Re: Dreams and Machines
Rex Allen wrote: Brent, So my first draft addressed many of the points you made, but it that email got too big and sprawling I thought. So I've focused on what seems to me like the key passage from your post. If you think there was some other point that I should have addressed, let me know. So, key passage: Do these mathematical objects really exist? I'd say they have logico-mathematical existence, not the same existence as tables and chairs, or quarks and electrons. So which kind of existence do you believe is more fundamental? Which is primary? Logico-mathematical existence, or quark existence? Or are they separate but equal kinds of existence? The way I look at it there is knowledge we gain from perception, including the inner perception of logical and mathematical facts. We make up theories that unify and explain these perceptions and which extend beyond what we perceive. These theories have ontologies: things they assume to exist - within the domain of the theory. There's no way to say that one is more fundamental than the other so long as they are in separate theories. Only if they are subsumed within one theory can there be some sense in which one is more fundamental than the other. I don't think we have such a theory yet. And note that even if we have theory including both mathematical and physical objects in its ontology it may turn out that either one can be used to explain the other; so it's not necessarily the case that one is more fundmental. In what way, exactly, does logico-mathematical existence differ from quark existence? You can kick quarks and they kick back. Is logico-mathematical existence a lesser kind of existence? Is logico-mathematical existence derivative of and dependant on quark existence? See above. Further, do tables and chairs even have the same kind of existence as quarks and electrons? Although the explanation of the macroscopic world from the quantum world is not worked out it is generally supposed that tables and chairs will eventually be explained in terms of quarks and electrons. The interesting thing is that from the standpoint of epistemology, the tables and chairs are more fundamental, while the theory makes the quarks and electrons more fundamental to the ontology. So there are different senses of fundamental too. A table is something that we perceive visually, but we intellectually take tables to be ultimately and fully reducible to quarks and electrons. So chairs and quarks certainly exist at different levels. Quarks would seem to be more fundamental than chairs. But obviously we don't actually perceive quarks or electrons...instead we infer their existence from our actual perceptions of various types of experimental equipment and from there associate them back with tables. As for our experience of logico-mathematical objects, we certainly can translate them into more chair-like perceptions by visualization via computer programs, right? I'm doubtful of that. Certainly many mathematical objects can be illustrated because they were invented to describe something we could perceive - like spheres or symmetries. But I don't see how you would visualize Shannon information or strings in ten dimensional space. This would put them very much on similar footing with our experience of quarks and electrons at least, which we also only visualize via computer reconstructions. But there's more than visualization. We can also manipulate and use quarks and electrons, i.e. we can make them kick each other and us. And, presumably it is possible for a human with exceptional visualization abilities to experience logico mathematical objects in a way that is even more chair-like than that. For instance, there are people with Synesthesia (http://en.wikipedia.org/wiki/Synesthesia), for whom some letters or numbers are perceived as inherently colored, or for whom numbers, months of the year, and/or days of the week elicit precise locations in space (for example, 1980 may be farther away than 1990). I don't think that's good example. Synesthesia comes from cross coupling in the brain of concepts that are usually separate. I synesthesia were like perception then all synesthesists would see the same numbers as having the same color, etc. The main thing that causes us to attribute a form of existence to mathematical objects is that everyone who understands them agrees on their properties. But what if this type of synesthesia had some use that strongly aided in human survival and reproduction? Then (speaking in materialist terms) as we evolved synesthesia would have become a standard feature for humans and would now be considered just part of our normal sensory apparatus. We would be able to sense numbers in a way similar to how we sense chairs. In this case we would almost certainly consider numbers to be unquestionably objectively real and existing.
Re: Dreams and Machines
Rex Allen skrev: Brent, So my first draft addressed many of the points you made, but it that email got too big and sprawling I thought. So I've focused on what seems to me like the key passage from your post. If you think there was some other point that I should have addressed, let me know. So, key passage: Do these mathematical objects really exist? I'd say they have logico-mathematical existence, not the same existence as tables and chairs, or quarks and electrons. So which kind of existence do you believe is more fundamental? Which is primary? Logico-mathematical existence, or quark existence? Or are they separate but equal kinds of existence? The most general form of existence is: All mathematical possible universes exist. Our universe is one of those mathematical possible existing universes. The inside of a specific universe constitutes an other form of existence. In a specific universe there are objects inside that universe. In the Game of Life universe, you have the Glider object, the Glider gun object, the Exploder object, the Tumbler object, etc. In a specific instance of the GoL-universe, there exist some objects and some objects does not exist there. In our own universe, there exist tables and chairs and quarks and electrons. This is the specific form of existence. But the mathematical objects does not exist in our universe, in this form of existence. You can not find the 17 object anywhere inside our universe. Then we have the general form of existence saying that our universe exists because it is a mathematical possibility. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
Hi,
Ma connection at home is no functioning. So I am temporarily
disconnected. I hope I will be able to solve that problem. I am sending
here some little comments from my office.
I include some more material for Kim and Marty, and others, just to
think about, in case I remain disconnected for some time. Sorry.
Bruno
Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :
Rex Allen skrev:
Brent,
So my first draft addressed many of the points you made, but it that
email got too big and sprawling I thought.
So I've focused on what seems to me like the key passage from your
post. If you think there was some other point that I should have
addressed, let me know.
So, key passage:
Do these mathematical objects really exist? I'd say they have
logico-mathematical existence, not the same existence as tables and
chairs, or quarks and electrons.
So which kind of existence do you believe is more fundamental? Which
is primary? Logico-mathematical existence, or quark existence? Or
are they separate but equal kinds of existence?
The most general form of existence is: All mathematical possible
universes exist. Our universe is one of those mathematical possible
existing universes.
This is non sense. Proof: see UDA. Or interrupt me when you have an
objection in the current explanation. I have explained this many times,
but the notion of universe or mathematical universe just makes no
sense. The notion of our universe is too far ambiguous for just
making even non sense.
I could say the same to Brent. First I don't think it makes sense to
say that epistemology comes before ontology, given that the ontology,
by definition, in concerned with what we agree exist independently of
the observer/knower ... Then what you say contradict the results in the
computationalist theory, where the appearances of universe emerges from
the collection of all computations
BTW, thanks to Brent for helping Marty.
Rex, when you say:
I would say that most people PERCEIVE logico-mathematical objects
differently than they perceive tables and chairs, or quarks and
electrons. But this doesn't tell us anything about whether these
things really have different kinds of existence. That we perceive
them differently is just an accident of fate.
We perceive them differently because observation is a different
modality of self-reference than proving. It has nothing to do with
accident or fate. The comp physics is defined by what is invariant,
from the observation point of view of universal machine. Later this
will shown to be given by the 3th, 4th, and 5th hypostases.
math lesson (2 posts):
Hi,
I wrote:
The cardinal of { } = 0. All singletons have cardinal one. All pairs,
or doubletons, have cardinal two.
Problem 1 has been solved. They have the same cardinal, or if you
prefer, they have the same number of elements. The set of all subsets
of a set with n elements has the same number of elements than the set
of all strings of length n.
Let us write B_n for the sets of binary strings of length n. So,
B_0 = { }
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
We have seen, without counting, that the cardinal of the powerset of a
set with cardinal n is the same as the cardinal of B_n.
And now the killing question by the sadistic math teacher:
What is the cardinal, that is, the number of element, of B_0, that is
the set of strings of length 0.
