What can we know of reality?

[Doctordick]

God it was nice to hear from you again Annsi; your mind is so clear and open you are a wonder to behold. And both my wife and I loved that “Verizon Wireless Has Trouble With Math video. Although my work is admittedly much more complex than that fellows problem, I have, on many occasions, run into exactly the same kind of difficulty he had. Whenever I have actually gone to show the solutions to my equations, everyone (so far) uses distorted interpretations of my definitions (distortions expressed in their personal picture of reality: i.e., very akin to that .02 cents is the same as .02 dollars thing) to bring all discussion back to those definitions or simply contend that I am wrong. I distinctly have the impression that their true purpose was to find a way in their own head to ignore what I was saying so they wouldn't actually have to question their beliefs. That is exactly the kind of interactions I was referring to when I made the following comment to Buffy:

So long as it is held to be a frivolous hypothesis, I have no intention of going forward. I have been there many times and I won't go there again.

Or when I refer to that “extra baggage”: i.e., trying to attach meanings to my representations when there are none. You seem to easily understand that issue. Thank you; I appreciate it very much.

 

Kriminal99, in case you have been wondering,I haven't been ignoring you; I simply find it quite obvious that you don't understand the issue of interest in this thread “What can we know of reality”. There is a problem here which everyone (save Anssi) seems determined to ignore. For example,

If I define honesty as "what people aren't when they knowingly fail to provide correct and useful information that someone needs to act upon".

You cannot so define honesty without first defining the words, "what”, “people”, “aren't”, “when”, “they”, “knowingly”, “fail”, “to”, “provide”, “correct”, “and”, “useful”, “information”, “that”, “someone”, “needs”, “to”, “act” and “ upon". Until I understand what you mean by those words, your definition is simply: honesty is “word #1”+ “word #2”+ “word #3”+ “word #4”+ “word #5”+ “word #6”+ “word #7”+ “word #8”+ “word #9”+ “word #10”+ “word #11”+ “word #12”+ “word #13”+ “word #14”+ “word #15”+ “word #16”+ “word #17”+ “word #18” + “word #19”.

 

The actual numbers I attach to those words is of utterly no significance. I could just as well have said: honesty is “word #25”+ “word #3303”+ “word #4399”+ “word #24”+ “word #7867”+ “word #2124”+ “word #675”+ “word #2”+ “word #345”+ “word #215”+ “word #2739”+ “word #2237”+ “word #10233”+ “word #2”+ “word #754”+ “word #390”+ “word #287”+ “word #5672” + “word #3490”. And, since I wouldn't know what you meant by the word “honesty” until after I understood your definition, I could simply express the information you intended to express in the above sentence as “word #8675” equals “word #25”+ “word #3303”+ “word #4399”+ “word #24”+ “word #7867”+ “word #2124”+ “word #675”+ “word #2”+ “word #345”+ “word #215”+ “word #2739”+ “word #2237”+ “word #10233”+ “word #2”+ “word #754”+ “word #390”+ “word #287”+ “word #5672” + “word #3490”.

 

In order to understand what you meant I would have to interpret a great number of very similar expressions (a sufficient number to understand the English language). Every year, millions upon millions of children manage to decipher that kind of information in only a period of a few short years (apparently coming up with very similar conclusions). That means the problem is solvable! And, the creation of AI will depend very seriously on being able to solve that exact problem. I am discussing inherent constraints on that problem expressed in a manner which does not presume your current answer (at time t) is correct but demanding that your current answer (at any given time t) is “flaw-free” (a rather different constraint). I use mathematics because it is the most unambiguous language available to me and we need a language to communicate. To quote Richard Feynman, “mathematics is the distilled essence of logic.” It is very nice that we possess such a language, limited as it may be.

 

That brings up another issue which I call “the power of ambiguity”. (See my post to saviourmachine February first 2005.)

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.

As Anssi says,

Relevant as this may be, it is leading us away from the core of the topic...

Perhaps someone would like to start another thread devoted to the issue.

The formulas are there just to extend our logical abilities. A mere tool. Like the formula for quadratic equation.

This is the very crux of my presentation; I am presenting a very small set of definitions (things which can be defined within any information set without saying word one about what that information expresses) and, from that set of definitions coming up with a mathematical tool capable of extending some rather simple logic to an almost infinite set of references. That's it, there is no more and there is nothing to “understand” except the problem itself.

All it gives you is a way to express some constraints that need to be met by any internally coherent worldview you could ever make about reality (when that worldview is expressed in the form of the x, tau, t-plane).

Again, Anssi has hit the veritable nail on the head! He is a very bright fellow; how about giving him a little help with the mathematics.

 

And, Buffy, I can't give you any examples because I don't know how to solve the problem of understanding reality. Nevertheless, that equation imposes some very interesting constraints on the possible relationships which can exist; but we can't talk about them until we can solve the equation and I am not going to start down that road until I at least feel that you understand the difference between an undefined and a defined structure and the constraints being imposed by that equation. The concept is actually no more complex than the difference between .0002 dollars and .0002 cents.

 

Have fun -- Dick

[Buffy]

And, Buffy, I can't give you any examples because I don't know how to solve the problem of understanding reality. Nevertheless, that equation imposes some very interesting constraints on the possible relationships which can exist; but we can't talk about them until we can solve the equation and I am not going to start down that road until I at least feel that you understand the difference between an undefined and a defined structure and the constraints being imposed by that equation. The concept is actually no more complex than the difference between .0002 dollars and .0002 cents.

Doctordick,

 

You obviously don't know what I am talking about: you have no idea how *useful* your last several posts have been *because* you have been forced into applying a few "examples." I'd urge you to do two things:

• Go back and read your last three posts.
  
• Think about revising what you appear to define the word "example" as.

Even the most theoretical math does not exist in a vacuum: most mathematicians abhor "applied mathematics," but they do *constantly* relate new concepts to existing ones by example. On the other hand, what you are doing in the next step is most certainly applied mathematics! You are indeed starting with a purely mathematical argument which is fine, but if you want to apply it to "what we know of reality" then mappings--even abstract meta-mappings--to "reality"--or meta-realities, which I know is *really* the point--have to be drawn and justified.

 

The crux of what Q and I both--I think, and maybe even Anissi--are trying to figure out is whether or not your equation maps onto anything at all, and whether that mapping is valid, even if it is pure logic and math. You have yet to address Q's question of why partial differentials are required, and my ongoing unstated question remains "why must it be zero?"

 

If this is all just an exercise in throwing around arbitrary formulas, then the answer "why not?" is perfectly valid, but if you're (eventually) go on to the next step of saying "this formula can be made a *valid assumption* in constructing internally consistent worldviews" then you need to start mapping the pieces of your formula on to the next step. If you don't its just a meaning-free arbitrary formula!

 

To apply this issue onto your thesis: your formula may or may not be consistent with any particular worldview, but it all depends on the [imath]\vec{\psi}[/imath] it exists within!

