Laying out the representation to be solved.

[Doctordick]

I am inserting this preamble because it has been quite evident that very few people comprehend the underlying essence of my work.

 

 

I was trained as a physicist so most everyone presumes I should be discussing physics. When I was young, I thought I was a physicist but when I came forward with my discovery, physicists said it was philosophy, philosophers said it was mathematics and mathematicians said it was physics. No one chose to see it as of any interest to them. I have come to the conclusion that the physicists were right; it is essentially a philosophical proof as it is a tautological construct. It has nothing to do with the field of mathematics as all the mathematics used constitutes well known relationships. And, as it makes utterly no predictions and does no more than establish constraints upon one's personal expectations required by internal consistency of our world view, it clearly is not physics.

 

 

I am currently of the opinion that philosophers have severely undercut the the reputations of their own arguments by failing to be exact with the actual facts they have to work with. In particular, they have grossly short changed their field by failing to be cognizant of all the advances in logical analysis achieved by what is now called the “exact sciences”. Philosophy was once held to be the queen of sciences; a status it has long since lost. I find it rather strange that I was awarded Doctorate of Philosophy in Physics whereas physicists want utterly nothing to do with philosophy.

 

 

The following is the fundamental basis of my tautological construct:

 

 

In many respects, my presentation is quite analogous to Alan Turing's proof that his “Turing machine” was capable of performing any conceivable mathematical computation if it were representable as an algorithm. I believe I have proved (in the proof that I will show later) that any conceivable explanation of anything must satisfy my fundamental equation if that explanation is internally consistent.

 

 

It should be understood that my construct is as abstract as was Alan Turing's “Turing machine” and must be viewed in terms of the exact definitions I provide. It is also considerably more complex than his machine and must be carefully understood line by line. Essentially, the method of representing things is called a language and what I am presenting in this post is an abstract language designed to be capable of representing any possible conventional explanation.

 

 

I will only concern myself with what I call absolutely flaw free explanations. By the term “flaw free”, I mean that there exists no known circumstance which contradict that explanation: i.e., it is not only absolutely internally self consistent but it is also perfectly consistent with all information which is presumed to be known.

 

 

Laying out the problem to be solved.

 

 

Section 1: My definition of an explanation:

 

 

An explanation is a procedure which will provide rational expectations for hypothetical circumstances.

A “procedure” constitutes some sort of instruction, “expectations” constitute an estimated probability of yes/no decisions and “circumstances” constitute a description of whatever it is we are concerned with expecting. As for my meaning of “rational” see my post Defining the nature of rational discussion! In that post I explain why I feel “rational” means that the the result does not generate an emotionally negative response as to its truth. I will presume the meaning of “hypothetical” is understood.

 

 

Part I

Clearly, the first thing required here is a notation capable of representing absolutely any possible circumstance in a form which makes no presumptions whatsoever about any aspect of that circumstance.

 

I assert that absolutely any circumstance conceivable can be represented by an expression of the form:

 

 

[math](x_1, x_2, x_3,\cdots, x_n)[/math]

 

 

 

where [math]x_i[/math] is a numerical label constituting a reference to a fundamental element of the circumstances being explained.

There exists a problem here which, if the explanation is to be both exact and absolutely flaw free, must be carefully handled. It is best to see both “x” and “i” as separate labels referring to the same element. The possibility always exists that another internally consistent explanation of exactly the same circumstances may exist. Although the same circumstances are being explained, it cannot be presumed that this alternate explanation uses the same fundamental concepts for the fundamental elements being represented: i.e., essentially the two labels may obey very different constraints.

 

 

I use “x” (the common mathematical symbol for an unknown) as a label for the actual underlying element behind the explanation as this label is essentially undefined: i.e., there exists no way of defining this label in the absence of an explanation so it essentially has the character of an unknown. I use “i” as a label for the same element as referred to by the explanation as these labels are specifically defined by the explanation and I show it as an index on x to establish the connection. Thus the expression, [math]x_i[/math], is to refer to a specific underlying element appearing in and identified by the specific explanation being represented.

 

 

There is a subtle difficulty with the notation suggested above which needs to be handled carefully. The difficulty I am talking about arises because I am essentially using the notation [math](x_1,x_2,x_3,\cdots,x_i,\cdots)[/math] which, taken at face value, implies that every labeled element defined by the explanation (as referenced by the numerical index “i” on x) is different: i.e., whatever is being referred to (and defined by the explanation) by [math]x_{i_a}[/math] is different from what would be referred to by [math]x_{i_b}[/math]. Such an interpretation would make my notation disallow multiple occurrences of any defined elements. The problem could certainly be solved by using a more complex notation; however, there is an easier way to handle that possibility which will satisfy any and all such complications generated by different explanations designed to explain a given set of “undefined underlying facts” referred to by the numerical labels denoted by “x”.

 

 

The original notation above is just fine for all possible explanations if we simply allow different subscripts to refer separate occurrences of the same defined element anytime such a duplication is needed. After all, the "i" numerical index is supposed to reference some elemental defined thing required by the explanation: i.e. the i'th thing being referenced is a specific defined element; that two different numerical indices have exactly the same defined element as the item being referred to is really of no real consequence. Think of these references as an enumerated list. Is there really any problem having the same referenced element appear twice in that list?

 

 

Also, since the explanation being represented must always define all these labels anyway, there is no real necessity to use any numerical labels beyond the normal counting set: [math]1, 2, 3, 4, \cdots, i, \cdots [/math].

 

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [math]x_i=x_j[/math]: i.e., the numerical reference to the undefined underlying element refers to exactly the same “x” element while the associated numerical index “i” may or may not refer to specifically different defined elements. The point here is to handle all possibilities. It must be recognized that, since the "x" label is undefined, we absolutely can not know if this is or is not the case; however, if the notation disallows such a thing we can't really say "all possibilities" can be represented by the notation: i.e., we cannot require [math]x_i \ne x_j[/math] for any given pair of given defined i, j elements.

 

 

It should be understood that these numerical labels are no more than reference labels (they can refer to any specific linguistic description required by the explanation under analysis including any “picture” required). The complete set of n such labels “[math]x_i[/math]” can describe any conceivable circumstance as each label refers to a specific element within the description of the circumstance of interest. If you can define the circumstance of interest, such indices can actually be specified: i.e., think of a computer file containing every piece of information pertinent to the explanation being represented.

 

 

I think I have shown that my assertion is indeed a fact; the notation defined is a possible way of representing any conceivable circumstance.

 

 

However, a second serious issue, not yet mentioned, must be discussed.

 

 

 

If an explanation is required, we cannot already know all the answers to all possible questions: i.e., the concept of expectations would, in that case, be meaningless. Thus it is that all possible circumstances representable by the notation [math](x_1, x_2, x_3,\cdots, x_n)[/math] can be divided into two sets: those who's probability are actual known facts and those who's probability is dependent upon the veracity of the explanation. For reasons of convenience I will attach the label “the past” to the set who's probability is known and attach the label “the future” to the set who's probability is not known. In addition, I will attach the label “the present” to any addition to the set who's probability is converted from not actually known to actually known.

Think of this in terms of the computer file mentioned above. If that file contains all possible circumstances then no explanation is necessary; the file itself contains the answers to all questions. I use the labels “past” and “future” as those labels are fairly well consistent with how we would tend to view such a file. Additions to such a file would constitute answers previously unknown: i.e., expectations (provided by the explanation) would be verified (by experiment or observation), that verification would thus be a specific present which could be indexed by an index I will call “t” appended to the specific circumstance. Symbolically, a specific circumstance will now be represented by the expression

 

 

[math](x_1, x_2, x_3,\cdots, x_n,t)[/math]

 

 

 

An index “t” can be appended to every hypothetical circumstance representable.

 

 

 

The number of “presents” contained in the circumstances standing as a defense of your explanation (what is defined to be the past) can be indexed. The number of changes (in the circumstances standing behind your explanation) must be finite as, if the number is infinite, you cannot make use of them: i.e., no matter how many you have to work with, you are not finished (that is the very definition of “infinite”). If they are finite, they may be ordered.

Note that “t” is merely an index on the circumstance and the actual value of t given by your explanation need not be related to the order with which these circumstances transform from “not known to known”.

 

 

On the other hand, regarding the unknown circumstances, they must also be indexed in order to refer to them as possibly to be known (the reference cannot have a different form or one would have to have some sort of change in notation taking place in the “present”). A number of very important issues arise here. First, the number of t indices required by the representation (when we include the future) must be infinite as no matter how many circumstances are known (contained in the past), there are (perhaps) others which are not known (contained in the future) and our notation must allow for that possibility. The situation described is the very definition of “infinite".

 

 

And secondly the notation must allow for the possibility that the explanation might assign an index t to a circumstance which would lie between two indices already assigned: i.e., there is always a possibility that the explanation would require one to assign some specific new information to the sequence already defined to be “the past”. For example, archaeologists often discover information which they assign to the past: i.e., the common scientific explanations do not presume those sites came into existence the day the archaeologist discovered them they instead assign a time consistent with their explanations.

 

 

Being free to assign a reference “t” between any two indices already assigned makes t a continuous variable. That is, in fact, the very definition of a continuous variable.

 

 

Finally, the index “t” is quite different from the [math]x_i[/math] indices as it relates to the order of circumstances as per your explanation (and the division between known and unknown circumstances) and actually has no underlying undefined component as does the reference symbolized by the “[math]x_i[/math]” label.

