So, use your model, given these sets B, how can I arrive at my "explanation" and get the set A?

Oh, I had not realized that you didn't understand my definition of an explanation. I defined "

**An explanation**" to be

**a method of obtaining expectations** from

**given known information**. First, you can not "get

**A**",

**A** is the source of your "valid" information not something you have the ability to "know". The central issue is that your expectations can be seen as a function of the numerical elements in

**B**, something you can "know". I named the function psi. First, although you have already decided on a numerical reference for the elements of

**A** one might think we could omit that step but your numbers are specific references to your set

**A** and we cannot presume these are the labels our thinker will attach to those elements (remember, to him they are undefined). Also, you have not laid out the order index t so I will set one down.

The set

**C** will consists of

**B**(1) = (4,9,6,10),

**B**(2) = (4,8,10,10,12),

**B**(3) = (0,4,11,12,12,13),

**B**(4) = (1,2,3,4,7,9,10). Now you suggest that the 0.665 and 0.775 (which I gave numerical labels 2 and 7) are additions to

**B**(4) which arise because of set

**D**. (Since we are apparently gods and thus know what

**A** actually is we can tell the difference but our thinker can not) The model will then start with a table of psi!

psi(4,9,6,10,t=1) = ? from their explanation prior to t=1 and 1 for t>1

psi(4,8,10,10,12,t=2) = ? from their explanation prior to t=2 and 1 when t >2

psi(0,4,11,12,12,13,t=3) = ? from their explanation prior to t=3 and 1 when t>3

psi(1,2,3,4,7,9,10,t=4) = ? from their explanation prior to t=4 and 1 when t>4

Which at least makes the "explanation" consistent with

**C**. Now 0.665 and 0.775 (2 and 7) are members of

**D**: i.e., part of the students expectations (a figment of his imagination). Since I don't know what his expectations are (that is, I don't know what his explanation actually is), I have no way of adding any entries to that table of psi. (In fact, the entries I have given are not necessarily his explanation as humans quite often give explanations inconsistent with what actually happened.) I will nonetheless assume they are, i.e., I will assume his explanation is consistent with the facts. The question arises in my head as to why he decided to make the assumption those references 2 and 7 (0.665 and 0.775) should be in the entries; in what way did his explanation seem better when they were there? (Remember,

**D** is part of the explanation and not actually derived from

**A**. They are inserted because they are essential to the explanation hypothesized by the thinker.)

At any rate, whatever his explanation is, he should be able to give me his expectations for all entries to that table. If I ask him, what is your expectation for (1,3,4,5,t=6) and he has an explanation, he should be able to provide me with that answer. I could also ask him about (1,1,1,1,t=6) and an infinite number of additional possibilities. The question is, does there exist a procedure which will be perfectly consistent with all the members of any conceivable

**C** derived from

**A** and yet, at the same time, yield a decent rational probability for the actual new information. That is, given

**C**+

**D** up through B(tn-1) is the actual B(tn) seen as being within the expectations of their explanation? Another way of saying, are those expectations consistent with what happened?

I hold that my equation constitutes a procedure for generating expectations perfectly consistent with

**C**+

**D**. I hope this makes it clear that considering actual data is not a route to understanding the issue I am talking about. My equation is a logical construct and is perfectly true so long as the definitions given are adhered to.

Dick, in order for us nitwits to get an abstract model straight, you'll have to accept that it might be necessary for us to see it applied to something simple.

First, I do not think anyone here is a nitwit. And second, I no longer believe you are intentionally trying to create straw men. I think the source of the difficulty is that you don't comprehend what I am trying to do; you are not really differentiating between the concept "an explanation" and the thing "an explanation". You think I am trying to model the second when I am concerned solely with the first. It is your attempts to apply my comments to the second which are confusing you. The essence of the abstract concept is that the explanation is explaining something which is unknown in the absence of the explanation.

There is an overwhelming flaw in any procedure which is an attempt to apply my thoughts to a defined

**A**. A definition of something is an explanation of what that thing is. Were you to give to an individual elements of something totally undefined to him (i.e., in the total absence of any other information), it is extremely unwarranted to assume that he would arrive at exactly the same definition you were using to produce that information. Particularly for a volume of information so small as to be presentable on a forum thread. Look at the exposition I laid out for Erasmus above. Now if you gave the same information to two different individuals who could discuss what they were getting, they could theorize about the algorithm behind the data and perhaps agree between themselves, but I doubt that explanation would bear much resemblance to that of the provider; at least not until their information had reached a rather exorbitant volume.

