Doctordick

I am presuming "Scientist" did not comprehend what I proposed!!

 

Sorry about that! If I have misinterpreted your response let me know!

 

Have fun anyway!! -- Dick

Have I misunderstood the word "speculation"? I thought the word referred to ideas which could possibly be wrong. If there is no possibility that a specific idea could be wrong then it could not possibly be speculation!

 

I do not understand your comment that counter evidence might be the vast infrastructure man has built using language. Do you mean that the vast infrastructure is evidence that language is not an issue to be examined? It is a fact that mankind has built a great number of languages many of which are no longer understood. My point is that there could exist an infinite number of possible languages. Does there exist any constraints applicable to all languages or is that an issue unworthy of thought?

The first issue I find interesting is that no one is born knowing a language. Every child must first experience a substantial collection of interactions with others who already know a language. This, together with other experiences they associate with that language leads them to eventually come to believe they know what the language is expressing. Without such a process, understanding of the relevant elements of any language is impossible. Misunderstandings are a very important aspect of any communications and I do not concern myself with that issue.

 

I want to discuss the significant issues of a language I do not know!

 

But I cannot discuss anything without using a language!! So I propose to use English to discuss the relevant issues. A language I feel I know pretty well.

 

The first issue I would like to bring up is the fact that the primary elements of a language are representations of "concepts". I have in mind here the idea expressed in English by the concept of "words". If we know (or at least think we know) the concept expressed by a particular word, then we can express a specific thought with a collection of such concepts. Of course I include in this collection of concepts elements not ordinarily seen as words in the English language. Those elements could be punctuation, spacing and any other concept meaningful to a writer in that language. (As I understand it, ancient Latin did not include spaces so the actual concepts being represented do not necessarily include all concepts being represented in a specific language.)

 

A second important aspect of any language is the idea of a dictionary (I am referring to the English concept usually embedded in the idea of a dictionary which provides the specific thoughts being represented by a specific word.)

 

If one knows (or at least thinks they know) the relevant concepts together with a dictionary defining those concepts they have the ability to express their thoughts in that relevant language.

 

So I have presented three aspects of any language essential to comprehending that language: concepts, thoughts and a dictionary.

 

If one knows the required collection of concepts and can list the thoughts essential to those concepts, they have sufficient knowledge to express their thoughts. This is the very essence of any conceivable language.

 

If you can comprehend what I have just proposed, I will produce a valid representation of any thought in any language. It turns out that the representation has some profound consequences.

 

Thank you -- Dick

They have given no reasons for refusing it!

There is one issue pretty well overlooked by the scientific community. That would be the issue of control by the scientific community itself. I have a Ph.D. in theoretical physics achieved in 1971. I went into theoretical physics because I wanted to understand the universe. As a graduate student, I had a bad habit of reading too much. Every time some professor required us to read a journal article relevant to his work (and some referred to work published back in the times hundreds of years ago), I had the habit of reading the specific journal from cover to cover. I can't say I read every journal in Vanderbilt's library but I certainly read most of them.

 

At any rate, reading all those articles gave me a rather unusual perspective on publication. In my opinion most of those publications were not worth the paper they were written on. By the time I got my degree, I had decided not to publish until I had something serious to say.

 

Now add to that the fact that 1971 was a rather special year for the scientific community. Because of complaints about the meaningless of much scientific work (sex life of a butterfly for example), President Nixon pulled the federal support for scientific endeavors and turned the money over to states to distribute. Almost universally, the states used the money to benefit their interests. Scientific research money almost vanished but lots of state offices got raises.

 

For the first time in history, there was unemployment among people with graduate degrees. One of the new faculty members in the physics department at Vanderbilt was pumping gas at a service station when I got my degree. (It was a new world.)

 

At any rate I earned my living outside the field of physics. However, I still spent serious time thinking about an idea I had back when I was a student,. Back when I was in my second year (when I was first introduced into quantum mechanics) I noticed an issue totally ignored by the scientific explanation of relativity. That evening I took my idea to the professor teaching that class and, after about three hours, he agreed that I was correct but I should not mention it to the other students as it would just confuse them. Besides, I couldn't deduce general relativity from it so I must be essentially wrong.

 

At any rate, I only have about three publications in my name. (With me as a party to some specific theoretical work.) As I said above, I continued to think about the issue I noticed back in 1967 and in 1982 I discovered a way to extend the issue to general relativity. So I wrote up an article and tried to publish. I ended up sending it to three different major physics journals. It was refused by all three with very similar notes. All three said it was philosophy and was of no interest to physicists. Their responses were very quick and I suspect the real problem was they didn't know what referee to send the thing to.

 

At any rate, since the professor who I had talked to back in 67 had died, I brought my presentation to the professor who was my adviser on my Ph.D. He refused to even look at the thing (I think he was upset because I didn't earn my living in physics).

 

Well after some discussions with a friend in 1987, I sent my article to two different philosophy journals. Both journals rejected it out of hand immediately. Again, I doubt a referee ever saw the thing. What I found extremely funny was the fact that both journals wrote the same reason for rejecting the thing. They both said it was mathematics and was of no interest to philosophers! I showed that response to a mathematician I knew at the time. He looked at the paper and said it would be of no interest to a mathematician as I presented no new mathematics as far as he was concerned it was physics and well over his head. So thus the physicists say it's philosophy, the philosophers say it's mathematics and the mathematicians say it's physics. All I can say is that all three refuse to even consider the thoughts.

 

In 2013 I composed a well thought out version and paid for publication of a book. The Publisher never sold a single copy and eventually required me to personally purchase every copy he had printed. So, at least the thing exists. If anyone wants to look at the thing, I will provide a free pdf copy if you send a note to my e-mail "doctordick01@yahoo.com".

