Science > Physics > Quantum Gravity Via Expansion-Contraction 35.0: n! As the Fundamental Knowledge/Causation Unit
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Science > Physics |
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"OsherD" |
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16 Nov 2006 06:59:46 PM |
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Quantum Gravity Via Expansion-Contraction 35.0: n! As the Fundamental Knowledge/Causation Unit |
From Osher Doctorow
From elementary probability theory, n! is the number of permutations of
n things taken n at a time, which is also the number of words of length
n that can be made from n different letters (symbols), where a word
need not be in a particular natural language dictionary of course.
Words are ordered, which is what "permutation" means.
Readers at all familiar with "standard" types of information theory or
information/entropy probably realize that such theory is mostly
concerned with the form rather than the content of messages as well as
the channels through which messages pass, which arguably explains why
n! is not part of a fundamental axiom of standard information theories.
In Probable Causation/Influence (PI), Knowledge is fundamentally taken
as Causal Knowledge in ordinary language. One way to think about
Causal Knowledge is to forget the usual definition of "word" in
linguistics and think of a symbol, here taken as a letter of the
English alphabet for simplicity, as embodying fundamental meaning
(semantics). Different symbols represent different fundamental
meanings (roughly, "ideas"), and of course there is no need to restrict
the number of symbols to 26 a priori. Why would one need words? One
reason is to indicate the direction of Causation (e.g., from left to
right), so that acd means that a causes c which causes d. We can even
replace "fundamental meanings" by "fundamental propositions", provided
that we keep track of the scenario by appropriate labels. Since
correlation is non-spurious (non-"erroneous" or non-"coincidental")
Causation, the ideas incorporate correlation as well.
In this scenario, n! is the number of possible "Causal concatenations"
or "Causal sentences", of which one example of a Causal sentence is acd
above. Even if the real (physical) world does not permit certain
orders of symbols to represent it, the possibility of other orders is
measured by n!.
Notice that if ab = ba, then a causes b and b causes a, which is to say
that a and b are correlated. But readers may realize by now that
correlations are only a proper subset of Causation because many Causes
precede their Effects in time (e.g., history).
Osher Doctorow
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| User: "Dr. Doctor" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 35.0: n! As the Fundamental Knowledge/Causation Unit |
16 Nov 2006 08:51:39 PM |
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"OsherD" <> wrote in message
news:1163725186.287006.236830@f16g2000cwb.googlegroups.com...
From Osher Doctorow
From elementary probability theory, n! is the number of permutations of
n things taken n at a time, which is also the number of words of length
n that can be made from n different letters
WRONGs
that is n*n*n*n*.....n*n is n^n, NOT n!
gos reads your books, it is on pages 312
<snips rests of mistakes>
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 35.0: n! As the Fundamental Knowledge/Causation Unit |
16 Nov 2006 07:13:44 PM |
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From Osher Doctorow
Notice that n! increases as n increases since n! is 1 times 2 times 3
times...times n. So if we take n! as a fundamental measure of Causal
Knowledge or Causal Semantic Information, it agrees with the idea that
each symbol represents different Knowledge (whether representing a
proposition or an Event or a process, etc.).
In other words, the larger n!, the more symbols and hence the more
Knowledge there are, Causally related by concatenation (writing one
symbol after the previous one, typically although not necessarily from
left to right in English).
Standard information/entropy theory has not the faintest clue regarding
such things, which is not surprising since it is interested in the form
rather than the content/meaning of messages. It is not a useless thing
since it has cryptographic and engineering applications except that in
engineering it again is concerned with channels and
transmission-reception probabilities rather than meanings or Causation.
From this viewpoint, why do black hole theorists take such joy in
discovering facts about black hole entropy/information? It is
arguably because they have never thought of any other type of
entropy/information than what the engineers have provided. Still, if
we ever try to decode black holes or hypothesize that there is a
"little man" inside a black hole trying to communicate with the
outside, we'll know who to look for to get guidance :>)
Osher Doctorow
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