Re: What are numbers? What is math?

2014-02-13 Thread Russell Standish
On Thu, Feb 13, 2014 at 10:23:14AM -0800, Edgar L. Owen wrote:
 Craig,
 
 I also suspect Bruno's math skills are superior to mine, but his 
 understanding of the place of math in reality seems pretty deficient, or 
 perhaps just rigid.
 
 As I've pointed out his 8 steps may well be mathematically consistent but 
 that doesn't mean they have anything to do with the fundamental structure 
 of reality at all. To meaningfully apply a purely mathematical or logical 
 proof to reality, one must establish an actual correspondence of the 
 variables in the proof to actual variables of reality. I don't see Bruno 
 doing that at all.

The strength of Bruno's approach is that that is implicit in the
assumption of COMP. Once you assume that one's consciousness can be
implemented by a computation, then necessarily ontological reality
(whatever that is) can also be implemented by a computation. This is a
simple consequence of the Church thesis.

 
 There is no way that anything happens in his static Platonia. And there is 
 no method of selecting the structure of our actual universe from what is 
 apparently his all possible universes.
 
 He told us his theory doesn't predict the fine tuning, as this type of 
 theory must, because the fine tuning is not important in hi view.
 

It is not important for the UDA. But it is, nevertheless, not
inconsistent with the Anthropic Principle either. Bruno would say it
is necessary for the manifestation of other conciousnesses to us. I
reserve my judgement on this...

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: What are numbers? What is math?

2014-02-13 Thread Craig Weinberg
I mostly agree Edgar. I would split hairs with you about using the word 
'relationships' as a noun for the fundamentals. I see relating as an aspect 
of sense and sense-making, so that it places the capacity to relate 
(pansensitivity) as the fundamental. I think you are right about R-bits 
being identical, however I would not say that they exist in an absolute 
sense, but are rather the most restricted type of sensory relationship that 
we can detect. In this way, R-bits are not actually what make up 
macroscopic experience in an absolute sense, because our native macroscopic 
perspectives have their own primitive thresholds of sensitivity. The 
universe senses and makes sense on every level, so that humans can live 
without knowledge of atoms or R-bits and have a relatively complete 
understanding of their world, just as microphenomenal experiences are 
relatively complete without having any hint of human existence.

Craig


On Thursday, February 13, 2014 1:23:14 PM UTC-5, Edgar L. Owen wrote:

 Craig,

 I also suspect Bruno's math skills are superior to mine, but his 
 understanding of the place of math in reality seems pretty deficient, or 
 perhaps just rigid.

 As I've pointed out his 8 steps may well be mathematically consistent but 
 that doesn't mean they have anything to do with the fundamental structure 
 of reality at all. To meaningfully apply a purely mathematical or logical 
 proof to reality, one must establish an actual correspondence of the 
 variables in the proof to actual variables of reality. I don't see Bruno 
 doing that at all.

 There is no way that anything happens in his static Platonia. And there is 
 no method of selecting the structure of our actual universe from what is 
 apparently his all possible universes.

 He told us his theory doesn't predict the fine tuning, as this type of 
 theory must, because the fine tuning is not important in hi view.


 Your abacus example is A Propos to the points in my post. 

 The important insight  in my post is that all R-bits, that make up all the 
 information that constitutes the current state of the universe, are 
 identical. 

 It is the RELATIONSHIPS of these R-bits, not the R-bits themselves that 
 give us the H-numbers used in H-math. This is obvious from a proper 
 understanding of binary numbers in particular, in which it is the bits that 
 are clearly elemental, and all numbers are relationships of a single type 
 of bit, rather than being elemental in themselves.

 H-math (and Bruno) assumes that these individual numbers are what is 
 elemental and actually real and extant in reality. That there is some 
 elemental thing called prime number 17 that is an actual fixed unalterable 
 component of fundamental reality. I don't see anyway that makes sense, or 
 is necessary. it confuses understanding of actual reality...

 What actually exists fundamentally, it seems to me, is a finite number of 
 identical R-bits, rather than H-math numbers. 

 It is unclear to what extent the R-math that actually computes reality in 
 terms of these R-bits, needs any concepts like H-numbers, but to the extent 
 it does, these are relationships, part of R-math, rather than elemental 
 R-numbers themselves.

 R-numbers are just the set of all identical R-bits among which R-math can 
 define the (small?) set of relationships it needs to compute actual reality.

 It is in this sense that I stated that all actual R-numbers are all just 
 the identical R-bits which are just related and computed into all the 
 information that constitutes the universe. 

 in this sense then everything can be said to be composed of numbers=bits, 
 and only of numbers=bits. Or more properly of numbers=bits and their 
 relationships.

 Edgar

 On Wednesday, February 12, 2014 3:07:48 PM UTC-5, Craig Weinberg wrote:



 On Wednesday, February 12, 2014 11:57:11 AM UTC-5, Edgar L. Owen wrote:

 Bruno, and Craig,

 Computational reality doesn't need any notion of primes, or 17 is a 
 prime. In fact I don't see any reason why reality needs any concept even of 
 17 to compute its current state. If this is true then individual numbers 
 such as 17 are not necessary for reality to compute the universe. I suspect 
 what reality does is more 1:1 comparisons.

 E.g. when reality makes a computation to conserve and redistribute 
 particle properties among the outgoing particles of a particle interaction, 
 it doesn't need to count up 17 of anything, it just has to know they are 
 all distributed which it can do with simple 1;1 comparisons. It can do that 
 by 1:1 comparisons, not by any notion of numbers such as 1, 2, or 17 much 
 less any notion of primes.


 I suspect that in this regard Bruno may have more insight, but 
 superficially I agree with you. Just as an abacus can be used to perform 
 H-Math functions, on a physical level, all that is happening is that beads 
 are sliding to one side or another (R-Math?). I consider H-Math not to be 
 limited to humans, but more along the 

Re: What are numbers? What is math?

2014-02-13 Thread Craig Weinberg


On Thursday, February 13, 2014 6:05:34 PM UTC-5, Russell Standish wrote:

 On Thu, Feb 13, 2014 at 10:23:14AM -0800, Edgar L. Owen wrote: 
  Craig, 
  
  I also suspect Bruno's math skills are superior to mine, but his 
  understanding of the place of math in reality seems pretty deficient, or 
  perhaps just rigid. 
  