 

 

There is one additional benefit of this additional t index. If, within the circumstance to be represented (i.e., the representation [math](x_1, x_2, x_3,\cdots, x_n,t)[/math]) there is any significance whatsoever to the order of the fundamental elements [math]x_i[/math] the index t can be used to indicate that order (the circumstance [math](x_1, x_2, x_3,\cdots, x_n,t)[/math] can be divided into multiple circumstances indexed by different t indices. As a consequence, within the notation [math](x_1, x_2, x_3,\cdots, x_n,t)[/math], exchange of position of any of the [math]x_i[/math] labels will no longer be of any significance whatsoever.

 

 

Before I close my argument regarding the notation I intend to use to represent the circumstances, there is one other common characteristic of explanations which must be included in the notation. If it is not included, the notation would not be capable of representing absolutely any explanation (which is the intention here). Many explanations contain presumed elements; elements not necessarily part of the actual underlying elements to be explained but rather, are elements required by the explanation itself. These elements may or may not be bona fide but are nonetheless an essential part of the explanation. The fact that an explanation is flaw-free (fits all known information) and continues to be flaw-free for a continuing collection of presents (more experiments) cannot be taken as proof that all fundamental elements of that explanation are bona fide: i.e., it is always possible that there exists an alternated explanation which does not rely upon those elements.

 

 

Of course, it is always possible these elements are indeed bona fide thus it is necessary to include an underlying x to provision this possibility. Essentially, that expands the number of elements represented by the numerical labels x_i from being a finite set to being an infinite set because, there may exist presumptions within the explanation itself which rely upon an infinite number of elements not actually part of the underlying known circumstances which the explanation was created to explain.

 

 

There are some subtle consequences of this infinite extension which will be brought up later when I construct my paradigm. For the moment, the notation will allow fictitious underlying elements so as to avoid the difficulty of elements required only by some specific explanations. Thus it is the primary conclusion of this presentation is that there exist no circumstances which cannot be represented by the purely numerical symbolic notation:

 

 

[math](x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]

 

 

 

I now assert that I have in fact designed a method of representing absolutely any possible circumstance required by any possible explanation in a form which makes absolutely no presumptions about any aspect of those circumstances nor the explanation of those circumstances.

 

 

 

Part II

 

 

The next thing required here is a method of representing the expectations generated by that explanation by any specific circumstance of interest.

 

I assert that any said “expectation” can be represented by a number greater than or equal to zero and less than or equal to one; where zero indicates the circumstance is not possible and one indicates that the circumstance will definitely occur. I will presume that the professional field of probability and statistics will yield a rational interpretation of numbers between zero and one.

What is interesting about this representation is the fact that the representation implies that the definition of an explanation (an explanation is a procedure which will provide rational expectations for hypothetical circumstances) is totally equivalent to “a procedure for obtaining a specific number (that probability referred to above) from a collection of specific numbers expressed by the numerical expression, [math](x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math].

 

 

This is, in fact, the definition of a mathematical function; thus all explanations may be identified with a mathematical expression. The explanation is in fact the function which provides the probability of the circumstance under examination. Thus our concern is with a function of the form:

 

 

[math]0\;\leq\; P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\;\leq \;1[/math]

 

 

 

The above constraint (that the value of the function is bounded by zero and one) has absolutely nothing to do with the circumstances being discussed (the numerical expression: [math](x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]) but is rather a purely mathematical constraint derived from the definition of probability. As such, it is in our interest to express that constraint by mathematical means outside the definition of the circumstance under examination as it cannot be a constraint upon the circumstances themselves.

 

 

There exists a simple method of avoiding that constraint. Let [math]\vec{G}(\vec{x})[/math] be a representation of an arbitrary function: i.e., a function is a method of mapping one set of numbers (what is normally called the “argument” of the function: i.e., what is here represented by [math]\vec{x}[/math]) into a second set of numbers (what is normally called the “value” of the function: i.e., what is here represented by [math]\vec{G}[/math]). The vector notation is used here merely for the convenience of succinctly displaying an unknown set of numbers as a vector in an abstract space.

 

 

Given any such function [math]\vec{G}(\vec{x})[/math], one can define a second function [math]\vec{G}^\dagger(\vec{x})[/math] such that the standard definition of a “scalar product”, [math]\vec{G}^\dagger(\vec{x})\cdot\vec{G}(\vec{x}),[/math] is a positive definite real number.

 

 

The dagger is there to denote the conversion of each specific number in the “value” of [math]\vec{G}[/math] to a representation whose product with identical specific number in the output of the original function is a positive definite number. This extension in possibilities for the specific numbers in the “value” of [math]\vec{G}[/math] (for example those values can now be imaginary numbers and, in fact, many other more complex constructs) allows us the option of building into [math]\vec{G}(\vec{x})[/math] some important internal correlations which will be shown to be of extreme value later. For the moment it should be recognized that those same correlations can be expressed by multiple real numbers: i.e., I am not changing the definition of [math]\vec{G}(\vec{x})[/math], I am merely allowing some very interesting (and it turns out necessary) expressions of internal correlations.

 

 

If we now define

 

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\propto \vec{G}^\dagger(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\cdot\vec{G}(x_1, x_2, x_3,\cdots, x_n, \cdots, t),[/math]

 

 

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math] is guaranteed to be greater than or equal to zero. The only remaining part of the constraint due to P being a probability is to define that constant of proportionality such that the upper bound is unity. In the definitions of probability in standard probability theory, that upper bound is obtained by requiring that the sum over all possibilities be one. We can do exactly the same thing here. We merely integrate (or sum) the function [math] \vec{G}^\dagger\cdot\vec{G}[/math] (which is [math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math] times some constant) over all possibilities and use the fact that P integrated (or summed) over all possibilities has to be one to establish that constant of proportionality. We then merely divide [math]\vec{G}[/math] by the square root of that integral (or sum) and obtain a new function (which I will call [math]\vec{\Psi}(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]). At this point the correct probability for the expectations predicted for our explanation can be written

 

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t) \equiv \vec{\Psi}^\dagger(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\cdot\vec{\Psi}(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]

 

 

 

A number of possible problems can occur with that procedure. First, the specified integral might be zero and division by zero is undefined; in that case, the division is unnecessary as [math] \vec{G}^\dagger\cdot\vec{G}[/math] cannot be greater than one and thus [math]\vec{\Psi}[/math] can be set equal to [math]\vec{G}[/math].

 

 

Secondly, the specified integral (or the specified sum) might be infinite and division by infinity is exactly zero causing the defined function (which is to be our explanation) to vanish exactly. From the perspective of probabilities, this second case actually appears to be quite reasonable. Anytime the number of possibilities goes to infinity (i.e., there are an infinite number of possibilities which do not vanish) the probability of a specific result must vanish. In that case, we concern ourselves not with specific cases but rather with ratios between integrals (or sums) taken over various ranges.

 

 

It should be recognized that the only issue of interest here is that the result must be interpretable as a probability. That property, and that property alone, allows us to consider any given algorithm as a possible solution to our problem: i.e., the above division is unnecessary as we can use [math]\vec{G}[/math] directly and examine ratios between integrals (or sums) over different ranges.

 

 

Another possibility is that integration (or sum, considering possible singularities) over [math]\vec{G}^\dagger\cdot\vec{G}[/math] is undefined. In that case, I would hold that the offending function simply cannot be seen as equivalent to an explanation: i.e., if one cannot define a probability from that function it simply cannot serve as a representation of an explanation. If anyone can show how to define a probability from an offending function then that operation will serve to transform that [math]\vec{G}[/math] into my [math]\vec{\Psi}[/math] and we are once more back to a mathematical expression of the explanation. It should be clear to the reader that, if a flaw free explanation of the known circumstances exists, a method of obtaining the expectations must exist and thus so must the analogous function.

 

 

To restate the above, our interest is to find, from the collection of all possible functions, the specific function [math]\vec{\Psi}[/math] which corresponds to a given explanation: i.e., the function must yield exactly the observed probabilities of the known circumstances (what I earlier defined to be the known past). mathematically speaking that would be for all circumstances where t is less than the current present (whatever index the explanation puts upon that present),

 

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)dV_x=\vec{\Psi}^\dagger \cdot\vec{\Psi}dV_x[/math]

 

 

 

where dV_x is the differential volume [math]dx_1dx_2\cdots dx_i \cdots [/math] if the possible circumstance constitute a continuous field or one if the circumstances are discreet. The function must yield a probability density or absolute probability totally consistent with what is known. If we knew the data exactly, that number would be either one for each possible circumstance and zero otherwise or, if our knowledge were inexact, a value consistent with the probabilistic representation of that expectation: i.e., the real problem is to find a function which fits the known circumstances (that would be the known past). The known circumstances, [math](x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math] and their respective probabilities can be represented by a table of values and arguments for the function [math]\vec{\Psi}[/math].

 

 

The issue of an infinite number of entries to that table arises. That event can only occur via the addition of elements required by the explanation but not actually required by the circumstances being explained. The issue there is that the infinite number of hypothesized elements could only be applied via mathematical methods and the consequent possibilities thus have to be obtained via integration (or sum) over the acceptable cases: i.e. the actual number of probabilities to be identified as past circumstances must still be finite. (If such a thing can not be done, the correct impact of the added elements can not be specified and the required elements will not serve the purpose assigned to them).

 

 

It is then clear, at this point, that the problem of finding [math]\vec{\Psi}[/math] is one of interpolation. We need to find a function which fits the known circumstances (known for specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances. The problem confronting us becomes quite obvious here: any mathematician knows that there exists an infinite set of solutions even for the simplest of such problems. Since every such solution is a flaw free explanation of the known circumstances, a blind search for a solution from the given perspective is clearly a complete waste of time.