The student: let see, you wrote above B_0 = { },, and you were kind
enough to recall that the cardinal of { } is zero (of course, there is
zero element in the empty set). So the cardinal of B_0 is zero. 'zero
said the student.
'zero' indeed, said the teacher, but it is your note. You are wrong.
B_0 is not empty! It *looks* empty, but beware the appearance, it looks
empty because it contains the empty string, which, if you remember some
preceding post is invisible (even under the microscope, telescope,
radioscope, ..).
A solution could have been to notate the empty string by a symbol like
_, and write all sequences 0111000100 starting from _:
_0111000100, with rules __ = _, etc. Then B_0 = { _ }, B_1 = {_0,
_1}, etc. But this is too much notation.
And now the time has come for contrition when the teacher feels guilty!
Ah..., I should have written directly something like
B_0 = { _ }, with _ representing the empty sequence.
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
OK?
Remember we have seen that the cardinal of the powerset of a set with n
elements is equal to the cardinal of B_n, is equal to 2^n.
The cardinal of B_0 has to be equal to to 2^0, which is equal to one.
Why?
if a is a number, usually, a^n is the result of effectuating (a times a
times a time a ... times a), with n occurences of a. For example: 2^3 =
2x2x2 = 8.
so a^n times a^m is equal to a^(n+m)
This extends to the rational by defining a^(-n) by 1/a^n. In that case
Re: Dreams and Machines
Bruno Marchal skrev:
Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :
Rex Allen skrev:
Brent:
Do these mathematical objects really exist? I'd say they
have
logico-mathematical existence, not the same existence as
tables and
chairs, or quarks and electrons.
So which kind of existence do you believe is more fundamental?
Which
is primary? Logico-mathematical existence, or quark existence? Or
are they separate but equal kinds of existence?
The most general form of existence is: All mathematical possible
universes exist. Our universe is one of those mathematical possible
existing universes.
This is non sense. Proof: see UDA. Or interrupt me when you have an
objection in the current explanation. I have explained this many
times, but the notion of universe or mathematical universe just makes
no sense. The notion of our universe is too far ambiguous for just
making even non sense.
What do you think about the GoL-universes? You can look at some of
those at http://www.bitstorm.org/gameoflife/ . If you have an initial
condition and you have an unlimited board, then you can compute what
will happen in the future in that universe. These universes are
universes with a two-dimensional space and a one-dimensional time.
These GoL-universes are mathematial universes. They have an initial
condition and a mathematical rule that defines how that universe will
look like in the next moment, and the next next moment, and so on.
Does this make sense for you?
Now look at a mathematical universe that have somewhat more complicated
rules, and that mathematical universe looks exactly the same as our
universe. The same things happens as in our universe, and there is an
object there that is calling himself Bruno, and there is another object
calling himself Torgny...
(By the way, I think it is better to use the notion 010110 for
strings. Then B_1 will be {0, 1}, and B_0 will be {}. Then it is
more clear that B_0 contains one element.)
--
Torgny
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Re: The seven step series
Hi Brent, I really appreciate the help and I hate to impose on your patience but...(see below) - Original Message - From: Brent Meeker meeke...@dslextreme.com To: everything-list@googlegroups.com Sent: Tuesday, July 21, 2009 5:24 PM Subject: Re: The seven step series Take all strings of length 2 00 01 10 11 Make two copies of each 00 00 01 01 10 10 11 11 Add a 0 to the first and a 1 to the second 000001 010 011 100 101 110 111 and you have all strings of length 3. I can see where adding 0 to the first and 1 to the second gives 000 and 001 and I think I see how you get 010 but the rest of the permutations don't seem obvious to me. P-l-e-a-s-e explain, Best, m. (mathematically hopeless) a. Brent m.a. wrote: *Thanks Brent,* * Could you supply some illustrative examples?* * marty a.* ** - Original Message - From: Brent Meeker meeke...@dslextreme.com mailto:meeke...@dslextreme.com To: everything-list@googlegroups.com mailto:everything-list@googlegroups.com Sent: Tuesday, July 21, 2009 3:57 PM Subject: Re: The seven step series Each binary string of length n has two possible continuations of length n+1, one of them by appending a 0 and one of them by appending a 1. So to get all binary strings of length n+1 take each string of length n, make two copies, to one copy append a 0 and to the other copy append a 1. Brent m.a. wrote: Hi Bruno, I'm not clear on the sentence in bold below, especially the word correspondingly. The example of Mister X only confuses me more. Could you please give some simple examples? Thanks, marty a. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
Ma connection at home is again functioning. I am happy to have solved
the problem rather quickly.
On 22 Jul 2009, at 13:54, David Nyman wrote:
2009/7/22 Bruno Marchal marc...@ulb.ac.be:
Ma connection at home is no functioning.
As a linguistic aside, Bruno has cleverly expressed the above
statement in perfect Glaswegian (i.e. the spoken tongue of Glasgow,
Scotland - my home town).
Indeed I am following an intense summer school in Glaswegian.
You thought you could make fun of the poor disconnected one?
Other well-known examples are: Is'arra
marra on yer barra Clarra? (Is that large vegetable on your barrow a
marrow, Clara?); and Gie's'a sook on yer soor ploom (Let me taste
the sour plum (a globular sweet-sour confection) that you are
presently sucking).
Perhaps he intends to continue further in this vein?
Once, on a list, someone thought I was using slang from New-York! Now
Glaswegian!
I am afraid I am just writing to quickly, and then when I read myself
I concentrate so much on the meaning ...
Most of the time I see the spelling errors when I read my mail, never
when I send it.
Sorry sorry sorry ...
Take care of the sense and the spelling will take care of itself. Well
*that* does not work!
Bruno
David ;-)
Hi,
Ma connection at home is no functioning. So I am temporarily
disconnected. I hope I will be able to solve that problem. I am
sending
here some little comments from my office.
I include some more material for Kim and Marty, and others, just to
think about, in case I remain disconnected for some time. Sorry.
Bruno
Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :
Rex Allen skrev:
Brent,
So my first draft addressed many of the points you made, but it
that
email got too big and sprawling I thought.
So I've focused on what seems to me like the key passage from your
post. If you think there was some other point that I should have
addressed, let me know.
So, key passage:
Do these mathematical objects really exist? I'd say they have
logico-mathematical existence, not the same existence as tables
and
chairs, or quarks and electrons.
So which kind of existence do you believe is more fundamental?
Which
is primary? Logico-mathematical existence, or quark existence? Or
are they separate but equal kinds of existence?
The most general form of existence is: All mathematical possible
universes exist. Our universe is one of those mathematical possible
existing universes.
This is non sense. Proof: see UDA. Or interrupt me when you have an
objection in the current explanation. I have explained this many
times,
but the notion of universe or mathematical universe just makes no
sense. The notion of our universe is too far ambiguous for just
making even non sense.
I could say the same to Brent. First I don't think it makes sense to
say that epistemology comes before ontology, given that the ontology,
by definition, in concerned with what we agree exist independently of
the observer/knower ... Then what you say contradict the results in
the
computationalist theory, where the appearances of universe emerges
from
the collection of all computations
BTW, thanks to Brent for helping Marty.
Rex, when you say:
I would say that most people PERCEIVE logico-mathematical objects
differently than they perceive tables and chairs, or quarks and
electrons. But this doesn't tell us anything about whether these
things really have different kinds of existence. That we perceive
them differently is just an accident of fate.