 

But essentially this note goes to the issue of "scientific publication". In today's world the scientific community has become an authority much as the religious authorities were back in the dark ages. The truth of their position is based on their authority and not upon their ability to back up their theories;

 

Have fun -- Dick

I was initially a bit disturbed by having my earlier post moved to "speculations" as I made no speculations whatsoever. But, on thinking about the issue I guess I made one serious speculation. That would be that there were people on this forum capable of thinking.

 

Have fun -- DoctorDick

First, regarding the "moderators" decision to move this thread to "Speculation", my thread contains no speculations whatsoever and the issue I want to discuss consists of absolutely nothing but cold hard facts. (Facts most people would rather ignore!) If anyone sees an assertion I make which is not a cold hard fact, please bring it up so we can discuss the issue.

 

Secondly, the only response so far (from Lord Antares) seems to totally ignore what I have said.

 

His response, that "establishing a mechanism for representing any conceivable language" is "language itself" rather misses the point. People generally presume they understand the language they use. Now that is "speculation" and not defensible fact (misunderstandings occur quite regularly and to deny that such things occur is rather foolish).

 

Secondly, Mr Antares apparently ignored the phrase "My attack requires two fundamental concepts", and simply presumed these concepts were readily available and (I guess) already known by him. Lastly, his assertion that "it will not be understood by another person just by defining it" seems to presume a rather ignorant comprehension on the part of the second party in the communication of interest.

 

What I said was, "My attack requires two fundamental concepts: first, establishing a mechanism for representing any conceivable language and second, establishing a mechanism capable of defining the concept of understanding within that representation of the language without actually defining the language itself." I did neither of these things in my opening post. That post was made for the purpose of finding someone interested in thinking about the issue and nothing more.

 

His further assertion that I can not define what I mean by "understanding" is again a rather extreme "presumption".

 

Finally his question, what is "the problem" I am talking about was (as far as I am concerned) quite clearly expressed. My opening comment was, "The issue of understanding reality is something I would like to seriously discuss." That he totally missed that fact is simply beyond my comprehension.

 

He also apparently missed my further comment that "I would like to discuss the issue without making any assumptions about the language being examined." It seems to me that even the most uneducated individual would comprehend difficulty inherent in such an attack! Without defining a language, discussion is simply impossible.

 

My comment that I would like to use English is an admission that I fully understand the problems embedded in the presumption that the language is "understood" by the reader. That is a problem I will do my best to work around, but recognition that it is a serious problem must be comprehended by the reader. Something which seems to be totally beyond Mr. Antares comprehension.

 

If anyone else reading this thread is interested in discussing the subject (in English, my native language which I think I understand pretty well) I will present the first fundamental concept essential to any conceivable language. That would be the fact that every conceivable language requires a collection of symbolic representations of concepts essential to representing specific thoughts via that language. If no such representations exist, the language does not exist.

 

Please, if anyone thinks that is not a fact, please give me an example of a contradiction of that assertion.

 

Thank you -- Dick

The issue of understanding reality is something I would like to seriously discuss. There is an aspect of that issue which no one seems to have any interest in thinking about. The issue I refer to is the fact that no one is born capable of considering the problem. Every person who has ever tried to think about that issue had to first learn the language spoken by their contemporaries. The underlying problem is that each and every one of them makes the assumption that they understand the language they have supposedly learned.

 

I would like to discuss the issue without making any assumptions about the language being examined. This constitutes a problem as even discussing the issues requires we use a language. I have a subtle means of working around that underlying issue which is apparently difficult for people to comprehend. My attack requires two fundamental concepts: first, establishing a mechanism for representing any conceivable language and second, establishing a mechanism capable of defining the concept of understanding within that representation of the language without actually defining the language itself.

 

In my discussion I would like to use English as the discussion mechanism in order to refer to some underlying aspects of the unknown language being represented.

 

If anyone is interested, let me know and I will make a serious attempt to explain my thoughts in English.

 

Thank you for taking the trouble to think about the issue.

The purpose of mathematical notation is to facilitate the making and communicating of statements in mathematics.

 

...

 

This is a complete waste of everyone's time.

 

 

 

Make your case that it is not. All you need to do is show where your formulation is taught in mainstream physics, i.e. where it shows up in textbooks.

 

 

 

Are you qualifying your statement about the x_i s?

 

If they are specific numbers then of course all the differential coefficients are zero, as they are for any constant.

 

But that is introducing new material, not before stated.

 

It is a pretty pedestrian statement that

 

0 + 0 + 0 + 0 +........................ = Well suprise, 0

 

Originally, you stated an identity concerning a bunch of variables, labelled x_i

 

This may be true for some values of x_i but not for others, nevertheless it could be a valid equation.

 

To qualify for an identity it must be true for all values of all the x_i s

 

This is elementary.

 

The [latex]x_i[/latex] have never been introduced as variables. They have been, from the very start, nothing more than numerical labels on that finite set of listed concepts. The representation [latex]P(x_1,x_2,\cdots,x_n)[/latex] is not a mathematical expression. It is an expression of the probability that the assertion represented by an ordered list of concepts [latex](x_1,x_2,\cdots,x_n)[/latex] is a valid assertion. It is a defined representation of supposed facts (the important point being that they are represented without defining those represented concepts).

 

The virtue of this representation is that, not being specifically defined, the representation applies to all conceivable explanations of any collection of facts. It is an absolutely general representation of facts to be comprehended.