  As I've pointed out his 8 steps may well be mathematically consistent 
 but 
  that doesn't mean they have anything to do with the fundamental 
 structure 
  of reality at all. To meaningfully apply a purely mathematical or 
 logical 
  proof to reality, one must establish an actual correspondence of the 
  variables in the proof to actual variables of reality. I don't see Bruno 
  doing that at all. 

 The strength of Bruno's approach is that that is implicit in the 
 assumption of COMP. Once you assume that one's consciousness can be 
 implemented by a computation, then necessarily ontological reality 
 (whatever that is) can also be implemented by a computation. This is a 
 simple consequence of the Church thesis. 


I understand that, but my argument has never been with Bruno's approach to 
Comp, it is with the assumption of Comp itself. I have a different 
understanding of the relation between information and consciousness which 
makes more sense, and it explains why Comp is false, and why it cannot be 
proved false logically.
 

Craig
 


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 Principal, High Performance Coders 
 Visiting Professor of Mathematics  hpc...@hpcoders.com.aujavascript: 
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Re: What are numbers? What is math?

2014-02-13 Thread LizR
On 14 February 2014 07:23, Edgar L. Owen edgaro...@att.net wrote:

 Craig,

 I also suspect Bruno's math skills are superior to mine, but his
 understanding of the place of math in reality seems pretty deficient, or
 perhaps just rigid.

 As I've pointed out his 8 steps may well be mathematically consistent but
 that doesn't mean they have anything to do with the fundamental structure
 of reality at all. To meaningfully apply a purely mathematical or logical
 proof to reality, one must establish an actual correspondence of the
 variables in the proof to actual variables of reality. I don't see Bruno
 doing that at all.


What you have to do is show that either his assumptions are wrong, or that
he has made a mistake in the logical inferences he draws from them. The
correspondence with reality comes down to whether the original
assumptions are realistic (i.e. accord with reality) or not.

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Re: What are numbers? What is math?

2014-02-13 Thread LizR
On 13 February 2014 08:45, Craig Weinberg whatsons...@gmail.com wrote:

 It's not the concept of prime numbers that is political, its the
 assumption that we must agree that they are important to understanding
 consciousness. usually scientists agree with is political. I would be
 more sympathetic with in spite of what scientists/authorities agree with.

 If you agree with the axioms of comp, you have agreed that numbers are
important to understanding consciousness. In particular, Yes Doctor
doesn't work unless consciousness is digital. Of course you may disagree
with Yes Doctor - I'm not sure that I would agree, given the choice!

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Re: What are numbers? What is math?

2014-02-13 Thread LizR
It seems to me that the situation summarises as follows.

Craig disagrees with the axioms of comp, in particular with Yes Doctor
and hence parts company with Bruno at step 0.

Edgar agrees with Yes Doctor (because in his view consciousness is the
product of a computation) and hence, if he is going to disagree with comp,
needs to find a flaw in Bruno's other axioms or his logical chain of
inferences. I suspect the weak link to attack here *might* be Peano
arithmetic...

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Re: What are numbers? What is math?

2014-02-13 Thread Russell Standish
On Fri, Feb 14, 2014 at 12:14:18PM +1300, LizR wrote:
 It seems to me that the situation summarises as follows.
 
 Craig disagrees with the axioms of comp, in particular with Yes Doctor
 and hence parts company with Bruno at step 0.
 
 Edgar agrees with Yes Doctor (because in his view consciousness is the
 product of a computation) and hence, if he is going to disagree with comp,
 needs to find a flaw in Bruno's other axioms or his logical chain of
 inferences. I suspect the weak link to attack here *might* be Peano
 arithmetic...
 

I don't see why - with the Church thesis, Peano arithmetic is just as
good as any other system capable of universal computation.

Bruno takes Arithmetical Realism precisely because it is so
uncontroversial. One could equally assert the reality of any system
capable of universal computation.

When it comes to step 8, of addressing the non-robust universe move,
ISTM that this move is actually one of denying arithmetical reality,
of denying the real existence of a universal computer in fact. But I think
that would do violence to the Church thesis also.

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: What are numbers? What is math?

2014-02-13 Thread LizR
On 14 February 2014 13:33, Russell Standish li...@hpcoders.com.au wrote:

 On Fri, Feb 14, 2014 at 12:14:18PM +1300, LizR wrote:
  It seems to me that the situation summarises as follows.
 
  Craig disagrees with the axioms of comp, in particular with Yes Doctor
  and hence parts company with Bruno at step 0.
 
  Edgar agrees with Yes Doctor (because in his view consciousness is the
  product of a computation) and hence, if he is going to disagree with
 comp,
  needs to find a flaw in Bruno's other axioms or his logical chain of
  inferences. I suspect the weak link to attack here *might* be Peano
  arithmetic...
 

 I don't see why - with the Church thesis, Peano arithmetic is just as
 good as any other system capable of universal computation.


That comment isn't my opinion, it was intended for Edgar. Since he thinks
human maths is different to reality maths, it seems like the obvious
starting point (for him) if he's going to disagree with comp.

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Re: What are numbers? What is math?

2014-02-13 Thread Edgar L. Owen
Russell,

But that assumes that consciousness is prior to ontological reality, to 
actual being. That's one of the things I find most ridiculous about both 
Bruno's comp and block universes, that they assume everything is 1p 
perspectives of conscious human observers.

To me, that's just solipsism in new clothes. And it implies there was no 
reality before humans.

I think the correct view is that reality is independent of human 
perception, that it being functioning quite fine for 13.7 billion years 
before humans came along. But that humans each have their own internal 
VIEWS or SIMULATIONS of reality, which they mistake for actual human 
independent reality.

Bruno, and a few others seem to MISTAKE those internal views of reality for 
human independent reality itself. 

That's a fundamental and deadly mistake in trying to make sense of 
reality...

Edgar




On Thursday, February 13, 2014 6:05:34 PM UTC-5, Russell Standish wrote:

 On Thu, Feb 13, 2014 at 10:23:14AM -0800, Edgar L. Owen wrote: 
  Craig, 
  
  I also suspect Bruno's math skills are superior to mine, but his 
  understanding of the place of math in reality seems pretty deficient, or 
  perhaps just rigid. 
  