We perceive them differently because observation is a different
modality of self-reference than proving. It has nothing to do with
accident or fate. The comp physics is defined by what is invariant,
from the observation point of view of universal machine. Later this
will shown to be given by the 3th, 4th, and 5th hypostases.
math lesson (2 posts):
Hi,
I wrote:
The cardinal of { } = 0. All singletons have cardinal one. All pairs,
or doubletons, have cardinal two.
Problem 1 has been solved. They have the same cardinal, or if you
prefer, they have the same number of elements. The set of all subsets
of a set with n elements has the same number of elements than the set
of all strings of length n.
Let us write B_n for the sets of binary strings of length n. So,
B_0 = { }
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
We have seen, without counting, that the cardinal of the powerset
of a
set with cardinal n is the same as the cardinal of B_n.
And now the killing question by the sadistic math teacher:
What is the cardinal, that is, the number of element, of B_0, that is
the set of strings of length 0.
The student: let see, you wrote above B_0 = { },, and you were kind
enough to recall that the cardinal of { } is zero (of course, there
is
zero element in the empty set). So the cardinal of B_0 is
Re: Dreams and Machines
On 22 Jul 2009, at 14:12, Torgny Tholerus wrote: The most general form of existence is: All mathematical possible universes exist. Our universe is one of those mathematical possible existing universes. This is non sense. Proof: see UDA. Or interrupt me when you have an objection in the current explanation. I have explained this many times, but the notion of universe or mathematical universe just makes no sense. The notion of our universe is too far ambiguous for just making even non sense. What do you think about the GoL-universes? You can look at some of those at http://www.bitstorm.org/gameoflife/ . If you have an initial condition and you have an unlimited board, then you can compute what will happen in the future in that universe. What is an unlimited board for an ultrafinitist. (Ok, that was perhaps easy). These universes are universes with a two-dimensional space and a one-dimensional time. These GoL-universes are mathematial universes. They have an initial condition and a mathematical rule that defines how that universe will look like in the next moment, and the next next moment, and so on. Does this make sense for you? Those are not universes, but computational histories. Assuming comp there is a first person indeterminacy, which makes physical appearances or physical universe emerging from the infinity of such computational and universal computation. I suggest you read the UDA papers. I guess you were not yet on the list when I explained why Wolfram sort of computational physics, based on cellular automata, does not work. And quantum mechanics confirms this by giving indirect but strong evidences on the existence of many statistically interfering computations. The question about the existence of a mathematical structure describing the physical appearance is open, but we know already it is not a structure such that it makes sense to say I belong to it, even if it makes sense to say he belongs to it. But he, from his first person point of view belongs to an infinity of such history (or comp is false, which is the case normally for an ultrafinitist). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
2009/7/19 Rex Allen rexallen...@gmail.com: In your view, Bruno (or David, or anyone else who has an opinion), what kinds of things actually exist? What does it mean to say that something exists? This is naturally the $64k question for this list - or any other, for that matter (pun intended). I don't know the 'answer' - of course - but it doesn't stop me banging on about it interminably, here and elsewhere. Anyway, I'll have another go, but naturally only on the basis that anything that follows is just a 'way of speaking' that might - or mightn't - be helpful in resolving apparent puzzles stemming from linguistic or logical confusions. Personally, I find it useful to start from a more primitive position prior to speculating about the status of say, mathematical formalisms. Like Schopenhauer, Spinoza, Schrodinger and very many others, I find dualism to founder hopelessly on the rock of interaction and explanatory redundancy. Hence I'm a monist (or a non-dualist) who - given the singular incorrigibility of first-person 'experiential reality' - concludes that though whatever underlies remains forever *unknowable* it must nonetheless perforce be 'real in the sense that I am real' (RITSIAR - a gnomic acronym that has surfaced before on this list). Other primitive intuitions are founded on this: 1) The unknowable is singular (i.e symmetrical, holistic, indivisible: e.g. Plotinus' One) 2) The unknowable is pluralistic (asymmetrical, differentiated: i.e. pattern and order manifested within the One) 3) 1 and 2 taken together are of course 'paradoxical' in the light of the logic of the 'excluded middle'. This, I believe, is not vicious, but rather points virtuously towards the limit of such logics. It situates an unresolvable mystery appropriately, rather than attempting speciously to dispel it or ignore it. 4) 1 and 2 taken together must be RITSIAR. For me, this comprises the intuition that 'existence' is fundamentally - and only - a 'personal and present way of being'. To put it another way, epistemology and ontology are enfolded into the unmediated intuition of 'the way one is' as follows: 5) 1 (uniqueness, symmetry) - relating to an intuition of bare 'reflexive presence' (i.e. the whole is 'present-to-self', as I am). 6) 2 (asymmetry, differentiation) - relating to orderings of 'motivated self-access' (i.e. an intuition that 'presence' manifests in recursive orders of reflexively-intimate self-relativisation. Note that this vitiates and replaces the notions of 'observation' and 'action' and thereby collapses otherwise infinite regresses. It also welds 'causal closure' to an indivisible primitive intuition that enfolds - of necessity - both 'perception' and 'intention'. 7) All subsets of being, as it were - including the first-personal - emerge as a consequence of the 'superset of being' (the '0-personal') 'getting a grip on itself' (or better: *oneself*). 8) Taken together, 5, 6 and 7 collapse into a basic intuition of existence as - always and everywhere - constituted by a 'personal self-actualisation' which is posited to be characteristic of reality 'from the ground up'. The foregoing treatment attempts to summarise a (well-known: e.g. Plotinus, Vedanta, etc.) set of intuitions intended to underpin other notions of 'existence' in all its forms - i.e. any other postulation of 'existence' whatsoever is parasitic on the 'master' intuition that whatever 'exists' must be 'personally present as an actualised way-of-being'. So, in this light, what of the 'existence' of mathematics, 'possible' worlds, and other such 'abstractions'? Well, they indeed qualify in this sense (trivially) in the form of our shared 'mental constructions'. But are they additionally present - in some other form - *in-their-own-right*? One's view on this will clearly depend on the way one's theories (implicit or explicit) posit how the particular zoo of worlds, universes etc. one favours emerges from the ground outlined above. I would dichotomise such views into two camps: necessitist and contingentist. COMP, I think (but I may be off-beam here: see below) falls into the first camp. As far as 'reality' goes in COMP, I'm reasonably sure that what Bruno (conceding that he is almost always way ahead of me on any of this) implies in the metaphysics (or theology) of COMP, is that 'arithmetical reality' should be regarded as 'real' and 'present' in more or less the sense of 'RITSIAR'. Hence, the 'Platonic existence' that underpins COMP is RITSIAR. By this I don't mean the 'numbers' and 'operators' that we denote verbally or in writing - these of course are just a 'way of speaking' - a language. Rather these symbols gesture towards an unknowable domain that nonetheless possesses these characteristics in some (rigorously definable?) sense. And this domain is inescapably 'personal' - it is 'us', and it is everything else, too. One astonishing consequence of this schema is that any 'possible world' derivable from such a
Re: Dreams and Machines
On 22 July, 16:01, Bruno Marchal marc...@ulb.ac.be wrote:
Ma connection at home is again functioning. I am happy to have solved
the problem rather quickly.