 

So please *do* think about the examples above and try to work with them: Maybe Q's example is too limited (although quite frankly your response to it was tremendously useful!), but anything you can do to provide analogies will assist us meatheads in "understanding what you're talking about."

 

I'm learning more about what you're talking about by your dismissive treatment of examples than you can ever imagine!

 

Recursively yours,

Buffy

[Kriminal99]

And in terms of our worldview, whatever math you use to describe reality, that math is describing the behaviour of some elements that you have decided to tack with identity. The problem being, we did not begin science with a set of "objects" whose behaviour we are just trying to probe. Instead, we decide what constitutes an "object" (or any defined entity like "space" or "time"), the large deciding factor in these definitions being "what makes it simple to understand/predict the behaviour of reality"

 

I mentioned space and time; notice that in most cases that math is describing the behaviour of those "sensible things" in some "space" (whose properties/essence you defined), and in some "time" (also that you defined). As a related note, it should be clear to see that there's no point in defending some arbitrarily chosen ontological take on spacetime, just because it happens to seem particularly aesthetical or elegant together with the rest of one's worldview.

 

Thank you for the response. IMO:

 

I am not sure what you are referring to when you talk about science defining objects. I am referring to, for example, an apple. Animals have concepts of things like apples, without having a concept of science. An animal or even unscientific human may wonder if he hits an apple from a tree, where will it land.

 

A minimalist will begin listing properties of apples, and seeking to measure additional properties of apples. Logic is only to be used in conjunction with these ascertained properties. Such a person may weigh an object. They may have, through previous such inquiries determined that certain rules apply even when you switch the object you are working with. Then they will combine these ascertained properties logically to better reason where the object will land.

 

Minimalism is a more general approach because the same thing can be done with introspective concepts like honesty...

 

Perhaps you have extracted a response to your arbitrary space time objection. You need not refer to space time to deem my concept of an apple arbitrary. I no doubt define the apple in terms of how I perceive it. If I had a bat's sonar array, or if I had an inverted spectrum, my definition would be different.

 

Realizing this does not change what I perceive regarding the apple. Trying to redefine apple to meet a new understanding of perception or space time is exactly the type of thing that minimalism is supposed to prevent for the sake of processing efficiency. Rather our understanding of such concepts should just be tacked on to the end of everything else we understand and left there. We can say that if we were a bat and had a sonar array, the same external object (assuming there are external objects) would look different. But an apple is still the colorful yummy fruit in front of us.

[Kriminal99]

Kriminal99, in case you have been wondering,I haven't been ignoring you; I simply find it quite obvious that you don't understand the issue of interest in this thread “What can we know of reality”. There is a problem here which everyone (save Anssi) seems determined to ignore. For example,

You cannot so define honesty without first defining the words, "what”, “people”, .....

 

.....+ “word #5672” + “word #3490”. And, since I wouldn't know what you meant by the word “honesty” until after I understood your definition, I could simply express the information you intended to express in the above sentence as “word #8675” equals “word #25”+ “word #3303”+ “word #4399”+ “word #24”+ “word #7867”+ “word #2124”+ “word #675”+ “word #2”+ “word #345”+ “word #215”+ “word #2739”+ “word #2237”+ “word #10233”+ “word #2”+ “word #754”+ “word #390”+ “word #287”+ “word #5672” + “word

#3490”.

 

In order to understand what you meant I would have to interpret a great number of very similar expressions (a sufficient number to understand the English language). Every year, millions upon millions of children manage to decipher that kind of information in only a period of a few short years (apparently coming up with very similar conclusions). That means the problem is solvable! And, the creation of AI will depend very seriously on being able to solve that exact problem. I am discussing inherent constraints on that problem expressed in a manner which does not presume your current answer (at time t) is correct but demanding that your current answer (at any given time t) is “flaw-free” (a rather different constraint). I use mathematics because it is the most unambiguous language available to me and we need a language to communicate. To quote Richard Feynman, “mathematics is the distilled essence of logic.” It is very nice that we possess such a language, limited as it may be.

 

Nah I do understand it I promise. In fact I already came up with the solution of how define those words (you don't need the whole language) and how children do it a long time ago. I was hinting at it when I mentioned that one only need accept that the frequency with which something has happened in the past affects the frequency of it occurring in the future... Though I suppose it requires a few other memory storing and fractioning abilities without which we could probalby do nothing but drool. I solved this problem by organizing simplified information, where simplified refers to a specific algorithm that I referred to as minimalism. It turns all further philosophical discussions into math and probably would allow for an AI. All my posts were trying to respond to your arguments.

 

I had tried to make posts regarding that system before, but I just got banned for repeatedly referring to reality in contradiction to things moderators stated.

 

Anyways, the way the system works is simple and contradicts what Wittgenstein argued. Witt failed to account for people's perception comparison and pattern recognition abilities.

 

For illustration I will use <> to encase a perceived memory and to denote coincidental perceptions, which have occurred # number of times. | will denote or. Certain simple memory related abilities are assumed to be hard wired, with our automatic ability to perform these tasks as adults for evidence.

 

If a child sees a room with a book in it, and simultaneously hears the word book, he hasn't learned anything yet but perhaps he stores the memory.

 

Somewhere in his head is the record:

 

<Sound of word book> & <Image of a room with a book in it>

 

The next day he is in a completely different room with a book also laying in front of him. (preferably the same one for simplicity's sake, but not necessarily) The child stores the memory:

 

<Sound of word book> & <Image of a different enviornment with a book in it>

 

Then the child simply compares the similar parts of the two images, which just happens to be the book. Then he removes the rest of the images because of the lesser frequency with which they coincide with the word book and is just left with

 

<Sound of word book> &2 <Image of book>

 

Of course it might take more than twice, especially if its a different book or the book is being looked at from a much different angle. But with the implied comparison and pattern recognition ability, many factors can be removed through repeated experiences.

 

Tomorrow someone says "open the book", and the child watches someone do so. Through similar repeated occurrences he removes factors and obtains the association:

 

<Open the book> &(X>1) <String of images involving someone opening the book>

 

Later, someone in front of the child asks someone to open a different object which the child has already been able to associate with it's image. A box perhaps. This verb has not changed, and is associated with a animation that is similar to the one the child saw coincide with opening the book. Thus:

 

<Sound of command "Open the <Book|Box>"> &(X>3) <String of images involving someone opening something>

 

Now the child has something to associate with the higher level concept object, even if he doesn't do so right away. Specifically what is to be an "object" is something that can be "open the" 'ed. It is a function of what the child has thus far perceived.

 

Then the child hears someone say, "Grab the book" and then, and watches them do. And then they see someone being told to and grabbing other things .

<"Grab the <object>"> &(X>1) <String of images of someone grabbing an object>

 

and also

 

<Verb> & <String of images involving a person doing something>

 

Mind you not the word verb, but just the underlying concept just as in the case of object. And also:

 

<"the"> &(X>1) <Word that comes before <object> and <verb>>

 

And it continues such that every high level concept can be defined as a function of things previously perceived.

 

Such memory abilities are implied by our ability to consider something like a unicorn, which consists of a horse that has had the horn of a goat appended to its head.