Now, I (being a god) happen to know that the information being given by Erasmus above is a random collection of elements from the set of real integers. Thus I can expand upon what information the thinker will be provided with over an extended period and can be pretty sure his eventual explanation of the information will be "it's random", which is not at all what I think Erasmus had in mind when he proposed the example but is the only conclusion possible given the constraints.

As for your challenge about the unknown x, I could tell you that x is an unknown ? (number?, real?, complex?, quaternion?, apple?, galaxy?) and insist that you just must understand how it is possible to determine it.

Once upon a time, say back when we were single celled animals, we had no idea of what the universe was (at least I suspect that is true) and reality could seriously be called an unknown! Now we have come a long way since then and I must insist that you understand that it is possible to get here from there (at least get a decent idea as to what reality is) by some method. I sincerely doubt a fertilized human egg comprehends the true nature of reality in all of its nuances. And yet, millions upon millions of those fertilized eggs grow up on a daily basis into entities which are able to make a great amount of sense of that undefined information they have received since the event of their fertilization. That problem is solved day in and day out by countless individuals who have spent less than twenty years on the issue; therefore, I conclude it is a solvable problem and is worth examining.

Is it really futile to apply the model to something as if it wasn't known?

No, what is futile is the idea of handling the information in small isolated pieces. When one does that, the conclusions which can be drawn are so limited as to be essentially useless. It is a problem which can only be handled in a holistic manner. Once it has been handled, it is then possible to deduce apparent results in limited cases but the reverse approach does not yield usable results. The problem here is that the scientific community always looks at the details under the presumption that their solution to the problem to date is correct. They need to step back to the very dawning of the problem and figure out how to solve it from scratch.

The critical issue here is that, when taken as a holistic problem, a valid solution to rational expectations must satisfy my equation. In fact, I have come to the conclusion that it is exactly the freedom to relabel (essentially redefine) the elements making up

**B** which makes it possible to solve the problem; now, if I am correct, that makes for some very strange and interesting thoughts. Meanwhile, I would like the opportunity to show you that I am correct.

... but you'll go blue in the face before understanding my method unless I say that it consists in knowing "something about the number, such as that 3x = 4".

And you are going blue in the face because you refuse to accept the idea that "absolute internal consistency" could possibly be such a demanding constraint. Against that position, please note that the black body spectrum was obtained by the simple requirement of demanding kinematic consistency. Internal consistency is a far more demanding constraint than is usually realized.

How about that as a simple case for applying your abstract model to?

We poah Injuns dunno wut da dang' woid 'aljubah' mean! Use yo' mahdul ta sho' us!

Again, you are confusing modeling the abstract logical concept, "an explanation" with modeling a specific instance of "an explanation". My model is not a source of explanations, it is a model of "an explanation": i.e., a model of "a method of obtaining expectations consistent with the given information". You give me the explanation (in all its gruesome detail, leaving utterly no questions to be asked) and I would give you psi which represents it; however, I would probably give it to you in tabular form and it would probably be longer than the forum would tolerate. My equation tells you how to interpolate between known data under the rule specified by the Dirac constraint.

Which is the fundamental equation, extracted from the model, that you deduce?

I would stick it in right here if I knew how. You seem to be aware of a method of inserting images of equations as evidenced by your quote of my other paper in your response in the

"What is time?" thread. Tell me how you did that and I'll quote the relevant material directly in this thread. Besides that, discussing the solutions will be much easier if I can quote the relevant equations in that procedure.

All appendix 2 says is what I had more or less reckoned from the Dirac times psi constraint, trivial enough, even I can understand it's the complement of a set (of B in the x-tau plane), but I don't get how this matches up with your more prosaic description: "a set I will call D which consists of information we presume is valid"

If the set

**D** were to consist of the complement of

**B** obtained from

**A** then the Dirac constraint would constrain

**B** obtained from

**A** to be exactly what was actually obtained in every detail. That is the most extreme possible case and, if that case can be obtained, any case less extreme can be obtained. As portions of that complement are omitted, the constraint allows those portions to be possibilities for

**B** obtained from

**A**: i.e., the elements in

**C** are less exactly set.

I don't think I am as upset as you think I am. I just get a little perturbed sometimes when I can't understand what they are missing. It occurs to me that it could be the simplest and most necessary truths which are the most difficult to explain.

Have fun -- Dick

"The simplest and most necessary truths are the very last to be believed."

by Anonymous