  As I've pointed out his 8 steps may well be mathematically consistent 
 but 
  that doesn't mean they have anything to do with the fundamental 
 structure 
  of reality at all. To meaningfully apply a purely mathematical or 
 logical 
  proof to reality, one must establish an actual correspondence of the 
  variables in the proof to actual variables of reality. I don't see Bruno 
  doing that at all. 

 The strength of Bruno's approach is that that is implicit in the 
 assumption of COMP. Once you assume that one's consciousness can be 
 implemented by a computation, then necessarily ontological reality 
 (whatever that is) can also be implemented by a computation. This is a 
 simple consequence of the Church thesis. 

  
  There is no way that anything happens in his static Platonia. And there 
 is 
  no method of selecting the structure of our actual universe from what is 
  apparently his all possible universes. 
  
  He told us his theory doesn't predict the fine tuning, as this type of 
  theory must, because the fine tuning is not important in hi view. 
  

 It is not important for the UDA. But it is, nevertheless, not 
 inconsistent with the Anthropic Principle either. Bruno would say it 
 is necessary for the manifestation of other conciousnesses to us. I 
 reserve my judgement on this... 

 -- 

  

 Prof Russell Standish  Phone 0425 253119 (mobile) 
 Principal, High Performance Coders 
 Visiting Professor of Mathematics  hpc...@hpcoders.com.aujavascript: 
 University of New South Wales  http://www.hpcoders.com.au 
  



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Re: What are numbers? What is math?

2014-02-13 Thread Russell Standish
On Thu, Feb 13, 2014 at 05:51:18PM -0800, Edgar L. Owen wrote:
 Russell,
 
 But that assumes that consciousness is prior to ontological reality, to 
 actual being. That's one of the things I find most ridiculous about both 
 Bruno's comp and block universes, that they assume everything is 1p 
 perspectives of conscious human observers.
 

That is most certainly not the case with COMP, which posits an
ontological reality that is computationally universal (in which case
it may as well be Peano arithmetic). It might be levelled at my world
view, described in Thoery of Nothingm although to be fair, I do not
make any sort of ontological commitment, but just argue that
ontological reality doesn't really have any empirical meaning.

 To me, that's just solipsism in new clothes. 

No - because in both COMP, and in my theory of nothing, the presence
of other observers is a predicted consequence. Hardly
solipsism. Perhaps you mean something else - idealism perhaps?

 And it implies there was no reality before humans.
 

If by human you mean observers in general, then yes - it does imply
that. There is no reality without observers.

 I think the correct view is that reality is independent of human 
 perception, that it being functioning quite fine for 13.7 billion years 
 before humans came along. But that humans each have their own internal 
 VIEWS or SIMULATIONS of reality, which they mistake for actual human 
 independent reality.

What evidence do you offer for this assumption?

 
 Bruno, and a few others seem to MISTAKE those internal views of reality for 
 human independent reality itself. 

It is intersubjective reality. But strictly speaking, not independent.

 
 That's a fundamental and deadly mistake in trying to make sense of 
 reality...
 

Actually, it has rather a lot of advantages for understanding as
compared with the alternatives. 


-- 


Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: What are numbers? What is math?

2014-02-13 Thread Craig Weinberg


On Thursday, February 13, 2014 8:51:18 PM UTC-5, Edgar L. Owen wrote:

 Russell,

 But that assumes that consciousness is prior to ontological reality, to 
 actual being. That's one of the things I find most ridiculous about both 
 Bruno's comp and block universes, that they assume everything is 1p 
 perspectives of conscious human observers.

 To me, that's just solipsism in new clothes. And it implies there was no 
 reality before humans.


I don't think anyone here (or anyone that I have ever spoken with, really) 
thinks that there was no reality before humans. Idealism, or the kind of 
Pansensitivity that I suggest need not have anything to do with human 
beings at all. The issue is whether anything can simply 'exist' 
independently of all possibility of experience. I think that if that were 
possible, then any form of perception or experience would be redundant and 
implausible. More importantly though, in what way would a phenomenon which 
has no possibility of detection be different than nothingness? We can 
create experiences that remind us of matter and energy just by imagining 
them, and we can derive some pleasure and meaning from that independently 
of any functional consideration, but what reason would the laws of physics 
or arithmetic have to accidentally make sensation and participation?
 


 I think the correct view is that reality is independent of human 
 perception, that it being functioning quite fine for 13.7 billion years 
 before humans came along. But that humans each have their own internal 
 VIEWS or SIMULATIONS of reality, which they mistake for actual human 
 independent reality.

 Bruno, and a few others seem to MISTAKE those internal views of reality 
 for human independent reality itself. 

 That's a fundamental and deadly mistake in trying to make sense of 
 reality...

 Edgar




 On Thursday, February 13, 2014 6:05:34 PM UTC-5, Russell Standish wrote:

 On Thu, Feb 13, 2014 at 10:23:14AM -0800, Edgar L. Owen wrote: 
  Craig, 
  
  I also suspect Bruno's math skills are superior to mine, but his 
  understanding of the place of math in reality seems pretty deficient, 
 or 
  perhaps just rigid. 
  
  As I've pointed out his 8 steps may well be mathematically consistent 
 but 
  that doesn't mean they have anything to do with the fundamental 
 structure 
  of reality at all. To meaningfully apply a purely mathematical or 
 logical 
  proof to reality, one must establish an actual correspondence of the 
  variables in the proof to actual variables of reality. I don't see 
 Bruno 
  doing that at all. 

 The strength of Bruno's approach is that that is implicit in the 
 assumption of COMP. Once you assume that one's consciousness can be 
 implemented by a computation, then necessarily ontological reality 
 (whatever that is) can also be implemented by a computation. This is a 
 simple consequence of the Church thesis. 

  
  There is no way that anything happens in his static Platonia. And there 
 is 
  no method of selecting the structure of our actual universe from what 
 is 
  apparently his all possible universes. 
  
  He told us his theory doesn't predict the fine tuning, as this type of 
  theory must, because the fine tuning is not important in hi view. 
  

