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Posted by Paul R. Martin on July 22, 2002 05:04:54 UTC

Hi again Mike,

***1) This is not an attack and I will not apologize for is not really confrontive, but I hope will surprise you positively: I really don't think you have demonstrated any process to determine scientifically or mathematically who could understand the paper.***

You are right. I have not demonstrated that.

***In fact, I don't think you have the background necessary to make such a judgement.***

Maybe I don't. But do you think I have the necessary background to form an opinion? After all, an opinion was all I offered.

***The ability to do math, itself, is not all that is needed in order to evaluate someone else's ability to understand. That is not intended as an attack...and certainly I'd welcome any good evidence to the contrary. ***

My opinion was based on my direct knowledge of how hard it was for me to follow and understand Chapter 1 of Dick's paper, and on my impressions from reading people's posts discussing Dick's paper. My ability to do math didn't enter very much into the process of forming my opinions.

Don't take my opinion on the matter too seriously, though. All it would take for someone to get on my list would be for them to say something like, "Hold on there, I should be on your list too." and he/she would immediately be added.

***2) We ought to have a better abstract and or definitive restatement of the gist of Dr. Dick's paper...a better summary of the logic of the paper's main points...even if the math itself still would have to be confirmed. IF, and only IF, we cannot clearly restate in words, say 250 or so, what (approx.) 1,000 math-squiggle marks of that article mean...then either we are dealing with a) "national security" b) a big practical joke or c) the parts don't add up to a whole and his work probably contains only some interesting, useful math work whose philosophical derivations need not stem from the original grand thesis we've seen implied.***

Yes, I agree. We ought to have a better abstract. It seems like I wrote one once, and Dick approved of it, but I can't remember where it is posted and I can't find a copy. Let me pull one together from an old post which I don't think anyone ever responded to. I'll see how close I can get to 250 words. The old post I'm talking about is at


In Chapter 1 of his paper, Dick defines a completely unspecified set of numbers, a collection of subsets of those numbers, and a finite subset of that collection with cardinality n. He then poses the question, "Could there be a function that can in all cases predict the makeup of the nth subset given a knowledge of the makeup of the other n-1 subsets?", (equation (1.2)), and proceeds to demonstrate logically that the answer to the question is "no".

Next, he poses the question, "Could there be a function that can predict the probability of the nth subset having a particular makeup, given a knowledge of the makeup of the other n-1 subsets?"

To answer this question, he assumes that such a function exists (equation (1.3)). This assumption raises two new questions. 1) Can we prove the existence of such a function? and 2) What, if anything, can we deduce about the nature of this function?

Then, by applying standard definitions from previous mathematics, (equation (1.4)), he defines yet another function which can be interpreted as producing what we might call probability density (equation (1.7)).

Finally, he proceeds, by strictly logical deductive arguments, to show that if such a function exists, it must obey a particular differential equation (various versions of his paper have labeled this equation as (1.27) and (1.29))

Dick chose notation in making his definitions that just happened to coincide with the notation used in modern physics to describe the Schroedinger and Dirac equations. That choice makes some of the important interpretations of Dick's results immediately evident.

If we view our access to the "universe" or "reality", (whatever they might be) as being a set of information available to "our senses", (whatever they might be) then that accessible set of information can be considered to be, or converted to, a set of numbers. Dick's differential equation applies to this set of numbers. Furthermore, the solutions to his differential equation, can be interpreted to mean that there are certain constraints imposed on any "universe" or "reality" that we can perceive via "our senses". The meanings of the terms in quotes, of course, have nothing to do with Dick's result or its derivation.

In Chapters 2-5, Dick has developed solutions to his differential equation which he shows to be equivalent to most of physics as it has been discovered so far by other methods. Armed with the differential equation and it's solutions, Dick has developed a completely general way of modeling the information available to us about our universe. This method involves plotting the numbers in the various subsets on a three-dimensional space, and parameterizing the subsets with a variable called 'time'.

By applying the solutions to his differential equation to this method of plotting, or displaying, the information, he shows that this model is consistent with the typical model that each of us develops naturally in our subconscious minds as a result of living in this world, and it is consistent with the model developed by conventional physics. N.B. This "Model" is not part of his formalism.


Oops! I blew it. That abstract is twice as long as what you requested at 506 words. Let me have a crack at writing a shorter one:


If we look at the problem of understanding our universe, we realize that all we have to work with are sense impressions. As we know from familiar computer technology, all sense impressions, such as meter readings, sounds, images, verbal descriptions, etc. can all be represented by numbers. So the general problem of understanding our universe is the same as the general problem of understanding a big set of numbers. If we know nothing about these numbers, we can't say much about them specifically. But, as it turns out, we can discover some constraints on statistical patterns within subsets of those numbers. Dick has discovered just such a constraint. He has proved that any set of numbers whatsoever must conform to a particular differential equation which describes the behavior of the probability density of any rule which might describe some order present in subsets of the numbers. Dick then went on to solve his differential equation and discovered that the solutions matched familiar laws of physics that had been laboriously evolved by trial and error over the centuries in an attempt to find rules that match observed data. One philosophical implication of his discovery is that any universe which can be described, i.e. whose features can be communicated among people, must conform to his equation, and thereby, must obey the laws of physics. God had no choice.


Okay. That one came in at about 225 by my count. On reading these, I am a little disturbed that Dick would object that I didn't mention his trick of including unknowable data along with the knowable data in the big set of numbers. But, after thinking about it more, I think that a description of that trick would push any abstract beyond not just your 250 word target, but the 500 words in my first abstract.

Now, if anyone has been interested enough to read through these abstracts, you will probably be interested in whether or not Dick thinks what I have written is a fair summary of his work. If so, please ask Dick to comment on their accuracy. There is a good chance I have misstated something somewhere, and it would be a shame not to have my errors corrected. And, Mike, if this is not what you were looking for, let me know.

Warm regards,


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