 

The meaning of the various "concepts" has to be learned from their usage and the patterns inherent in that usage. A result which could be accomplished were one given the list of circumstances represented by [latex](x_1,x_2,\cdots,x_n)[/latex] which are held to be valid (you could call that an experience of reality if you wish). The fact that those numerical labels are entirely arbitrary leads to a very significant relationship. Given the entire list [latex]P(x_1,x_2,\cdots,x_n)[/latex], the expression [latex]P(x_1+a,x_2+a,\cdots,x_n+a)[/latex] becomes a defined mathematical function of "a". Since the simple addition of a constant makes no changes whatsoever in the patterns represented in those relevant lists, learning the meanings of the various "concepts" is a problem identical to the original problem. That implies that [latex]P(x_1+a,x_2+a,\cdots,x_n+a)[/latex] must be identical to [latex]P(x_1,x_2,\cdots,x_n)[/latex] as they are deduced from exactly the same patterns.

 

It follows that [latex]\frac{d\;}{da}P(x_1+a,x_2+a,\cdots,x_n+a)[/latex] must vanish for all such representations of any coherent understanding of any collections of facts.

 

Regarding -- 0 + 0 + 0 + 0 +........................ = Well suprise, 0

 

You are apparently defining [latex]\frac{\partial \;}{\partial x_1}P(x_1,x_2,\cdots,x_n)=0[/latex] whereas I am regarding it as undefined since [latex]x_1[/latex] is a numerical label and not a variable. You are jumping to the conclusion that because it looks like a mathematical function [latex]P(x_1,x_2,\cdots,x_n)[/latex] is a mathematical function.

 

The next step of my argument concerns changing my representation into a valid mathematical expression in such a manner that it's generality is conserved without altering the underlying meaning of the representation. That is not a trivial issues.

 

 

I would have thought that was obvious. For example, Newtonian gravity and GR are completely different explanations and yet, in the appropriate domains, produce identical results.

 

I don't know about anyone else, but I find your definitions totally incomprehensible.

 

"In the appropriate domains" is the critical limitation there. I gave my "child's perspective on relativity" because it gave exactly the same results as Einstein's 'theory of special relativity" throughout the entirety of exactly the same domain. Oh, outside that domain they don't agree but at least mine is perfectly consistent with quantum mechanics. That seems to me to be at least an interesting aspect. The moderators here put this into speculation, not I. I wish someone would comment upon where they think I have made a speculation.

 

If you find my definitions incomprehensible, I suggest you ignore me. That won't bother me at all.

 

And finally, imatfaal, what are those "recondite riddles" are you referring to?

 

Have fun --Dick

Some people are I interested but are having difficulty following your line of thought.

I've read George Gamows "one,two,three infinity". I still have a copy as some of his mathematics I find useful.Though that book is very basic math (I also tend to collect a lot of textbook in physics subjects, my earliest was written on 1921)

You might try showing how the formulas you posted thus far compare to the GR methodology.

 

First of all, nothing I have said has anything to do with GR methodology and furthermore, there appear to be a number of competent people out there complaining about GR. In essence, it seems to me to be a subject of little importance to my general analysis.

 

 

 

 

There is a difference between being equal to and being identical to.

 

When one is speaking of specific numbers, please explain to me the difference between being equal and being identical?

 

Have fun -- Dick

I still don't quite see why this is not a mathematical expression. What is the difference between 'numerical label' and 'real variable' in this context? I don't know if what you have written is well-defined or exactly what it is, you have not said what it is. From your notation it looks like we have a function on R^n that is at least C1. What this function represents and how we interpret whet we can get from it, you will have to spell out.

 

As I said, "they are mere numerical labels of the concepts necessary to express the circumstance of interest". They are simple references to your solution. The specific concepts required to express the facts, information, knowledge, --whatever-- which you have come to hold as necessary to understanding your mental image of reality. When you have found what you think is a solution (that is, there is some aspect of reality you feel is true) the final issue is to express that solution via a language. The language is part of the solution! The elements of that language are not variables, they do not change, they are fixed concepts.

 

There are two very important issues here. First, the number of concepts required to express anything you know is finite and, second, once you have decided what those concepts are, they can be listed and labeled, but they do not change. Being "arbitrary" and "changing" are two totally different concepts.

 

Consider your statement (You seem very verbose and this is distracting from the points you are trying to make.)

represented by the circumstance (15,7,8,13,3,6,2,14,9,4,11,15,5,12,1,10,0) in my notation.

 

Then P(15,7,8,13,3,6,2,14,9,4,11,15,5,12,1,10,0) would represent the probability (in your understanding) that the circumstance was true.

 

Given that meaning of the representation, please explain to me what you think could possibly mean.

 

Have fun --Dick

 

(By the way guys, that is my real name and not a comment. And "Doctor Dick" has been my nickname most all of my adult life.)

 

 

Not so. Perhaps you should revise some mathematics, rather than insulting me (and others), since this is the second time you have done it, in this thread.

 

Please explain that comment!!

 

Well, no responses but a decent number of views. I will take it that some people are interested. I like a comment made by tar in post #41 of the closed thread “Is philosophy relevant to science”:

 

By my thinking there is no door between my mind and reality. My brain is real' date=' my senses pick up real actual patterns from and about reality and perceive them and store them in an analog fashion as to represent rather acurately what is going on around me. I can build maps and models of it, use transforms and analogies, and get a pretty good "idea" of what it is that I am in and of. I can put "myself" in the shoes of any entity I chose, and imagine what they might be experiencing. I can "imagine" unseen others.

 

It is in light of these thoughts that I "understand" other's philosophies, religion and psychology.

And from my personal point of view, the scientific method is a fine way for us to utilize the explorations of reality that others have made, and to add those explorations to my own understanding of the nature of "the thing in itself".

[/quote']

Add to that a comment made by a friend of mine from Finland:

 

In some important ways' date=' our world views always are; the chosen terminology can be anything, as long as it is a self-coherent way to express valid predictions. That is just another way to say, it's chosen expression form is bunch of circularly understood concepts. And that is another way to express why I think it is so childish when people argue about the correctness of the circle they most like to use.