[Qfwfq]

Your comment is that all I know of reality is “three pairs of numbers” or, if one includes post #90 you could add three more pairs. That means the information consists of twelve valid ontological elements. Since you have apparently decided that the order of the pairs and the order of the exchange is known (i.e., the information on which to build your model has increased), there exists but one element in each [imath](x,tau)_t[/imath] plane. The only rational conclusion is that there will probably be another down the road. My analysis needs to be working with “all of the information” available and the problem you have presented contains such a dearth of information that practically no conclusions of value can be arrived at. There isn't even enough information there to conclude those ontological elements are numbers. This is exactly what I was talking about when I said, “Your example is chock full of assumptions (presumed valid ontological concepts) which you take no trouble to explicitly list (because the size of such a list would probably be beyond accomplishment)”.

It took me a while to find this useful paragraph in the plethora. What I wanted was for you to DO it, for the numbers and forget about the rest of the spy's universe. You can add anything that's in the story that you consider essential and specify anything else that would be needed, but I wasn't asking you to do what you're making out. It's of no use to me if you tell me to build the [imath](x,\tau)_t[/imath] planes, I need to know HOW you build them and then how you get the constraints, in the latest form you put them into, which I'm not yet able to justify. There's no point in asking people to believe the validity of these constraints and accusing them of denial and of fighting you tooth and nail to deny the possibility that “there always exists an interpretation of any flaw-free explanation of reality which will obey your equation" if you don't help us get through the arguments.

 

I'm not asking you to provide more links to a sequence of long past posts that I have no time to go through. Try to say the essential and don't accuse me of misunderstanding, just try to help me get the details straight. The problem is that we always run into semantic troubles and you don't earnestly throw the bridge, which would be up to you. In the above quote for example I see the discrepancy in what you meant about assumptions and what I understood it to mean, in the English language. You did not mean what you said: “Your example is chock full of assumptions...” but instead that I didn't describe all the spy knows about his entire universe. It's also a semantic discrepancy when you say the model can't be applied to "specific examples" when instead you meant the same as above. When you say:

You actually mentioned, “a spy”, “is sent”, “to gather”, “intelligence”, “for”, “planners”, “attack”, “against”, “a castle”, “they”, “need”, “to know”, “how”, “fake”, “patrol” “guard”, a “patrol commander”...

and the further thing you said to Krim:

You cannot so define honesty without first defining the words, "what”, “people”, “aren't”, “when”, “they”, “knowingly”, “fail”, “to”, “provide”, “correct”, “and”, “useful”, “information”, “that”, “someone”, “needs”, “to”, “act” and “ upon". Until I understand what you mean by those words, your definition is simply: honesty is “word #1”+ “word #2”+ “word #3”+ “word #4”+ “word #5”+ “word #6”+ “word #7”+ “word #8”+ “word #9”+ “word #10”+ “word #11”+ “word #12”+ “word #13”+ “word #14”+ “word #15”+ “word #16”+ “word #17”+ “word #18” + “word #19”.

I know exactly what you mean and I've been aware of it for a long time, so have other people; I found an amusing example in one of Hofstadter's books where he illustrates the idea with the word "love". He takes a dictionary definition of the word and then replaces even only the most essential words of it with their definitions in the same dictionary and maybe even the next recursion of this process. This results in an entire paragraph, about which he remarks "How romantic!". Obviously there's no point in continuing with further replacements.

 

When babies are being brought up properly, words are repeated to them while they are being shown simple things, until they start to make associations. I can remember when I was already old enough to speak fairly well but had difficulty understanding the difference between cat and dog when being shown some real live ones running around a yard. I remember figuring that it seemed like cats have rounder heads while dogs have a snout and the dog was maybe a bit larger, then they pointed out to me that dogs bark while cats meow, I was also told about how they differ in when they wave their tails. It was still somewhat confusing to me.

 

However, when I posted the story, and said all that I said about it, I was using a well known language called English, expecting it to be understood by members of this forum including DoctorDick. I wasn't "making assumptions" I was using words that we all already know the meaning of. I took this great humongous liberty only to make it a humanly possible feat, it wasn't a matter of arrogance on my part. I was only attempting to accomplish the possible, instead of the impossible. My humble apologies.

 

This whole exchange is nothing if not tiresome. You all seem to think that I am saying something that I am not saying; you are all looking for applications of my ideas within your personal paradigm. All I ask is that you admit that it appears to be a true representation of reality under my definitions: i.e., there exists a paradigm where my equation is a valid representation of certain specific constraints on reality.

Yes it is tiresome and I can't waste too much time either, try to throw the bridge instead of expecting it from everyone else, and accusing them of things.

 

The story with the spy isn't my personal paradigm, it is a fictional story, it may be regarded as existing in a fictitious universe which may even be similar to yours in many respects, compatibly with what the story specifies. Anything the story doesn't specify is a degree of freedom for you. I did not ask you to build the complete "what is, is what is" table for that universe, only one that includes the specified pairs of numbers and whatever you will, that can either be made out from what I (the story's author) posted or compatibly chosen and, if you should so deem, suggest anything specific that should be added (like, perhaps, we would need to know what kind of tubs they bath their feet in). Surely you can do it with some information, as if it were all the available information. Specify what the arbitrary labels are and how the mapping may be chosen. Show me what is consequential, I need to catch up with Anssi before his math skills improve enough to get him even further ahead.

 

I would further like to clear up a misconception to avoid it adding confusion to the discussion:

 

Logic does not depend on reality. Mathematics is a type of constructing on logic and certain definitions, in essence choices, and therefore does not depend on reality. Logic and mathematics are not a belief about reality. Whether or not the definitions are chosen to describe some aspect of (a given) reality (in a given universe) is of no whatsoever concern to a mathematician. Reality is of no influence on the validity of mathematics; any valid mathematical construct is valid "in" any reality or universe.

[Doctordick]

• Go back and read your last three posts.
  
• Think about revising what you appear to define the word "example" as.

I have done that and I think I understand what you are trying to say; however, I think much of what you are thinking is beside the point.

You are indeed starting with a purely mathematical argument which is fine, but if you want to apply it to "what we know of reality" then mappings--even abstract meta-mappings--to "reality"--or meta-realities, which I know is *really* the point--have to be drawn and justified.

The problem is that such mappings or even abstract meta-mappings need to rest upon the behavior of solutions to that equation. Without those solutions, I am merely talking about the nature of representation itself. I am sure you have heard of the Ancient tablets with the cuneiform texts. There are apparently two versions referred to as linear A and linear B. One has been translated and, in spite of diligent effort, the other has not. We have a collection of symbols which are not defined and the information content just isn't sufficient to decipher them. Perhaps someone in the future will make a lucky guess and find some pattern within the known data which makes sense and then his (or her) start will lead to other rational interpretations. But meanwhile, it is merely a problem to be analyzed.

 

Normally, the very first step in analyzing such a problem is to label the various symbols under examination so that they can be easily referred to. The significant fact of interest to me is that the actual label used in such a circumstance is totally immaterial and that fact itself has consequences.