On 22 Jul 2009, at 13:54, David Nyman wrote:
2009/7/22 Bruno Marchal marc...@ulb.ac.be:
You thought you could make fun of the poor disconnected one?
Dinna fash yursel laddie, ah was'na makin sport o' ye. It wus a
compliment!
Further lessons available on application.
Hoots mon
David -;
Ma connection at home is no functioning.
As a linguistic aside, Bruno has cleverly expressed the above
statement in perfect Glaswegian (i.e. the spoken tongue of Glasgow,
Scotland - my home town).
Indeed I am following an intense summer school in Glaswegian.
You thought you could make fun of the poor disconnected one?
Other well-known examples are: Is'arra
marra on yer barra Clarra? (Is that large vegetable on your barrow a
marrow, Clara?); and Gie's'a sook on yer soor ploom (Let me taste
the sour plum (a globular sweet-sour confection) that you are
presently sucking).
Perhaps he intends to continue further in this vein?
Once, on a list, someone thought I was using slang from New-York! Now
Glaswegian!
I am afraid I am just writing to quickly, and then when I read myself
I concentrate so much on the meaning ...
Most of the time I see the spelling errors when I read my mail, never
when I send it.
Sorry sorry sorry ...
Take care of the sense and the spelling will take care of itself. Well
*that* does not work!
Bruno
David ;-)
Hi,
Ma connection at home is no functioning. So I am temporarily
disconnected. I hope I will be able to solve that problem. I am
sending
here some little comments from my office.
I include some more material for Kim and Marty, and others, just to
think about, in case I remain disconnected for some time. Sorry.
Bruno
Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :
Rex Allen skrev:
Brent,
So my first draft addressed many of the points you made, but it
that
email got too big and sprawling I thought.
So I've focused on what seems to me like the key passage from your
post. If you think there was some other point that I should have
addressed, let me know.
So, key passage:
Do these mathematical objects really exist? I'd say they have
logico-mathematical existence, not the same existence as tables
and
chairs, or quarks and electrons.
So which kind of existence do you believe is more fundamental?
Which
is primary? Logico-mathematical existence, or quark existence? Or
are they separate but equal kinds of existence?
The most general form of existence is: All mathematical possible
universes exist. Our universe is one of those mathematical possible
existing universes.
This is non sense. Proof: see UDA. Or interrupt me when you have an
objection in the current explanation. I have explained this many
times,
but the notion of universe or mathematical universe just makes no
sense. The notion of our universe is too far ambiguous for just
making even non sense.
I could say the same to Brent. First I don't think it makes sense to
say that epistemology comes before ontology, given that the ontology,
by definition, in concerned with what we agree exist independently of
the observer/knower ... Then what you say contradict the results in
the
computationalist theory, where the appearances of universe emerges
from
the collection of all computations
BTW, thanks to Brent for helping Marty.
Rex, when you say:
I would say that most people PERCEIVE logico-mathematical objects
differently than they perceive tables and chairs, or quarks and
electrons. But this doesn't tell us anything about whether these
things really have different kinds of existence. That we perceive
them differently is just an accident of fate.
We perceive them differently because observation is a different
modality of self-reference than proving. It has nothing to do with
accident or fate. The comp physics is defined by what is invariant,
from the observation point of view of universal machine. Later this
will shown to be given by the 3th, 4th, and 5th hypostases.
math lesson (2 posts):
Hi,
I wrote:
The cardinal of { } = 0. All singletons have cardinal one. All pairs,
or doubletons, have cardinal two.
Problem 1 has been solved. They have the same cardinal, or if you
prefer, they have the same number of elements. The set of all subsets
of a set with n elements has the same number of elements than the set
of all strings of length n.
Let us write B_n for the sets of binary strings of length n. So,
B_0 = { }
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
We have seen, without counting, that the cardinal of the powerset
of a
set with cardinal n is the same as the cardinal of B_n.
And now the killing
Re: The seven step series
Marty,
Brent wrote:
On 21 Jul 2009, at 23:24, Brent Meeker wrote:
Take all strings of length 2
00 01 10 11
Make two copies of each
00 00 01 01 10 10 11 11
Add a 0 to the first and a 1 to the second
000001 010 011 100 101 110 111
and you have all strings of length 3.
Then you wrote
I can see where adding 0 to the first and 1 to the second gives 000
and 001 and I think I see how you get 010 but the rest of the
permutations don't seem obvious to me. P-l-e-a-s-e explain, Best,
m
. (mathematically hopeless) a.
Let me rewrite Brent's explanation, with a tiny tiny tiny improvement:
Take all strings of length 2
00
01
10
11
Make two copies of each
first copy:
00
01
10
11
second copy
00
01
10
11
add a 0 to the end of the strings in the first copy, and then add a 1
to the end of the strings in the second copy:
first copy:
000
010
100
110
second copy
001
011
101
111
You get all 8 elements of B_3.
You can do the same reasoning with the subsets. Adding an element to a
set multiplies by 2 the number of elements of the powerset:
Exemple. take a set with two elements {a, b}. Its powerset is {{ } {a}
{b} {a, b}}. How to get all the subset of {a, b, c} that is the set
coming from adding c to {a, b}.
Write two copies of the powerset of {a, b}
{ }
{a}
{b}
{a, b}
{ }
{a}
{b}
{a, b}
Don't add c to the set in the first copy, and add c to the sets in the
second copies. This gives
{ }
{a}
{b}
{a, b}
{c}
{a, c}
{b, c}
{a, b, c}
and that gives all subsets of {a, b, c}.
This is coherent with interpreting a subset {a, b} of a set {a, b, c},
by a string like 110, which can be conceived as a shortand for
Is a in the subset? YES, thus 1
Is b in the subset? YES thus 1
Is c in the subset?NO thus 0.
OK?
You say also:
The example of Mister X only confuses me more.
Once you understand well the present post, I suggest you reread the
Mister X examples, because it is a key in the UDA reasoning. If you
still have problem with it, I suggest you quote it, line by line, and
ask question. I will answer (or perhaps someone else).
Don't be afraid to ask any question. You are not mathematically
hopeless. You are just not familiarized with reasoning in math. It is
normal to go slowly. As far as you can say I don't understand, there
is hope you will understand.
Indeed, concerning the UDA I suspect many in the list cannot say I
don't understand, they believe it is philosophy, so they feel like
they could object on philosophical ground, when the whole point is to
present a deductive argument in a theory. So it is false, or you have
to accept the theorem in the theory. It is a bit complex, because it
is an applied theory. The mystery are in the axioms of the theory,
as always.
So please ask *any* question. I ask this to everyone. I am intrigued
by the difficulty some people can have with such reasoning (I mean the
whole UDA here). (I can understand the shock when you get the point,
but that is always the case with new results: I completely share
Tegmark's idea that our brain have not been prepared to have any
intuition when our mind try to figure out what is behind our local
neighborhood).
