Thanks for taking the time to do that.
What I have bolded in your quote describes what somebody might learn over time through practice in dealing intelligently with a large number of people.
It's not just self-referentiality there's quite a lot of coreferentiality involved I think it's safe to say.
How does an algorithm pack in what seems like the potentially infinite amount of info needed to make the formalization you laid out?
Thanks in advance for dealing with my questions.
Well it obviously needs to be very complex -- but that isn't necessarily as big a deal as you might think.
Because you need to understand that there is a distinction between the complexity of an
instance of an algorithm and the "original" or "base" or "class" or whatever you want to call it, algorithm.
For example, your DNA contains the algorithm(s) needed to describe you exactly as you are -- kind of. But they are only the "template" part of the algorithm, the part people talk about when they say "this algorithm was used to arrive at this state" or something like that. What is omitted in such a statement, but what is implied, is all the
data that is
included in a particular "run" or "instance" of the algorithm. In the case of you, the "template" of your DNA has produced an instance that has been "running" on data -- the environment of you and your cells -- for a long time.
Obviously, the latter is much more complex than your DNA. It would be impossible to store very much about your current state in your DNA -- there is just too much complexity in you as you are now. People think DNA has tons of storage but they are wrong -- it had tons of storage in 1970 when people's segmented core drives had only kilobytes of memory, but now when you can get terabyte drives for under $50 DNA isn't the masterpiece it used to be. The trick is that evolution led to DNA that relies upon
the laws of nature to do most of it's heavy lifting.
For instance, does DNA instruct most biochemicals on how to react? No, of course not. There is no need to -- as long as DNA instructs the cells to make the chemicals, and maybe get them in proximity, basic chemistry takes over and the reactions take place. DNA doesn't even instruct enzymes on how to catalyze -- it just instructs the cells how to make the enzymes and then nature takes over. If you wanted to embed *every* step of such an algorithm in the instructions of DNA it would require orders of magnitude more complexity than is available.
And does DNA instruct your brain on how to act given a certain situation? Does DNA instruct you on how to drive a car, or speak English, or even make fundamental inferences about causation (the most basic task of any brain) ? No, of course not. All DNA has done is given your neurons a very primitive topographical arrangement -- that of a baby. The laws of nature, combined with the environment you grew up in, leads to everything else.
So, long story short, the same kind of tricks can be used to specify a formal algorithm that has
emergent behavior vastly more complex than the formalization itself. Yes, the formalization your are asking for would be very complex, but it might not be as complex as you envision, because all that is required is the formalization of steps that
are not implicit given the laws of nature. All the other stuff -- the steps that
are implicit, that combine with the basic algorithm to generate an instance that has emergent properties and behavior -- can be omitted, and there are very many such steps.
That means you can describe an
infinite set of behavior with a
finite algorithm. Then what ends up being infinite are the various
instances of the algorithm that occur.