[/quote']

The real issue here is “language”. Language is entirely a “collection of circularly understood concepts”. When tar says, “my senses pick up real actual patterns from and about reality and perceive them and store them”, he is actually presuming that his concept of “senses” and the “perception of reality” obtained from them are correct. That is a belief and is not necessarily a fact. However, there is a way of handling the issue without actually succumbing to the belief.

 

Communications are achieved via a language. Knowing the language involves understanding those circularly defined concepts represented by the symbols going to make up that language. The important point here is that the actual symbols used to represent that language are an immaterial issue. Absolutely any concept representable in a language is just as easily represented by a set of numerical labels attached to the conceptual elements represented by the symbols going to make up that language.

 

Now a lot of people will complain about that assertion. But, before you jump to the conclusion that such a representation cannot be absolutely general, consider two very important issues. First, all internet communications rely on the ability to convert anything to be communicated into a collection of binary numbers (and that includes words, pictures, mechanical interactions and even could include smells and taste via the technology possibly becoming available to us). And secondly, almost everyone's view of the universe includes the concept of nerve signals connecting their brain to reality. Now those nerve signals themselves could certainly be represented by numerical labels.

 

If follows, from the above, that absolutely any possible communication conceivable can be represented by a set of numerical labels which, in turn, can be represented by the mathematical notation [math](x_1,x_2,\cdots,x_n)[/math]. The language being represented is not an issue here because, the problem of understanding the language is fundamentally identical to understanding anything.

 

I think it is quite evident that the mental view one possesses of reality is clearly acquired via “practical thinking” not by analytical analysis: i.e., babies simply display no expertise at analytical analysis. Furthermore, you should note that “beliefs” are an acquired thing; children are not born with “beliefs”. Think about that for a moment. It implies that understanding (at least initially) is acquired in the complete absence of beliefs.

The real beauty of this representation is the fact that the supposed language plays no role in the problem at all: i.e., this means that any generalization which can be made from this representation applies even to issues not yet thought of. It is possible that future views of the universe might very well be quite different from those we currently hold. That is simply not an issue; the communications of those views could still be represented in the notation [math](x_1,x_2,\cdots,x_n)[/math].

 

Oh, as an aside, I have left the number of numbers in that representation finite. That will turn out to be a very important factor. It arises directly from the definition of “infinite”. If the number of elements in a collection is infinite then it follows that, no matter how many you have considered, you have not finished considering them. Essentially, all communications must be finite in extent. Note that this does not require that the concepts being communicated are finite but merely that the number of elements used to communicate the issues be finite.

 

If anyone has any complaints with what I have said so far, let me know; I will try to clarify anything you find difficult to understand. And, DrRocket, I am already well aware of your brilliant and insightful comprehension of my work and the detailed proof reading you have made of my earlier posts so it really serves no useful purpose for you to comment further. I wholly appreciate all the hard work you have already done.

 

I have reproduced this load of crap to avoid letting you edit it after the fact. But it is still just a load. There is absolutely nothing here of any mathematical or physical interest. In fact it is not clear that there is even a lucid thought.

Thank you for your kind support.

 

Have fun -- Dick

Geometric proof of what?

(The following has been corrected for typo errors in the original)

 

With regard to "weak emergence" (that is with regard to the definition of "weak emergence") I feel it can also be dispensed with via the following proof. That is, emergence is emergence and there is nothing either weak or strong about it! People begin to think about weak "emergence" when what they are looking at is more complex than what they can deduce from "known laws". What they seem to forget is that physics is applicable only to problems which can be reduced to one body problems by some procedure.

 

 

I am of the opinion that the following proof is of great significance when one goes to consider "emergent" phenomena and the complexity achievable from simple constructs. The proof concerns a careful examination of the projection of a trivial geometric structure on a one dimensional line element.

 

 

The underlying structure will be an n dimensional rigid entity defined by a collection of n+1 points connected by lines (edges) of unit length embedded in an n dimensional Euclidean space (i.e., a minimal n dimensional equilateral polyhedron; the generalized concept of a higher dimensional equilateral triangle with unit edges). The universe (the collection of information to be analyzed) of interest will be the projection of the vertices of a that polyhedron on a one dimensional line element. The logic of the analysis will follow the standard inductive approach: i.e., prove a result for the cases n=0, 1, 2 and 3. Thereafter prove that if the description of the consequence is true for n-1 dimensions, it is also true for n dimensions. The result bears very strongly on the range of complexity of "emergent" phenomena given an extremely simple source.

 

 

First of all, the projection will consist of a collection of points (one for each vertex of that polyhedron) on the line segment of interest. Since motion of that polyhedron parallel to the given line segment is no more than uniform movement of every projected point, we can define the projection of the center of the polyhedron to be the center of the line segment: i.e., linear motion of the polyhedron has no real consequences. Furthermore, as the projection will be orthogonal to that line segment and the n dimensional space is Euclidean, any motion orthogonal to that line segment introduces no change in the projection whatsoever. It follows that the only motion of the polyhedron which provides any interesting changes in the distribution of points on the line segment will be rotations of the polyhedron in the n dimensional space.

 

 

The assertion which will be proved is that every conceivable distribution of points on the line segment is achievable by a specifying a particular rotational orientation of the polyhedron relative to the line segment of interest. Before we proceed to the proof, one issue of significance must be brought up. That issue concerns the scalability of the distribution. I referred to the collection of points on the line segment as the "universe of interest" as I want the student to think of that distribution of points as a universe: i.e., any definition of length must be arrived at via some defined characteristic of the the distribution itself or some subset of the distribution. Thus any two distributions which differ only by a scale factor will be considered to be identical distributions.