The crux of what Q and I both--I think, and maybe even Anissi--are trying to figure out is whether or not your equation maps onto anything at all, and whether that mapping is valid, even if it is pure logic and math. You have yet to address Q's question of why partial differentials are required, and my ongoing unstated question remains "why must it be zero?"

I had thought I had answered both those questions a number of times. I will try to explain it in another way.

 

I have set things up so that “what is to be explained” is a set of numbers (those arbitrary numerical labels) which are displayed as a set of points in the [imath](x,\tau,t)[/imath] plane. I have defined "an explanation" to be a method of obtaining expectations from given known information. Your expectation (which are actually a specific subset of of those numerical labels) can be represented as a probability (a number bounded by zero and one) with which you expect a given specific subset.

 

Thus it is that the solution (an explanation; that method of obtaining expectations which is in fact the epistemological construct to be discovered) can be seen as a mathematical function: the argument of the function consists of the set of specific labels and the output of the function is the probability that set will appear in a future [imath](x,\tau)[/imath] plane (the future being defined to be “not part of the given known information”).

 

Since I want to omit not a single possibility for that “mathematical function”, I represent the “method” via a scalar product of an abstract vector function [imath]\vec{\psi}[/imath] which can represent any possible transformation from one set of numbers to another set of numbers (any set of information into a second set of information) and where the transformation into a number bounded by zero and one is an easy thing to define.

 

Now, the important thing in all this is that the given known information is actually the things being labeled, not the labels themselves. Since it can be represented as a mathematical function of those numerical labels, we know certain symmetries must exist in that representation. In particular we know shift symmetry must be a property of the representation. If we have discovered a solution, (a method of obtaining expectations from given known information) that method must yield the same result if we were to change all of our numerical labels by simply adding some number a to each and every numerical reference label (the three axes of our representation can be considered independent sets here). The point being that the output of the function is a function of the things being labeled and not actually of the labels themselves. By making the representation a function of the labels, we have introduced the shift symmetry.

 

To put it another way,

[math]\vec{\psi}(x_1+a,\tau_1,x_2+a,\tau_2,\cdots, x_n+a,\tau_n,t)=\vec{\psi}(x_1,\tau_1,x_2,\tau_2,\cdots, x_n,\tau_n,t)[/math]

 

or

[math]\vec{\psi}(x_1+a,\tau_1,x_2+a,\tau_2,\cdots, x_n+a,\tau_n,t)-\vec{\psi}(x_1,\tau_1,x_2,\tau_2,\cdots, x_n,\tau_n,t)=0.[/math]

 

Since a can be any number, it should be obvious that

[math]\frac{d}{da}\vec{\psi} = \lim_{\Delta a \rightarrow 0}\frac{ \vec{\psi}(x_1+a+\Delta a,\tau_1,x_2+a+\Delta a,\tau_2,\cdots, x_n+a+\Delta a,\tau_n,t)-\vec{\psi}(x_1+a,\tau_1,x_2+a,\tau_2,\cdots, x_n+a,\tau_n,t)}{\Delta a}=0.[/math]

 

Notice that, in the above, the arguments of [imath]\vec{\psi}[/imath] are themselves shown as functions of the shift parameter. Any rudimentary knowledge of partial differentiation should include the fact that the above has to require that

[math]\frac{d}{da}\vec{\psi}=\sum_{i=1}^n \frac{\partial}{\partial x_i}\frac{\partial x_i}{\partial a}\vec{\psi}=0[/math]

 

and, adding the fact that [imath]\frac{\partial}{\partial a}x_i = 1[/imath], one is clearly led to the conclusion that

[math]\sum_{i=1}^n \frac{\partial}{\partial x_i}\vec{\psi}=0.[/math]

 

You might be bothered by the fact that the [imath]x_i[/imath] are discreet numbers and the partials above treat them as continuous variables. This shouldn't be bothersome as no new information (which would add possible new values) can violate any of the steps given. It follows that, in the continuous limit, we should expect the result to be valid. Plus that, it provides about the simplest possible extension of information into unknown regions. Lastly, the above can be done in each of the orthogonal axes of our representation. As to the question, why are these differentials required? I don't see that they are except for the fact that they lead to a convenient way of expressing the constraints required by the existence of that shift symmetry.

If this is all just an exercise in throwing around arbitrary formulas, then the answer "why not?" is perfectly valid, but if you're (eventually) go on to the next step of saying "this formula can be made a *valid assumption* in constructing internally consistent worldviews" then you need to start mapping the pieces of your formula on to the next step. If you don't its just a meaning-free arbitrary formula!

I would agree with that 100%. At the moment, it is absolutely nothing more than a meaning-free formula. I don't know that I would use the word “arbitrary” as it is somewhat strongly dependent upon the definitions I have already put forth.

To apply this issue onto your thesis: your formula may or may not be consistent with any particular worldview, but it all depends on the [imath]vec{psi}[/imath] it exists within!

I won't comment on this because I do not understand what you had in mind when you wrote it. My thesis is that there always exist an interpretation of the facts known to me which satisfies my representation. In no way does that make it consistent with “any particular world-view”. It can be no more than an interpretation of what I know of a specific world-view and it rests upon a paradigm which insures that as more information becomes available to me, the new information will not lead to a violation of that interpretation.

So please *do* think about the examples above and try to work with them: Maybe Q's example is too limited (although quite frankly your response to it was tremendously useful!), but anything you can do to provide analogies will assist us meatheads in "understanding what you're talking about."

The problem here is that any problem which can be solved at all requires such a large base of information that that the actual process required is far beyond anyones physical capability (at least on a conscious level). And I certainly don't regard anyone here as a “meathead”. I am very willing to work on trying to communicate. I think you may find my following response to Q enlightening. If not, I apologize.

 

Qfwfq, I may have misjudged you. You may be trying to resolve a problem which I have not yet mentioned. I have avoided the issue because, once it is broached, most everyone refuses to take me seriously. I will try and clarify exactly what I have in mind.

Specify what the arbitrary labels are and how the mapping may be chosen. Show me what is consequential, I need to catch up with Anssi before his math skills improve enough to get him even further ahead.

The arbitrary labels are “arbitrary labels” and the mapping may be chosen anyway at all. Essentially, nothing is consequential; the consequences are entirely in your epistemological construct (your interpretation of what is going on). It makes utterly no difference what that epistemological construct is, if it is internally consistent, the temporal behavior of the ontological elements can be interpreted such that my equation is a valid constraint.

 

I suspect you may have noticed that there need be no underlying rules to reality at all: i.e., essentially embedded in my work is the question “what would reality appear to look like if it were absolutely and totally random?”. Most everyone is quite confident that “it certainly wouldn't appear as it does”. I do not know “what it would look like”; however, I do know that any explanation you could develop for it could be interpreted in a way which would guarantee the ontological elements would obey my equation. That leads to the conundrum, “how could I possibly achieve an explanation of a totally random reality. Actually, the answer is quite simple.