 It is not important for the UDA. But it is, nevertheless, not 
 inconsistent with the Anthropic Principle either. Bruno would say it 
 is necessary for the manifestation of other conciousnesses to us. I 
 reserve my judgement on this... 

 -- 

  

 Prof Russell Standish  Phone 0425 253119 (mobile) 
 Principal, High Performance Coders 
 Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
 University of New South Wales  http://www.hpcoders.com.au 
  




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Re: What are numbers? What is math?

2014-02-13 Thread LizR
On 14 February 2014 14:51, Edgar L. Owen edgaro...@att.net wrote:

 Russell,

 But that assumes that consciousness is prior to ontological reality, to
 actual being. That's one of the things I find most ridiculous about both
 Bruno's comp and block universes, that they assume everything is 1p
 perspectives of conscious human observers.


What on earth has this got to do with block universes???

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Re: What are numbers? What is math?

2014-02-13 Thread LizR
On 14 February 2014 15:40, Russell Standish li...@hpcoders.com.au wrote:

  And it implies there was no reality before humans.

 If by human you mean observers in general, then yes - it does imply
 that. There is no reality without observers.

 What about the CMBR? When it was created there were (presumably) no
observers in existence in the universe. Are you saying it wouldn't exist if
we hadn't evolved to detect it (e.g. if humans hadn't evolved, or if we had
never invented radio telescopes) ?

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Re: What are numbers? What is math?

2014-02-13 Thread Russell Standish
On Fri, Feb 14, 2014 at 04:23:00PM +1300, LizR wrote:
 On 14 February 2014 15:40, Russell Standish li...@hpcoders.com.au wrote:
 
   And it implies there was no reality before humans.
 
  If by human you mean observers in general, then yes - it does imply
  that. There is no reality without observers.
 
  What about the CMBR? When it was created there were (presumably) no
 observers in existence in the universe. Are you saying it wouldn't exist if
 we hadn't evolved to detect it (e.g. if humans hadn't evolved, or if we had
 never invented radio telescopes) ?

Yes - exactly.

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: What are numbers? What is math?

2014-02-12 Thread Bruno Marchal


On 11 Feb 2014, at 17:07, Edgar L. Owen wrote:


All,

In a computational reality everything consists of information in the  
computational space of reality/existence, whose presence within it  
gives it its reality. By taking place within reality these  
computations produce real universe results.


All this information is ultimately quantized into a basic unit I  
call an R-bit. Thus all of reality is constructed of different  
arrangements of R-bits.


Now the basic insight is that R-bits are actually just numbers,  
let's call them R-numbers to distinguish from the H-numbers of human  
mathematics which are quite different.


This means that the actual numbers of reality are actually the real  
elemental constituents OF reality. Numbers make up reality, and  
everything in reality is constructed only of these R-numbers. R- 
numbers = R-bits.


This neatly addresses the problem of how there can be abstract  
concepts such as number that describe but aren't an actual part of  
reality. In this view there can't be, since the actual numbers of  
reality are the actual constituents of everything in reality.


As Pythagoros claimed, all is number, in the realest sense possible.


That begin to looks like comp. But still, by the FPI, the physical  
cannot appears to be made of numbers (and they are not). Physics is  
an inside view.


If you use computational reality in the standard sense, all you need  
to postulate is elementary arithmetic, but you have to retrieve both  
mind and matter from only the arithmetical relation.


Reading UDA would save a lot of time, if, like here, you seem to agree  
with the computationalist hypothesis in the cognitive science.







Now what do these R-numbers look like?

1. Every R-number is exactly the same as every other R-number. They  
are fungible or interchangeable. They do not exist in any sequences  
such as 1, 2, 3 ... They don't have ordinal or cardinal 'tags'  
attached to distinguish them. There are not different numbers, or  
different kinds of number. All numbers are exactly the same.


But this looks like nonsense to me. You are using number in a non  
standard sense, like computation.






What human H-math calls ordinal or cardinal characteristics of  
number are not intrinsic to R-numbers themselves, but are  
relationships between R-number groups and sets. These concepts are  
part of R-math, not characteristics of R-numbers.


2. R-numbers are finite. The universe contains only some finite  
number of basic R-bits, and since R-bits are themselves numbers, the  
number of numbers in the computational universe is finite. There are  
no R-number infinities.


That is ultrafinitism, probably of the physicalist type. Why not, but  
there will be difficulties with step 8.







3. The only R-numbers that exist correspond to what human H-math  
would try to think of as the non-zero positive integers up to the  
finite limit of R-bits in existence. There is no R-number 0, no  
negative R-numbers, no fractional or irrational R-numbers. These are  
examples of how human H-math generalizes and tries to extend the  
basic relational concepts of R-math to H-numbers. It is by making  
these kind of extensions and generalizations that H-math diverges  
from R-math and thus has real problems in accurately describing  
reality.


If comp is true, both physics and consciousness are independent of  
such detail.







What does R-math look like?

1. R-math is the actual computations that compute actual reality  
that compute the real empirical objective state of the information  
universe. H-math, while originally modeled on R-math has greatly  
expanded beyond that to enormous complexities which though they  
sometimes can accurately describe aspects of reality, do NOT  
actually COMPUTE it. R-math is what actually actively COMPUTES  
reality, and only what is necessary to do that.


That is magical thinking. You must avoid uses of real, reality,  
etc. This beg the entire discussion.






2. R-math is probably a rather small set of logico-mathematical  
rules, just what is necessary to actually compute reality at the  
elemental level.


You will need a universal machine or number, and you can't define what  
that means without some infinity, at least at the epistemological level.




It will include active routines such as those that compute the  
conservation of the small set of particle properties that make up  
all elemental particles, and the rules that govern the binding of  
particle properties in atomic and molecular matter.


Where do such particles come from? What are they?





3. Thus R-math consists of the logical operators of the active  
routines that actively compute reality, rather than the static  
equations and principles of H-math.



So the take away is that :

1. The universe, and everything in it, consists of information only.


What does that mean?



And that information consists only of different arrangements of  
elemental R-bits. And 

Re: What are numbers? What is math?