 

 

Case n=0 is trivial as the polyhedron consists of one point (with no edges) and resides in a zero dimensional space. It's projection on the line segment is but one point (which, from the above constraints, is at the center of the line segment by definition) and no variations in the distribution of any kind are possible. Neither is it possible to define length within that "universe". It follows trivially that every conceivable distribution of a lone point on a line segment where the center of the distribution is defined to be the center of the line segment is achievable by a particular rotational orientation of the polyhedron (of which there are none). Thus the theorem is valid for n=0 (or at least can be interpreted in a way which makes it valid). I said it was trivial; it is only here for continuity in that it lets me begin with one point.

 

 

Case n=1 is also trivial as the polyhedron consists of two points and one edge residing in a one dimensional space. Since the edge is to have unit length, one point must be a half unit from the center of the polyhedron and the other must be a half unit from the center in the opposite direction. Since rotation is defined as the trigonometric conversion of one axis of reference into another, rotation can not exist in a one dimensional space. It follows that our projection will consist of two points on our line segment. We can now define both a center (defined as the midpoint between the two points) and a length (define it to be the distance between the two points) in this universe but there is utterly no use for our length definition because there are no other lengths to measure. It follows trivially that every conceivable distribution of two points on a line segment (which is one) is achievable by a particular rotational orientation of the polyhedron (of which there are none). Thus the theorem is valid for n=1.

 

 

Case n=2 is the first case which is not utterly trivial. Fabrication of an equilateral n dimensional polyhedron is not (in general) a trivial endeavor. In order to keep our life simple, let us construct our equilateral polyhedron in such a manner so as to make the initial orientation of the lower order polyhedron orthogonal to the added dimension. Thus we can move the lower order entity up from the center of our new coordinate axis and add a new point on the new axis below the center. In this case, the coordinates of previous polyhedron (as displayed in the n Euclidean space) remain exactly what they were for the n-1 established coordinates and are all shifted by the same distance from zero along the new axis. The new point has a position zero in all the old coordinates (it is on the new axis) and an easily calculated position on in the negative direction on that new axis (that distance must be equal to the new radius of the vertices of the old polyhedron as measured in the new n dimensional space).

 

 

The proper movement is quite easy to calculate. Consider a plane through the new axis and a line through any vertex on the lower order polyhedron. If we call the new axis the x axis and the line through the chosen vertex the y axis, the y position of that vertex will be the old radius of the vertex in the old polyhedron. The new radius will be given by the square root of the sum of the old radius squared and the distance the old polyhedron was moved up in the new dimension squared. That is exactly the same distance the new point must be from the new center. Assuring the new edge length will be unity imposes a second Pythagorean constraint consisting of the fact that the old radius squared plus (the new radius plus the distance the old polyhedron was moved up) squared must be unity.

 

 

[math]r_n = \sqrt{x_{up}^2 + r_{n-1}^2}[/math]

 

 

and

 

 

[math] 1 = \sqrt{r_{n-1}^2 + (x_{up} + r_n)^2 }[/math]

 

 

The solution of this pair of equations is given by

 

 

[math]r_n = \sqrt{\frac{n}{2(n+1)}} [/math]

 

 

and

 

 

[math]r_{up} = \frac{1}{\sqrt{2n(n+1)}}[/math]

 

 

 

The case n=0 was a single point in a zero dimensional space. The case n=1 can be seen as an addition of one dimension x_1 (orthogonal to nothing) where point #1 was moved up one half unit in the new dimension and a point #2 was added at minus one half in the new dimension (both the new radius and "distance to be moved up" are one half). The case n=2 changes the radius to one over the square root of three and the line segment (the result of case n=1) must be moved up exactly one half that amount. A little geometry should convince you that the result is exactly an equilateral triangle with a unit edge length. Projection of this entity upon a line segment yields three points and the relative positions of the three points are changed by rotation of that triangle.

 

 

In this case, we have two points to use as a length reference and a third point who's distance from the center can be specified in terms of that defined length reference. Using those definitions, two of the points can be defined to be one unit apart and the third point's position can vary from any specific position from plus infinity to minus infinity. The infinities are approached when the edge defined by the two vertices being used as our length reference approaches orthogonality to the line segment upon which the triangle is being projected (in which case the defining unit of measure falls towards zero). Plus infinity would be when the third point is on the right (by convention) and minus infinity when the third point is on the left (by common convention, right is usually taken to be positive and left to be negative). It thus follows that every conceivable distribution of three points on a line segment is achievable by a particular rotational orientation of the polyhedron (our triangle). Thus the theorem is valid for n=2.

 

 

Case n=3 consists of a three dimensional equilateral polyhedron consisting of four points, six unit edges and four triangle faces: i.e., what is commonly called a tetrahedron. If you wish you may show that the radius of vertices is given by one half the square root of three halves and the altitude by the radius plus one over two times the square root of six (as per the equations given above).

 

 

In examining the consequences of rotation, to make life easy, begin by considering a configuration where a line between the center of our tetrahedron and one vertex is parallel to the axis of projection on our reference line segment. Any and all rotations around that axis will leave that vertex at the center of our line segment and actually consist of rotation in the plane of the face opposite to that point. Essentially, except for that particular point, we obtain exactly the same results which were obtained in case n=2 (that would be projection of the triangle face opposite the chosen vertex). Using two of the points on that face to specify length, we can find an orientation which will yield the third point in any position from minus infinity to plus infinity while the forth point remains at the center of the reference line segment.

 

 

Having performed that rotation, we can rotate the tetrahedron around an axis orthogonal to the first rotational axis and orthogonal to the line on which the projection is being made. This rotation will end up doing nothing to the projection of the first three points except to uniformly scale their distance from the center. Since we have defined length in terms of two of those points, the referenced configuration obtained from the first rotation does not change at all. On the other hand, the forth point (which was projected to the center point) will move from the center towards plus or minus infinity depending on the rotation direction (the infinite positions will correspond to the orientation where the line of projection lies in that face opposite the fourth point: i.e., the scaled reference distance approaches zero). It follows that all possible configurations of the four points in our projection can be reached via rotations of the tetrahedron and the theorem is valid for n=3.