 

Essentially the circumstance implies something very significant: your explanation of reality must actually be a data compression algorithm which, in reality, (to use the word in a slightly differently way) says nothing about reality other than “what is” is, “what is”. Most everyone immediately drops into the “that can't possibly be true” mode when they realize this and want to hear not another word of it. In their opinion, I must be nuts to even consider such a thing: i.e., to make a metaphor, it doesn't even mention the god of science “causality”. I suspect there is not a single professional scientist who would even dream of considering the possibility as his professional standing would immediately vanish were he to do so. The position of the scientific community is that “an absolutely random universe could not have any rules”. The really significant issue here is that I am not talking about reality, I am talking about your interpretation of reality (your explanation of your experiences), quite a different thing. The fact is that it is your interpretation of reality which must have rules and the ”what is”, is “what is” is the only interpretation which exists without rules.

Logic does not depend on reality. Mathematics is a type of constructing on logic and certain definitions, in essence choices, and therefore does not depend on reality. Logic and mathematics are not a belief about reality. Whether or not the definitions are chosen to describe some aspect of (a given) reality (in a given universe) is of no whatsoever concern to a mathematician. Reality is of no influence on the validity of mathematics; any valid mathematical construct is valid "in" any reality or universe.

It is valid even if that universe is totally and absolutely random. Nevertheless, such an assertion quite often brings forth nothing except total rejection, quite analogous to that “I burned my math book because it had no mention of God.” Modern science is indeed a religion as they think they understand the universe and believe there cannot be another perspective as successful as theirs.

 

Just an interesting comment. Many years ago, when the Internet first became available, I ran across a very interesting web site. I have searched for it many times since but have never been able to find it again. I was a mathematical presentation which proved that, for any given pattern of numbers, there existed a number of numbers within which that pattern could not be avoided. This was a long time ago and I didn't really examine his proof carefully so I cannot stand behind it but I think a simple example of what he was talking about could be “two numbers the same distance apart”. If you try to construct such a set of integers where the pattern absolutely does not appear, you will always run into difficulties.

 

Start with [imath]x_1[/imath] and [imath]x_2[/imath]. Then no number which differs from either of them by [imath](x_1-x_2)[/imath] or [imath](x_2-x_1)[/imath]can be used. (In fact, no pairs which differ by those amounts can be included in the set; there may be subtleties to this extension which have far flung import.) There are still a lot of numbers available so we can add [imath]x_3[/imath] to our collection. Now no number which differs by [imath](x_1-x_2)[/imath], [imath](x_2-x_1)[/imath], [imath](x_1-x_3)[/imath], [imath](x_3-x_1)[/imath], [imath](x_2-x_3)[/imath] or [imath](x_3-x_2)[/imath] can be used. As I said, I do not remember the proof but it seems to me the result was a consequence of the fact that the number of numbers which could not be used expanded much more rapidly than the number of numbers in the collection (every time one number is added, the number of additional numbers to be excluded exceed the total number of numbers already in the set). As I said, I wish I could find that paper so I could examine it carefully (I haven't been able to prove it myself). It is nevertheless quite clear that, with a sufficiently large set of random numbers, the probability that any specific repeated patterns will be found becomes closer and closer to one.

 

This implies that, even in a totally random universe, patterns will exist in any collection of numerical labels given to those elemental entities if the number of elemental entities is sufficiently large. Considering that ”what is”, is “what is” table (that set of points in my [imath](x,\tau,t)[/imath] space) must reflect some [imath]10^{20}[/imath] references for [imath]10^7[/imath] years means that “no recognizable patterns” is a very improbable possibility: i.e.. even a totally random universe will most probably have a great number of recognizable patterns even if no rules are given as to how the mapping is to be chosen. I think this issue will become much clearer if we can get to the solutions of that equation.

 

And finally, as to expectations, considering the volume of information represented by the past compared to that which constitutes the present, one should certainly understand that the probability that the present will make any significant contribution to any pattern based description of the past, has to be negligibly small: i.e., the best statement of your expectation should be “the patterns I see in the future should look a lot like the patterns I used to describe the past”. This implies a good data compression mechanism is most probability the best representation of the universe possible and is probably the rational which stands behind our view of reality. We notice patterns and mark them with labels and begin to deal, not with the patterns themselves but, with patterns in those names. That is almost the definition of a data compression mechanism.

 

Now, I have proved that certain constraints must be imposed upon such a solution and that those constraints are embedded in my “fundamental equation”. The issue is, have I sufficiently defended that position that you will take the trouble to look at solutions to that equation without scoffing at the applicability of my constraints?

 

Have fun -- Dick

[Qfwfq]

The arbitrary labels are “arbitrary labels” and the mapping may be chosen anyway at all. Essentially, nothing is consequential; the consequences are entirely in your epistemological construct (your interpretation of what is going on). It makes utterly no difference what that epistemological construct is, if it is internally consistent, the temporal behavior of the ontological elements can be interpreted such that my equation is a valid constraint.

:shrug:

 

Well, I suppose I didn't word my post very well and you misunderstood it.

i should have said which are the arbitrary labels, not what. In the spy's case there are some non-arbitrary numbers and I don't see what the arbitrary labels would be. I don't see what you would map those numbers on to and I don't know what the table would be. I'm therefore unable to deduce the validity of your constraints.

[AnssiH]

I am not sure what you are referring to when you talk about science defining objects. I am referring to, for example, an apple. Animals have concepts of things like apples, without having a concept of science. An animal or even unscientific human may wonder if he hits an apple from a tree, where will it land.

 

I didn't mean to imply that we are defining objects only when we do science, rather we are defining objects in all our attempts to understand anything about reality.

 

When you perceive that apple, the definition has already been made since you can understand some pattern as an "apple". Note that we don't necessarily do this "defining" consciously.

 

Think about the avalanche of sensory data that is flowing into your brain. You recognize things like apples, reflections, glares, waves on an ocean, rivers, tornados and all sorts of stable patterns that you have tacked with identity. Your comprehension of reality rests on these "sensible things", and it is the interplay of these things that you draw your predictions from.

 

But you were not born with the knowledge that these things exist, instead you defined them. I.e. certain spatial/temporal features of your sensory data become tacked with identity so you understand them as the "same thing"; a thing which preserves its identity through "time" and "space".

 

Whatever behaviour you find from reality will affect how you break it into components. When you see certain familiar behaviour (pattern), you perceive that as an "object X" that you defined.

 

(btw, this is relevant also to your example about babies learning language. You cannot suppose the baby just knows what constitutes a "word" or that there even are such things as "words". That is part of your worldview)

 

So I hope this clears up what I mean by us deciding what constitutes an object. For more philosophical aspects of this, take a look at "Ontological perspective" and "Epistemological perspective" at post #34. (really take a look, I spent a lot of time on that one ;)

 

Let's take a quick look at physics still. Look at the different ontological interpretations of quantum mechanics. They are each a different set of "ontological elements", and they define "space" and "time" differently; they define them exactly the way they need to so to produce correct predictions/expectations for reality. These views are self-coherent but do not mix with one another; one paradigm cannot be investigated from within another paradigm.