 

 

However, sometimes ignorance can be a powerful analytical tool. I am speaking here of symmetry arguments. Let us take a careful look at the representation I have laid out. Essentially I have proved that, if an explanation exists for a known set of circumstances, there exists a mathematical function (which I will represent as [math]\vec{\Psi}[/math]) which will yield exactly the expectations implied by that explanation. At the moment, it does not seem to be a very useful fact but it must be recognized as a fact nonetheless.

 

 

 

For those who find the above acceptable I will continue this theme in another thread some time down the road, explaining exactly how one can fabricate an excellent paradigm expressible via the above notation which will set some very exact constraints on the required algorithm without imposing any presumptions whatsoever on the circumstances nor the explanation being represented.

 

 

Meanwhile, I would like to know of any confusion generated by the above opus. Please don't worry about its usefulness as I am only concerned about one issue at this moment. Is there anything above which is not clear? I want to be as clear as possible before I go on and please help me in that effort. I will be appreciative.

 

 

If anyone can point out and/or prove that something I have said is in error please allow me first to respond by private message before you clutter up the thread with poorly thought out complaints. I am just trying to keep things as clear as possible and have no intention of blocking well thought out complaints. I simply believe they are more apt to be misunderstandings than errors.

 

 

Have fun -- Dick

[lemit]

I think that, as in a marriage that fails after a number of years, philosophy and the sciences have drifted apart in the last few centuries.

 

I have chosen the philosophy (maternal?) side of the family. You suggest you believe your construct is most likely philosophy. I have a question for which I have no preconceived answer: which branch of philosophy do you think your construct best fits?

 

Thanks.

 

--lemit

[Doctordick]

I have a question for which I have no preconceived answer: which branch of philosophy do you think your construct best fits?

Regarding my personal opinion, I think modern philosophy is a pretty worthless endeavor and that would apply to all of the “branches”. “The main subjects of ancient philosophy are: understanding the fundamental causes and principles of the universe; explaining it in an economical and parsimonious way...” Think of me as trying to pick up from where they left off.

 

Lawcat has sent me a private message indicating severe misunderstanding of the issues here and, presuming others have jumped to some of these same conclusions, I am answering his questions here.

1. You have created a space[/b] X(x1,x2, x3, . . . , xn, . . . )

No I have not created a space. You have done so in your imagination. My representation is no more than a list of numbers and these numbers are no more than reference labels to the concepts with which your explanation is fabricated. As I said at the beginning, it is essentially an abstract language. No matter what these numbers refer to, being numbers they can be taken to be arguments to some (as yet undefined) mathematical function. Any computer file may be seen as a collection of hexadecimal numbers and, as such, could be used as an argument to a mathematical function. Any other conclusion (unless you defend it) constitutes jumping to a conclusions as to my intentions.

In other words, even though you intend to stay away from knowing what X is, you already have preconceived idea of what it is which becomes a part of the solution?

No. It is you who is jumping to unwarranted conclusions as to what x is: i.e., you are beginning with a preconceived idea as to what these numbers represent. That is to say, you are attempting to intuitively develop some way of seeing these labels other than just numerical labels (you are attempting to incorporate them into your world view in some way).

2. Circumstance is the explanation itself, [/b]the space X(x1, x2, . . , Xn, . . ). Right? If no, then what represents the explanation as distinct from circumstance?

No, the circumstance is not the explanation itself. The circumstance is what is being explained. The explanation is the method of generating your expectations (I defined these terms at the very beginning) regarding questions not answered in the known circumstances. The opening issue was that any acceptable explanation of anything must yield exactly the circumstances you know. Otherwise it is invalid from the get go: i.e., any explanation which fails to be consistent with given circumstances is initially inconsistent with the stuff it is supposed to explain and is thus certainly not flaw-free.

 

Now the circumstances might include what you might term an explanation but long before you could come to such a conclusion, you would first have to be able to explain those circumstances: i.e., you must, from the circumstances themselves, decipher the existence and meaning of that explanation. If I told you there was an explanation withing a collection of Egyptian hieroglyphics or some undecipherable language, what would be your reaction?

Then, I have a question about this from your post: "it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by xi = xj"

 

How is presumption different from circumstance or the explanation itself when all we have to work with is the circumstance space (x1, x2, . . . xn, . . .)? Where is the presumption differentiated from reality in this space?

If the explanation is flaw-free then it is consistent with absolutely all that is known. In such a circumstance, what method do you propose to differentiate between what is presumed and what is fact? The explanation is flaw-free until an expectation it predicts for an unknown circumstance turns out to be wrong: i.e., when that unknown circumstance becomes a known circumstance which invalidates the explanation.

 

The rest of your message makes it quite clear that you do not comprehend what I am talking about. I have just proved one thing (all specific flaw free explanations of anything may be mapped into some specific mathematical function) and you are attempting to force that proof into saying something about your personal world view.

 

By the way, regarding the possibility that xi = xj, there is the possibility that there exists only one electron. That concept was put forward long ago and I am aware of no proof that it is wrong.

 

Remember, I am talking about “any possible explanation”, not about any specific explanation and the notation must be able to handle any possible set of circumstances.

 

I hope that removes some of your confusion.

 

Have fun -- Dick

[lawcat]

Remember, I am talking about “any possible explanation”, not about any specific explanation and the notation must be able to handle any possible set of circumstances.

 

I see it differently. You are beginning with a preconceived notion that your set is about "any possible explanation."

 

Your concern, your ultimate point, is about circumstances, about reality, about explanations, about possibilities, probabilities. Most of your posts, if not all, is about persuading the reader that you are talking about explanations and their probability of being yes/no as to circumstance.

 

Look, EVERYTHING (ALL) and ANYTHING of ALL, can be represented as (x1, x2, x3, . . . , xn, . . . ). But you chose only one specific interpretation of that set. You chose to interpret it as circumstances and explanations. Of course, then, your final conclusion is that the whole universe is about explanations. How surprising!

 

As to philosphy, your expose is pure political rhetoric. Lobbying for a certain interpretation.

 

Mathematically it is of value if indeed it is a synthesis of "all" fundamental equations.

 

Physically, it must be tested and proven to have any value, which I suppose to the extent all fundamental equations are tested and proven, yours would be as well.

 

But explanation has nothing to do with the with the validity of your equations, as hard as you try to persuade the reader that it does.

[Rade]

The validity of DD equation comes from the philosophic Law of Identity, A = A. The equation of DD is a subset of this general law. Thus, I find it more than amusing that DD claims:

 

I think modern philosophy is a pretty worthless endeavor

 

while at the same time holding as true:

 

I have come to the conclusion that the physicists were right; it [my Fundamental Equation] is essentially a philosophical proof as it is a tautological construct

 

Even, more, not only is the Fundamental Equation derived via worthless Philosophy, it:

 

has nothing to do with the field of mathematics as all the mathematics used constitutes well known relationships.

 

And of course the final nail in the logic about the worthlessness of the Fundamental Equation (well, for sure in the mind of DD)

 

And, as it makes utterly no predictions and does no more than establish constraints upon one's personal expectations required by internal consistency of our world view, it clearly is not physics

 

Thus, I think it a good thing that DD concludes

 

I think modern philosophy is a pretty worthless endeavor

 

then proceeds to explain his worthless "philosophic proof" he calls his Fundamental Equation. At least we finally understand what he has been trying to tell us for some one year now.

[Rade]

Being free to assign a reference “t” between any two indices already assigned makes t a continuous variable. That is, in fact, the very definition of a continuous variable.

I would like to point out that this idea of DD was stated by Aristotle. The "t" of DD is the "time" of Aristotle. Aristotle defined time as "that which is intermediate between moments". The words used by DD--"between" and "two" show the connection in thinking. The "two indices" of DD = any "two moments" of Aristotle. As with the "t" of DD, the "time" of Aristotle is continuous, thus also infinite, since it is always possible to add another "t" between any two indices, same as it is always possible to add another "time" between any two moments. Note also that DD requires that a "t" be assigned, same as Aristotle requires that "time" be measured between moments. The,"assign" operation of DD = the "measure" operation of Aristotle. The "t" of DD is a type of number "assigned" by a human, the "time" of Aristotle is a type of number "measured" by a human. I think it important then to realize that the DD concept of "t" is nothing new to philosophy.

 

Also, if you read p. 384 of Roger Penrose book, "The Road to Reality" (2004) you will see that Penrose has an explanation of Aristotelian Spacetime, such that, "time" ranges over a Euclidean 1D-space[ which would be the "t" of DD], and some set of elements (x) [which would be the indices of DD] ranges over a Euclidean 3D-space.

 

Penrose continues...."time [for Aristotle] is represented as a Euclidean space, .... a one-dimensional space E1. Thus, we can think of "time", as well as space, as being a Euclidean geometry, rather than being just a copy of the real line R".

 

Thus, I conclude (until someone shows me where I error in thinking), that the approach of DD to assign a "t" derives from the "time" of Aristotle and "t" is then a one-dimensional Euclidean geometry. If true, then a read of Penrose on spacetime (Chapter 17) may well help with understanding the approach being taken by DD.

[AnssiH]

Laying out the problem to be solved.

 

Section 1: My definition of an explanation:

 

An explanation is a procedure which will provide rational expectations for hypothetical circumstances.

 

A “procedure” constitutes some sort of instruction, “expectations” constitute an estimated probability of yes/no decisions and “circumstances” constitute a description of whatever it is we are concerned with expecting. As for my meaning of “rational” see my post Defining the nature of rational discussion! In that post I explain why I feel “rational” means that the the result does not generate an emotionally negative response as to its truth. I will presume the meaning of “hypothetical” is understood.

 

I have three comments about that.

