Steve, I hope I haven't upset you by moving the comments you made by private message back to the thread. I think some of those comments are very important and if you misunderstood what I was saying then others probably misconstrued the same issues.
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Originally Posted by ldsoftwaresteve
DoctorDick:Isn't that one of the functions of an abstraction, of a concept? We think in terms of the concept rather than all of the elements in the set which it subsumes.
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Yes, I would agree; that is essentially what we mean by the term abstraction. Coming up with mental categories (and symbols for the same) for the aspects common to certain collections of significant things.
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Originally Posted by ldsoftwaresteve
So we need a machine that can take input and perform the abstractions and drop it on the mountain in the right place.
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Yeah, but as you say that's not an easy thing to implement. In order to implement it, you need an abstract idea of what abstraction is all about and that would be to comprehend the purpose of abstraction itself. In essence, the abstraction lays aside the essential aspects of the information which allow us to operate via that lesser body of information Korzybski was talking about. That is, it establishes the elements necessary to an explanation: i.e., allows us to come to conclusions without considering all the known information in its entirety. And, yes, that is exactly where I am trying to go with my analysis.
Just as an aside dealing with AI, there is another way to look at the problem of abstraction. First, let us consider the problem of making a prediction based on a situation which exists exactly somewhere in the known information (a rare but significant concern; history does in fact sometimes repeat itself). If it didn't, induction would be worthless.

If this is the case, our problem is actually quite simple: all we have to do is find that the specific example itself and simply assume the new results will be the same as the old results.
That situation can be seen as looking up the solution in the log of all known situations. Or, from another perspective, trying to figure out were we are (at the particular instant) in that log of all known things. Clearly, the more closely the current situation resembles the found situation, the more faith we can put in the idea that what happened last time will happen again. Sort of like looking at a piece of a sentence (or several sentences) and finding where that piece is repeated in the Library of Congress. The longer our sample gets, the more constrained the possibilities are. Given a list of all possibilities and what follows each of them, we can estimate a probability on what the next word will be. As our sample gets large, either we hone down to a particular case or we generate a new entry which appears nowhere. The more data we have in our base (that Library of Congress) the more improbable a "new" entry will occur. (Unless we are talking about a million monkeys on a million typewriters.
So what we want is some organized collection specific sequences which occur often enough to be of interest; the reoccurring phenomena are things which can be abstracted. In order to implement such a performance, let our AI device record a log of everything which occurs; both those data events internal to the device itself and obtained external inputs. After a sufficient time (with a complex device), that log can get quite long and involved. As it does so, the probability of repeated patterns rises. Suppose we start compressing that log under the following procedure:
We start with a collection of data events in that log which are repeated somewhere else in the log. If compression is viable (that is, if we can replace every entry of that repeated segment with the address of a reference to that sequence [together with some additional information] and obtain a net reduction in storage consumption) it would be possible to build a selection of entries ordered by how often they occur together with a list of most probable following entries (that would be there as additional information to give us our expectations).
Now think of that compressed file as a new log to be searched and similarly processed. We know the current incoming data (and our manufactured compression library) so we can generate a list of possibilities as to where we might be in that log. Taking a list of the most probable states, we can predict our expectations and construct the possible branches we might be on. Those predictions can be used to step the process further. So we generate a number of possible sequences into the future.
Within those sequences occur some internally generated events. The importance of those internally generated events is that they are under the control of the device itself. The device is thus able to evaluate the desirability of possible end points and choose it's activity to make whatever it "desires" to occur to be more probable than the alternatives. Ah, but how do we decide which outcome is more desirable? How about the result which leads to better data compression? Think about that one for a while. What is abstraction anyway?
When we start looking at devices with multigigibyte states and logs in the multiterrabyte range with the processing speed of a super computer, the possible outcomes of such a process start to become very interesting. I would also like to point out that such a system could also determine what information was internal and what was external (i.e., the program itself does not need to have that information in the initial set up). Internal events would be events with a very high probability of occurring. That is to say, if the device could control those events, their probability of occuring would be one.
This last point has to do with learning how to do something. Learning how to drive a car amounts to discovering the collection of events under one's control which lead to events normally not under control occurring with very high probability. That is to say, one becomes "one with the car" or it essentially begins to be part of the internal device. (It always bugged me when people would tell me "you have to become one with the ..." as if it were a choice when it is really a consequence of learning the skill being referred to.)
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Originally Posted by ldsoftwaresteve
Hi Dick. Forgive me for being so slow.
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I would call your response quite rapid. Note that I am considerably slower than you. The following comments in blue were part of a private communication but I think they need to be cleared up for everyone.
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Originally Posted by ldsoftwaresteve
An abstract model would be an identification of how all explanations are similar. Each term in the model would have to be an abstraction representing the set to which it refers.