 

Note that we always have multiple valid options as to how to break it into "objects". It may not be trivial, but it can be done. Also note that it certainly seems, that to break reality into components at all is inherent to how our understanding of reality works, not inherent to how reality itself works. I.e. what Kant said. In brief:

 

Each worldview or model functions by us having first defined its components, without having any idea about what is the "real way" to define reality into components (or rather, without having any reason to believe reality actually is, ontologically speaking, a set of components)

 

So, assuming you understand how I mean the above, you can understand that world seems very much different when seen through different worldviews (that have tacked identities onto different features of the data, including defining space and time differently). Yet they both can have the exact same explanation power; just they work with different terms.

 

The question is now, is there something that is common to each and every possible (valid) worldview. By valid I mean they do not contain self-conflict. So, how do we express the constraints that arise from the simple fact that each worldview, whatever it may be, needs to be internally coherent. If it contains self-conflict, it cannot be a good description of reality can it?

 

Now we are moving closer to where Qwfwq is already standing (I think). Onto the next post ->

 

-Anssi

[AnssiH]

;)

Well, I suppose I didn't word my post very well and you misunderstood it.

i should have said which are the arbitrary labels, not what. In the spy's case there are some non-arbitrary numbers and I don't see what the arbitrary labels would be. I don't see what you would map those numbers on to and I don't know what the table would be. I'm therefore unable to deduce the validity of your constraints.

 

The "arbitrary labels" are referring to names that you give to the components of reality that you have tacked with identity (look at my previous post). In Doctordick's treatment the names are just numbers. I.e. a guard could be a number 5, a spy could be a number 3, etc... They are arbitrary because guard could be any number and it would not have an effect on the predictions of the worldview.

 

This can be a confusing example because the guards also happen to be shouting "numbers" at each others. The numbers that the guards shout at each others need to be understood as elements in the worldview as well and in this treatment they could be labeled with any number. A shouted word "thirteen" could be labeled as "7856" or whatever. The only reason it would have a label is so that its existence can be marked down into the x,tau,t-space.

 

If that was confusing, please ignore it and let me explain this properly :) I think I know what you are asking about as I tried to take the same route to figure out what the "x,tau,t"-table is for when Doctordick first mentioned it to me. I.e. I tried to figure out how would some simple system be described by it.

 

Unfortunately that is going besides the point. The point is precisely that there is NO "one and only" correct way to map some physical system onto that table.

 

Let's say you map a dual slit experiment onto it, then each different ontological interpretation would map different ontological elements to exist at different certain moment. That is to say, two different people with different worldviews could produce completely different looking tables when describing the same system. The tables might look like they have absolutely nothing in common. It would look like completely different entities would be moving through time in different tables. (Remember, they have merely marked down what entities (that they defined) exist at specific moments)

 

Case example: I think a particularly interesting case is Milo Wolff's attempt to model reality by having defined everything in terms of "spherical standing waves" that are like "ripples of space" (i.e. here space is defined as something that can have 3 dimensional "ripples"). I don't know if that's valid, the point is simply that any physical system mapped through that worldview (where the waves or the standing waves have identity) would look quite a bit different from one where elementary particles move around (relativistically or otherwise).

 

Now the point is that whatever that table might look like, it will have certain properties if it is self-coherent. For example that shift symmetry regarding the probability function arises from the fact that the labels we assigned to the features (that we defined) were completely arbitrary to begin with and cannot affect the behaviour of the probability function (whatever it might be). In common terms, our predictions of reality would be the same even if we called apples oranges and vice versa, or if we perceived red as blue and vice versa.

 

The "x,tau,t"-table will NOT be able to tell you which of all possible models is somehow "correct one". The purpose is to investigate the common properties of all valid models.

 

-Anssi

[Doctordick]

Well, I suppose I didn't word my post very well and you misunderstood it.

i should have said which are the arbitrary labels, not what. In the spy's case there are some non-arbitrary numbers and I don't see what the arbitrary labels would be. I don't see what you would map those numbers on to and I don't know what the table would be. I'm therefore unable to deduce the validity of your constraints.

There is no such thing as a non-arbitrary label. Labels are what the “person who is trying to understand” uses to identify or refer to specific patterns he or she has identified (or decided are significant). They are a consequence of some epistemological construct he believes necessary to solving the problem. When you say, “in the spy's case there are some non-arbitrary numbers” you are in fact saying, “there is additional information here which is not being taken into account” (the meaning of the word spy, the meaning of the utterance your refer to as “13”, etc.). If that is indeed the case, then it is necessary (if you want to communicate the information the epistemological construct is based upon) that you provide that additional information. When you go to do that, the symbols you use can be arbitrarily labeled.

 

Otherwise, your description of the problem is biased by your assumption that some epistemological construct (in this case, I would suspect your presumption that your world view and the expression of the problem in English) is a valid basis within which to consider the puzzle. That epistemological construct may very well be a flaw-free construct but I have no interest in the constraints presumed by some successful epistemological construct; my interest is the constraints required by ALL flaw-free epistemological constructs.

 

And Anssi, you are, as usual, dead on with your interpretation of the situation. Thanks for the help; I hope it does some good.

 

Have fun -- Dick

 

PS This is an addition which occurred to me upon rereading this post. Perhaps it will never be read but I will add it anyway (with a reference to it later). Qfwfq is overlooking the fact that I have said many times that “an interpretation exists” which conforms to my equation. He apparently wants a solution, not an interpretation of a solution: if he were to give me a solution (complete enough that I could reason out his expectations in detail from it) then, with sufficient time, I could present him with a [imath]\vec{\Psi}[/imath] which would yield those expectations (i.e., an interpretation of his solution which satisfied my equation). All I have to do is write a computer program which yields those expectation (if his explanation is sufficient to reason out his every expectation) and then set down the output of that computer program for every possible set of inputs (that would be a table representation of [imath]\vec{\Psi}[/imath]. Exactly what numerical label I attach to each input (the address where that variable is to be stored is immaterial: i.e., consider the inputs to be the information bits themselves).

 

Please let me know if this act violates any rules of the forum. If it does, I apologize. -- Dick

[Kriminal99]

(btw, this is relevant also to your example about babies learning language.

 

On to your response to QFQW...

 

You cannot suppose the baby just knows what constitutes a "word" or that there even are such things as "words". That is part of your worldview)

 

So I hope this clears up what I mean by us deciding what constitutes an object. For more philosophical aspects of this, take a look at "Ontological perspective" and "Epistemological perspective" at post #34. (really take a look, I spent a lot of time on that one :weather_snowing:

 

....

 

The question is now, is there something that is common to each and every possible (valid) worldview. By valid I mean they do not contain self-conflict. So, how do we express the constraints that arise from the simple fact that each worldview, whatever it may be, needs to be internally coherent. If it contains self-conflict, it cannot be a good description of reality can it?

