Dear Friends,
we keep talking in different systems of references. Nevertheless, there are
points about which some clarification is helpful, to connect the
translucent picture of numbers to the movies you see. Let us talk some
absolute numbers, in the hope of clarifying the background.
Dai wrote a few days ago:
“ … To my mind the note which is heard is far richer than the note on the
score. The difference includes everything that goes into the interpretation
of a piece of music. I am not arguing that numbers could not describe this
difference, but claiming that hugely more numbers would be required to
adequately describe it. … “
Now Stanley brings up following perspective:
“ … But my point was simply that the observer cannot be 'objective', but
always brings in many constraints to any observation, which might have been
made from yet another perspective, of which we cannot imagine the number or
qualities of. … “
Both injections deal with the numeric extents that are available to
perceive or express a state of the world. Assuming that the neurology works
ideally, the perception or expression of the state of the world is not
influencing anything: as many different states of the world are there, as
many can be flawlessly perceived and expressed.
The question that has to be addressed is, then, how many different states
of the world there are. We know that about a limited number of things only
a limited number of nonredundant sentences can be said (otherwise one would
start repeating oneself). These sentences are only meaningful, if they
convey something that could be otherwise (there is nothing to say about a
standalone tautology, like there is nothing to say about Kant’s
thing-as-such). So, the assumption is that the sentence details the place
of the element, relative to which and what kind and how any symbols the
element carries, which make that element commutative to some other
elements, and commutative-cum-sequential to some specific elements, which
are presently relevant. In this context, there is always something to
remark on and make idle predictions about the future.
Nevertheless, about a limited number of things only a limited number of
different sentences can be said, be these sentences stating something about
a sequential position of elements, relative to the patterns of distribution
of commutative symbols, or be they of the kind that they detail the
patterns of distribution of commutative symbols, relative to the sequential
positions that the elements have; in both cases one hits an upper
limit of *rien
ne va plus*, all that can be said, has been said.
The monoideismus this person labours with is connected to the two upper
limits not agreeing with each other. One should indeed refer to
www.oeis.org/A242615 to see the numeric relations pictured.
For the present discussion it does well to mention, that we deal here with
different cases of probabilities the numbers of which are in the order of
magnitude of 3.6E+94 and 1.3E+95. These are really big numbers. There is,
by Jupiter!, sufficient number of alternatives for a sound’s timbre,
enchantment, finest innuendo, etc.
It is not easy to raise hell by running around and holding up placates that
say: “There is an intricate inexactitude in our counting system! We count
incorrectly to the tune of 3.4E-94%!” There are many, to whom other
problems appear more urgent.
Among the corollaries of the steps to put this inexactitude in clean cloths
is, that there exists a maximal number of aspects (perspectives,
viewpoints) that can be used while describing all possible states of the
world. Commutative statements appear to be independent of each other. We
might have counted a case under *{(k elements carry symbol w, among these,
j elements carry also symbol q), (r elements carry symbol t, among these, k
elements also carry symbol z), … etc} *as we met it at any of its partial
descriptions, therefore classifications that come *later*, repeat
redundancies (which may be the method to force registry in the memory).
There is always a *first* describing aspect that segments the cases. The
*second* aspect deals with cases that are already categorised in some ways.
The *last *aspect finds the last cases that were indistinguishable
previously and assigns identifying symbols to them. Any subsequent searches
would turn up only such cases that have already been entered in the
databases. This is a query language, but also in that language only a
limited number of sentences can be said of a collection that is limited in
numbers.
Yes, we indeed can very well imagine the number and the qualities of
categorising perspectives, at least in idealised cases. There is an inner
granularity to the logical world, things are not spread uniformly in space.
Things congregate by very simple rules, at least on the numeric level.
The main points again: we compare the maximal number of DNAs with the
maximal diversity of organisms. We find that the upper limits do not match.
There is an inherent inexactitude, caused by our presently used rules of
counting, in the counting system. The extent of this inexacitude is
extremely small. The bias can be fixed, if one uses symbols that are
concurrently commutative and sequential. These are found when one uses
cycles.
There are cycles that can co-exist, and some that can not co-exist. Knowing
that some elements of the cycle have already been the case allows
predictions, when, where and which elements will appear next. This property
of ordered collections is used by the nervous system as the basis for
remembering and learning.