2014-02-12 Thread Bruno Marchal


On 11 Feb 2014, at 19:58, Craig Weinberg wrote:

I think that the opposite of everything that you are saying makes  
more sense.:


On Tuesday, February 11, 2014 11:07:07 AM UTC-5, Edgar L. Owen wrote:


So the take away is that :

1. The universe, and everything in it, consists of information only.  
And that information consists only of different arrangements of  
elemental R-bits. And these elemental R-bits are the actual numbers  
on the basis of which R-math continually computes the current state  
of the universe.


The universe, and everything in it, consists of no information, but  
only experiences which are informed through aesthetic acquaintance.  
Information consists of no elemental structures at all, but rather  
is distributed metaphorically in gaps between experiences using a  
variety quantitative shortcuts.


That makes sense with comp.





2. Thus everything in the universe is made up of numbers and only  
numbers.


Thus nothing in the universe is made up of numbers, which is why  
we have developed mathematics to enumerate what has no number itself.


Correct with comp.





3. All the things in the universe are just various arrangements and  
relationships between these numbers.


Nothing in the universe is merely an arrangement or relationship  
between numbers.


OK. (Nothing in the physical and mental universe is merely an ...)






4. These are continually being recomputed by all the interactive  
programs (all just aspects of a single universal program) that make  
up all the processes in the universe.


There are no processes in the universe which are only computations.  
Nothing in the universe depends on a continuous computation and  
nothing that interacts can be purely a program.


OK.





5. These processes follow fundamental logico-mathematical rules  
which are part of what I call the extended fine tuning (the set of   
every non-reducible aspect of reality including the rules of logic  
it follows). These are analogous to the basic machine operations of  
silicon computers.


Logico-mathematical rules are abstracted from approximation and  
insensitivity, and are appropriate only for controlling forms and  
functions from the outside in.


Correct.






6. The programs of reality are complex sequences of these elemental  
operations acting on R-numbers which are just R-bits. In general  
these sequences incorporate standard routines such as the particle  
property conservation routine.



The reality of programs is simple logical elements operating on each  
other with no profoundly meaningful application to the actual  
presence of the universe or ourselves.


Here you depart from comp.






The aggregate result is the universe we exist within which consists  
entirely of different types of information, a fact  which can be  
verified by direct objective observation.


The result is that the concepts we call number and information  
consist entirely of the same type of reductive expectations, a fact  
which can be verified by direct subjective participation.


Self-referentially relative numbers agree with you.






Our minds each internally simulate this information universe as the  
physical, dimensional universe in which mind tells us we live. These  
simulations are a convenient evolutionary illusion that enables us,  
as programs within a universe of programs, to more effectively  
compute our lives and function more successfully. They enable our  
survival as individuals and as a species. That is why they have  
evolved, even as they conceal the true underlying information nature  
of reality.



Our internal experience is informed directly by opportunities for  
quasi-veridical sensory entanglement from within, without, and  
beyond our neurology. It is the idea of information and numbers  
which is a meta-simulative technology that allows us to project our  
control beyond our physical limitations. Computation accelerates and  
amplifies existing tendencies of individual and collective users,  
both threatening and supporting our survival.


Locally. But to do a scientific (modest and sharbale) theory, we need  
to start from 3p agreement, and usually scientists agree with  
statements like 17 is prime, but not on sense, quasi-veridical,  
entanglement, etc.


Bruno




Craig


Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Craig Weinberg


On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal wrote:


 On 11 Feb 2014, at 19:58, Craig Weinberg wrote:



 Our internal experience is informed directly by opportunities for 
 quasi-veridical sensory entanglement from within, without, and beyond our 
 neurology. It is the idea of information and numbers which is a 
 meta-simulative technology that allows us to project our control beyond our 
 physical limitations. Computation accelerates and amplifies existing 
 tendencies of individual and collective users, both threatening and 
 supporting our survival.  


 Locally. But to do a scientific (modest and sharbale) theory, we need to 
 start from 3p agreement, and usually scientists agree with statements like 
 17 is prime, but not on sense, quasi-veridical, entanglement, etc.


I agree that it is an important political consideration, but I don't think 
it is a scientific consideration. At one time the starting point statements 
that authorities agree with were found in the book of Genesis.

Craig


 Bruno



 Craig


 Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Bruno Marchal


On 12 Feb 2014, at 13:24, Craig Weinberg wrote:




On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal wrote:

On 11 Feb 2014, at 19:58, Craig Weinberg wrote:




Our internal experience is informed directly by opportunities for  
quasi-veridical sensory entanglement from within, without, and  
beyond our neurology. It is the idea of information and numbers  
which is a meta-simulative technology that allows us to project our  
control beyond our physical limitations. Computation accelerates  
and amplifies existing tendencies of individual and collective  
users, both threatening and supporting our survival.


Locally. But to do a scientific (modest and sharbale) theory, we  
need to start from 3p agreement, and usually scientists agree with  
statements like 17 is prime, but not on sense, quasi-veridical,  
entanglement, etc.


I agree that it is an important political consideration, but I don't  
think it is a scientific consideration. At one time the starting  
point statements that authorities agree with were found in the book  
of Genesis.





The analogy does not work, because the statement that 17 is a prime  
number is everything but political. But if you want start a party on  
the idea that 17 is not prime, you are free to make it political. You  
will need propaganda, torture, terror, and many things like that to  
keep power, but then why not, we are used to this.


My point was only that if you want to communicate something to others,  
you have to adopt a language they understand, and start your theory  
from statement on which they can agree for the sake of the argument  
or not (that's private for the others).


If not, all what you do is already a sort of propaganda. I'm afraid.

Bruno








Craig


Bruno




Craig


Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Edgar L. Owen
Bruno, and Craig,

Computational reality doesn't need any notion of primes, or 17 is a prime. 
In fact I don't see any reason why reality needs any concept even of 17 to 
compute its current state. If this is true then individual numbers such as 
17 are not necessary for reality to compute the universe. I suspect what 
reality does is more 1:1 comparisons.

E.g. when reality makes a computation to conserve and redistribute particle 
properties among the outgoing particles of a particle interaction, it 
doesn't need to count up 17 of anything, it just has to know they are all 
distributed which it can do with simple 1;1 comparisons. It can do that by 
1:1 comparisons, not by any notion of numbers such as 1, 2, or 17 much less 
any notion of primes.

