Hi Genie,
I just got back from a strenuous 3-day hike and I haven't even unpacked my gear, or taken a shower yet. But when I looked at the forum, I just had to respond to a couple of things.
The easy one is a first attempt at your request for a summary of Dick Stafford's work. Mike Pearson (who is part of the second item I want to talk about) made a similar request back in July. I answered him with two summaries at
http://www.astronomy.net/forums/god/messages/20032.shtml?base=60
The shorter was,
"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."
The longer one was,
"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."
So far, Dick has not said that he has found anything wrong with either of these summaries. But that may be because he didn't read them. You should only consider these as starting points for discussion representing my personal take on what Dick has done. I would be delighted if anyone, especially Dick, would point out any errors I may have made.
In your request, Genie, you asked, "Is there a one page summary or abstract of Doctor Dick's paper anywhere?" In the spirit of completeness, I should point out that in a personal communication to Chris Langan, which you answered, I included yet another such summary. I quote it here for the benefit of other readers of this forum:
"Here's my take on his discovery: The problem is to understand the universe. To "understand" it means to be in a position to explain it in a communicable way. So, one assumption is made at the outset that the universe, or at least the part we are interested in, is communicable. That is, it is describable to the degree that the descriptions can be communicated from one human-like mind to another. Since we find that our universe is describable in that way, the assumption is not vacuous. If there are other universes, or aspects of our own or any other, which are not describable, the constraints discovered by Dick do not apply to them.
"Since the universe is describable, all physical facts, patterns among those facts, and concepts involving the facts and patterns, can all be described. These descriptions can be represented by sets of numbers.
"Dick approached the problem by examining a completely arbitrary set of numbers. He discovered a set of constraints on the probabilities of finding certain patterns within the set of numbers. Since the set of numbers was completely general, the constraint he found applies to any set of numbers, including the set described above as representing descriptions of physical facts about our universe and patterns and concepts involving those facts. This means that the physical facts themselves and the patterns and concepts all fall under the constraints Dick discovered. Sure enough, when solutions to the equation stating the constraints were found, they turned out to be the familiar laws of physics."
Now, for the second item of business, I was very disappointed at how you and Mike Pearson introduced yourselves to each other. Mike is a good guy, and a smart one. But the way his persona comes through via the words he types sometimes has a way of rubbing people the wrong way and getting him off on a bad foot. Please don't pre-judge him from what he has written to you so far.
And, Mike, if you read this. C'mon, give the lady a chance and try to be polite at least until you get to know Genie. She is not anonymous.
More later; I've just got to take a shower.
Warm regards,
Paul |