Hope that this brings you a context relating to the system of consistent
counting.
Karl
2018-03-23 13:57 GMT+01:00 Stanley N Salthe <ssal...@binghamton.edu>:
> Bruno -- That is an interesting, creative move! But my point was simply
> that the observer cannot be 'objective', but always
> brings in many constraints to any observation, which might have been made
> from yet another perspective, of which we cannot
> imagine the number or qualities of.
>
> STAN
>
> On Thu, Mar 22, 2018 at 11:41 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>>
>> Dear Stan,
>>
>>
>> On 20 Mar 2018, at 20:22, Stanley N Salthe <ssal...@binghamton.edu>
>> wrote:
>>
>> Bruno -- In this context I like to point out the constraints on our
>> abilities of perception. First, we are physical.
>>
>>
>> That is a strong metaphysical assumption. See my paper for showing this
>> is not compatible with the Digital Mechanist hypothesis in the cognitive
>> science, which is my working hypothesis.
>>
>> Perception is a relative indexical relation between a (digital) machine
>> (number, combinators, pattern of game of life, whatever) and other
>> plausible, from its perspective, universal or not entities (infinitely many
>> below the substitution level, making both matter and consciousness not
>> Turing emulable (in the Mechanist perspective).
>>
>> There are evidences for a physical reality, but I am not sure there are
>> evidence for a primary physical reality. The use of math in physics is well
>> explained if the physical appears to be a mathematical reality seen from
>> internal creature represented, relatively incarnated or implemented in that
>> mathematical reality.
>>
>> I can prove, if you agree with very elementary arithmetic, the existence
>> of the computations and the machine running them. I cannot prove the
>> existence of a physical universe, but if Mechanism is true, the physical
>> universe appearance can and must be explained by a statistics on all
>> computations (seen in a first person way). That makes mechanism testable
>> and indeed, thanks to Quantum Mechanics (without collapse) it fits very
>> well up to now.
>>
>>
>>
>>
>>
>> Thus:
>>
>> {physical {material {biological {animal {mammal {primate {human
>> {socialized {with accumulated personal history }}}}}}}}}
>>
>>
>>
>> Ok, but you will need “magical” (non Turing emulable, nor Recoverable)
>> ability in your matter to select some computation.
>>
>> You invoke the God “Matter", but if it plays a role, I am no more sure I
>> can say yes to …the doctor and survive qua computation.
>>
>> Mechanism and Materialism, which are often used together, can be shown
>> incompatible (it is basically my PhD thesis, and it is summed up in most of
>> my papers).
>>
>> So it is more like
>>
>> {arithmetical{dream-like{biological{conscious{physical{{animal {mammal
>> {primate {human {socialized {with accumulated personal history }}}}}}}}}
>>
>>
>>
>>
>> Hence, actuality is for us non-existent.
>>
>>
>> ?
>> Is not actuality existent *for us*, phenomenologically, and non-existent
>> Ontologically, I guess you mean. I am not sure I understand well.
>>
>>
>> We live in a constructed reality.
>>
>>
>> The whole physicalness is indeed the arithmetic seen from the internal
>> arithmetical beings, but the person attached to them are not arithmetical
>> not even analytical (not even third person describable in any way).
>>
>> I am aware that what I say contradicts 1500 years of (Aristotelian)
>> theology, but then it was enforced by 1500 years of argument per authority,
>> sometimes violent.
>>
>> Best,
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>> STAN
>>
>> On Tue, Mar 20, 2018 at 12:23 PM, Bruno Marchal <marc...@ulb.ac.be>
>> wrote:
>>
>>> Hi Dai, Hi Carl, Hi colleagues,
>>>
>>> > On 19 Mar 2018, at 16:22, Dai Griffiths <dai.griffith...@gmail.com>
>>> wrote:
>>> >
>>> > On 15/03/18 10:11, Karl Javorszky wrote:
>>> >
>>> > >To me, it does not appear necessary to make a distinction between
>>> “reality” and “data”
>>> >
>>> > That's a defensible position, but it does constrain 'reality' to 'that
>>> which we can perceive'. Which would rule out the reality of things that we
>>> cannot perceive, e.g. explanatory mechanisms, or the insides of black holes.