Ordinal and cardinal number, and all their properties such as odd, even or 
prime are thus characteristic of human H-math, not of the actual R-math of 
reality that actually computes the current state of the universe, at least 
so far as I can see.

Edgar



On Wednesday, February 12, 2014 11:36:29 AM UTC-5, Bruno Marchal wrote:


 On 12 Feb 2014, at 13:24, Craig Weinberg wrote:



 On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal wrote:


 On 11 Feb 2014, at 19:58, Craig Weinberg wrote:



 Our internal experience is informed directly by opportunities for 
 quasi-veridical sensory entanglement from within, without, and beyond our 
 neurology. It is the idea of information and numbers which is a 
 meta-simulative technology that allows us to project our control beyond our 
 physical limitations. Computation accelerates and amplifies existing 
 tendencies of individual and collective users, both threatening and 
 supporting our survival.  


 Locally. But to do a scientific (modest and sharbale) theory, we need to 
 start from 3p agreement, and usually scientists agree with statements like 
 17 is prime, but not on sense, quasi-veridical, entanglement, etc.


 I agree that it is an important political consideration, but I don't think 
 it is a scientific consideration. At one time the starting point statements 
 that authorities agree with were found in the book of Genesis.



 The analogy does not work, because the statement that 17 is a prime number 
 is everything but political. But if you want start a party on the idea that 
 17 is not prime, you are free to make it political. You will need 
 propaganda, torture, terror, and many things like that to keep power, but 
 then why not, we are used to this.

 My point was only that if you want to communicate something to others, you 
 have to adopt a language they understand, and start your theory from 
 statement on which they can agree for the sake of the argument or not 
 (that's private for the others).

 If not, all what you do is already a sort of propaganda. I'm afraid.

 Bruno







 Craig


 Bruno



 Craig


 Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Bruno Marchal

Edgar,


On 12 Feb 2014, at 17:57, Edgar L. Owen wrote:


Bruno, and Craig,

Computational reality doesn't need any notion of primes, or 17 is a  
prime.



Which confirms that you are using computational in a mysterious  
idiosyncratic personal sense, and I recall you that you have never  
answered my question: what do you mean by computational, reality,  
and in this case needs.






In fact I don't see any reason why reality needs any concept even of  
17 to compute its current state. If this is true then individual  
numbers such as 17 are not necessary for reality to compute the  
universe. I suspect what reality does is more 1:1 comparisons.


E.g. when reality makes a computation to conserve and redistribute  
particle properties among the outgoing particles of a particle  
interaction, it doesn't need to count up 17 of anything, it just has  
to know they are all distributed which it can do with simple 1;1  
comparisons. It can do that by 1:1 comparisons, not by any notion of  
numbers such as 1, 2, or 17 much less any notion of primes.


Ordinal and cardinal number, and all their properties such as odd,  
even or prime are thus characteristic of human H-math, not of the  
actual R-math of reality that actually computes the current state of  
the universe, at least so far as I can see.


In the theory according to which my brain (or more general) is Turing  
emulable, there is no such universe.
We don't need, and worst, cannot use, the 1p-plural evidence, for its  
existence, but we can find the stable logic of the observable (and  
normally all physical *laws*).


In my franc opinion, if you don't mind, you do a similar mistake than  
Craig, reifying your own 1p intuition. Yu have not learn how to  
communicate in the scientific matter. You seem unable to make clear  
your assumption, and you miss the opportunity to test your theory by  
comparing it with the one based on the standard definition of  
computation.


You do bad philosophy of science if you mistreat the basic definitions  
everyone agree on.


Bruno






Edgar



On Wednesday, February 12, 2014 11:36:29 AM UTC-5, Bruno Marchal  
wrote:


On 12 Feb 2014, at 13:24, Craig Weinberg wrote:




On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal  
wrote:


On 11 Feb 2014, at 19:58, Craig Weinberg wrote:




Our internal experience is informed directly by opportunities for  
quasi-veridical sensory entanglement from within, without, and  
beyond our neurology. It is the idea of information and numbers  
which is a meta-simulative technology that allows us to project  
our control beyond our physical limitations. Computation  
accelerates and amplifies existing tendencies of individual and  
collective users, both threatening and supporting our survival.


Locally. But to do a scientific (modest and sharbale) theory, we  
need to start from 3p agreement, and usually scientists agree with  
statements like 17 is prime, but not on sense, quasi-veridical,  
entanglement, etc.


I agree that it is an important political consideration, but I  
don't think it is a scientific consideration. At one time the  
starting point statements that authorities agree with were found in  
the book of Genesis.





The analogy does not work, because the statement that 17 is a prime  
number is everything but political. But if you want start a party on  
the idea that 17 is not prime, you are free to make it political.  
You will need propaganda, torture, terror, and many things like that  
to keep power, but then why not, we are used to this.


My point was only that if you want to communicate something to  
others, you have to adopt a language they understand, and start your  
theory from statement on which they can agree for the sake of the  
argument or not (that's private for the others).


If not, all what you do is already a sort of propaganda. I'm afraid.

Bruno








Craig


Bruno




Craig


Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Craig Weinberg


On Wednesday, February 12, 2014 11:36:29 AM UTC-5, Bruno Marchal wrote:


 On 12 Feb 2014, at 13:24, Craig Weinberg wrote:



 On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal wrote:


 On 11 Feb 2014, at 19:58, Craig Weinberg wrote:



 Our internal experience is informed directly by opportunities for 
 quasi-veridical sensory entanglement from within, without, and beyond our 
 neurology. It is the idea of information and numbers which is a 
 meta-simulative technology that allows us to project our control beyond our 
 physical limitations. Computation accelerates and amplifies existing 
 tendencies of individual and collective users, both threatening and 
 supporting our survival.  


 Locally. But to do a scientific (modest and sharbale) theory, we need to 
 start from 3p agreement, and usually scientists agree with statements like 
 17 is prime, but not on sense, quasi-veridical, entanglement, etc.


 I agree that it is an important political consideration, but I don't think 
 it is a scientific consideration. At one time the starting point statements 
 that authorities agree with were found in the book of Genesis.



 The analogy does not work, because the statement that 17 is a prime number 
 is everything but political.