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I am not sure of exactly what you are saying here. I do not understand the applicability of "representing the set to which it refers". What I would have said would be more like "each 'component' (instead of term) in the model would have to be an abstraction of some essential component which exists in all explanations and displayed the fundamental behavior of that component".
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Originally Posted by ldsoftwaresteve
Interesting, you have to use an explanation to explain itself.
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Not really. What I am doing is explaining the procedure I went though to isolate those abstract components of an explanation. The object was not to "explain and explanation" but rather to define what constituted an explanation. I have been interested in definition since the third grade when I saw something astonishing in the dictionary. A long story behind it but essentially the teacher told us that it was against the rules to use a word in it's own definition as to do so defeats the purpose of definition (without knowing what the word means, you cannot understand the definition). Now I was smart enough to know that, if you went far enough, any dictionary would be circular but I was curious how long it would take to find a circle. I was too young and ignorant to understand how complex that question really was and I went to the dictionary in the class room to check it out for myself. Since, in my head, where I started made no difference, I started at the beginning. I was astonished when I read the first entry, "a: the first letter of the alphabet; a pronoun ...". I closed the dictionary and went back to my desk and have thought about definition ever since. Most people do not worry about how they come to know the meanings of words. Fundamentally it is equivalent to answering the question, "how do we know what we know about anything?"
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Originally Posted by ldsoftwaresteve
“I will begin by pointing out that all “explanations” result in a set which is to be characterized by the explanation.”[/COLOR]
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No, the explanation does not
result in a set! The idea of an explanation is meaningless without something to be explained. What is significant here is that the most abstract representation of anything is the concept of a set. A "set" can be absolutely anything. I get the feeling you are mixing up the significant roles of components here.
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Originally Posted by ldsoftwaresteve
Interesting, that implies that in the one case (‘to’) we can change the landscape of the mountain by filling in the gaps and from what you say below that is performed using our ‘understanding’.
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Or create new gaps in that landscape! You have to keep your mind open; the input is information and the output is information. The output may be things you already know, things you didn't know or falsification of things you thought you knew. We all have "expectation" which we can't explain, have learned of explanations which confirm our expectations and we have learned explanations which changed our expectations.
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Originally Posted by ldsoftwaresteve
Relational databases can be modified and queried.
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I don't know what you had in mind when you wrote this.
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Originally Posted by ldsoftwaresteve
An explanation provides the formula for a ‘query’.
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Yes and no! Certainly it can be seen as such with regard to known information (the information can be queried), but unknown information cannot be "queried" so the explanation provides something more than a mere "query". The explanation, whether that explanation is right or wrong, yields real expectations for circumstances outside the known information.
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Originally Posted by ldsoftwaresteve
(ah, very subtle difference from ‘known’ – I like),
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Thank you.
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Originally Posted by ldsoftwaresteve
‘understood’, then, implies an abstract on the nature of the set under consideration. If I understand the nature of the set of all locations that a ball in orbit has, i.e. gravity, time, motion, etc. I can predict (have an expectation of) where the ball in orbit will be even though I don’t now know where it will be at some point in the ‘future’. By knowing why and how it behaves over ‘time’, my expectation is that it will be right ‘there’.)
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Now I would say that "an abstract on the nature of the set under consideration" is essentially a phrase equivalent to "an explanation" and really doesn't add anything: i.e., one could just as well have said, "'understood', then, implies you can explain it". Remember, my definition of "an explanation" is that it provides a method of specifying your expectations (the "future").
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Originally Posted by ldsoftwaresteve
(a function, process, etc.)
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Yes! To this and the next couple of statements.
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Originally Posted by ldsoftwaresteve
The beginning of my disconnect. Yes, and it is followed by a ‘let’ statement. We’ve jumped to another level of abstraction. Let "A" be what is to be explained and proceed with the following primitive definitions: 1.A is a set. Tables.2. B is a set, defined to be an unordered finite collection of elements of A. Kitchen tables, Dining room tables, living room tables, patio tables.3. C is defined to be a finite collection of sets B. Indoor tables.
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"If you have learned to add two and five without asking "Two and five what?" you already have both feet off the ground--higher than you think. You are now air-born. The rest is just a matter of gaining altitude."
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Robert M. Hutchins and Mortimer J. Adler in "Gateway to the Great Books".
The issue here is the fundamental nature of abstraction: removing the "real foundation" of a concept without removing the essence of that concept itself thus leaving the "real foundation" an open and unanswered question. You are trying to reestablish a possible "real foundation" for the abstract concept I have proposed. That can be done with my abstract definition as it can be done with arithmetic though what I am doing is a far more complex abstraction than simple arithmetic. But when you try to construct a "real" example, you need to be very careful to fulfill the definition of these sets,
A,
B and
C exactly.
First,
A is a set (as I said, a set can be anything).