>>>
>>> If not the whole of mathematics.
>>>
>>> To be provocative, I would me more like thinking that the data are an
>>> observer tiny distorted part of reality, especially that we can never
>>> distinguishes possibly genuine data with hallucinations and dreams.
>>>
>>> In the computationalist theory, a data is the input to some
>>> machine/number program, the execution is the arithmetical semantic of some
>>> universal number getting the machine and the data has its input.
>>>
>>> Now a data can be anything, and can be interpreted, and handled, quite
>>> differently, if at all, by different universal, or not, programs. I
>>> identify the person by its set of beliefs, and the first person by its
>>> subset of true beliefs. Incompleteness makes this working well.
>>>
>>>
>>> >
>>> > > just like there is no necessity for musicians to distinguish between
>>> the note printed on the partiture,
>>> > > and the acoustic sound, or for Chess champions to distinguish
>>> between the description of the position
>>> > > in the protocol of the game and the actual pieces one can hold in
>>> his hands.
>>> >
>>> > I do not think that these are the same case.
>>>
>>> I think that equating reality and data would lead to solipsism (which is
>>> phenomenologically correct but ontologically incorrect).
>>>
>>> Also, is there a reality?
>>>
>>> And what could it be?
>>>
>>> We can’t answer, but we can do hypothesis/theory, and with mechanism the
>>> physical reality becomes a phenomenological mode of self-reference of the
>>> universal (in the sense of Post, Church, Kleene, Turing, …) machine/number.
>>>
>>> The biological evolution explains the biological origin of the humans,
>>> but to avoid the behaviourist error of avoiding consciousness, eventually,
>>> we get a “physical evolution”, where the physical laws somehow percolate
>>> from the dreams of all universal numbers. The key is that from the
>>> universal machines' first person perspectives it is “executed” by
>>> infinitely many universal numbers below their computationalist substitution
>>> level. A fact that I saw a long time before this is confirmed by Everett
>>> quantum mechanics (which is the old one minus the collapse of the wave
>>> packet postulate).
>>>
>>> Data are indexicals, defined relatively to the universal machine/number
>>> which interpret it, correctly, or incorrectly, relatively to its most
>>> probable computations (among an infinity of them).
>>>
>>> With mechanism the big picture is very simple, arithmetic and its
>>> enumerable, but non mechanically enumerable set of universal numbers. But
>>> the first person phenomenology is “uncertain” on non enumerable
>>> computations, making them “living” on the border of the uncomputable.
>>>
>>> Related to this is that the original doubt of the greek
>>> theologians/metaphysicians was between "is reality what we see” or is
>>> reality something else from which what we see is the shadow, the border,
>>> the symptom, ...
>>>
>>>
>>> >
>>> > The description of the configuration of a chess game is lossless. I
>>> could note down the distribution of the pieces, take them off the board,
>>> mix them up and put them back again, and the game would not be changed for
>>> the players. The physical chess set and the physical context are also
>>> largely irrelevant. Players could leave one room, have a relaxed coffee or
>>> aquavit, go back into another room with a duplicate of the game with
>>> different pieces on another board, and continue with little disturbance.
>>> >
>>> > But sheet music is not a lossless representation of a performance.
>>> From the starting point of the sheet music, the performer has to decide on
>>> volumes, intonation and timing, and in some cases also ornament and
>>> variations. These issues arouse deep passions and ferocious debate! Nor
>>> would we be happy to buy a recording of a symphony in which different
>>> orchestras played different movements in different concert halls (although
>>> it might be interesting to hear).
>>>
>>>
>>> I might agree with Karl, but as expressing a first person phenomenology.
>>> With mechanism that keeps enumerability, but loss “recursive enumerability.
>>> Even the simple Gödel-Löbian self-observing universal system/number/machine
>>> is confronted to the uncomputable main part of the (arithmetical) Truth by
>>> just this introspection. The senses comes from the multi-relations in
>>> between different universal machine.
>>>
>>> Best Regards,
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>>>
>>> >
>>> > Dai
>>> > _______________________________________________
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>>>
>>>
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>>
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