Bruno
http://iridia.ulb.ac.be/~marchal/
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Re: The seven step series
m.a. wrote: Hi Brent, I really appreciate the help and I hate to impose on your patience but...(see below) - Original Message - From: Brent Meeker meeke...@dslextreme.com mailto:meeke...@dslextreme.com To: everything-list@googlegroups.com mailto:everything-list@googlegroups.com Sent: Tuesday, July 21, 2009 5:24 PM Subject: Re: The seven step series Take all strings of length 2 00 01 10 11 Make two copies of each 00 00 01 01 10 10 11 11 Add a 0 to the first and a 1 to the second 000001 010 011 100 101 110 111 and you have all strings of length 3. *I can see where adding 0 to the first and 1 to the second gives 000 and 001 and I think I see how you get 010 but the rest of the permutations don't seem obvious to me. P-l-e-a-s-e explain, Best,* ** * m. (mathematically hopeless) a.* They aren't permutations. They're just sticking a 0 or 1 on the end. One copy of 01 becomes 010 and the other become 011. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
On 22 Jul 2009, at 17:56, David Nyman wrote:
2009/7/19 Rex Allen rexallen...@gmail.com:
In your view, Bruno (or David, or anyone else who has an opinion),
what kinds of things actually exist? What does it mean to say that
something exists?
This is naturally the $64k question for this list - or any other, for
that matter (pun intended). I don't know the 'answer' - of course -
but it doesn't stop me banging on about it interminably, here and
elsewhere. Anyway, I'll have another go, but naturally only on the
basis that anything that follows is just a 'way of speaking' that
might - or mightn't - be helpful in resolving apparent puzzles
stemming from linguistic or logical confusions.
Personally, I find it useful to start from a more primitive position
prior to speculating about the status of say, mathematical formalisms.
Like Schopenhauer, Spinoza, Schrodinger and very many others, I find
dualism to founder hopelessly on the rock of interaction and
explanatory redundancy. Hence I'm a monist (or a non-dualist) who -
given the singular incorrigibility of first-person 'experiential
reality' - concludes that though whatever underlies remains forever
*unknowable* it must nonetheless perforce be 'real in the sense that I
am real' (RITSIAR - a gnomic acronym that has surfaced before on this
list).
Hmm... OK. Nice. Not completely convinced yet.
Other primitive intuitions are founded on this:
1) The unknowable is singular (i.e symmetrical, holistic, indivisible:
e.g. Plotinus' One)
unknowable?
or unprovable, uncommunicable, that is unbelievable, unjustifiable.
2) The unknowable is pluralistic (asymmetrical, differentiated: i.e.
pattern and order manifested within the One)
3) 1 and 2 taken together are of course 'paradoxical' in the light of
the logic of the 'excluded middle'. This, I believe, is not vicious,
but rather points virtuously towards the limit of such logics. It
situates an unresolvable mystery appropriately, rather than attempting
speciously to dispel it or ignore it.
Hmm... The excluded middle is what makes us modest.
It makes possible to prove the existence of some object x by showing
that x belongs to {a, b, c} , without any means to decide which of a,
b and c x is.
The excluded middle principle is what you need to recognize unknowns
and capture them in some set, hopefully not to big.
In the theoretical computer science, and especially in theoretical
learning many theorems are necessarily non constructive.
You abandon the excluded middle principle when you want to build
something, or extend yourself, with the exclusion of the other.
The excluded middle principle is what you need to think and dream
about what you build, and what can follow, and talk on it with others.
You need it somehow to believe in another one. Also, it prevents not
the falsity of solipsism, but the falsity of any doctrinal (3-
communicable) solipsism.
4) 1 and 2 taken together must be RITSIAR. For me, this comprises the
intuition that 'existence' is fundamentally - and only - a 'personal
and present way of being'. To put it another way, epistemology and
ontology are enfolded into the unmediated intuition of 'the way one
is' as follows:
5) 1 (uniqueness, symmetry) - relating to an intuition of bare
'reflexive presence' (i.e. the whole is 'present-to-self', as I am).
6) 2 (asymmetry, differentiation) - relating to orderings of
'motivated self-access' (i.e. an intuition that 'presence' manifests
in recursive orders of reflexively-intimate self-relativisation. Note
that this vitiates and replaces the notions of 'observation' and
'action' and thereby collapses otherwise infinite regresses. It also
welds 'causal closure' to an indivisible primitive intuition that
enfolds - of necessity - both 'perception' and 'intention'.
7) All subsets of being, as it were - including the first-personal -
emerge as a consequence of the 'superset of being' (the '0-personal')
'getting a grip on itself' (or better: *oneself*).
Nicely said.
8) Taken together, 5, 6 and 7 collapse into a basic intuition of
existence as - always and everywhere - constituted by a 'personal
self-actualisation' which is posited to be characteristic of reality
'from the ground up'.
? This belongs to the incommunicable part. If you communicate it, you
bet on the existence of someone else, and on something sharable. But
then you do science, and in honest science you share only doubts.
Do you see what I see?
Do you believe what I believe?
The foregoing treatment attempts to summarise a (well-known: e.g.
Plotinus, Vedanta, etc.) set of intuitions intended to underpin other
notions of 'existence' in all its forms - i.e. any other postulation
of 'existence' whatsoever is parasitic on the 'master' intuition that
whatever 'exists' must be 'personally present as an actualised
way-of-being'. So, in this light, what of the 'existence' of
mathematics, 'possible' worlds, and
Re: Dreams and Machines
2009/7/22 Bruno Marchal marc...@ulb.ac.be: explanatory redundancy. Hence I'm a monist (or a non-dualist) who - given the singular incorrigibility of first-person 'experiential reality' - concludes that though whatever underlies remains forever *unknowable* it must nonetheless perforce be 'real in the sense that I am real' (RITSIAR - a gnomic acronym that has surfaced before on this list). Hmm... OK. Nice. Not completely convinced yet. Let's try to be clear(!) I don't intend 'RITSIAR' to refer merely to the 1-person, but to the 0-person and all the other persons you can think of. Why? Because given that I am indubitably RITSIAR, then whatever I emerge from must also subsist in a status that is also RITSIAR in some uneliminable *ontological* sense. Naturally I don't intend by this that either the One, or 3-person descriptions, literally call themselves I, but rather that what is ontologically RITSIAR in the 1-person is irreducibly so in the whole, and vice versa. As an analogy, if - merely for the sake of argument - we were to choose to ascribe fundamental 'materiality' to the world', then we also must consistently hold that all and any constituent parts and sub-wholes subsist in ontological 'materiality' by the same token. Not to do this would be equivalent to accepting sudden non-linear step-changes in *ontological* status merely as a function of scale - which AFAICS is incoherent - i.e. I wouldn't have a clue what this could possibly mean. I don't want us to talk past each other merely on the basis of incommensurable jargon - if there's anything I can do to make this point clearer, I'll go on trying. 1) The unknowable is singular (i.e symmetrical, holistic, indivisible: e.g. Plotinus' One) unknowable? or unprovable, uncommunicable, that is unbelievable, unjustifiable. Here I'm saying that the *undifferentiated* One is unknowable, because 'knowing' is here posited precisely to subsist in differentiated ways-of-being adopted by the One *posterior* to its bare, undifferentiated 'presence'. Hence, this 'bare presence' or personal ground is a priori both unknowing and unknowable. 'Knowledge' subsists in the multiplicity of distinguished ways-of-being that emerge from the bare presence of the One: i.e. 