A is supposed to be the abstract representation of "what is to be explained". You have labeled the set "Tables". Though you haven't taken the trouble to say it, the common interpretation of labeling the set that way would be to presume that each of the elements (the "elementary" components) of the set would each be a table of some sort.
Second,
B (also a set) is defined to be an unordered finite collection of elements of
A. You have titled
B with the phrase
Kitchen tables, Dining room tables, living room tables, patio tables.. What you mean by this is simply unclear. Do you mean that the elements of
B are Kitchen tables, Dining room tables, living room tables, patio tables or that these are possible labels for particular sets "
B". The problem is that either interpretation is inconsistent with the implied definition of
A.
A better representation of a particular
B in this case would be for example, a small blue kitchen table, a large varnished Dining room table, a second small blue kitchen table, and a patio table. (A set of specific tables, a finite collection of elements of
A: tables.) There are many ways in which one could construct possible
B's and each of those sets
B become elements of the set
C and you would certainly not be reasonable if you were to label
C "Indoor Tables". A much better title would be "a specific collection of shipments of tables" (each shipment being a particular
B).
At this point, it would be better to constrain the label of
A a bit in order to make better sense of what your expectations might be. Instead of "Tables" (which is a pretty general label) let us instead call
A "Tables from the Basset Furniture Co.". At that point the question of your possible expectations (and what you are trying to explain) might make a little more sense. What you want to explain are tables which can be obtained from the Basset Furniture Co. And what information is your explanation to be based on? A finite collection of shipments of tables (each which we could label with a shipment number for reference). And what are your expectations? Given a number, and a list of tables, what is the probability you will find a shipment with that shipment number (where the invoice matches that list) either among the shipments you have already received or expect to receive. If you can provide a method of obtaining that probability then you have provided an explanation of
A.
Even at this point it is not a very good example of "an explanation" as, in dealing with shipments of tables, having nothing to go on except invoices of known shipments is not a very realistic situation. Remember
C, by definition, constitutes the entirety of the information upon which your expectations are to be based. It pretty well follows that any realistic situation you want to seriously consider requires a much larger information set than can reasonably be written down. You need to work the truth of these propositions out in the abstract, not in the particular as a reasonable example constitutes a problem far more complex than anything we could write down in an e-message.
Does that provide a clearer picture of what I am trying to communicate?
And "TIDUSGIYA", I have no idea of what you are talking about! To me it most resembles a shot gun blast of assorted phrases with no theme.
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Originally Posted by Pyrotex
Korzybski says we have NO access to the Territory. None, zip. We ONLY have access to the Map. That is where we live, think, have our minds, and discuss reality.
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I agree with Korzybski one hundred percent with regard to that issue. Many many years ago I realized that human intelligence is totally isolated from the outside world. The only contact which exists is via interactions, the real meaning of which cannot be known a-priori. Our mental image of the universe is constructed from data received through mechanisms (our senses) which are also part of that image. I think any scientist in the world would hold it as obvious that one could not possibly model the universe until after some information about that universe were obtained. The problem with this position is that we cannot possibly model our senses (the fundamental source of that information) until after we have modeled the universe. This is a subtle problem far deeper than the old chicken and egg conundrum.
In fact I will contend that the problem of explaining the universe is exactly equivalent to the problem of constructing a rational model of a totally unknown universe given nothing but a totally undefined stream of data which has been transcribed by a totally undefined process.
The very fact that we possess a mental image of the universe implies that it is possible to construct a coherent rational model of the universe via nothing more than patterns observed in a totally undefined collection of data. (Remember, the data must be undefined if our senses are undefined.) Since we have such an image, we must conclude that it is possible to construct one. In order to understand our view of the universe and discover the true nature of our presumptions, we must first comprehend the solution of this problem. The only way we can hope to accomplish that result is to solve the problem directly. I have solved that problem and have been attempting to explain the solution to you.
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Originally Posted by Turtle
___I have some familiarity with mathematics, which is why I asked about a Venn diagram. As far as I know, they have the facility to represent the unions, conjunctions etc. of sets in an algorithmically reliable fashion; moreover as Dr Dick introduced specific sets, I rationally concluded I may construct a Venn diagram to model them.
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I apologize for misunderstanding your comment which I now think I did. It had not occurred to me that someone would make the mistake made by Steve. If you examine my answer to him you should understand that Venn diagrams are not applicable here at all. The "elements" of the three sets are not taken from the same collection of things. The elements of
C consist of entire sets
B and the elements of
B need not be a subset of
A. It is entirely possible that an element which exists only once in
A may occur many times in
B.
The abstractions I am presenting in my definition of "an explanation" are quite simple; but the complexity of what can be represented by those abstractions is almost beyond belief. As I told you when I started, we are off into that swamp of confusion out of touch with reality. We are working with nothing beyond what may be deduced from my definitions.
Have fun -- Dick
What I am saying is really quite simple; it is the consequences which become complex and far reaching.