RE: Why is there something rather than nothing? From quantum theory to dialectics?

Wed, 28 Jan 2015 22:23:11 -0800 

 

 

From: [email protected] 
[mailto:[email protected]] On Behalf Of Bruno Marchal
Sent: Wednesday, January 28, 2015 6:44 AM
To: [email protected]
Subject: Re: Why is there something rather than nothing? From quantum theory to 
dialectics?

 

 

On 28 Jan 2015, at 08:21, 'Chris de Morsella' via Everything List wrote:





 

 

From: [email protected] 
[mailto:[email protected]] On Behalf Of John Clark
Sent: Monday, January 26, 2015 2:23 PM
To: [email protected]
Subject: Re: Why is there something rather than nothing? From quantum theory to 
dialectics?

 

On Sun, Jan 25, 2015  'Chris de Morsella' via Everything List 
<[email protected]> wrote:

 

 > I agree it is devilishly hard to produce a truly random stream and a lot of 
 > brain power has gone into trying to do so, because of the strategic 
 > importance of doing so.

 

>>It's not merely hard it can't be done, you will never be able to produce true 
>>randomness in a computer with just software, you'll need to add a hardware 
>>gadget for that.

 

Yes, granted but the best pseudo random algorithms can produce pretty good 
facsimiles that would be very hard to differentiate from a true random stream.

 

> Ten divided by three results in a non-computable number

 

Ten divided by three is a computable number, Turing meant something else by a 
non-computable number. There are algorithms that will allow you to compute a 
decimal that is arbitrarily close to 10/3 or the square root of 2 or PI or e, 
or any other real number that has a name; tell me how close you want to get 
(provided the distance isn't zero) and I'll give you a finite decimal for it. 
But Turing proved that most numbers on the Real number line, nearly all in 
fact, are not like that at all; there are no algorithms that can even give 
approximations for them.

 

I realize now, I should have used the term irrational number.

 

It's sort of ironic that although these non-computable numbers are vastly, in 
fact infinitely, more common than the computable numbers that everybody is 
familiar with nobody can point to and name a single one of them... well Chaitin 
managed to name one and called it Omega, but he couldn't point to it.

 

Omega is a construction  measures the probability that a randomly constructed 
program will halt and that “measurement” can take on an infinite number of 
values. So though it is treated as a non-computable value; it is more of a 
conceptual construction.

 

Well, there are many others, more simple than omega. Take any programming 
language, generate all the programs, on all finite imputs by lexicographical 
order (= by length, and by alphabetical order for those having the same 
length). This gives P_0, P_1, P_2, ... Then the sequence of b-inary digit 
defined by saying that the nth digit is 0 if P_n stops, and 1 if it does not 
stop gives an example of non computable sequence. Or list the sequence which 
says if P_i is the program computing a total (everywhere defined on N) function 
(I assume the programs without the inputs here): this leads to a different non 
computable sequence.

 

Note that with the first sequence as Oracle, you can still not compute the 
second (but with the second, you can compute the first). Both are 
non-computable sequence, but the second one is more "non-computable" than the 
first.

 

The non-computable is thus organized on a ladder of degrees of 
non-computability. This was studied by turing, notably, and there is en entire 
field consecrated to the study of degree of unsolvability/non-computability. 

 

This index of non-computability,… what an interesting non-apparent dimension; 
nicely put, thanks.

 

 

>>The computable is a very small portion of the truth, and universal machines 
>>are confronted to it, and they live on the border of the computable and the 
>>non-computable.

 

That seems intuitively correct. Living processes as well thrive within the edge 
zone between chaos and order, and die off when conditions become either too 
chaotic or too ordered. This is similar for many other complex catalytic 
processes as well; being in that zone seems to be a recurring emergent 
distribution pattern of most complex phenomena.

 

 

 

 

 





 

It makes perfect sense for non-computable (I refreshed myself on this) numbers 
to be vastly more numerous than computable numbers (including irrational ones); 
when you begin to think of the kinds of algorithms and program complexity to 
generate some randomly chosen very large number – say a billion digit number -- 
without special inside knowledge (e.g. no X - “the non-computable number”- is 
equal to the number one less than X plus one… or anything of that nature)

A computable but irrational number is an algorithmic bull’s eye really, the 
relatively rare case of a relatively simple recipe cooking up this endless 
numeric soup.

 

The fact that nature exhibits only computable numbers, like pi, e, gamma, etc. 
is rather strange, even with computationalism. Apparently, our existence does 
not rely on oracle, others than the stopping oracle, well emulated by ... time. 
(Thanks to that oracle, we know that the program "earthly-dinosaurs" stopped!

 

 

IF QM is correct, then we can build a circuit generating "real randomness", but 
it is not different from the first person indeterminacy, like with an iterated 
self-duplication, which illustrate without the quantum, that we can generate 
non computable numbers in a way verifiable (in some sense) by collection of 
people, like with quantum + Everett, but without assuming the quantum.

 

I find it amusing how most people mistakenly think that making a random number 
is easy, when in fact doing so – purely with software – is more than just hard; 
it has so far proven out of reach. Perhaps quantum computers may be able to. 
Otherwise we need a hardware detector of physical quantum phenomena to generate 
a random value.

 





 

> take any local section of the stream – of square root of two is instead very 
> difficult to compress

 

That's true, the entire square root of 2 decimal expansion would be easy to 
compress, but a local section of it, say just the digits from digit 1000 to 
digit 2000, would be far more difficult to compress. 