 

Now we are moving closer to where Qwfwq is already standing (I think). Onto the next post ->

 

-Anssi

 

I am not sure if you were agreeing with my example or proposing there was a problem with it. Just in case, in that example the baby doesn't need to know what a word means. All that matters is that the word is being uttered at the same time as the object is being seen. This is why the & sign was used to denote a coincidental connection.

 

It doesn't have meaning until they start to be repeatedly heard at the same time as they see the object or chain of events. Thus an idea of an object is just a collection of related perceptions, with no special status attributed to any one of those perceptions based on what sense they came from or anything else. This simple system explains why no arcane understanding of time/space is needed to begin defining the world around them. Everything is just defined in terms of each other, which of course makes perfect sense considering that:

 

1) There is no end to a chain of explanations of "why", so a better instinctual understanding would require infinite brain mass to support...

 

2) Neural networks seem to indicate that things work this way

 

This approach doesn't really require the assumptions you mention in the other post you referenced. It is simply recognizing coincidences. Once we are old enough to question these coincidences by realizing our parents could have called those things something different, we also realize that they "make the interpretation of the consequent patterns meaningful" enough that it is pointless to change them.

 

On to your response to QFQW and DD's post...

 

I don't think the problem is explaining that every world view needs to be internally coherent. Everyone knows that, they just don't know how or care to know how to test it.

 

People are not by nature rational beings. They are after animal related goals and too much reasoning doesn't seem to allow them to reach those goals. What we need to do is create an enviornment that forces people to accept rationality to achieve their animal goals. That is basically what is behind people like you and me.

 

Otherwise, your description of the problem is biased by your assumption that some epistemological construct (in this case, I would suspect your presumption that your world view and the expression of the problem in English) is a valid basis within which to consider the puzzle. That epistemological construct may very well be a flaw-free construct but I have no interest in the constraints presumed by some successful epistemological construct; my interest is the constraints required by ALL flaw-free epistemological constructs.

 

So given that a person cares about doing so, how would they do this?

 

Everyone involuntarily uses the same basic system to understand their surroundings up to a certain point, and they always use this system to some degree.

 

Because of this, the same rules are necessary for everyone.

 

Completeness is not one of those rules. You can never achieve it. However you should always look for more information than you currently have, especially if you think it might have relevance to the integrity of your belief set.

 

No logical contradictions obviously is one of those rules. However, we cannot perceive infinite logical consequences of any given claim. Thus I propose several "efficiency" rules to best allow us to use what little resources we have.

 

Cut anything from definitions of words other than the context the word is meant to refer to. Then determining logical consequences simply becomes math, instead of dealing with a pile of spaghetti that you have to untangle. And then you can actually see logical contradictions. An important part of this is cutting out metaphorical definitions of words.

 

If anything unnecessary cannot be removed (such as the label), then be aware that infinite other labels could be used without affecting the core beliefs.

[Qfwfq]

The "arbitrary labels" are referring to names that you give to the components of reality that you have tacked with identity (look at my previous post).

Which is the semiotic issue, and my choice of example had more to do with this than you might have imagined. But I still can't figure out what help the x, [imath]\tau[/imath], t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

 

The point is precisely that there is NO "one and only" correct way to map some physical system onto that table.

I wasn't asking for the one and only way, I was asking for some indication of how the the things can be organized into tables in a way that actually reflects what is to be explained and a justification of the constraints.

 

The "x,tau,t"-table will NOT be able to tell you which of all possible models is somehow "correct one". The purpose is to investigate the common properties of all valid models.

Obviously, and I'm trying to justify the constraints.

[Buffy]

Dick,

 

Thanks for the extended explanation. I'm going to try to stick to something simple to focus on that still gets at the core of my lack of clarity about what you are doing:

Now, the important thing in all this is that the given known information is actually the things being labeled, not the labels themselves.

Got that. Meta versus meta-meta versus meta-meta-meta is not problem for me. I've had it from philosophy to math to computer science and I'm really good at it! I'm meta-gal!

 

But:

Since it can be represented as a mathematical function of those numerical labels, we know certain symmetries must exist in that representation. In particular we know shift symmetry must be a property of the representation.

WHY?

 

This is why I thought your example of non-associative algebras was so useful! I can come up with lots of excuses as to why those mathematical functions should show no shift symmetry whatsoever!

 

From my point of view so far, this is an unjustified assumption, that makes agreeing on your formula in the abstract impossible without further explanation as to why this restriction would hold.

 

As I think both Q and I are trying to do, it seems that a better understanding of the justification--indeed *mapping* even if it is one or two meta levels above a concrete example--is necessary before justifying such a restriction can be seen as valid.

 

A side note: I can definitely see how this can degrade into the "'what is' is 'what is'" argument, but I appreciate and *agree* with you that its not really relevant, nor is it "preposterous." On the other hand, I think its evidence that there is something missing in your math here, because it may be the case that that conclusion is only showing an incompleteness in the mapping: much like quantum mechanics shows "illogical" or "inconclusive" "infinities" when applied to gravity. The conclusions drawn may or may not be wrong, but the math is inadequate to justify those conclusions.

 

I'm fond of noting that the list of logicians who have seriously proposed formal systems that turned out to be inconsistent reads like an honor roll: Frege, Church, Curry, Quine, Rosser, :snow:

Buffy

[AnssiH]

I am not sure if you were agreeing with my example or proposing there was a problem with it.

 

There was not enough information for me to say if there's a problem or not :snow: (presumably your idea has got more details to it than were voiced)

 

I was just trying to steer the conversation from an AI model more towards the original subject.

 

Thus an idea of an object is just a collection of related perceptions, with no special status attributed to any one of those perceptions based on what sense they came from or anything else. This simple system explains why no arcane understanding of time/space is needed to begin defining the world around them. Everything is just defined in terms of each other

 

Yes, everything is defined in terms of each others [in self-coherent manner]. That is the crux of what I was calling "semantical worldview".

 

So it seems we agree, and I suppose the only thing you have reservations of is whether all that math is how we build our worldviews. I'm fairly sure it is not I should have stressed before that Doctordick is not exactly proposing that this is how we do our worldviews. Rather this should be viewed as a fairly high-level analysis about our worldviews. What consequences there are as a result of that analysis, is a different matter. (Certainly it could lead to methods for building self-coherent predictive models out of completely unknown information, and those methods could be completely different from how brain does it...)

 

-Anssi

[AnssiH]

Which is the semiotic issue, and my choice of example had more to do with this than you might have imagined. But I still can't figure out what help the x, [imath]tau[/imath], t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

 

I can't remember where there would be a good succinct post defining these so;

 

Let's say you were to map down a worldview where reality is identified as bunch of electrons and protons, then electrons would get different X label than protons. Let's say electrons are "1" and protons are "2" on the X-axis.

 

If a certain moment consisted of three electrons and four protons (according to that worldview), you'd need to mark down three 1's and four 2's -> to do that you need the tau axis.

 

So to answer your question, different sorts of elements are labeled with different X (what is different sort depends on your worldview), and each individual element would be labeled with (x, [math]\tau[/math]).