 

1. I don't understand why do you say "yes/no decisions".

 

2. It would make this statement a lot easier to understand if you found a way to eliminate the use of the word "rational" the way you are using it; since its meaning is something slightly different than how people generally interpret it. I mean having to read a post about how it's meant exactly - in order to not misinterpret the statement - does make this seem a little bit more complicated than it is. I believe you are trying to communicate that "rational" doesn't mean that the expectations must be based on purely logical conclusions, it suffices that they provide a meaningful basis for good survival decisions... (Could we say approximately valid?)

 

3. When you say '“circumstances” constitute a description of whatever it is we are concerned with expecting', it gives the unintented implication that "circumstance" refers to some defined form of the underlying information. Whereas in the rest of the post it seems to be explicitly meant to refer to the underlying "undefined" information. It is obviously imperative that the reader understands exactly what "circumstance" is supposed to mean.

 

Part I

Clearly, the first thing required here is a notation capable of representing absolutely any possible circumstance in a form which makes no presumptions whatsoever about any aspect of that circumstance.

 

I assert that absolutely any circumstance conceivable can be represented by an expression of the form:

 

[math](x_1, x_2, x_3,\cdots, x_n)[/math]{/center]

 

where [imath]x_i[/imath] is a numerical label constituting a reference to a fundamental element of the circumstances being explained.

 

There exists a problem here which, if the explanation is to be both exact and absolutely flaw free, must be carefully handled. It is best to see both “x” and “i” as separate labels referring to the same element. The possibility always exists that another internally consistent explanation of exactly the same circumstances may exist. Although the same circumstances are being explained, it cannot be presumed that this alternate explanation uses the same fundamental concepts for the fundamental elements being represented: i.e., essentially the two labels may obey very different constraints.

 

I use “x” (the common mathematical symbol for an unknown) as a label for the actual underlying element behind the explanation as this label is essentially undefined: i.e., there exists no way of defining this label in the absence of an explanation so it essentially has the character of an unknown. I use “i” as a label for the same element as referred to by the explanation as these labels are specifically defined by the explanation and I show it as an index on x to establish the connection. Thus the expression, [imath]x_i[/imath], is to refer to a specific underlying element appearing in and identified by the specific explanation being represented.

 

If a circumstance of interest contains multiple appearances of a specific underlying element defined by the explanation; different i labels will be used to denote those occurrences: i.e., different “i” subscripts can be used to refer to the same element in the explanation. This procedure will handle the situation where elements presumed to be the same underlying elements by one explanation are to be different underlying elements in an alternate explanation.

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [imath]x_i = x_j[/imath]. The underlying element labeled by “x” is the same, whereas that same element in the explanation is labeled by “i” in one case and “j” in the other (the explanation presumes the elements are different).

 

It should be understood that these numerical labels are no more than reference labels (they can refer to any specific linguistic description required by the explanation under analysis including any “picture” required). The complete set of n such labels “[imath]x_i[/imath]” can describe any conceivable circumstance as each label refers to a specific element within in the description of the circumstance of interest. If you can define the circumstance of interest, such indices can actually be specified: i.e., think of a computer file containing every piece of information pertinent to the explanation being represented.

 

I think I have shown that my assertion is indeed a fact; the notation defined is a possible way of representing any conceivable circumstance.

 

Excuse a long quote, I felt it was necessary.

 

I read that thing very carefully, and I think there are few problems regarding its clarity.

 

One thing that people evidently have problems with - I did too early on if you remember - is that they immediately try to understand it in terms of how a given explanation they know of (say, a given physics model) would translate into that notation.

 

I think it is evident that some people believe they understand how such a translation occurs - under some intuitive assumptions - and they end up voicing objections that have nothing to do with the analysis.

 

So, it should be emphasized even more that this notation is not set up for the purpose of being able to translate existing explanations into its terminology. The notation will be used for analyzing universal properties of explanations; the aim is to use this notation to express those universal properties in mathematically exact form; not for expressing specific explanations themselves

 

In fact the preamble does not very clearly state the reason for setting up an absolutely general notation, and I think a new reader would find themselves wondering about that. Understanding early on what you are trying to express with the notation/fundamental equation should make it much easier for the reader to understand the meaning of it all, and why it's important that the notation itself is not supposed to be seen as defining any aspect of an explanation; we just want all possibilities to be expressable.

 

A second problem I had with its clarity is that, for any reader who has not carefully followed your earlier presentations, and did not understand the idea of representing the undefined information in this notation as well, would probably find that whole quoted part very difficult to understand. I mean, try to read that with the assumption in mind that it is talking about an expression of a single specific explanation. It becomes impossible to understand most of it.

 

I think it would be a good idea to explain something about that whole idea of "representation of undefined information in this notation". And also clarify again that it is not the issue to actually know how some information would be thus mapped out; it is only important that the notation itself does not exclude any possibilities regarding whatever information an explanation might be based on.

 

I underlined the last two words, because I think you should emphasize how the "underlying information" in this context is NOT referring to reality itself per se; it is referring to whatever information was actually used in the construction of a given explanation, and thus we know it is of finite amount, and thus we know that a representation of that information could exist in the notation under discussion.

 

I'm saying that because I think a lot of readers have jumped to conclusion that your referring to "underlying information" is to refer to reality, and then they object to you making assumptions about "what reality is" so to speak.

 

I think after understanding the above, it is much easier for the reader to understand what you mean by different explanations referring to the same elements in different ways (in terms of the notation), and understand how the idea of "identity of the elements", and how they differ between different explanations, is handled in this the notation.

 

However, a second serious issue, not yet mentioned, must be discussed.

If an explanation is required, we cannot already know all the answers to all possible questions: i.e., the concept of expectations would, in that case, be meaningless. Thus it is that all possible circumstances representable by the notation [imath](x_1, x_2, x_3,\cdots, x_n)[/imath] can be divided into two sets: those who's probability we know and those who's probability is to be given by our explanation. For reasons of convenience I will attach the label “the past” to the set who's probability is known and attach the label “the future” to the set who's probability is not known. In addition, I will attach the label “the present” to any addition to the set who's probability is converted from not known to known.

 

I think that should be more carefully worded, because you are jumping from referring to the future as the set "whose probability is given by an explanation" and as the set "whose probability is not known".

 

It could be problematic that typically people would say that the probabilities given by an explanation are "known probabilities", and those lacking an explanation are "unknown probabilities"... So I just see a chance for a lot of misinterpretations right here.

 

Plus it is confusing to me that you refer to information that is already "set" (the past) as information that has got "probability" assigned to it. I am not sure why do you use the concept of probability to set information...

 

In general, I thought the way the "t" parameter is introduced makes things perhaps seem a bit more complicated than they need to be, but after spending a lot of time thinking about this, I'm not sure how it could be changed...

 

Well, I've been reading this very carefully and put a lot of thought to it so it's a bit slow... I decided to have a pause here and post my thoughts thus far, I hope it's helpful...

 

-Anssi

[Rade]

Thus it is that all possible circumstances representable by the notation (x_1, x_2, x_3,...x_n) can be divided into two sets: those who's probability we know and those who's probability is to be given by our explanation

I have a comment about this statement. I think all will agree that any argument is only as valid as the basic premise(s) upon which it based. Thus, I ask, can the human mind "know" a "probability" for a possible circumstance a priori ? Or, is it more correct to say the human mind can "know" a "probability" for an actual circumstance after the fact ? I think the latter.

 

Take for example the circumstance of flipping 1000 coins either heads or tails. Each flip is represented by the notation (x_1, x_2, x_3,...x_n). Now, DD tells us there are only two logical divisions for this possible circumstance, that is a priori to the circumstance (1) the one who's probability we know (2) the one who's probability is given by an explanation. Is this logical ? I think not.

 

Of course after the 1000 flips, a probability of H&T will result--but clearly this probability was not "known" a priori to the operation of flipping. Thus, the first explanation of DD fails this example. Now, is this an example of the DD set "who's probability is to be given by our explanation" ? Or, is the probability that we know given by the reality that only two expectations are possible for the operation under investigation ? Clearly the latter applies. Therefore, I conclude that the simple coin toss example falsifies the basic premise of DD concerning his labels of "past", "future", "present" as concerns all "possible circumstances" not yet actual.

[JMJones0424]

Rade, you are truly grasping at straws. Given your example of flipping coins...

 

The results of flipping 1000 coins can be divided into two sets.

 

1) Those who's probability we know. We know the probability of ending up with that set because the flipping of coins has already taken place, and we have observed the results.

 

2) Those who's probability is to be given by our explanation. The flipping has not yet occurred, so the best we can do is to determine the probability of the resulting set of coin flips.

 

I do not understand your point of contention. Please release yourself from all preconceived notions and read DD's post again. I do not think there is anything resembling a conflict in what he has written in this post, rather I think you are looking for mis-understandings in order to generate a conflict. You appear to be quote mining. The entire quote from DD-

 

If an explanation is required, we cannot already know all the answers to all possible questions: i.e., the concept of expectations would, in that case, be meaningless. Thus it is that all possible circumstances representable by the notation (x_1, x_2, x_3,..., x_n) can be divided into two sets: those who's probability we know and those who's probability is to be given by our explanation. For reasons of convenience I will attach the label “the past” to the set who's probability is known and attach the label “the future” to the set who's probability is not known. In addition, I will attach the label “the present” to any addition to the set who's probability is converted from not known to known.

 

Clearly contradicts the conclusion you accuse him of, and makes your argument seem strained.

 

The problem is once again that English words have more than one meaning. DD has gone to great pains to specifically define what he means by the terms he uses, but you are entirely ignoring those definitions and drawing conclusions that are contradicted by the sentences immediately following the quote you pulled.