 

 

The final part of the proof (if it is true for an n-1 dimensional figure, it is true for an n dimensional figure) requires a little thought:

 

 

Since the space in which the n dimensional polyhedron is embedded is Euclidean, we can specify a particular orientation of that polyhedron by listing the n coordinates of each vertex. That coordinate system may have any orientation with respect to the orientation of the polyhedron. That being the case, we are free to set our coordinate system to have one axis (we can call it the x axis) parallel to the line on which the projection is to be made. In that case, except for a scale factor (which must be obtained from the distribution), a list of the x coordinates of each point correspond exactly to the apparent positions of the projected points on our reference line. Thus I will henceforth use the x axis in the n dimensional space as a surrogate for my reference line segment.

 

 

If the theorem is true for an n-1 dimensional polyhedron, there exists an orientation of that polyhedron which will correspond to any specific distribution of n points on a line (where scale is established via some procedure internal to that distribution of points). If that is the case, we can add another axis orthogonal to all n-1 axes already established, move that polyhedron up along that new axis a distance equal to

 

 

[math]x_n = \frac{1}{\sqrt{2n(n+1)}}[/math]

 

 

 

and add a new point at zero for every coordinate axis except the nth axis where the coordinate will be set to

 

 

[math]-r_n = x_n = - \sqrt{\frac{n}{2(n+1)}}[/math].

 

 

 

The result will be an n dimensional equilateral polyhedron with unit edge which will project to exactly the same distribution of points obtained from the previous n-1 dimensional polyhedron with one additional point at the center of our reference line segment.

 

 

If our n dimensional polyhedron is rotated on an axis perpendicular to both the reference line segment and the nth axis just added, the only effect on the original distribution will be to adjust the scale of every point via the scale factor [math]cos\theta[/math]. That is, the new x_i is obtained by

 

 

[math]x_{1i New} = x_{1i Old}cos\theta + \sqrt{\frac{n}{2(n+1)}}sin\theta [/math],

 

 

 

where theta is the angle of rotation (notice that the sin term yields a simple shift exactly the same for all points which is quite meaningless as far as the pattern of those points is concerned). Meanwhile, the x_1 position of the added point will be given exactly by [math]-r_n sin \theta[/math] (the cos term vanishes as it started on the origin of x_1). Once again, the added point may be moved to any position between plus and minus infinity which occur at plus and minus ninety degrees of rotation. Once again, the length scale is to be established via some procedure internal to the distribution of points. It follows that the theorem is valid for all possible n.

 

 

QED

 

 

There is an interesting corollary to the above proof. Notice that the rotation specified in the final paragraph changes only the components of the collection of vertices along the x axis and the nth axis. All other components of that collection of vertices remain exactly as they were. Since the order used to establish the coordinates of our polyhedron is immaterial to the resultant construct, the nth axis can be a line through the center of the polyhedron and any point except the first and second (which essentially establish the x axis under our current perspective). It follows that for any such n dimensional polyhedron for n greater than three (any x projection universe containing more than four points) there always exists n-2 axes orthogonal to both the x and y axes. These n-2 axes may be established in any orientation of interest so long as they are orthogonal to each other and the x,y plane. Thus, by construction, for any point (excepting the first and the second which establish the x axis) there exists an orientation of these n-2 axes such that one will be parallel to the line between that point and the center of the polyhedron. Any rotation in the plane of that axis and the y axis will do nothing but scale the y components of all the points and move that point through the collection, making no change whatsoever in the projection on the x axis.

 

 

We can go one step further. Within those n-2 axes orthogonal to the x and y axes, one can choose one to be the z axis and still have n-3 definable planes orthogonal to both the x and the y axes. That provides one with n-3 possible rotations which will leave the projections on the x and y axes unchanged. Since, in the construction of our polyhedron no consequences of rotation had any effect until we got to rotations after addition of the third point, these n-3 possible rotations are sufficient to obtain any distribution of projected points on the z axis without altering the established projections on the x and y axes.

 

 

Thus it is seen that absolutely any three dimensional universe consisting of n+1 points for n greater than four can be seen as an n dimensional equilateral polyhedron with unit edges projected on a three dimensional space. That any means absolutely any configuration of points conceivable. Talk about "emergent" phenomena, this picture is totally open ended. Any collection of points can be so represented! Consider the republican convention at noon of the second day (together with every object and every person in the rest of the world; and all the planets; and all the galaxies ...) where the collection of the positions of all the fundamental particles in the universe is no more than a projection of some n dimensional equilateral polyhedron of unit size on a three dimensional space. Talk about emergent phenomena!

 

 

On top of that, if nothing in the universe can move instantaneously from one position to another, it follows that the future (another distribution of that collection of positions of all the fundamental particles in the universe) is no more than another orientation of that n dimensional polyhedron and the evolution of the universe in every detail must correspond to continuous rotation of that figure. Think about that view of a rather simple geometric construct and the complex phenomena which is directly emergent from the fundamental perspective.

 

 

Have fun -- Dick

You guys should be asking "thinking - how does it work?'

 

So how do we deal with thinking in the day to day world of getting by? Are we "plagued" by the shortcuts we use, or are they a practical necessity due to the sheer volume of information? I think it would be interesting to explore practical thinking in general.

So then, why don't we do that?

 

One thing about practical thinking; much of the thought processing is done at an unconscious level by the mainframe of the brain. The unconscious compares the absorbed data, does the data crunching, and spits out a bottom line; Eureka!. But it occurs so fast, one may not be able to formulate the solution to the final answer, in a conscious way.