'getting-a-grip-on-Oneself'. The excluded middle principle is what you need to think and dream about what you build, and what can follow, and talk on it with others. You need it somehow to believe in another one. Also, it prevents not the falsity of solipsism, but the falsity of any doctrinal (3- communicable) solipsism. I'm not abandoning the principle, rather I was pointing to the fact that in analysis at this level, there is something deeply mysterious - apparently paradoxical in terms of mutually exclusive 'opposites' - about a 'seamless' unity nevertheless being 'differentiable'. As a matter of personal psychological compulsion, I feel it necessary to point this out, to forestall someone else asking how can you claim that 'parts' ultimately subsist in the context of a 'seamless' whole? If you like, I consider myself to be a sort of dualist in this sense: that there seems to me ultimately to be an inescapable duality (meaning two irreducible ways of being) between intuitions of 'whole' and 'part'. Once we have reasoned as far as we can in terms of 'ultimates', we're left with nothing to 'separate' the 'whole' into 'parts'. If we believe we can 'actually' *sever* the 'whole', what do we suppose 'lies between' the 'parts' (e.g. the old notion of 'atoms in the void')? Nothing? One may simply say that this of course is the well known tension between intuitions of the 'continuous' and the 'discrete'. But at this level of discourse, there seems to be something wrong that can't be fixed by invoking higher-order 'limit' theories unavailable even in principle at this depth of analysis. Nonetheless, the unknowable - unknowably - somehow resolves this paradox. But maybe I'm the only one who cares about this. Or maybe it's just gibberish. 8) Taken together, 5, 6 and 7 collapse into a basic intuition of existence as - always and everywhere - constituted by a 'personal self-actualisation' which is posited to be characteristic of reality 'from the ground up'. ? This belongs to the incommunicable part. If you communicate it, you bet on the existence of someone else, and on something sharable. But then you do science, and in honest science you share only doubts. Do you see what I see? Do you believe what I believe? Hm, I think there may be a misstep in emphasis here. The key intuition, which I was deriving step-by-step up to that point, is that whatever it is that we take to be 'real' or 'existent' - and by that token fundamentally RITSIAR - must thereby be both 'personally present' and 'self-actualising'. In my terms, this would have to be so whether we take RITSIAR to be based on Number, 'matter' or spiritual green cheese. I agree this isn't science, and hence is
Re: Dreams and Machines
David Nyman wrote: 2009/7/22 Bruno Marchal marc...@ulb.ac.be: explanatory redundancy. Hence I'm a monist (or a non-dualist) who - given the singular incorrigibility of first-person 'experiential reality' - concludes that though whatever underlies remains forever *unknowable* it must nonetheless perforce be 'real in the sense that I am real' (RITSIAR - a gnomic acronym that has surfaced before on this list). Hmm... OK. Nice. Not completely convinced yet. Let's try to be clear(!) I don't intend 'RITSIAR' to refer merely to the 1-person, but to the 0-person and all the other persons you can think of. Why? Because given that I am indubitably RITSIAR, then whatever I emerge from must also subsist in a status that is also RITSIAR in some uneliminable *ontological* sense. Naturally I don't intend by this that either the One, or 3-person descriptions, literally call themselves I, but rather that what is ontologically RITSIAR in the 1-person is irreducibly so in the whole, and vice versa. As an analogy, if - merely for the sake of argument - we were to choose to ascribe fundamental 'materiality' to the world', then we also must consistently hold that all and any constituent parts and sub-wholes subsist in ontological 'materiality' by the same token. Not to do this would be equivalent to accepting sudden non-linear step-changes in *ontological* status merely as a function of scale - which AFAICS is incoherent - i.e. I wouldn't have a clue what this could possibly mean. I don't want us to talk past each other merely on the basis of incommensurable jargon - if there's anything I can do to make this point clearer, I'll go on trying. 1) The unknowable is singular (i.e symmetrical, holistic, indivisible: e.g. Plotinus' One) unknowable? or unprovable, uncommunicable, that is unbelievable, unjustifiable. Here I'm saying that the *undifferentiated* One is unknowable, because 'knowing' is here posited precisely to subsist in differentiated ways-of-being adopted by the One *posterior* to its bare, undifferentiated 'presence'. Hence, this 'bare presence' or personal ground is a priori both unknowing and unknowable. If I understand you correctly, this is similar to the explication of I by Thomas Metzinger in his book The Ego Tunnel. He expresses it as the self being transparent. We look *through* it but not *at* it, and necessarily so. 'Knowledge' subsists in the multiplicity of distinguished ways-of-being that emerge from the bare presence of the One: i.e. 'getting-a-grip-on-Oneself'. The excluded middle principle is what you need to think and dream about what you build, and what can follow, and talk on it with others. You need it somehow to believe in another one. Also, it prevents not the falsity of solipsism, but the falsity of any doctrinal (3- communicable) solipsism. I'm not abandoning the principle, rather I was pointing to the fact that in analysis at this level, there is something deeply mysterious - apparently paradoxical in terms of mutually exclusive 'opposites' - about a 'seamless' unity nevertheless being 'differentiable'. As a matter of personal psychological compulsion, I feel it necessary to point this out, to forestall someone else asking how can you claim that 'parts' ultimately subsist in the context of a 'seamless' whole? This paradox arises in quantum cosmogony. The universe (or multiverse) evolves as the rotation of a single ray in Hilbert space. But relativistic horizons separate different local projections so that we see decohered, classical objects (and we are such objects). At least that's the speculation - there is both unity and diversity: different aspects of the wave-function of the universe which is unknowable. If you like, I consider myself to be a sort of dualist in this sense: that there seems to me ultimately to be an inescapable duality (meaning two irreducible ways of being) between intuitions of 'whole' and 'part'. Once we have reasoned as far as we can in terms of 'ultimates', we're left with nothing to 'separate' the 'whole' into 'parts'. If we believe we can 'actually' *sever* the 'whole', what do we suppose 'lies between' the 'parts' (e.g. the old notion of 'atoms in the void')? Nothing? One may simply say that this of course is the well known tension between intuitions of the 'continuous' and the 'discrete'. But at this level of discourse, there seems to be something wrong that can't be fixed by invoking higher-order 'limit' theories unavailable even in principle at this depth of analysis. Nonetheless, the unknowable - unknowably - somehow resolves this paradox. But maybe I'm the only one who cares about this. Or maybe it's just gibberish. 8) Taken together, 5, 6 and 7 collapse into a basic intuition of existence as - always and everywhere - constituted by a 'personal self-actualisation' which is posited to be characteristic of reality 'from the ground up'.
Re: The seven step series
Going a step further... (see below) - Original Message - From: Brent Meeker meeke...@dslextreme.com To: everything-list@googlegroups.com Sent: Wednesday, July 22, 2009 12:57 PM Subject: Re: The seven step series m.a. wrote: Hi Brent, I really appreciate the help and I hate to impose on your patience but...(see below) - Original Message - From: Brent Meeker meeke...@dslextreme.com mailto:meeke...@dslextreme.com To: everything-list@googlegroups.com mailto:everything-list@googlegroups.com Sent: Tuesday, July 21, 2009 5:24 PM Subject: Re: The seven step series Take all strings of length 2 00 01 10 11 Make two copies of each 00 00 01 01 10 10 11 11 Add a 0 to the first and a 1 to the second 000001 010 011 100 101 110 111 and you have all strings of length 3. *I can see where adding 0 to the first and 1 to the second gives 000 and 001 and I think I see how you get 010 but the rest of the permutations don't seem obvious to me. P-l-e-a-s-e explain, Best,* ** They aren't permutations. They're just sticking a 0 or 1 on the end. One copy of 01 becomes 010 and the other become 011. Then I assume the next step would be making two copies of each of those: 000000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 ...and sticking a 0 or 1 at the end: 000100100011 01000101011001111000 1001 1010 1011 1100 1101 1110 and this is the binary sequence of length 4. How do these translate into ordinary numerals? 1,2,3,4... Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Seven Step Series
Bruno,
See desperate questions below.
marty a.