 

The beforementioned "moment" could look like this:

(1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (2,4)

 

Or obviously you can conceive it as points on an x,tau -plane

 

I'm sure you can figure out that the t is there so we can index different "moments", i.e. multiple x,tau -planes. (Doctordick calls them "presents")

 

And I'm sure you realize immediately that it's not quite that simple; typically worldviews have some definition for "space" too so the mapping needs to contain that specific definition as well one way or another.

 

I actually asked about this in the PF forums (post#422) but it got drowned between other issues, so Doctordick needs to clarify on that. (Let's say one's interpretation of a situation is that "an electron is bouncing between two protons in an euclidean space"; how would that be mapped, as an example).

 

-Anssi

[Doctordick]

But I still can't figure out what help the x, tau, t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

The [imath](x,\tau,t)[/imath] table is no more than a tabular representation of exactly the same data displayed as points in the [imath](x,\tau,t)[/imath] abstract Euclidean space. The actual points in the [imath](x,\tau,t)[/imath] space are nothing more than a way of representing the references specific to some epistemological construct. Any collection of references to the ontological elements underlying a specific epistemological construct can be displayed in such a structure. Think of it as a collection of references defining the language used to describe one's epistemological solution: i.e., used to display the basic data sufficient to decipher the solution you have in mind.

I was asking for some indication of how the the things can be organized into tables in a way that actually reflects what is to be explained and a justification of the constraints.

It just takes a lot of data and each element of that data can be referred to by any label you wish to use as figuring out the meaning of the labels is a very real part of figuring out the epistemological solution you have in mind. For example, (and Buffy, here is another example) consider your problem of the spy and the code with the guards only, instead of giving it to me, give it to a two day old infant. What response would you expect?

 

Certainly that infant has the innate ability to understand what you are talking about. The problem is that it would take you maybe ten to twenty years to provide him with sufficient data to decipher exactly what the question was. Now, your presentation of that data, had it been carefully documented could be labeled with arbitrary [imath](x,\tau,t)[/imath] labels. When his actions eventually became consistent with your expectations (i.e., what you would expect of someone who understood what you were talking about) you would come to believe he understood you. Then, and only then, could you talk about the issues you want to talk about. The issue here is that your concern is only meaningful within a rather complex specific epistemological construct.

Obviously, and I'm trying to justify the constraints.

Then you are looking in all the wrong places for that justification. The justification is not to be found in any epistemological construct as it lies not in the epistemological construct but rather is a consequence of the fundamental symmetries of the references system used to express that epistemological construct. Those constraints are a direct consequence of the embedded symmetry of that arbitrary reference system and have absolutely nothing to do with any specific [imath](x,\tau,t)[/imath] table related to reality.

 

We have a subtly significant structure here. The epistemological construct is a function of the ontological elements themselves, not the actual numerical references chosen to display them in the [imath](x,\tau,t)[/imath] table. Yet, independent of how those numerical labels are created, if the epistemological construct may be deduced from the ontological elements themselves, it can be deduced from that collection of numerical labels. The constraints I am referring to are a consequence of the symmetry necessarily embedded in that representation no matter how that representation is created.

 

By the way, as another example for Buffy, in attaching reference indices to data, consider the following hypothetical situation. We have a flaw-free epistemological solution to archeology: i.e., it is perfectly consistent with all the data available to us. Under that solution, fire was not used by humans prior to 65,000 years ago (I just pulled that out of my hat so don't quibble with its accuracy). An archaeologist digging at a site already definitely dated as being prior to 75,000 years ago discovers a charcoal bed together with chewed bones and other indications of human habitation. This is new information: i.e., by my definition of time we are talking about the future (i.e., a "new" present). Relative to the epistemological construct he was working with, this is a future event: i.e., his finding this stuff occurred in the future, not in the past of his epistemological construct; however, in order to maintain the overall structure of his epistemological construct, he will probably assign a t index of this bed of charcoal to somewhere in the vicinity of -75,000 years.

 

What is significant here is that the division between past and future (a specific “present”) contains this new information; his assignment of this information to -75,000 years in his [imath](x,\tau,t)[/imath] table is an assumption and not exactly an objective representation of his experiences. He has eliminated the possibility that the charcoal bed came into existence the moment he uncovered it. Note that I am not saying his assumption is wrong, I am merely saying that it is an assumption; the real question being “what other assumptions is he inadvertently making?” It is certainly true that the assignment for t may nevertheless lead to a new flaw-free epistemological construct but that is not the issue under discussion. The issue here is that, in the absence of an epistemological solution, those reference indices are open undefined numerical labels.

 

This is why I thought your example of non-associative algebras was so useful! I can come up with lots of excuses as to why those mathematical functions should show no shift symmetry whatsoever!

Again, you are scumming to the overwhelming urge to look at epistemological constructs. The issue here is the embedded symmetries in the reference system used to express the information on which those epistemological constructs are built.

 

Certainly you will accept the fact that one can use numerical labels to refer to the specific elements of that information. If you had that entire collection of references, including the time index which yields changes in that collection, it is quite clear that patterns would occur (that's pure finite numerology). If your explanation (your epistemological construct) is actually no more than a data compression mechanism (which it certainly must be since the collection of numerical labels, in the absence of an epistemological construct, cannot possibly contain any information themselves) then it is quite reasonable to presume that such data compression mechanisms are feasible.

 

So, start with a set of such numerical labels (that hypothetical ”what is”, is “what is” table and nothing more) and create an epistemological construct which yields a flaw-free explanation of your experiences (recreates the table). Now you have solved the problem; you have explained your experiences! Now take that original table and add the number a to every [imath]x_i(t)[/imath] element. In what way have you changed the problem confronting you? That is called shift symmetry. You cannot remove that symmetry from the problem and it follows that the symmetry must be likewise embedded in the solution.

 

Thanks for trying Anssi but I suspect your presentation will sway few.

 

Have fun -- Dick

[Qfwfq]

Actually Dick, I found Anssi's presentation quite clarifying. Considering it with his remark:

And I'm sure you realize immediately that it's not quite that simple; typically worldviews have some definition for "space" too so the mapping needs to contain that specific definition as well one way or another.

 

I actually asked about this in the PF forums (post#422) but it got drowned between other issues, so Doctordick needs to clarify on that. (Let's say one's interpretation of a situation is that "an electron is bouncing between two protons in an euclidean space"; how would that be mapped, as an example).

it seems that the "what is, is what is" table begins to look a bit like Fock space. Since he found no answer to his query as of post#422 in the PF forums, I'll say to his benefit that it is defined in any good book of field theory. The most pedestrian treatment is perhaps the one in Schweber's book, of which I believe this should be a recent edition and it seems an accessible price too, especially for us € folks these days. It does suppose quite a bit of calculus, linear algebra and stuff to be familiar, but I wouldn't be surprised if Anssi could follow the overall line of reasoning concerning his query. :)

 

It didn't really take all that much after all, to give me a useful bit of insight.