 

Precisely, and another way of making the point I was trying to make that point 
of view is often the critical driver of a contextual complexity; e.g. the 
complexity of square root of 2 is low from the bird’s eye point of view of the 
entire (infinite) output, but becomes high for points of view constrained to 
local zones somewhere along the infinite output stream.

 

>>This is not obvious. We may find an algorithm computing quickly decimals at 
>>anyy place of a computable numbers. That has been proven for the 
>>(transcendent) number PI, and it would be astonishing it could not been 
>>proven for sqrt(2), but I have not heard if that has been proved.

 

It seems to me that those proofs depend on knowledge of the algorithm/program. 
That I can see being the case. If you possess the knowledge that it is PI you 
are computing the given range in the output stream for, you have a privileged 
point of view. 

However, what if you have absolutely no knowledge of the algorithm/program that 
is responsible for generating the resultant output. It could be any infinite 
number of programs (or random collections of programs, you the observer does 
not know). All you have is a seemingly purely random series of number strings. 
If the individual number strings were kept rather short (say under 1000 
digits), then it would be unlikely that any kind of subtle patterns could 
become discernable for such a small sample size. The number of such small 
strings could be vastly numerous, with each representing a truly random order 
scrambled packet. 

The key point I am trying to make is that without a priori privileged knowledge 
of the f() being run (along an infinite recursion; resulting in infinite 
output) if the resulting output stream is highly disordered -- and hence has a 
very low quotient of compressibility -- then it would be extremely hard if not 
impossible to work back from -- even a massive -- repository of such data 
packets to the actual f() or array of f() that generated the scrambled packets. 

-Chris

 

Bruno

 





 

 

Is there a algorithm that will produce just those digits that is shorter than a 
list of those 1000 digits? Maybe there is, or maybe not, Turing also proved 
that in general there is no way to know if there is a algorithm that will 
produce a sequence of numbers that is shorter than the sequence itself; and 
even if there is and you happened to find a algorithm that worked Turing also 
proved that in general there is no way to know if it is the shortest algorithm. 
.

 

Different chunks of the output stream may be compressible to varying degrees 
(even if perhaps minutely varying degrees), but based on the highly chaotic 
nature of this particular stream – to as far out as it has been calculated by 
us – my guess is that there could be no significant compression.

Turing was a math genius; information science owes him a great deal.

 

>> By "seemingly random" I assume you mean it came from a algorithm.

 

> Yes, it is not truly random, but the chunks have been randomly scrambled in 
> the transmission

 

OK.

 

>> How is the data stream scrambled, by another algorithm or a physical random 
>> process such as radioactivity decay?  

 

> Assume by some physical random process – assume for the sake of discussion 
> that the ordering of the packets has been truly scrambled.

 

OK 

> Also need to assume that the key first packet containing the portion of the 
> number to the left of the ‘dot’ is explicitly excluded from the transmission. 
> Only packets of numbers are transmitted; no other symbols.


OK

 

> now I am not sure, perhaps square root of two will leave subtle patterns in 
> the apparently random series that a clever algorithm could pull out. This 
> possibility increases as the chunk size increases,

 

The square root of 2 has been calculated to, I don't know probably about a 
trillion digits, but regardless of the chunk size if the chunks were picked at 
random from the entire infinite sequence of digits then the probability that 
any chunk you received came from those first trillion digits that you would 
recognize would be zero. And even supposing one of the chunks you got did 
contained a sequence of 1000 digits that were identical to the first 1000 
digits of the square root of 2 that doesn't prove it came from a algorithm that 
produces the square root of 2. It has been proven that any finite sequence of 
digits you can name exists somewhere in the decimal expansion of PI or e, your 
social security number will be out there a finite distance into the expansion 
and so will the first 1000 digits of the square root of 2. So maybe the number 
they're sending you didn't come from a algorithm for the square root of 2 at 
all, maybe it came from a PI algorithm, or a e algorithm.

 

 

Exactly – you never know what algorithm, or even some other stretch of the 
infinite output stream resulting from the infinite evaluation of  2^(1/2). Any 
such coincidental knowledge could not lead back to a proof, because it could be 
produced by an infinite number of algorithms. The most that could be said is 
that the square root of 2 generates this given ordered set of digits at some 
given range of its output. But correlation does not by itself prove causation.

Now supposing these unfortunate researchers began trying to build a map of 
these data chunks mapping correlating regions of the vast array of all of their 
known physical constants and math algorithms  trying to see by brute force 
correlation if a winner would emerge. I feel that instead no winner would 
emerge. Many candidates would be eliminated, if their output was predictable 
and any one of the growing collection of perceived packets could be proved to 
be an impossible series of values for that candidate; however the ones that 
would be left would be very large (theoretically potentially infinite).

No matter how many regions of correlation were found nothing more could be said 
than that.

 

  

>> In other words will the recipient ever be able to predict what the next 
>> digit will be?

 

> I was thinking more of the strong challenge of reassembling the packets into 
> their correct order;  by working back to a proof of the function that 
> generated the output stream,

 

That would be pretty much the same thing, if you can reliably predict the next 
digit you must have figured out what the algorithm was that produced the 
digits..

 

Yes, I can see that.

-Chris

 

 John k Clark







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http://iridia.ulb.ac.be/~marchal/

 

 

 

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