized the ignorance aspect of symetry. The symetry here (or the ignorance) is the fact that we are free to label things any way we want and that fact has real consequences.

Please, think that all over a little and let me know if you have any problems with it.

Have fun -- Dick

**saviourmachine** · May23-05, 10:24 AM

Derivation

Originally Posted by Doctordick

There are two very simple relabeling procedures with very significant consequences: since I am using numerical labels, I can either add some given number to every label in any given B or multiply every given label by an arbitrary number.

Yes, how cool! Using numeric labels, adding as well as multiplying is possible.

Adding a number to every label in every B doesn't change the probability P. That's right. P(x₁+b, ..., x_n+b) should have the same outcome. Differentiating to b (or a) results in zero. I also agree with the ultimate equation [1]:

$LaTeX Code: \\sum_i \\frac{\\partial}{\\partial x_i}P(x_1,x_2,\\cdots,x_n)=0.$

Symmetry, Noether's theorem, equation [1]

The only reason I changed the variable back to x was to be consistent with my earlier notation. What is above is nothing more than a consequence of the Noether theorem. That is why I brought up her theorem earlier and emphasized the ignorance aspect of symetry. The symetry here (or the ignorance) is the fact that we are free to label things any way we want and that fact has real consequences.

Sorry, this is too fast for me. It's difficult for me to connect these two themes: this formula and Noether's theorem. Can you recapitulate shortly?

~~Doctordick~~ · May23-05, 04:05 PM

Originally Posted by saviourmachine

Yes, how cool!

My feelings exactly. I will never forget the first time I ever saw it. It is utterly astonishing that no one noticed that prior to the twentieth century. Think of all the math done prior to her discovery. It just goes to convince one that everything has not yet been done (even some mighty simple things).

Originally Posted by saviourmachine

Symmetry, Noether's theorem, equation [1]
Sorry, this is too fast for me. It's difficult for me to connect these two themes: this formula and Noether's theorem. Can you recapitulate shortly?

It shouldn't be. You seem to understand exactly what I did and that is the very essence of Noether's theorem. The central issue is the relationship between symmetry (which I see as a particular kind of ignorance) and conserved quantities. A "conserved" quantity is something which doesn't change. In mathematics, change is represented by differentials so, "a conserved quantity" means that there is a differential which does not change. If we can show that a symmetry leads to a differential of something which must be zero, then we have an example of Noether's theorem. John Baez (who I think is a member of this forum) has an excellent discussion of Noether's theorem on his web site (from the purely conventional perspective).

I admit my view is a bit askew of the norm but it might be worth while for you to review my original post to you on this subject together with selfAdjoint's response and my response to him. I got no further complaint from him so I presume he had no further argument with what I said.

As I said in the post you are responding to:

It can be thought of as the consequence of the fact that the solution can be expressed in different languages; this is just a very specific and very subtle change in language (specific labels) not easily expressed in term of the ordinary concepts used in the translation between human languages I am aware of (other than secret codes that is).

I am pretty sure you have a decent idea of what is going on here because of your "Cool" comment above. It is very much the sign of that little light going on.

Exactly the same relationship can be used to generate a conserved quantity related to that "j" we attached to those B's which represent a change in C. The universe we are trying to explain (with that function which is going to yield our expectations) is derived from all the information embedded in the set C. Certainly no one will argue that the order with which we receive that information is an unimportant aspect of solutions we might propose; however, in the general case, that cannot be a fundamental issue. Remember, it is A we are trying to explain and the only thing we have to go on is C. Again, in the general case, we cannot presume that order is significant. Not unless the fact of that order is implicitly embedded in the data itself. We can assure that is the case by adding "unknowable" data which explicitly sets that order. Since we have already made sure (by adding imaginary entries in the B's we are working with – unknowable data) that all B's are different, we can simply add a numerical label which is to have a different value in every B and will indicate the order significant to the solution.

Now (having added that new label) our solution to the problem contains another (totally imaginary component) numerical label which I will call "time" and represent with the letter t. Again, multiplying that label by a constant or adding a constant to all t cannot alter the order and we once again have a fundamental symmetry in our representation. The fact that we can add any number to that t label yields another conserved quantity represented by the differential expression:

$LaTeX Code: \\frac{\\partial}{\\partial t}P(x_1,x_2,\\cdots,x_n,t)=0.$

Once again, the critical issue is that the particular B being referred to does not change nor does the order of those sets. These facts are true, no matter what order the information was received in. Since this is an ordering parameter on received changes B, this leads me to some very simple definitions. A particular value of t will be called "the present". Any t less than that particular t will be called "the past" and any t greater than that particular value of t will be called the future. This is the simplest definition of time which can be made and, in the end, I will show that it is also sufficient to all usages known. Since B represents a change in the information we have to work with, the "past" constitutes what we have to work with and the "future" constitutes what is not yet known.

Note that $LaTeX Code: P(x_1,x_2,\\cdots,x_n,t)$ is the probability of B being $LaTeX Code: (x_1,x_2,\\cdots,x_n,t)$ when t was the present: i.e., if nothing was known about about any B's beyond the one referred to by that "t". Note that "time" as here presented is nothing but a parameter indicating the order in which you came to know things. Note also that "time travel" is pretty well a ridiculous concept under this picture as it amounts to going from knowing what we know to knowing less (the common idea of time travel is to "go into the past" and still know what you know).

If anything I have said confuses you, let me know. I will be happy to clarify anything.

Have fun -- Dick

**saviourmachine** · Jun7-05, 05:44 PM

Originally Posted by Doctordick

In mathematics, change is represented by differentials so, "a conserved quantity" means that there is a differential which does not change. If we can show that a symmetry leads to a differential of something which must be zero, then we have an example of Noether's theorem.

Aha, it's that simple!

Not unless the fact of that order is implicitly embedded in the data itself. We can assure that is the case by adding "unknowable" data which explicitly sets that order.

Aha, that makes some things clear.

Now (having added that new label) our solution to the problem contains another (totally imaginary component) numerical label which I will call "time" and represent with the letter t. Again, multiplying that label by a constant or adding a constant to all t cannot alter the order and we once again have a fundamental symmetry in our representation. The fact that we can add any number to that t label yields another conserved quantity represented by the differential expression:

$LaTeX Code: \\frac{\\partial}{\\partial t}P(x_1,x_2,\\cdots,x_n,t)=0.$

That's straightforward.

Note that "time" as here presented is nothing but a parameter indicating the order in which you came to know things. Note also that "time travel" is pretty well a ridiculous concept under this picture as it amounts to going from knowing what we know to knowing less (the common idea of time travel is to "go into the past" and still know what you know).

Yes, that makes sense. Providing the items in reversed order is still in order.

Looking forward,

Andy