- Original Message -
From: Bruno Marchal marc...@ulb.ac.be
To: everything-list@googlegroups.com
Sent: Wednesday, July 22, 2009 11:01 AM
Subject: Re: Dreams and Machines
Ah..., I should have written directly something like
B_0 = { _ }, with _ representing the empty sequence.
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
OK? Yes.
Remember we have seen that the cardinal of the powerset of a set
with n
elements is equal to the cardinal of B_n, is equal to 2^n.
The cardinal of B_0 has to be equal to to 2^0, which is equal to one.
Why?
if a is a number, usually, a^n is the result of effectuating (a
times a
times a time a ... times a), with n occurences of a. For example:
2^3 =
2x2x2 = 8.
so a^n times a^m is equal to a^(n+m)
This extends to the rational by defining a^(-n) by 1/a^n. In that
case
a^(m-n) = a^m/a^n. In particular a^m/a^m = 1 (x/x = 1 always), and
a^m/a^m = a^(m-m) = a^0. So a^0 = 1. So in particular 2^0 = 1.
Do you really expect us to understand this?
But we will see soon a deeper reason to be encouraged to guess that
a^0
= 1, but for this we need to define the product and the
exponentiation
of sets. if A is a set, and B is a set: the exponential B^A is a very
important object, it is where the functions live.
Or this?
Take it easy, and ask. Verify the statements a^n/a^m = a^(n-m),
with n
= 3 and m = 5. What is a*a*a/a*a*a*a*a / = division, and * =
times).
Or this?
Bruno
http://iridia.ulb.ac.be/~marchal/
-
Hi,
I am thinking aloud, for the sequel.
There will be a need for a geometrical and number theoretical
interlude.
Do you know what is a periodic decimal?
Do you know that a is periodic decimal if and only if it exists n and
m, integers, such that a = n/m. And that for all n m, n/m is a
periodic decimal?
Could you find n and m, such that
12.95213213213213213213213213213213213213 ... (= 12.95 213 213 ...)
Solution:
Let k be a name for 12.95213213213213213213213213213213213213213 ...
Let us multiply k by 100 000.
100 000k = 1295213.213213213213213213213213213213213213 ... =
1295213
+ 0.213213213 ...
Let us multiply k by 100
100k = 1295.213213213213... = 1295 + 0.213213213213213..
We have 10k - 100k = 1295213 + 0.213213213... - 1295
- 0.213213213... = 1295213 - 1295 = 1293918
So 99900k = 1293918
Dividing by 99900 the two sides of the egality we get:
k = 1293918/99900
We have n and m such that k = n/m = 12.95213213213213213...
n = 1293918, and m = 99900.
This should convince you that all periodic decimal are fractions.
Exercice: find two numbers n and m such that n/m =
31,2454545454545454545... = 31, 2 45 45 45 45 ...
Convince yourself that for all n and m, n/m gives always a periodic
decimal.(hint: when n is divided by m, m bounds the number of
possible
remainders).
And now geometry (without picture, do them).
Do you know that the length of the circle divided by its diameter is
PI? (PI = 3.141592...)
Do you know that the length of the square divided by its diagonal is
the square root of 2? (sqrt(2)= 1,414213562...)
- can you show this?
- can you show this without Pythagorus theorem? (like in Plato!)
Do you know if it exists n and m such that n/m = the square root of 2
(relation with incommensurability)
Do you know if the Diophantine equation x^2 = 2y^2 has a solution?
No.
I think I will prove this someday, if only to have an example of
simple, yet non trivial, proof.
This entails that the sqaure root of 2 cannot be equal to any
fraction
n/m.
And it means the square root of 2 is a non periodic decimal. (its
decimal will provide a good example of a non trivial computable
function).
Bruno
http://iridia.ulb.ac.be/~marchal/
http://iridia.ulb.ac.be/~marchal/
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Re: The seven step series
m.a. wrote:
*Going a step further... (see below)*
**
- Original Message -
From: Brent Meeker meeke...@dslextreme.com
mailto:meeke...@dslextreme.com
To: everything-list@googlegroups.com
mailto:everything-list@googlegroups.com
Sent: Wednesday, July 22, 2009 12:57 PM
Subject: Re: The seven step series
m.a. wrote:
Hi Brent,
I really appreciate the help and I hate to impose on
your patience but...(see below)
- Original Message -
From: Brent Meeker meeke...@dslextreme.com
mailto:meeke...@dslextreme.com
mailto:meeke...@dslextreme.com
To: everything-list@googlegroups.com
mailto:everything-list@googlegroups.com
mailto:everything-list@googlegroups.com
Sent: Tuesday, July 21, 2009 5:24 PM
Subject: Re: The seven step series
Take all strings of length 2
00 01 10 11
Make two copies of each
00 00 01 01 10 10 11 11
Add a 0 to the first and a 1 to the second
000001 010 011 100 101 110 111
and you have all strings of length 3.
*I can see where adding 0 to the first and 1 to the second gives 000
and
001 and I think I see how you get 010 but the rest of the permutations
don't seem obvious to me. P-l-e-a-s-e explain, Best,*
**
They aren't permutations. They're just sticking a 0 or 1 on the end.
One copy
of 01 becomes 010 and the other become 011.
*Then I assume the next step would be making two copies of each of those:*
**
*000**000 001 001 010 010 011 011
100 100 101 101 110 110
111 111*
**
*...and sticking a 0 or 1 at the end:*
**
* 000100100011 0100010101100111
1000 1001 1010 1011 1100 1101
1110 *
**
*and this is the binary sequence of length 4.*
Right, it's all the binary strings of length 4
**
*How do these translate into ordinary numerals? 1,2,3,4...*
Bruno's using them to represent sets and subsets. So if we have a set {a b c}
we can represent the subset {a c} by 101 and {a b} by 110, etc. That's quite
different from using a binary string to represent a number in positional
notation. I'll leave it to Bruno whether he wants to go into that.