[AnssiH]

However, a second serious issue, not yet mentioned, must be discussed.

If an explanation is required, we cannot already know all the answers to all possible questions: i.e., the concept of expectations would, in that case, be meaningless. Thus it is that all possible circumstances representable by the notation [imath](x_1, x_2, x_3,\cdots, x_n)[/imath] can be divided into two sets: those who's probability we know and those who's probability is to be given by our explanation. For reasons of convenience I will attach the label “the past” to the set who's probability is known and attach the label “the future” to the set who's probability is not known. In addition, I will attach the label “the present” to any addition to the set who's probability is converted from not known to known.

 

Think of this in terms of the computer file mentioned above. If that file contains all possible circumstances then no explanation is necessary; the file itself contains the answers to all questions. I use the labels “past” and “future” as those labels are fairly well consistent with how we would tend to view such a file. Additions to such a file would constitute answers previously unknown: i.e., expectations (provided by the explanation) would be verified (by experiment or observation), that verification would thus be a specific present which could be indexed by an index I will call “t” appended to the specific circumstance . Symbolically, a specific circumstance will now be represented by the expression

[math](x_1, x_2, x_3,\cdots, x_n,t)[/math]

 

 

An index “t” can be appended to every hypothetical circumstance representable.

 

So, I left last time thinking that that introduction of "t" seems a bit overly complicated. Because we are already talking about procedures for predicting up-coming information, based on the accumulated information, so it should be obvious that a method for handling and ordering "changes" or "time-wise evolution" is required by the universal notation. I understand you are trying to keep it analytically correct, and I can't immediately suggest a better way to introduce it, but perhaps it suffices to explain early on that we are indeed talking about the requirement for a time-wise evolution parameter.

 

The additional clarification about "t" I found to be pretty clear.

 

But after reading that part, I think many people would find themselves wondering how relativistic simultaneity would be expressable in this notation, so I think it might be a good idea to mention something about that. Maybe just to say that the availability of relativistic definitions of simultaneity are discussed later on when special relativity arises in the analysis.

 

Before I close my argument regarding the notation I intend to use to represent the circumstances, there is one other common characteristic of explanations which must be included in the notation. If it is not included, the notation would not be capable of representing absolutely any explanation (which is the intention here). Many explanations contain presumed elements; elements not necessarily part of the actual underlying elements to be explained but rather, are elements required by the explanation itself. These elements may or may not be bona fide but are nonetheless an essential part of the explanation. The fact that an explanation is flaw-free (fits all known information) and continues to be flaw-free for a continuing collection of presents (more experiments) cannot be taken as proof that all fundamental elements of that explanation are bona fide: i.e., it is always possible that there exists an alternated explanation which does not rely upon those elements.

 

Of course, it is always possible these elements are indeed bona fide thus it is necessary to include an underlying x to provision this possiblity. Essentially, that expands the number of elements represented by the numerical labels x_i from being a finite set to being an infinite set because, there may exist presumptions within the explanation itself which rely upon an infinite number of elements not actually part of the underlying known circumstances which the explanation was created to explain.

 

I think, if you manage to explain well enough in the earlier parts of the presentation what the "underlying elements" or "underlying x" means, the reader should be able to understand that pretty well.

 

Maybe I should mention that I find myself thinking of this issue simply in terms of, some explanations containing some "hypothetical" defined elements whose role is simply to explain the behaviour of some other defined elements, and thus those "hypothetical" elements implying the existence of underlying information, while no such underlying information might exist (not all explanations need to explain those bits of information).

 

I have no idea if anyone finds that above paragraph any clearer though...

 

Part II

The next thing required here is a method of representing the expectations generated by that explanation by any specific circumstance of interest.

 

.

.

.

 

The dagger is there to denote the conversion of each specific number in the “value” of [imath]\vec{G}[/imath] to a representation whose product with identical specific number in the output of the original function is a positive definite number.

 

I found that above sentence to be very hard to read. In fact I'm still not sure what it says... I just remember that the dagger denoted a complex conjugate.

 

This extension in possibilities for the specific numbers in the “value” of [imath]\vec{G}[/imath] (for example those values can now be imaginary numbers and, in fact, many other more complex constructs) allows us the option of building into [imath]\vec{G}(\vec{x})[/imath] some important internal correlations which will be shown to be of extreme value later. For the moment it should be recognized that those same correlations can be expressed by multiple real numbers: i.e., I am not changing the definition of [imath]\vec{G}(\vec{x})[/imath], I am merely allowing some very interesting (and it turns out necessary) expressions of internal correlations.

 

Yes, but "necessary" only in making it easier to recognize the connections between modern physics and the universal characteristics of explanations?

 

I am saying that because in the above paragraph you are first commenting that "it should be recognized that those same correlations can be expressed by multiple real numbers" - which is just the right place to make that comment as I think people would start to wonder - but then you are a bit careless when you refer to those expressions of internal correlations as "necessary", I think that might create some unfortunate confusion.

 

Maybe you should replace the last sentence with "I am merely allowing for a simpler expression of certain internal correlations" or something, and/or possibly comment that the real interest here is to allow similar representations as are used by modern physics, without limiting possibilities as to what is being represented.

 

Okay, I read the rest of it through and have no additional comments, it all seemed pretty clear to me, only saw couple of trivial typos...

 

-Anssi

[Doctordick]

1. I don't understand why do you say "yes/no decisions".

”Yes” and “No” are totally equivalent to “it happened” and “it didn't happen” (see JMJones0424 post #9 on this thread) and, at the same time conveniently extend directly to “it will happen” and “it won't happen” (your expectations). It is a convenient and short English expression of exactly that relationship.

2. It would make this statement a lot easier to understand if you found a way to eliminate the use of the word "rational" the way you are using it; since its meaning is something slightly different than how people generally interpret it.

Really? Are you saying that my assertion, “that the the result does not generate an emotionally negative response as to its truth”, does not capture what they mean? If you can find a more succinct expression of what they mean, let me know. My reference was only in there to allow people who disagree with that assertion to get an understanding of what I mean. If they find no problem with “irrational means, doesn't make sense” they should find no problem with my somewhat more exact assertion.

I believe you are trying to communicate that "rational" doesn't mean that the expectations must be based on purely logical conclusions, it suffices that they provide a meaningful basis for good survival decisions... (Could we say approximately valid?)

Now that appears to me to be more wordy than my assertion and is also much more likely to open the door to meaningless philosophical arguments which is what I am trying my hardest to avoid.

3. When you say '“circumstances” constitute a description of whatever it is we are concerned with expecting', it gives the unintented implication that "circumstance" refers to some defined form of the underlying information. Whereas in the rest of the post it seems to be explicitly meant to refer to the underlying "undefined" information. It is obviously imperative that the reader understands exactly what "circumstance" is supposed to mean.

I think you are misinterpreting the purpose of this post. The purpose is to prove that every explanation can be mapped into a mathematical function; nothing more. You are trying to bring in issues not relevant to that proof.

 

In this case, we are dealing with “any explanation” and I am merely stating that the explanation explains observed circumstances. If you have an explanation, those circumstances are defined. It is in fact the intended implication at this point in the proof. The issue of not defining the underlying elements has to do with “not making presumptions” as to exactly what these circumstances are. That is the issue brought up and handled in part I. It has no place in the definition of an explanation and it seems to me would generate confusion and argument!

So, it should be emphasized even more that this notation is not set up for the purpose of being able to translate existing explanations into its terminology. The notation will be used for analyzing universal properties of explanations; the aim is to use this notation to express those universal properties in mathematically exact form; not for expressing specific explanations themselves

Again, I think you are missing the point of this post. You want it to lead into my proof of my fundamental equation. It is indeed my purpose to set up a way to translate existing explanations into a mathematical terminology without implying any purpose whatsoever. I am specifically not setting them up to deduce my equation. I want this post to stand on its own.

 

Yes, I agree that “they immediately try to understand it in terms of how a given explanation they know of (say, a given physics model) would translate into that notation”. That is exactly why I say, “think of a computer file containing every piece of information pertinent to the explanation being represented”. My purpose is to lead them into the idea that any collection of circumstances can be represented through mathematical notation. I specifically want to avoid the problem of trying to convince them of any further ideas. It is my purpose to avoid the arguments such a presentation would induce, not to avoid them worrying about how to translate into that notation.

 

The central issue here is to prove that a mathematical representation of any circumstance is feasible; something they really don't doubt at all. What I bring up are some subtle problems in such a representation which constitute presumptions (ideas which I suspect would not occur to them on their own) and provide mechanisms to overcome those possible problems. The issue is one of exactness and avoidance of presumptions within that representation. The issue of “where I am going” is being specifically avoided as that is the issue everyone wants to fight me on.

I mean, try to read that with the assumption in mind that it is talking about an expression of a single specific explanation. It becomes impossible to understand most of it.

It is only meaningful if one is trying to find a notation for any conceivable explanation. It seems to me that the comment, “Clearly, the first thing required here is a notation capable of representing absolutely any possible circumstance in a form which makes no presumptions whatsoever about any aspect of that circumstance”, should make it quite clear that I am not talking about “a single specific explanation”. In fact, in part I, I am not talking about an explanation at all; I am talking about representation of “any possible circumstance”.

 

I think you are confusing where I intend to go with where I am going in this post.

I think that should be more carefully worded, because you are jumping from referring to the future as the set "whose probability is given by an explanation" and as the set "whose probability is not known".

Essentially, there is utterly no difference between those two probabilities. What is known and what is unknown may bear upon the apparent validity of the explanation but has utterly nothing to do with the explanation itself: i.e., the explanations job is to explain both what you know and, via the assumption the explanation is correct, what you expect to know.

