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Author
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Topic: Questions on Reality Models and automata in Computation Theory
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gedanken
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Member # 594
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posted 29. October 2003 23:19
Russel's post shows why mathematics per se does not necessarily represent the real world.
Rather one must examine whether what is represented actually obeys the properties we can observe. For example real world particles are neither infinitely small nor infinitely numerous. But a set of points can be defined in our mathamatical models that can be decomposed as described above. The real world of particles does not obey this model, nor its problems.
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Aliet Jacob
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Member # 908
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posted 31. October 2003 09:24
Russel,
When you write about a finite universe under axiom of choice, do you mean the hubble volume (visible universe) or you mean some abstract mathematical construction?
And why are we talking about spheres?
Has the baloon analogy totally infected the way we think about the universe?
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chimp
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Member # 333
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posted 01. November 2003 06:50
quote:
Gedankin:
Rather one must examine whether what is represented actually obeys the properties we can observe. For example real world particles are neither infinitely small nor infinitely numerous. But a set of points can be defined in our mathamatical models that can be decomposed as described above. The real world of particles does not obey this model, nor its problems.
The Scientific Method:
http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html
quote:
The scientific method has four steps
1. Observation and description of a phenomenon or group of phenomena.
2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.
3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.
If the experiments bear out the hypothesis it may come to be regarded as a theory or law of nature (more on the concepts of hypothesis, model, theory and law below). If the experiments do not bear out the hypothesis, it must be rejected or modified. What is key in the description of the scientific method just given is the predictive power (the ability to get more out of the theory than you put in; see Barrow, 1991) of the hypothesis or theory, as tested by experiment. It is often said in science that theories can never be proved, only disproved. There is always the possibility that a new observation or a new experiment will conflict with a long-standing theory.
According to the scientific method, absolute certainty cannot exist.
This reduces to the statement:
"The only certainty, is uncertainty"
This appears to be a tautological statement. So the scientific method itself, employs a type of circular reasoning.
In fact, there seems to be no escaping certain types of circular logic. It is built into the very structure of our cognitive machinery ![[Wink]](wink.gif) :
We can be absolutely certain or we can be not absolutely certain
A or ~A
Is always true.
Gedankin, we are absolutely certain or we are not absolutely certain. It is absolutely true...?
[ 04. November 2003, 02:42: Message edited by: Russell E. Rierson ]
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gedanken
Member
Member # 594
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posted 01. November 2003 16:51
Russell, I don't want to hijack Aliet's thread for another topic, so I will be very brief.
Logic is of models. They have crisp terminology, including logics by definition. (But even definitions must be communicated, and that even gives for lack of clarity.)
The more related point to this thread is that the problems of "logic" and its clarity are closely related to the issues of language and semantics and mapping from language syntax to meanings (semantics). I've been accused of "playing semantic games", which is of course more or less true, but it was to make the point of difficulty in crisp clarity in mapping of language elements to what we think of as their meaning that is at heart, even somewhat in the main topic of this thread.
But indeed, one cannot be certain that one could never be certain in science--just because apparently one has never yet been completely certain does not imply that as an absolute. The same is said of death and taxes. Do we really mean what we say?
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Aliet Jacob
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Member # 908
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posted 03. November 2003 11:19
quote:
I don't want to hijack Aliet's thread for another topic, so I will be very brief
Hijack away! am done.
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chimp
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Member # 333
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posted 04. November 2003 03:31
quote:
The more related point to this thread is that the problems of "logic" and its clarity are closely related to the issues of language and semantics and mapping from language syntax to meanings (semantics). I've been accused of "playing semantic games", which is of course more or less true, but it was to make the point of difficulty in crisp clarity in mapping of language elements to what we think of as their meaning that is at heart, even somewhat in the main topic of this thread.
Gedankin, are you saying that reality is both objective and subjective? Or are you saying that the subjective component must be totally and antiseptically removed from science and mathematics? It would seem almost impossible to remove the observer completely from the system. There is no way to step outside the universe and take a look at it.