Brent
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Re: Dreams and Machines
David Nyman wrote: 2009/7/23 Brent Meeker meeke...@dslextreme.com: If I understand you correctly, this is similar to the explication of I by Thomas Metzinger in his book The Ego Tunnel. He expresses it as the self being transparent. We look *through* it but not *at* it, and necessarily so. Well, I haven't read it, but yes, what I've been saying certainly implies this. This paradox arises in quantum cosmogony. The universe (or multiverse) evolves as the rotation of a single ray in Hilbert space. But relativistic horizons separate different local projections so that we see decohered, classical objects (and we are such objects). At least that's the speculation - there is both unity and diversity: different aspects of the wave-function of the universe which is unknowable. Yes, the wave function indeed expresses just such 'paradoxical partness in wholeness'. You make the self fundamental, but is it so. Maybe the self is a mathematical construct or a statistical ensemble or experiences. RITSIAR may not be real in the ontology of the best theory. No, I emphatically do not make 'the self' fundamental. In fact, taking my lead from Plotinus, Vedanta et al, I would deny the existence or necessity of any such independent existent as 'the self'. The I that I take to be real in RITSIAR is the reflexive I of the 'personally present' unity. I'm not sure I can even parse this paragraph. An I that is reflexive is one that refers to itself. So what is RITSIAR can refer to itself. So it implicitly entails a unity to refer to. Our is the unity the unity of perception, i.e. all my perceptions cohere so they are mine. They constitute a world being present to me from my point of view. 'Reflexive' because it is unique; Why would being unique imply it can refer to itself - or whatever reflexive means in this context (unconscious reaction?)? 'personal' because it is the superset out of which 'persons' (subsets) emerge; 'present' because - given that such 1-persons self-assert 'presently' Does everything RITSIAR self-assert? I understand asserting proposition, i.e. assigning a value true to it. I don't understand self-assert. - the background from which they can be said, for certain purposes, to distinguish themselves a fortiori constitutes a more inclusive 'presence'. ??? Hence I claim that 'the best theory' - whatever else it encompasses - can't help but be ontologically RITSIAR. But that's where I would appeal to two different senses of basic. Basic to epistemology is perception/intuition/experience/cognition. But based on that knowledge one may develop theory in which the ontology is different. No, I emphatically think not. This is the point of my 'collapse' of epistemology and ontology. My claim is that 'knowing' and 'being' are cognates - more specifically, 'knowing' is a 'way-of-being'. We can only know - reflexively - what we are and we can't know what we aren't. Of course one can't know a falsehood. Or are you saying we can't know anything but ourselves (a step toward solipism). Or are you saying we can only know what we are through introspection (reflection)? AFAICS this is the only way to avoiding the otherwise infinite regress between 'observer' and 'observed'. Furthermore, through the intuition or insight that 'ways-of-being' are equivalent to instances of 'self-motivated-relativisation' of the One, we situate 'causal closure' inescapably in an indivisible unity of reflexive 'perception' and 'action'. The consequence of this of course is 'no brains without minds, and vice-versa'. These are the minimal requirements, IMO, of any foundational ontology capable of going on to account for a 'mind' or 'body' that is RITSIAR - as opposed to being the kind of 'Cheshire Cat' or 'arm's length' abstraction that can't help conjuring 'philosophical zombie worlds' and other such monstrosities. To many scare quotes. Physics gains knowledge from physicists looking at records and instrument readings. But the theory built on this knowledge is in terms of elementary particles and fields. The positivists wanted to build physics on an ontology of perceptions and instrument readings, but it was not at all fruitful and has been abandoned. The trouble here, I'm convinced, is the attempt to ground the argument at a level of analysis that is already much too 'sophisticated' - what one author recently called an 'adultocentric' viewpoint. What I'm trying to do by contrast is to base my foundational theorising solely on what a 'philosophical neonate' would be able - or need - to lay claim to: IOW, the simplest and most irreducible logical pre-requisites necessary to justify the 'appearances' that our later theorising will rely on. You are concerned that RITSIAR can't be recovered if it's not asserted in the beginning, but the alternative is that the ontology of the world is real in a
Re: Dreams and Machines
Hi Brent, You are asserting monism. But the One, the ur-stuff, is ineffable/unknowable. So when we place ourselves in the world it is by making distinctions within the unity. To become distinct from the background (the One) is what it means to be RITSIAR. Right? Brent How do you know that the One, the ur-stuff, is ineffable/unknowable? If your being, for example, was the ur-stuff (I assume you mean akin to urelements in set theory), then it is effable and knowable. You have written about it, and at least two of its properties, and so it is not completely ineffable, yes? So I think it is effable even if it is exceedingly difficult to describe fully. What I'm having trouble believing is that it is unknowable. Cheers Brian --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
Brian Tenneson wrote: Hi Brent, You are asserting monism. But the One, the ur-stuff, is ineffable/unknowable. So when we place ourselves in the world it is by making distinctions within the unity. To become distinct from the background (the One) is what it means to be RITSIAR. Right? Brent How do you know that the One, the ur-stuff, is ineffable/unknowable? If your being, for example, was the ur-stuff (I assume you mean akin to urelements in set theory), then it is effable and knowable. You have written about it, and at least two of its properties, and so it is not completely ineffable, yes? So I think it is effable even if it is exceedingly difficult to describe fully. What I'm having trouble believing is that it is unknowable. In the above I was trying to paraphrase what David wrote. I don't have a final theory, but if I did it would include some ontology and that would be effable (no point in having a theory you can't use to theorize). But even if I did I don't think it would be possible to *know* that it was the final theory. So it's unknowable in that sense. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Dreams and Machines
Brent Meeker wrote: Brian Tenneson wrote: Hi Brent, You are asserting monism. But the One, the ur-stuff, is ineffable/unknowable. So when we place ourselves in the world it is by making distinctions within the unity. To become distinct from the background (the One) is what it means to be RITSIAR. Right? Brent How do you know that the One, the ur-stuff, is ineffable/unknowable? If your being, for example, was the ur-stuff (I assume you mean akin to urelements in set theory), then it is effable and knowable. You have written about it, and at least two of its properties, and so it is not completely ineffable, yes? So I think it is effable even if it is exceedingly difficult to describe fully. What I'm having trouble believing is that it is unknowable. In the above I was trying to paraphrase what David wrote. I don't have a final theory, but if I did it would include some ontology and that would be effable (no point in having a theory you can't use to theorize). But even if I did I don't think it would be possible to *know* that it was the final theory. So it's unknowable in that sense. Brent That's a very interesting point. The way science goes is that it continually doubts itself and consequently revises itself when new data come in, even if that data is paradigm-shattering. They'll gleefully justify starting a new theory that is closer to the final theory. Due to this aspect of the nature of science, science would never be able to prove its own final theory /is /a final theory. Someone like me would say, no new data has contradicted our final theory for a thousand years does *not* imply there will be a need for revision after 1,001 years. That's a form of scientific uncertainty. This uncertainty among the scientific community (ie science can't prove final theory is final) could possibly yield to other avenues of investigation such as AI, math, philosophy, and perhaps some theoretical physics (eg Tegmark). Perhaps the final theory will be completely mathematical in nature, like how mathematical M-theory is now. Then it stands to reason that the only people who could prove it is final are the mathematicians, the cog sci people, the AI computer science people, etc.. Whether it could be proven final depends on that final theory; ie the final theory should make as one of its predictions that it is the final theory. Then mathematicians (and whoever else) try to prove that theory is satisfiable which would mean it (the theory) is consistent. However, something surprising might be true, that the final theory is undecidable in the following sense: for the final theory, along with This theory is final as a statement in the theory, there is no effective procedure for determining if a generic statement is true or false. Consistency combined with undecidability is an interesting for a set of formulas (like the final theory), because while every statement is either true (or false), it may very well be that it is true (or false) and no matter how clever you are, you won't prove it true (or false, as the case may be). If knowable means you have to know the proof, then there are some statements are true but you'll never have a proof that it is true. However, there still might be an escape from not knowing:: an omniscient thing (like a perfect Turing-like machine) explaining to you how to know what was previously not known. An answer key, if you will, on any statement. You can ask what is God or what is my purpose and it will tell you something that is true but there is no proof for. But... You can't prove the answer key is the answer key. Then it becomes a question of doubt: why should I believe the answer key before me is correct? IDK, I think I'm going off on wild tangents now. My apologies. -Brian --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