It could be problematic that typically people would say that the probabilities given by an explanation are "known probabilities", and those lacking an explanation are "unknown probabilities"... So I just see a chance for a lot of misinterpretations right here.

I just searched my post and found no occurrence of the word “unknown”. I suspect you are intuitively mixing this post with other posts I have made.

Plus it is confusing to me that you refer to information that is already "set" (the past) as information that has got "probability" assigned to it. I am not sure why do you use the concept of probability to set information...

If you are going to describe all possible circumstances, how do you propose to describe a circumstance where the possibility is not known for sure? Or are you making the assumption that such a thing can not occur? Was that John or Jim I saw driving the car yesterday? Handling circumstances without making presumptions is the central issue here and one needs to provide for every possibility.

Well, I've been reading this very carefully and put a lot of thought to it so it's a bit slow... I decided to have a pause here and post my thoughts thus far, I hope it's helpful...

Well, I think you are missing the reason I made this post. What I was attempting to do is to prove that every explanation can be mapped into a mathematical function; nothing more. As I said earlier, you are trying to bring in issues not relevant to that proof. Notice the number of “thanks” I have received on that OP. That is something I seldom receive and I take it to indicate those people found that post clearer than my other posts: i.e., I think separating out the many different independent issues is a beneficial approach here.

Because we are already talking about procedures for predicting up-coming information, based on the accumulated information, so it should be obvious that a method for handling and ordering "changes" or "time-wise evolution" is required by the universal notation. I understand you are trying to keep it analytically correct, and I can't immediately suggest a better way to introduce it, but perhaps it suffices to explain early on that we are indeed talking about the requirement for a time-wise evolution parameter.

I think that issue should be clear after I make that comments about archaeologists assigning a t different from the time they actually make their discovery. The variable t is assigned by the explanation itself, not by any specific circumstances.

But after reading that part, I think many people would find themselves wondering how relativistic simultaneity would be expressable in this notation, so I think it might be a good idea to mention something about that.

I disagree. This post is concerned only with creating a numerical representation of any possible circumstance. The issue of time and its definition in relativity is a burden of the explanation itself, not my numerical representation of that explanation. As you should understand, my definition of t, though it does turn out to fulfill exactly the service provided by the common concept of time, is definitely not the common definition. The issue being that the common definition contains additional presumptions which are simply not required. I do not want to complicate things by introducing things not relevant to what I am actually proving: that any circumstances can be expressed via my notation.

I think, if you manage to explain well enough in the earlier parts of the presentation what the "underlying elements" or "underlying x" means, the reader should be able to understand that pretty well.

First, before I complicate the post with additional verbiage, I would want you to explain to me why the common meaning of “underlying elements” will not sufice.

Maybe I should mention that I find myself thinking of this issue simply in terms of, some explanations containing some "hypothetical" defined elements whose role is simply to explain the behaviour of some other defined elements, and thus those "hypothetical" elements implying the existence of underlying information, while no such underlying information might exist (not all explanations need to explain those bits of information).

Once again, I think you are trying to extend what I am proving here into things better covered later as they essentially have nothing to do with what I am proving here.

I found that above sentence to be very hard to read. In fact I'm still not sure what it says... I just remember that the dagger denoted a complex conjugate.

That is not correct. Complex conjugation is only one of the possibilities there. The problem here is that there can exist relationships which can be mathematically embedded in the notation which require the first vector of the dot product to be related to the second vector in certain specific ways in order to insure the elemental products are all positive definite. That dagger is there only to take care of those embedded relationships. It is quite analogous to complex conjugation but need not be identical. Complex numbers constitute a two dimensional relationship. There are higher dimensional relationships which can serve the same (as yet unexplained) purpose of those complex numbers.

 

Please notice that I comment that, “for the moment it should be recognized that those same correlations can be expressed by multiple real numbers”. People who are well trained in mathematics will pick up on the fact that there exists a large number of internal relationships which can be embedded via that mechanism; but, it serves no purpose in this proof except perhaps to denote the fact that specific manipulation might be necessary were one to use such embedded relationships. The issue will come up much later. For the moment please just ignore it.

Yes, but "necessary" only in making it easier to recognize the connections between modern physics and the universal characteristics of explanations?

Not really. There is another issue here which is quite significant; but it is quite subtle and requires some pretty advanced mathematics to understand. It is more significant when it comes to addressing symmetry issues.

... - but then you are a bit careless when you refer to those expressions of internal correlations as "necessary", I think that might create some unfortunate confusion.

Well maybe I should not have mentioned it but it turns out providing another requirement very similar to the fact that probability must be bounded by zero and one: i.e., it will provide a way of satisfying a valid mathematical constraint which has absolutely nothing to do with the circumstances being discussed, but is rather another purely mathematical constraint also derived from some subtlies in the definition of probability. The necessity will appear in some later complications; for the moment, let it go.

Maybe you should replace the last sentence with "I am merely allowing for a simpler expression of certain internal correlations" or something, and/or possibly comment that the real interest here is to allow similar representations as are used by modern physics, without limiting possibilities as to what is being represented.

No, the real interest here is to eliminate a very real problem; however, the actual problem does not appear yet but it will show its ugly head later.

Okay, I read the rest of it through and have no additional comments, it all seemed pretty clear to me, only saw couple of trivial typos...

Now I just spent almost an hour carefully reading my original post and was unable to find those typos. Sometimes it is quite difficult for the author of a paper to see his own typos as his mind jumps directly to what he meant. Not that I am demanding your service but I sure do appreciate it.

 

Please don't take this post badly. I don't want you to think I am criticizing you; I think your comments are very accurate but I think you are missing my intentions here. I think that the fact that Buffy and Tormod approved gives evidence that I did accomplish my intentions. I am sorry Qfwfq is not around to comment. I would very much be interested in his take on what I said.

 

Have fun -- Dick

[AnssiH]

”Yes” and “No” are totally equivalent to “it happened” and “it didn't happen” (see JMJones0424 post #9 on this thread) and, at the same time conveniently extend directly to “it will happen” and “it won't happen” (your expectations). It is a convenient and short English expression of exactly that relationship.

 

Ah, okay, so by "an estimated probability of yes/no decisions" you essentially refer to the probabilities regarding the existence or absence of individual indices that make up a description of a given circumstance?

 

I was not sure if you were implying to actual decision making in one way or another and that confused me. I'm not sure if it would confuse others the same way.

 

Really? Are you saying that my assertion, “that the the result does not generate an emotionally negative response as to its truth”, does not capture what they mean?

 

Sure I think it does, albeit I had to read the referred post to be sure what you meant. But my actual concern is that people who are engaged in arguments that arise from differences in their underlying beliefs (let's say evolution vs. creationism), would see the arguments of the other party as "irrational", while seeing their own argument as based on sound logic and thus "rational". In your terms, the arguments of both sides would be called "rational".

 

So I am concerned that for a lot of people the word "rational" there implies immediately that you are talking about expectations springing from sound logic. I realize you are aware of this problem since you comment on it and refer to the post explaining that this is not the case.

 

My reference was only in there to allow people who disagree with that assertion to get an understanding of what I mean. If they find no problem with “irrational means, doesn't make sense” they should find no problem with my somewhat more exact assertion.

 

Yeah, right now it only slightly increases the threshold for understanding this thing, but if you ever want to place this elsewhere from these forums, the problem would become larger I think. People don't think every sentence they read that carefully, and wrong implications can become very harmful especially if they happen at the get-go.

 

I believe you are trying to communicate that "rational" doesn't mean that the expectations must be based on purely logical conclusions, it suffices that they provide a meaningful basis for good survival decisions... (Could we say approximately valid?)

Now that appears to me to be more wordy than my assertion and is also much more likely to open the door to meaningless philosophical arguments which is what I am trying my hardest to avoid.

 

Yeah, I didn't mean it as a suggestion for replacement, I just wanted to make sure I had understood what you meant by "rational". Partially the reason I felt uneasy with that word was that I really had to stop and read another post carefully through to be sure I understood exactly why you had it in there.

 

In any case, english is not my first language so its doubly hard for me to give good suggestions... I could say though, that in my mind, if you said "An explanation is a procedure which will provide reasonable expectations for hypothetical circumstances", then I at least would have take the "reasonable" to mean something akin to "valid most of the time". I.e. I'd intuitively take it to imply exactly what you mean to say with "rational".

 

But again, I don't see this as a huge issue, just a small hump worth mentioning.

 

3. When you say '“circumstances” constitute a description of whatever it is we are concerned with expecting', it gives the unintented implication that "circumstance" refers to some defined form of the underlying information. Whereas in the rest of the post it seems to be explicitly meant to refer to the underlying "undefined" information. It is obviously imperative that the reader understands exactly what "circumstance" is supposed to mean.

 

I think you are misinterpreting the purpose of this post. The purpose is to prove that every explanation can be mapped into a mathematical function; nothing more. You are trying to bring in issues not relevant to that proof.

 

In this case, we are dealing with “any explanation” and I am merely stating that the explanation explains observed circumstances. If you have an explanation, those circumstances are defined. It is in fact the intended implication at this point in the proof. The issue of not defining the underlying elements has to do with “not making presumptions” as to exactly what these circumstances are. That is the issue brought up and handled in part I. It has no place in the definition of an explanation and it seems to me would generate confusion and argument!

 

Ah I see. I found myself thinking about which way you meant "circumstances" for quite some time because that statement that I quoted felt a bit ambiguous to me, and after reading how you were using it in the rest of the post, I came to decide you meant undefined circumstances. Unfortunately for me, it had bit of a double meaning...