Now this seems to be an excellent starting point. We should not go adding to the difficulty by presuming beliefs built by that process. That attack is clearly not analytical: i.e., not something we can logically discuss. Let's get back to the underlying issue; exactly what do we mean by “thinking” and, can we formulate a logical solution embodying that final answer? I say the answer is yes!

 

I don't really know the answer padren. I take it that experience, knowledge, peer pressure and culture play a large part in what we term pragmatic thinking. If I am correct in my premise then pragmatism to a Zulu warrior would be very different from an Inuit. I also find that pain and hurt are good teachers

Now I think your comment is quite on point. It just doesn't provide a lot to work with.

 

This is true for big issues too, not just small ones. For example, I am fairly sure that evolution occurs (not necessarily 100% according to Darwin, but pretty close) even though I haven't personally sifted through all the evidence. I sounds like a reasonably believable idea and I trust the scientists that have done the analysis.

Ah, trust! But aren't you just adding to the difficulty by presuming beliefs built by the process? In other words, it seems to me that you are simply avoiding the original issue. That serves no purpose at all.

 

Well someone somewhere should be rigorously skeptical of every new idea, but once several people with good credentials accept it most of us will believe them. Anything else is just too impractical. Of course its also good to have some people constantly skeptical of each idea, but I don't think there's a shortage of that.

Oh, I would differ with you; I think there is a major shortage of real skeptics! In my old age, I have come to the conclusion that “belief” is a totally unnecessary philosophical concept. As Bertrand Russell once said, “most people would rather die than think”. (I may have paraphrased that, but he did say something like that.) In fact, conscious analysis is not really a necessary aspect of success at all. I have known many successful people who never gave even the first thought to logical analysis of anything. But I am a rather strange person and perhaps I should tell you a little about myself.

 

When I was three years old, I witnessed an argument my father had with my aunt's husband concerning aliens from outer space. (It was always quite clear to me that my father had utterly no respect for my uncle.) When my uncle left, slamming the door as he went, my father turned to me and said, "anyone who believes more than ten percent of what he hears, or more than fifty percent of what he reads, or more than ninety percent of what he sees with his own eyes is gullible!" At the time, I had no idea as to what percent was nor what the word gullible meant but the comment was none the less absolutely engraved on my mind in every detail, never to be forgotten. The one thing I knew is that I didn't want to be one (at the time I think I had the impression it was a birth defect of some sort that required absolute disrespect).

 

My dad's comment may have had more impact on my life than any other experience I ever had. My single biggest worry has always been, "just how does one determine what one is supposed to believe?" I have to add to that the fact that adults just love to "pull kids legs". When I would catch them at it, they were always delighted. As a consequence, long before I even began school, I came to believe adults always lied to kids. I never saw it as malicious but rather presumed it as training not to be gullible (and, believe me, I was firmly convinced that I was indeed gullible; a problem I made every effort to hide). I simply could not tell when I was being told the truth and when I was being lied to.

 

Now, all children like to think they are grown up and so did I. By the time I was five or six, I stopped openly catching adults in their bullshit: I began to pretend I believed everything they said (just like a real adult). Oh, I didn't act on it but I certainly didn't tell them when I thought what they said was bullshit. My mother once told me one learns a lot more by listening than they do by talking. Oh, she also told me that if I did something which I really felt was right but turned out to be wrong, I could be forgiven; however, if I ever did something which I myself felt was wrong, that was unforgivable so I always went with what felt like the right thing to do (I never made an attempt to justify it). I think she was a very intelligent person.

 

I only brought this up to explain something about the way I lived my life and what I have to add to this thread. I thought about things all the time but I absolutely never thought out what I was supposed to do. What I always did was to "go with my gut!" All my life, I have never made decisions based on logic applied to my beliefs (because I had no idea as to what I was supposed believe, other than my gut instincts); I have always simply done what seemed to be the right thing to do emotionally. In essence I just turned control of my actions over to my subconscious. I think that was, to a great extent, exactly what padren meant by pragmatic living in his opening post and why I think what I have to say is worth listening to.

 

I lived my life as an unthinking thoughtless entity while, at the same time, always trying to figure out how to determine what should and shouldn't be believed. Before I got to High School, the only subject I was good at was mathematics. That subject (as taught) made it quite clear, what is and is not to be believed. But, as practically every thoughtful person says, mathematics has nothing to do with reality. That is why I ended up in Physics. Physicists seemed to be the only people who provided any way to test their beliefs. I ended up with a Ph.D. in Theoretical Nuclear Physics from Vanderbilt University. One problem I had was that, by the time I got into graduate school, they ceased providing tests for their beliefs. As Mr Skeptic said above, when people with good credentials accepted things, we were expected to believe them (in spite of the fact that, time after time throughout history, the authorities were shown to be wrong). Believing them began to get difficult if not impossible.

 

It is now my opinion that the source of the difficulty is belief itself. Belief is the single most potent corrupter of intellectual analysis which exists. I now find it clear that "belief" is simply not necessary in order to solve the problem confronting us. It turns out that the solution is simply sitting there in mathematics. Mathematics could, in fact, be defined to be the invention and study of internally consistent concepts. That is why physicists have consistently contributed to mathematics time after time. Our view of reality is supposed to be a collection of internally consistent concepts so, every time a scientist comes up with a new set of useful internally consistent concepts, the mathematicians adopt a representation of those concepts into their field.

 

It follows directly that, if and when a solution is found, it will be expressible in mathematics. I have found a solution and it turns out that asking the right question is the key to the difficulty. If you ask the right question and approach the possibilities without any prejudice of belief (i.e., making sure no possibility is omitted), the solution will unravel itself.

 

The solution is to define exactly what we mean by “understanding”. If anyone is really interested in seeing how such a thing rolls out, I will explain exactly what I am talking about. I am of the opinion that it is a serious answer to the question, "thinking - how does it work?'