An extremely trivial truth, but, a quantity exists or a quantity does not exist. In that respect the correspondence is exact, because there cannot be degrees of existence. It is a [YES] or [NO] relation. Fuzzy logics enter the picture with regards to parametrization of already existing quantities.
Of course you may try to say that a quantity can be observed to fuzzily be only 1/2 existing but that is totally incorrect. If it can be percieved then it is 100% existing. Or you may say that non existence does not exist, since non existence cannot be observed, and I would say you are correct, non existence does not exist by definition! Existence or non existence. A V ~A.
There is nothing new in your realization that semantics can be twisted, garbled, and confused, Goedel already proved it with his undecidability-incompleteness theorems!
Causality is general and specific and the general contains the specific, so, causal isomorphism must also exist in the general relationships formed by the logical syntax, yes?
[ 04. November 2003, 03:38: Message edited by: Russell E. Rierson ]
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gedanken
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Member # 594
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posted 04. November 2003 11:12
The “reality is” sort of question may be somewhat beyond what I discussed. But I’ll see if I can relate to this question in what follows. For example I’ve been accused of being a solipsist, which is of course quite far from my position, almost opposite. I ‘believe’ that there is a single unified reality that we all interact with. This comes from experience, including that with careful communication that multitudes of people can describe similar experiences of the same objects and other aspects of “reality” with increasing precision as they work carefully in their understanding.
But I agree that “There is no way to step outside the universe and take a look at it.” Rather we must view reality as part of reality ourselves. But that does not erase the subjective nature of observation. The notion of “objective” is one of degree, wherein we try by repetition, communication, and other techniques of viewing subject matter in different manners and by different persons, so as to find as much commonality of experience as possible—that is what is meant in large part by “objective”.
As to
quote:
An extremely trivial truth, but, a quantity exists or a quantity does not exist. In that respect the correspondence is exact, because there cannot be degrees of existence. It is a [YES] or [NO] relation. Fuzzy logics enter the picture with regards to parametrization of already existing quantities.
Yes, I understand that is your model. I have no problem with using that sort of model of reality—in fact I often use such a model. I find it to be a very useful model! But I wonder what you mean about a “quantity”? Do you mean that an object exists, and that it is measurable? (If so, being measurable was the point at which the concept of “quantity” came into relevance, and hence “quantity” was associated with “parameterization”. Since that was the order, how was the “quantity” already “existing”, when its existence is in model once the model was defined? Do you mean to say that models simply exist out there in reality, and we simply find them and at that time parameterize them?)
Since the body of many pages of argument that relate are in another thread, I am hesitant to re-argue this here.
PS, can you define “causal isomorphism”? That might be useful in another thread as well.
[ 04. November 2003, 12:32: Message edited by: gedanken ]
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chimp
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Member # 333
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posted 04. November 2003 14:49
Rex defines it here:
http://www.iscid.org/boards/ubb-get_topic-f-6-t-000397-p-13
Also:
Isomorphism: a correspondence that preserves the .html"algebraic structure", which is a map that is one to one and onto. The isomorphism is realized with the hology principle, where the SCSPL syntax is logically and geometrically self replicating up to certain determinant factors. The identity is distributive. The SCSPL grammatical syntax is part of the evolutionary process called conspansion, an alternation of quantum "coherence - decoherence". Intersecting sheets of potential collapse, and "re-expand". This is also known as re-quantization - inner expansion which self configures the spacetime geometry. Time processes space as cognition processes information.
If my interpretation, and "memory", is correct, the correspondence of logical tautology to reality, is analogous to the way a curve can be transformed into a fractal by substituting a geometrical reduction of the curve for its elementary relations. So, a tautology itself may be substituted for the sentenial variables of the tautology. The geomentric - logic iteration of invariant SCSPL syntax, is a fractal effect with spatiotemporal self similarity. The holographic aspect of CTMU is known as a "supertautology". The holographic[hology] principle is most likely different than regular [secondary] types of holgrams, and it does not suffer the the holographic difficulties as explained by Gedankin. Geometry is reduced to logic. Logic takes priority over ...geometry
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