 

I guess that's a problem too, I think other people could fall for it as well. Actually it seems to me that lawcat's question (that you quote in post #3) about circumstance being the explanation, and your reply about the explanation arising from the circumstances is ambiguous communication arising from this same confusion. (He was clearly thinking about the inability to refer to a circumstance without having an explanation)

 

I think it could be remedied by slightly more explicit statement in the beginning, something like "circumstances" constitute a description, in the terminology of a given explanation, of whatever it is we are concerned with expecting.

 

And then not using the same word to refer to the underlying information, because once the reader has accepted that "circumstance" refers to a representation of the underlying information (a representation married to a specific explanation), it is confusing to read something like The possibility always exists that another internally consistent explanation of exactly the same circumstances may exist. Although the same circumstances are being explained, it cannot be presumed that this alternate explanation uses the same fundamental concepts for the fundamental elements being represented

 

So what went on in my mind after reading that was; since "circumstance" is defined to be a description of some information - i.e. a product of an explanation - what does it mean that multiple explanations explain the same circumstances? I think I understand now how you meant it, but it was hard for me to interpret correctly.

 

Again, I think you are missing the point of this post. You want it to lead into my proof of my fundamental equation. It is indeed my purpose to set up a way to translate existing explanations into a mathematical terminology without implying any purpose whatsoever. I am specifically not setting them up to deduce my equation. I want this post to stand on its own.

 

Yeat, I am probably reading too much into it since I know where it is going. I'll try to view it as an independent thing.

 

Yes, I agree that “they immediately try to understand it in terms of how a given explanation they know of (say, a given physics model) would translate into that notation”. That is exactly why I say, “think of a computer file containing every piece of information pertinent to the explanation being represented”. My purpose is to lead them into the idea that any collection of circumstances can be represented through mathematical notation. I specifically want to avoid the problem of trying to convince them of any further ideas. It is my purpose to avoid the arguments such a presentation would induce, not to avoid them worrying about how to translate into that notation.

 

The central issue here is to prove that a mathematical representation of any circumstance is feasible; something they really don't doubt at all. What I bring up are some subtle problems in such a representation which constitute presumptions (ideas which I suspect would not occur to them on their own) and provide mechanisms to overcome those possible problems. The issue is one of exactness and avoidance of presumptions within that representation. The issue of “where I am going” is being specifically avoided as that is the issue everyone wants to fight me on.

 

Right, I see.

 

It is only meaningful if one is trying to find a notation for any conceivable explanation. It seems to me that the comment, “Clearly, the first thing required here is a notation capable of representing absolutely any possible circumstance in a form which makes no presumptions whatsoever about any aspect of that circumstance”, should make it quite clear that I am not talking about “a single specific explanation”. In fact, in part I, I am not talking about an explanation at all; I am talking about representation of “any possible circumstance”.

 

It seems to me that most of the difficulties I had with reading that whole section had to do with the apparent double meaning of "circumstances". I was trying to find an interpretation that made sense to me, and where "circumstance" meant either a description of the data or the underlying data itself.

 

Now that I know how you meant it, I'm reading the paragraph again carefully. I am getting the impression that you are essentially talking about something analogous to mapping of the information from a data file into this notation, setting up how an explanation of the data is to denote the association between its defined elements with the data itself.

 

I think the most helpful thing I can do right now is to explain what goes in my mind when I read different parts of it, so you get a feel of how I interpret things;

 

It is best to see both “x” and “i” as separate labels referring to the same element. The possibility always exists that another internally consistent explanation of exactly the same circumstances may exist. Although the same circumstances are being explained, it cannot be presumed that this alternate explanation uses the same fundamental concepts for the fundamental elements being represented: i.e., essentially the two labels may obey very different constraints.

 

I use “x” (the common mathematical symbol for an unknown) as a label for the actual underlying element behind the explanation as this label is essentially undefined: i.e., there exists no way of defining this label in the absence of an explanation so it essentially has the character of an unknown. I use “i” as a label for the same element as referred to by the explanation as these labels are specifically defined by the explanation and I show it as an index on x to establish the connection. Thus the expression, [imath]x_i[/imath], is to refer to a specific underlying element appearing in and identified by the specific explanation being represented.

 

(Is there a word missing after "...specific underlying element appearing in..."?)

 

I'm trying to ignore where this is headed, so I take it that the above is just to say that the "x" is the number referring to something in the underlying data, and the "i" is the number referring to a defined element associated with that data.

 

If a circumstance of interest contains multiple appearances of a specific underlying element defined by the explanation; different i labels will be used to denote those occurrences: i.e., different “i” subscripts can be used to refer to the same element in the explanation. This procedure will handle the situation where elements presumed to be the same underlying elements by one explanation are to be different underlying elements in an alternate explanation.

 

I immediately hanged on the phrase "specific underlying element defined by the explanation", because it sounds oxymoronic to me (I presume you know why I'd tend to take it that way). I am not sure if that refers to a defined element or to the underlying data, but I suppose you must mean that an explanation can contain multiple defined elements that each are attached to the same data point, i.e. the same value for "x". In that case you would find, in the description of the circumstance, different defined elements denoted with different "i", each having the same value in the "x".

 

At least that's how I took it, until I read:

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [imath]x_i = x_j[/imath]. The underlying element labeled by “x” is the same, whereas that same element in the explanation is labeled by “i” in one case and “j” in the other (the explanation presumes the elements are different).

 

Now I'm thinking something's awry in my interpretation, as you are explicitly saying that "a reverse situation" would be marked exactly how I thought the earlier situation would be marked, i.e. different "i" indices having the same value for "x".

 

Going back to the earlier paragraph, I think I interpreted it wrong. "Different "i" subscripts can be used to refer to the same element in the explanation" sounded to me exactly like [imath]x_i = x_j[/imath].

 

But I guess you meant essentially "Different "i" subscripts can be used to refer to the same element OF the explanation" (as oppose to "by the explanation")? If so, the only way I can interpret that sensically is that different elements with different values in "i" can refer to different instances of SIMILAR defined elements (since different "i" is by definition denoting a different instance)

 

Hmm, actually at this point I am still very unsure of where my interpretation goes wrong, I think I should wait for your response before I say more. I think there's some ambiguity somewhere that I tripped over, not sure where.

 

Now I just spent almost an hour carefully reading my original post and was unable to find those typos. Sometimes it is quite difficult for the author of a paper to see his own typos as his mind jumps directly to what he meant. Not that I am demanding your service but I sure do appreciate it.

 

Heh, yeah, it is certainly hard to spot those things after a while, I'll post a PM pointing out the ones I saw.

 

Please don't take this post badly. I don't want you to think I am criticizing you; I think your comments are very accurate but I think you are missing my intentions here.

 

Yeah don't worry, I am certainly jumping ahead in my attempts to interpret your post, but even without doing that, I do think there are real ambiguity issues there still, albeit it is always possible they are just caused by my particular alignment to this issue.

 

Nevertheless, I'm just doing what I think would be most helpful in making these issues as clear as possible, as I don't think they are that complicated by themselves... It's just the communication of the issues that becomes bothersome. :P

 

-Anssi

[AnssiH]

Oh, one more thing I forgot to mention.

 

I think that should be more carefully worded, because you are jumping from referring to the future as the set "whose probability is given by an explanation" and as the set "whose probability is not known".

Essentially, there is utterly no difference between those two probabilities. What is known and what is unknown may bear upon the apparent validity of the explanation but has utterly nothing to do with the explanation itself: i.e., the explanations job is to explain both what you know and, via the assumption the explanation is correct, what you expect to know.

 

It could be problematic that typically people would say that the probabilities given by an explanation are "known probabilities", and those lacking an explanation are "unknown probabilities"... So I just see a chance for a lot of misinterpretations right here.

I just searched my post and found no occurrence of the word “unknown”. I suspect you are intuitively mixing this post with other posts I have made.

 

I was referring to:

 

Thus it is that all possible circumstances representable by the notation [imath](x_1, x_2, x_3,\cdots, x_n)[/imath] can be divided into two sets: those who's probability we know and those who's probability is to be given by our explanation. For reasons of convenience I will attach the label “the past” to the set who's probability is known and attach the label “the future” to the set who's probability is not known.

 

You did not say "unknown", it was "not known". I think Rade's confusion had to do with interpreting that wrong.

 

So I meant to say, "probability given by an explanation" would be called in many people's minds "known probability" (i.e. you can assign a probability), while "not known probability", would imply that no probability can be assigned at all.

 

I believe I understand how you mean it, that in the absence of an explanation the probability of that set is "not known". I just also see a chance for confusion there. I think Rade's comments arose from misinterpreting this. Thinking about this, I think part of the difficulties that I see in this has to do with the double meaning of "circumstances".

 

Plus it is confusing to me that you refer to information that is already "set" (the past) as information that has got "probability" assigned to it. I am not sure why do you use the concept of probability to set information...

If you are going to describe all possible circumstances, how do you propose to describe a circumstance where the possibility is not known for sure? Or are you making the assumption that such a thing can not occur? Was that John or Jim I saw driving the car yesterday? Handling circumstances without making presumptions is the central issue here and one needs to provide for every possibility.

 

That comment also arose from my erroneous interpretation that "circumstance" explicitly referred to the undefined data, i.e. "what is to be explained".

 

-Anssi

[Doctordick]

(Is there a word missing after "...specific underlying element appearing in..."?)

The problem you are having here is with a rather standard English grammar construct. When one runs into a phrase which under normal circumstances would be followed by some specific continuation (i.e., in this case the answer to, “appearing in what?”) is instead followed by the word “and”, the following phrase is included as part of the preamble to the question: i.e., “appearing in and identified by” is simply regarded as a more complex categorization. Essentially the phrase you are reading constitutes the delineation (the specific underlying element) both appears in and is identified by the specific explanation.

