March 8, 2012
to be posted on

Barry Cooper
School of Mathematics
University of Leeds
Leeds LS2 9JT
United Kingdom

Dear Barry Cooper:
I have read your article (Barry Cooper The Incomputable Reality NATURE vol. 482 no. 7386 February 23 2012 page 465) and was delighted with the puzzle you raised in the context of the 100th birthday of Alan Turing.  Can information increase in computation?  Well obviously not in an ordinary computation done by a Turing-type computer.  But I shall take the bait and attempt a “yes” answer.  Of course you will think I am loony.  But you must recognize that this is inescapable in the current context.

I was reading about the life of Turing in the other essays in the journal and thinking in a melancholy sort of way that I needed his mind to help me with an idea I am working on.  Then I thought no, I have driven strong young men to hysterics.  Sometimes they get religion.  Turing had enough emotional trouble without me.  Fear not.  I shall not get into just what this particular idea is.  Instead I shall rephrase your challenge.

Is it possible to have a new idea? 

I should think it possible.  I must distinguish between a new idea and simply putting old ideas together.  In principle that is subject to calculation.  If you could somehow encode an idea in computer language and specify what you are looking for, the computer could ring the changes on any possible idea and let you know if there is a match.  Copying and pasting seem to be what computers do best.

Darwin, much as I sometimes rail against him, had a new idea.  Evolution can be very gradual.  Aristotle said things happen by chance and what works persists, but he did not address the issue of slow change.  Newton had the idea of mass as distinct from weight.  That was new, at least so far as I know. 

Turing, according to one essay, felt that one could not be productive except in an environment with other bright people.  That is not my own experience.  My new ideas come usually after long periods of solitude obstinately maintained.  But since he had so many new ideas we must take his opinion seriously.  New ideas seem to come from outside. 

Now let me propose that if you introduce a disturbance into a chaotic system you get little effect.  Throw a wooden shoe on the trash heap and it remains a trash heap.  Throw the sabot into a mechanical loom and you get a fine mess.

As a corollary I would suggest that if you introduce an orderly element into a chaotic system you get little effect.  But if you introduce an orderly element into a system that is already highly orderly, you might get something new.  So how might the “outside” imprint new information on the brain?

By “outside” I suggest we take the knowable universe.  That universe, to all appearances, is expanding.  Now, in defiance of the formalism of thermodynamics, let as assume that an object has a location, at least an approximate location, that is independent of its temperature. 

So as the universe “expands” (the quotes mean that I am leaving an enormous amount out) energy in the form of electromagnetic radiation is diluted.  The wavelength of light gets stretched.  That is the same phenomenon as the red shift.  But an object does not change a whole lot.  It cools, on average, but we are ignoring that.  Since there is more space in which the object can lie, it takes more information to specify the location of the object, just as a telephone book for a city (back when we had telephone books) would be bigger and each number longer than an old fashioned telephone book and number when phones were few. 

Of course you run into trouble with units.  The laws of thermodynamics dictate that the knowledge of the location of an object has value, has an energy equivalent, that is dependant of the temperature of the object.  And the units work out.  But if you say the object is confined by dimensions Done, Dtwo and Dthree meters and it’s location is known for Timedwell seconds, then the units do not come out in units of energy, at least in my hands, or maybe this sign is wrong.  But if you say the Done is the diameter of the universe minus the dimension measured and Tdwell is the age of the universe minus the time the object is known about, then the units (or sign) seem to me to come out all right.

So it takes ever more information to specify the universe.  Monday predicts Tuesday only within limits.  You might say time is simply the universe expanding.  There is a subtle change in the curvature of space that is reflected in our perception of time.  Put a watch in a bank vault and it will keep time just fine.  The universe reaches right through the walls. 

The new information that keeps appearing in the universe quickly degrades.  Maybe it’s vacuum energy.  It has to start out as information.  So look into the bank vault.  There is no evidence of information accumulating.  The vault contains mostly air and is made of metal atoms well specified by the blueprint from which the bank was built but otherwise unordered, not ordered atom by atom.

But the brain is of substantial size, is highly ordered and often repeats computations so the secular target is finite.  Put new information into it and it can be manifest as a new ordering of an already orderly system.  Thus ideas seem to emerge fully formed.  They seem to come from outside.  A computer cannot do it.  It would require changing some signal being passed between elements, and that would simply crash the system.  The brain, on the other hand, has an enormous number of chemical gradients and enormous parallelism.  It won’t crash from a trifling disturbance.  (Please do not ask my friends whether that is quite true.)  And these miniscule gradients are prepared to accept orderly input.

That would mean of course that there is constant new information materializing in the brain all the time.  Only rarely does it alight on a pattern with which it can do business. 

So I would say yes, there are insights that cannot be gained, information that cannot be achieved, by Turing style computation but which the brain may be capable of harvesting. 

I would advise against applying the logic to spirituality.  It will take you scary places and then, I think if you get it right, you’ll wind up believing just what you did at the start, whatever that might be.  But what about dreams?


M. Linton Herbert

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