It's not the concept of prime numbers that is political, its the assumption 
that we must agree that they are important to understanding consciousness. 
usually scientists agree with is political. I would be more sympathetic 
with in spite of what scientists/authorities agree with.
 

 But if you want start a party on the idea that 17 is not prime, you are 
 free to make it political.


You're straw manning me. I don't see that anything that I have said has to 
do with the content of arithmetic statements, only that the popularity of 
arithmetic among scientists is no reason to insist that is where we must 
begin in an investigation of consciousness.
 

 You will need propaganda, torture, terror, and many things like that to 
 keep power, but then why not, we are used to this.


Really laying on thick there. It doesn't bode well for the argument if any 
hint of a peek behind the curtain of arithmetic supremacy brings an 
evocation of cataclysmic consequences.
 


 My point was only that if you want to communicate something to others, you 
 have to adopt a language they understand, and start your theory from 
 statement on which they can agree for the sake of the argument or not 
 (that's private for the others).


I don't have a problem with that principle in general, but in this case, 
you are asking me to begin the conversation about insects by blanketing the 
garden with insecticide. You aren't factoring in the possibility that the 
framing of the discussion itself is a key component of what can be 
discussed. Once we agree to enter the silk flower greenhouse of 
mathematics, we have already lost the living meadow.


 If not, all what you do is already a sort of propaganda. I'm afraid.


I'm afraid that is more projection than you will admit.

Craig
 


 Bruno







 Craig


 Bruno



 Craig


 Edgar


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Re: What are numbers? What is math?

2014-02-12 Thread Craig Weinberg


On Wednesday, February 12, 2014 11:57:11 AM UTC-5, Edgar L. Owen wrote:

 Bruno, and Craig,

 Computational reality doesn't need any notion of primes, or 17 is a prime. 
 In fact I don't see any reason why reality needs any concept even of 17 to 
 compute its current state. If this is true then individual numbers such as 
 17 are not necessary for reality to compute the universe. I suspect what 
 reality does is more 1:1 comparisons.

 E.g. when reality makes a computation to conserve and redistribute 
 particle properties among the outgoing particles of a particle interaction, 
 it doesn't need to count up 17 of anything, it just has to know they are 
 all distributed which it can do with simple 1;1 comparisons. It can do that 
 by 1:1 comparisons, not by any notion of numbers such as 1, 2, or 17 much 
 less any notion of primes.


I suspect that in this regard Bruno may have more insight, but 
superficially I agree with you. Just as an abacus can be used to perform 
H-Math functions, on a physical level, all that is happening is that beads 
are sliding to one side or another (R-Math?). I consider H-Math not to be 
limited to humans, but more along the lines of a Bruno-Platonic set of all 
possible groupings of quantitative patterns. As enormous as that UD is, it 
is still, in my view, only a language of theoretical relations, not a 
concrete presence in the universe. What I see with comp is that, if human 
quality of consciousness were a calendar, comp takes the R-Math of January 
and the H-Math of December and assumes that February through November will 
be filled in automatically. What I see instead is that February through 
November cannot be substituted with low level 1:1 comparisons or high level 
eternal schemas, but instead must be developed in real time through real 
experiences. There can be no skipping experiences, so that even a fish does 
not have the experience of a fish if it does not arise from a context of 
inheriting lifetimes from invertebrate ancestors. I suspect that these 
experiences are not available in any structures to be simulated or modeled.

Craig


 Ordinal and cardinal number, and all their properties such as odd, even or 
 prime are thus characteristic of human H-math, not of the actual R-math of 
 reality that actually computes the current state of the universe, at least 
 so far as I can see.

 Edgar



 On Wednesday, February 12, 2014 11:36:29 AM UTC-5, Bruno Marchal wrote:


 On 12 Feb 2014, at 13:24, Craig Weinberg wrote:



 On Wednesday, February 12, 2014 5:18:21 AM UTC-5, Bruno Marchal wrote:


 On 11 Feb 2014, at 19:58, Craig Weinberg wrote:



 Our internal experience is informed directly by opportunities for 
 quasi-veridical sensory entanglement from within, without, and beyond our 
 neurology. It is the idea of information and numbers which is a 
 meta-simulative technology that allows us to project our control beyond our 
 physical limitations. Computation accelerates and amplifies existing 
 tendencies of individual and collective users, both threatening and 
 supporting our survival.  


 Locally. But to do a scientific (modest and sharbale) theory, we need to 
 start from 3p agreement, and usually scientists agree with statements like 
 17 is prime, but not on sense, quasi-veridical, entanglement, etc.


 I agree that it is an important political consideration, but I don't 
 think it is a scientific consideration. At one time the starting point 
 statements that authorities agree with were found in the book of Genesis.



 The analogy does not work, because the statement that 17 is a prime 
 number is everything but political. But if you want start a party on the 
 idea that 17 is not prime, you are free to make it political. You will need 
 propaganda, torture, terror, and many things like that to keep power, but 
 then why not, we are used to this.

 My point was only that if you want to communicate something to others, 
 you have to adopt a language they understand, and start your theory from 
 statement on which they can agree for the sake of the argument or not 
 (that's private for the others).

 If not, all what you do is already a sort of propaganda. I'm afraid.

 Bruno







 Craig


 Bruno



 Craig


 Edgar


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Re: What are numbers? What is math?

2014-02-11 Thread ghibbsa

On Tuesday, February 11, 2014 4:07:07 PM UTC, Edgar L. Owen wrote:

 All,

 In a computational reality everything consists of information in the 
 computational space of reality/existence, whose presence within it gives it 
 its reality. By taking place within reality these computations produce real 
 universe results.

 All this information is ultimately quantized into a basic unit I call an 
 R-bit. Thus all of reality is constructed of different arrangements of 
 R-bits.

 Now the basic insight is that R-bits are actually just numbers, let's call 
 them R-numbers to distinguish from the H-numbers of human mathematics which 
 are quite different.

 This means that the actual numbers of reality are actually the real 
 elemental constituents OF reality. Numbers make up reality, and everything 
 in reality is constructed only of these R-numbers. R-numbers = R-bits.

 This neatly addresses the problem of how there can be abstract concepts 
 such as number that describe but aren't an actual part of reality. In this 
 view there can't be, since the actual numbers of reality are the actual 
 constituents of everything in reality.