 

I have been told that English is one of the most complex languages out there. And it is a lot simpler today than it was a hundred years ago. My grandfather was a high school English teacher back in the eighteen hundreds and used to correct my English all the time, pushing me into constructs no one would use today. I get a kick out of watching movies and seeing how they have the nineteenth century characters speak. They are totally off the wall wrong; at least for middle America. It is my understanding that English used to have a lot of different dialects. But that's another story for another day. :D

Hmm, actually at this point I am still very unsure of where my interpretation goes wrong, I think I should wait for your response before I say more. I think there's some ambiguity somewhere that I tripped over, not sure where.

Go read it again, I changed it a bit while I was editing my typos.

You did not say "unknown", it was "not known". I think Rade's confusion had to do with interpreting that wrong.

I also made some small changes in that wording which might make the thing a little clearer.

Thinking about this, I think part of the difficulties that I see in this has to do with the double meaning of "circumstances".

Actually, it was the more broadended meaning of the word “circumstance” which drew me to use it. My dictionary had the following entries.

 

1. A fact or event accompanying another fact or event, either incidentally or as an essential condition or determining factor.

2. Conditions surrounding and affecting a person.

3. Ceremony or show.

4. Accompanying or surrounding detail, especially fullness of detail.

 

Even that one "Ceremony" has impact from the perspective that explanations can be seen as procedures which could easily be interpretable as ceremony and the underlying data to be explained can easily be seen as itself containing subsidiary explanations. It seems to me that all aspects of the word need to be included in the idea as to what kinds of elements [imath]x_i[/imath] is supposed to label. Please note that the word "element" means the explanation does not require any brake down of the labeled thing: i.e., it is elemental with regard to the explanation. I only said that because I can see the issue being overlooked.

[AnssiH]

The problem you are having here is with a rather standard English grammar construct.

 

Yup, we have similar structures in finnish so I did recognize it, I just wasn't quite sure if that's how you meant it.

 

Since you mention it, I find myself sometimes clarifying those like this "...refer to a specific underlying element appearing in - and identified by - the specific explanation being represented."

 

Anyway;

 

Go read it again, I changed it a bit while I was editing my typos.

I also made some small changes in that wording which might make the thing a little clearer.

 

I don't know if it's just me, but I'm still having troubles interpreting it.

 

The part we are discussing is;

 

If a circumstance of interest contains multiple appearances of a specific underlying element defined by the explanation; different i labels will be used to denote those occurrences: i.e., different “i” subscripts can be used to refer to the same element in the explanation. This procedure will handle the situation where elements presumed to be the same underlying elements by one explanation are to be different underlying elements in an alternate explanation. (This kind of problem can only occur if specific element appears more than once in a single specific defined circumstance labeled by a given t. If such a thing does occur, the explanation should have some reason for this occurrence and thus it is reasonable to give the different occurrences different labels.)

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [imath]x_i = x_j[/imath]. The underlying element labeled by “x” is the same, whereas that same element in the explanation is labeled by “i” in one case and “j” in the other (the explanation presumes the elements are different).

 

So the way I interpret this now is, that the first paragraph is talking about a situation, that could be denoted by an explanation as (for instance); [math](16_1, 16_2, 16_3, \cdots, x_n)[/math]

 

In that case, the three first elements defined by the explanation, are referring to something labeled as "16" in the underlying information (as per their definitions).

 

My interpretation of the second paragraph is essentially the same, that in the case that an explanation refers to the same thing in the underlying information via multiple different defined elements, it would mean that multiple defined elements would have the same value for "x", so it could also look like this; [math](16_1, 16_2, 16_3, \cdots, x_n)[/math]

 

Consequently I find myself asking, what is the difference between "an explanation referring to the same underlying element via multiple defined elements" (my interpretation of first paragraph), and "an explanation erroneously referring to the same underlying element via multiple defined elements" (my interpretation of second paragraph)

 

And I find myself asking, what do you mean by "same" element. Do you mean, "same" in type, or "same" in identity (instance)?

 

I suspect my interpretation of the first paragraph is wrong...

 

Actually, it was the more broadended meaning of the word “circumstance” which drew me to use it. My dictionary had the following entries.

 

1. A fact or event accompanying another fact or event, either incidentally or as an essential condition or determining factor.

2. Conditions surrounding and affecting a person.

3. Ceremony or show.

4. Accompanying or surrounding detail, especially fullness of detail.

 

Even that one "Ceremony" has impact from the perspective that explanations can be seen as procedures which could easily be interpretable as ceremony and the underlying data to be explained can easily be seen as itself containing subsidiary explanations. It seems to me that all aspects of the word need to be included in the idea as to what kinds of elements [imath]x_i[/imath] is supposed to label.

 

Okay, I'll interpret the word in its broader sense from this point on.

 

Please note that the word "element" means the explanation does not require any brake down of the labeled thing: i.e., it is elemental with regard to the explanation. I only said that because I can see the issue being overlooked.

 

Yeah, and it should perhaps be mentioned in the OP too...

 

What makes things perhaps a bit tricky to interpret is that there is no telling about what sort of information the definition of an element is based on, i.e. the concept of "underlying elements" is something that can trip over a lot of people... (I mean it sounds like a real 1:1 mapping to reality, in some sense, is being suggested)

 

-Anssi

[Rade]

you did not say "unknown", it was "not known". I think Rade's confusion had to do with interpreting that wrong.So I meant to say, "probability given by an explanation" would be called in many people's minds "known probability" (i.e. you can assign a probability), while "not known probability", would imply that no probability can be assigned at all.I believe I understand how you mean it, that in the absence of an explanation the probability of that set is "not known". I just also see a chance for confusion there. I think Rade's comments arose from misinterpreting this. Thinking about this, I think part of the difficulties that I see in this has to do with the double meaning of "circumstances".

Yes, exactly the problem I had with the use by DD of the word "circumstances"--thank you for making mention of this, because some believe I am out only to cause trouble for DD, while the exact opposite is true. I would like to see DD to succeed--thus I will do all that I can to falsify each and ever one of his arguments, question his every word, every statement, every comment, etc--it is my duty as a scientist. Then, if I (and of course others) cannot falsify his logic--well then, DD philosophy will move forward.

 

One other issue AnssiH...I see that DD over time changes his definitions of the "past" and "future". Now, this is fine, because the words "past" and "future" relate to concepts, and definitions of concepts must change as new information becomes available. However, most recently, I see he now adds the word "probability" to his definitions of "past" and "present". Do you know why ?

 

Finally, DD refuses to answer me how he defines these two concepts (1) know (2) believe. Would you have a clear understanding how DD thinks these two concepts differ ? I find this very important, because the word "know" and the opposite "not know" is used to define the two concepts "past" and "future"----but for me, I think DD would better his argument if he used the word "belief" rather than know in this context. Hope this makes sense to you.

[AnssiH]

Yes, exactly the problem I had with the use by DD of the word "circumstances"--thank you for making mention of this, because some believe I am out only to cause trouble for DD, while the exact opposite is true. I would like to see DD to succeed--thus I will do all that I can to falsify each and ever one of his arguments, question his every word, every statement, every comment, etc--it is my duty as a scientist. Then, if I (and of course others) cannot falsify his logic--well then, DD philosophy will move forward.

 

Well the problem is just that it's just almost impossible to discuss this via english language. You just get hopelessly entangled into all sorts of semantics. The situation is sort of similar to almost any online argument about relativity, where the other party does not understand the definitions behind relativity, but instead tries to understand the arguments in terms of their personal intuition.

 

"If the moving observer slows down in time, then he must see the external world as speeding up. Otherwise the idea is illogical". <- That right there is exactly analogous to the arguments that people usually give, and that is why DD is getting frustrated and feels that people just want to argue for arguments sake, without really even understanding what they are arguing about.

 

And just like is the case with those relativity arguments, I'm sure people see their own objections as logically solid, with no further need to think about the issue.

 

One other issue AnssiH...I see that DD over time changes his definitions of the "past" and "future".

 

I don't know what you mean, but I have strong suspicion this has got something to do with some unfortunate semantics with english language.

 

Now, this is fine, because the words "past" and "future" relate to concepts, and definitions of concepts must change as new information becomes available. However, most recently, I see he now adds the word "probability" to his definitions of "past" and "present". Do you know why ?

 

I think he wants to stick to the terminology related to "generating expectations". I don't read too much into it, but I did think it can generate confusion, as I commented earlier.

 

The main issue to keep in mind with the whole "future" and "past" thing is that this is purely an epistemological perspective taken on some information that is to be explained. The information "yet to be received" is "the future", and the information that is accumulated thus far, is "the past".

 

The "information yet to be received" is the same as saying "information that you don't yet know" (simply because you have not yet received it). There are many ways to interpret that wrong. Just remember what the whole point of those definitions is. (i.e. just remember what this is related to generating explanations via inductive deductions from some information)

 

Finally, DD refuses to answer me how he defines these two concepts (1) know (2) believe. Would you have a clear understanding how DD thinks these two concepts differ ? I find this very important, because the word "know" and the opposite "not know" is used to define the two concepts "past" and "future"----but for me, I think DD would better his argument if he used the word "belief" rather than know in this context. Hope this makes sense to you.

 

I think that "know" is such a common english word that it would be almost impossibly to use it unambiguously. I mean it's meaning depends heavily on the context and it would be hard to avoid its unintentional use. The same applies to "belief" to an extent. I think I do understand his perspective enough to be able to explain what he means by those words in some specific context though, if you want to point me to some paragraph that you find confusing.

 

-Anssi