 

It is probably also a major clue to real AI. Oh, by the way, I think it is quite evident that the mental view one possesses of reality is clearly acquired via “practical thinking” not by analytical analysis: i.e., babies simply display no expertise at analytical analysis. Furthermore, you should note that “beliefs” are an acquired thing; children are not born with “beliefs”. Think about that for a moment. It implies that understanding (at least initially) is acquired in the complete absence of beliefs. If you want to be rational, you should at least give me the opportunity to express what I have discovered.

 

Have fun -- Dick

This is the Dirac equation. I would first change notation, but that doesn't matter.

Been a while since I posted here but thought I might look around again. I actually have a Ph.D. in Theoretical Nuclear Physics from Vanderbilt University. I posted this thread because I wanted to see if there was anyone here who understood things at that level. I am afraid that is not Dirac's equation; Oh it looks a lot like Dirac's equation (and it is relatively easy to show Dirac's equation is an approximation to it) but there are important differences with profound consequences. Apparently there is no one here capable of comprehending the consequences of those subtle differences.

 

One exact solution I discovered leads to a rather significant geometric proof.

 

The proof concerns a careful examination of the projection of a trivial geometric structure on a one dimensional line element.

Also shown is an interesting corollary consisting of the fact that three (and only three) such projections can be made on three orthogonal axes thus a three dimensional collection of absolutely arbitrary points can always be seen as a projection of that same trivial n dimensional structure. It follows that any collective motion of such a collection of points can be seen as a projection of that trivial structure under complex rotation in that n dimensional space.

 

Another post which seems to have gone totally over everyone's head.

 

Have fun -- Dick

Just out of pure curiosity, can anyone here give me any advice on the problem of solving the following differential equation

 

where,

 

[math][\alpha_{ix} , \alpha_{jx}] \equiv \alpha_{ix} \alpha_{jx} + \alpha_{jx}\alpha_{ix} = \delta_{ij}[/math]

 

[math][\alpha_{i\tau} , \alpha_{j\tau}] = \delta_{ij}[/math]

 

[math][\beta_{ij} , \beta_{kl}] = \delta_{ik}\delta_{jl}[/math]

 

[math][\alpha_{ix}, \beta_{kl}]=[\alpha_{i\tau}, \beta_{kl}] = 0 \text{ where } \delta_{ij} =

\left\{\begin{array}{ c c }

0, & \text{ if } i \neq j \\

1, & \text{ if } i=j

\end{array} \right.

[/math]

 

Any advice on approaching this problem would be greatly appreciated.

 

Thank you very much!

I disagree with a large part of that…

Well, then let me know what part you disagree with. It certainly cannot be the second paragraph

Essentially I hold that "an explanation" is something which provides you with expectations (take that as my definition of an explanation: i.e., it is what I mean when I use the word "explanation"). If the universe is totally random, then your expectation should be "anything can happen" and there exist a number of explanations which yield exactly that result.

as all I am doing there is telling you what I mean when I use the word “explanation” you certainly can’t contend that I am lying to you,. So you must be disagreeing with my assertion that a difference exists between the value of an explanation and the existence of an explanation. If you are referring to something else, you need to clarify your intentions. I can not make heads or tails of the rest of your post.

I contest that you Can have Random within Parameters…

To contest, is to disagree with! So you are saying that you cannot have random within parameters: i.e., there is no such thing as a random selection from a defined set? That seems to me to be a position quite at odds with the common understanding of the word “random”. But you then say, “but it`s still non the less Random.” I have utterly no idea as to what you are trying to say.

if we take for example White Noise, generated by the reverbias breakdown voltage of a Zener diode and then heavily amplified, what you`ll hear is purely random noise "White noise".you`ll never get an Elephant or a all the dishes washed for a month, you will only ever get white noise.

The only thing I can grasp from this is that you are simply asserting that reality is not random. That has absolutely nothing to do with the question, “what would an explanation of the universe look like if the universe were absolutely and unconditionally random”.

now if we can accept this, Then this chat can move on, towards something a Little more Productive

I take this comment to be an assertion that the universe is not totally random and that my failure to accept that as a fact is an abomination to science: i.e., you certainly are opposed to thinking about it.

 

And yet you want to continue your pontification about Ockham's Razor VS Randomness. Now Ockham’s Razor has to do with simplicity and if there exists any hypothesis simpler than “it is just random”, I am unaware of it. And yet the entire scientific community utterly refuses to examine the consequences of such a hypothesis.

 

I am just dumfounded by their absolute belief that examination of such a thing cannot possibly be of any value. It is exactly the same as the medieval scholars refusing to consider a thesis omitting God.

 

Have fun -- Dick

And that's my point -- anything that's truly random is something we cannot explain ...

You are in error! I can give you a very simple explanation of anything you wish: i.e., "That is what the gods desired!" Now I am not being silly there. I am making the point that you are speaking of the value of an explanation, not the existence of an explanation. They are quite different issues.

 

Essentially I hold that "an explanation" is something which provides you with expectations (take that as my definition of an explanation: i.e., it is what I mean when I use the word "explanation"). If the universe is totally random, then your expectation should be "anything can happen" and there exist a number of explanations which yield exactly that result.

 

Now my question was very specific, what would you expect an explanation of the universe to look like if that universe were totally random?

... and accepting something as being truly random seems like giving up. So IMO we cannot ever accept something as truly random, even if we always model it as something effectively random.

So you refuse to even think about the matter?

 

If I gave you a specific explanation (i.e., a specific method which would yield an exact match to everything you had ever experienced) consistent with your known past (no matter what that past was), you would not consider that a valid explanation of a totally random universe? I am ready to do that, in detail, if you are willing to examine each logical step objectively.

 

Have fun -- Dick