 As Pythagoros claimed, all is number, in the realest sense possible.


 Now what do these R-numbers look like?

 1. Every R-number is exactly the same as every other R-number. They are 
 fungible or interchangeable. They do not exist in any sequences such as 1, 
 2, 3 ... They don't have ordinal or cardinal 'tags' attached to distinguish 
 them. There are not different numbers, or different kinds of number. All 
 numbers are exactly the same. 

 What human H-math calls ordinal or cardinal characteristics of number are 
 not intrinsic to R-numbers themselves, but are relationships between 
 R-number groups and sets. These concepts are part of R-math, not 
 characteristics of R-numbers.

 2. R-numbers are finite. The universe contains only some finite number of 
 basic R-bits, and since R-bits are themselves numbers, the number of 
 numbers in the computational universe is finite. There are no R-number 
 infinities.

 3. The only R-numbers that exist correspond to what human H-math would try 
 to think of as the non-zero positive integers up to the finite limit of 
 R-bits in existence. There is no R-number 0, no negative R-numbers, no 
 fractional or irrational R-numbers. These are examples of how human H-math 
 generalizes and tries to extend the basic relational concepts of R-math to 
 H-numbers. It is by making these kind of extensions and generalizations 
 that H-math diverges from R-math and thus has real problems in accurately 
 describing reality.


 What does R-math look like?

 1. R-math is the actual computations that compute actual reality that 
 compute the real empirical objective state of the information universe. 
 H-math, while originally modeled on R-math has greatly expanded beyond that 
 to enormous complexities which though they sometimes can accurately 
 describe aspects of reality, do NOT actually COMPUTE it. R-math is what 
 actually actively COMPUTES reality, and only what is necessary to do that.

 2. R-math is probably a rather small set of logico-mathematical rules, 
 just what is necessary to actually compute reality at the elemental level. 
 It will include active routines such as those that compute the conservation 
 of the small set of particle properties that make up all elemental 
 particles, and the rules that govern the binding of particle properties in 
 atomic and molecular matter.

 3. Thus R-math consists of the logical operators of the active routines 
 that actively compute reality, rather than the static equations and 
 principles of H-math.


 So the take away is that :

 1. The universe, and everything in it, consists of information only. And 
 that information consists only of different arrangements of elemental 
 R-bits. And these elemental R-bits are the actual numbers on the basis of 
 which R-math continually computes the current state of the universe.

 2. Thus everything in the universe is made up of numbers and only numbers.

 3. All the things in the universe are just various arrangements and 
 relationships between these numbers.

 4. These are continually being recomputed by all the interactive programs 
 (all just aspects of a single universal program) that make up all the 
 processes in the universe.

 5. These processes follow fundamental logico-mathematical rules which are 
 part of what I call the extended fine tuning (the set of  every 
 non-reducible aspect of reality including the rules of logic it follows). 
 These are analogous to the basic machine operations of silicon computers. 

 6. The programs of reality are complex sequences of these elemental 
 operations acting on R-numbers which are just R-bits. In general these 
 sequences incorporate standard routines such as the particle property 
 conservation routine.


 The aggregate result is the universe we exist within which consists 
 entirely of different types of 

Re: What are numbers? What is math?

2014-02-11 Thread Craig Weinberg
I think that the opposite of everything that you are saying makes more 
sense.:

On Tuesday, February 11, 2014 11:07:07 AM UTC-5, Edgar L. Owen wrote:



 So the take away is that :

 1. The universe, and everything in it, consists of information only. And 
 that information consists only of different arrangements of elemental 
 R-bits. And these elemental R-bits are the actual numbers on the basis of 
 which R-math continually computes the current state of the universe.


The universe, and everything in it, consists of no information, but only 
experiences which are informed through aesthetic acquaintance. Information 
consists of no elemental structures at all, but rather is distributed 
metaphorically in gaps between experiences using a variety quantitative 
shortcuts. 


 2. Thus everything in the universe is made up of numbers and only numbers.


Thus nothing in the universe is made up of numbers, which is why we have 
developed mathematics to enumerate what has no number itself.
 


 3. All the things in the universe are just various arrangements and 
 relationships between these numbers.


Nothing in the universe is merely an arrangement or relationship between 
numbers.
 


 4. These are continually being recomputed by all the interactive programs 
 (all just aspects of a single universal program) that make up all the 
 processes in the universe.


There are no processes in the universe which are only computations. Nothing 
in the universe depends on a continuous computation and nothing that 
interacts can be purely a program.
 


 5. These processes follow fundamental logico-mathematical rules which are 
 part of what I call the extended fine tuning (the set of  every 
 non-reducible aspect of reality including the rules of logic it follows). 
 These are analogous to the basic machine operations of silicon computers. 


Logico-mathematical rules are abstracted from approximation and 
insensitivity, and are appropriate only for controlling forms and functions 
from the outside in.
 


 6. The programs of reality are complex sequences of these elemental 
 operations acting on R-numbers which are just R-bits. In general these 
 sequences incorporate standard routines such as the particle property 
 conservation routine.


The reality of programs is simple logical elements operating on each other 
with no profoundly meaningful application to the actual presence of the 
universe or ourselves.
 


 The aggregate result is the universe we exist within which consists 
 entirely of different types of information, a fact  which can be verified 
 by direct objective observation.


The result is that the concepts we call number and information consist 
entirely of the same type of reductive expectations, a fact which can be 
verified by direct subjective participation.
 


 Our minds each internally simulate this information universe as the 
 physical, dimensional universe in which mind tells us we live. These 
 simulations are a convenient evolutionary illusion that enables us, as 
 programs within a universe of programs, to more effectively compute our 
 lives and function more successfully. They enable our survival as 
 individuals and as a species. That is why they have evolved, even as they 
 conceal the true underlying information nature of reality.


Our internal experience is informed directly by opportunities for 
quasi-veridical sensory entanglement from within, without, and beyond our 
neurology. It is the idea of information and numbers which is a 
meta-simulative technology that allows us to project our control beyond our 
physical limitations. Computation accelerates and amplifies existing 
tendencies of individual and collective users, both threatening and 
supporting our survival.  

Craig


 Edgar



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