2.14 Abstract constructors
The classic philosophical puzzle of the ‘ship of Theseus’ concerns the legend that after Theseus’s adventure in Crete, the Athenians made his ship a monument, replacing any plank that decayed. Eventually, none of the original planks were left. Was it still the same ship, and if not, when did it stop being so?
Though the original puzzle has little substance (being hardly more than an essentialist exercise about the meaning of ‘same’), it does illustrate a fact about the physical world which, in the prevailing conception, is counter-intuitive. Let us approximate the ship as a substrate on which a constructor, the city of Athens, is repeatedly performing the task of restoring it to its original state. To prevent it from gradually changing shape with successive renovations, some blueprint must exist, specifying the correct shape. So Athens must be a programmable constructor, with the blueprint in a program whose physical representation (say, on a scroll) is a additional substrate that Athens must keep from deteriorating. Another part of the program would be the ideas that cause generations of Athenians to keep doing that. And since different Athenians perform the task in each generation, they, too, are among the substrates on which the task is being repeatedly performed.
So, since the ship, the scroll, and Athens are all substrates, what is the constructor? By hypothesis, none of the physical objects effecting the repair survives unchanged for many generations. Only the program does: the abstract information expressed in the scroll and the ideas. So that information meets the definition of a constructor more closely than anything else in the situation. It is an abstract constructor.
There seem to be constructor-theoretic laws, such as the interoperability principle for information (Section 2.6 above), that refer directly to abstract constructors. If there are such laws, then abstract constructors cannot be omitted from fundamental physics in the constructor-theoretic conception. Readers who baulk at the idea of an abstraction causing something physical need only substitute a weaker term for ‘can cause’ in the definition of a constructor in Section 1.1, such as ‘can cause, or codes for’.
The most important kind of abstract constructor is knowledge. Knowledge is information which, once it is physically instantiated in a suitable environment, tends to cause itself to remain so: it survives criticism, testing, random noise, and errorcorrection. (Here I am adopting Popper’s (1972) conception of knowledge, in which there need be no knowing subject.) For example, the knowledge encoded in an organism’s DNA consists of abstract genes that cause the environment to transform raw materials into another instance of the organism, and thereby to keep those abstract genes, and not mutations or other variants of them, physically instantiated, despite the mutation and natural selection that keep happening. Similarly, the ideas constituting the abstract constructor for preserving the ship of Theseus would have had to include not only some relatively arbitrary information about the historical shape of the ship, but also knowledge of how to cause Athenians to preserve those ideas themselves through the generations, and to reject rival ideas.
Now consider again the set of all physically possible transformations. For almost every such transformation, the story of how it could happen is the story of how knowledge might be created and applied to cause it. Part of that story is, in almost all cases, the story of how people (intelligent beings) would create that knowledge, and of why they would retain the proposal to apply it in that way while rejecting or amending rival proposals (so a significant determinant is moral knowledge). Hence, from the constructor-theoretic perspective, physics is almost entirely the theory of the effects that knowledge (abstract constructors) can have on the physical world, via people. But again, the prevailing conception conceals this.
In constructor theory it is natural to define the wealth of an entity in a nonanthropocentric way as the set of transformations that the entity would be capable of performing without generating new knowledge. Wealth has always consisted fundamentally of knowledge, even though it has been limited by the capacity of relatively fixed installations for harnessing naturally occurring resources. Once universal constructors exist, it will consist almost entirely of knowledge.
3.15 Are we universal constructors?
I guess that neither a typical human nor human civilisation as a whole approximates a universal constructor – not because we are something less but because, I hope, we are something more: we cannot be programmed – and especially not programed to carry out arbitrary instructions for an arbitrarily long time – because we may not want to.
Since we do not have hardware to upload arbitrary information into our brains as programs, the issue comes down to this: for each possible task A , does there exist information M(A) such that if we received a message instantiating M(A) , from space, followed by the substrates of A in a legitimate input state, and a supply of naturally-occurring raw materials, we would reliably transform the substrates to the corresponding output states, and then be ready to do so again for another possible task? What would M(A) have to say, to cause us to do this?
Presumably the effective part of M(A) would be in its preamble. Could it be a threat: ‘we are immensely powerful and will destroy you unless you obey the following instructions faithfully…’? Or a trade: ‘we offer you the secret of immortality if you pass this test…’? Presumably neither would be sufficient to cause us to be just as capable of performing A again afterwards in response to another instance of M(A) . Among other things, M(A) would have to cause changes in our civilisation that prevented our ideas from moving in directions that would make us disinclined to obey future commands. Perhaps there exists some way of fooling us into making something that would destroy us after causing us to build a more straightforward universal constructor. But again, could that be done with high reliability? I think that in reality, our creativity makes it implausible that we approximate a universal constructor very closely, despite our presumed ability to build one.
If a universal constructor is possible, there must be a smallest one. It would be interesting to know what it is, and how it works. Is it at the scale of molecules? If so, it may become the centrepiece of nanotechnology. If it is much larger, then generalpurpose nanotechnology will never be independent of macroscopic control and support systems. Will it just be a curiosity (like the simplest Turing machine)? Or will it rapidly become the commonest pattern of matter in the universe, the vehicle by which knowledge comes to dominate everything that happens?
Siberia said:Thanks, Laura, after I've read yesterday's article on SoTT by Pierre, I will definitely put this book on the top of my reading list. I was absolutely shocked to learn all this: http://www.sott.net/article/279645-Mummy-why-is-Daddy-wearing-a-dress-Daddy-why-does-Mummy-have-a-moustache. I didn't know that things are SO BAD
Laura said:Pierre's book is out! It includes a discussion on Information Theory and whole bunch of other stuff.
Hard copy available within days.
Is this "Free Will"? (or an analogue of it?)Muxel said:I like the cover art of Pierre's new book. Nice!
[quote author=Reconstructing physics: The universe is information]And it has a "counterfactual" character: a message cannot carry information unless a different message is also possible.
pegasus said:Pierre, I know I was a bit jokey or breezy in my prior post but truly want you to know that I do know all the hard work and effort that went into your work.