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

Tue, 27 Jan 2015 23:22:30 -0800 

 

 

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. 

 

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. 

 

> 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.

 

 

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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