On 29 Dec 2009, at 20:57, John Mikes wrote:

> excuse me if I suggest some circularity in you reply.

You are welcome.

> A "learning machine" is by def. learning SOMETHING

Yes. Usually a total computable function, or a mechanically generable  
set, or things represented by those things.

> and that SOMETHING comes from its inside, if we do not specify an  
> 'outside' it may explore (which would not be learning, rather  
> exploring - a quite different ballgame - maybe followed by 'and  
> learning IT').

Hmm... I would say yes, and indeed much of learning procedure are  
based on exploration of some spaces of possible solutions.

And the geometry or the math of those spaces can help to accelerate  
the search, etc.

A learning machine is a machine which do the operation inverse of  
programming. An learning machine is a machine which receive as input  
the input-outputs of another machine, and which regularly output, from  
time to time, a sequence of machine M1, M2, M3, ... If that sequence  
converge on a machine having the same input/output than the one of the  
presented machine, we say that the second machine has learn the first.
Trivially, all total computable function are learnable, (by the  
constant "its program"), and the interesting concept is the study of  
classes of functions which can be recognized by a machine.
All mechanically generable classes of total computable functions are  
quasi-trivially recognized by dovetailers on those classes. There are  
no universal learner, unless you weaken the identification of function  
criteria (actually allowing an indeterminate finite number of error,  
and the right to change the explanation an infinity of times!). See  
the paper by Case and Smith.

> The applied (ball)game of 'machine' (substituted for 'learning  
> machine', excluded per se from the 'exploring' function)


> reminds me of the puzzle of my midle-school grandkid: which word is  
> the ONE spelled always incorrectly in every good dictionary? (My  
> wife found it out, immediately, not me). For the lucky guessers I  
> allow a Coke on NewYear's Eve at his own expense, of course.
> It depends on 'machine'. Independent? that. too, has to be  
> explained. Maybe B&B did.
> Your question: "Can a machine find a new thing(?)".

Can a spider find a new thing? Without judgment, nor metaphysical  
identity problem for the spider, I would say obviously "yes". Look at

Some naturalist will explain the spider did not invent anythings. I  
think they are confusing levels. If it is obvious that no individual  
spider invented the lasso, it is a fact that a lineage did it.
Eventually from deep inside, there is novelty at each instant.

> I refer to Russell's "patentable" which I wanted to address: a  
> 'new' ('patentably new'?) thing is not necessarily a (sorry for the  
> Ger.) "noch nie dagewesen" - it can be not yet described (but  
> knowable - a new combination of elements usually applied for  
> different patterns etc.). A good example is in this thread about  
> "electricity" as NOT describable to a medieval scientist: it might  
> have been "brand new" and unknown, but it still fits into the  
> 'knowables', so I think about more 'real' novelty.

Real novelty? You talk like if the dreamer could never awaken. For a  
platonist, there is a sense of saying there is no novelty at all,  
indeed there is no time, nor space. Just the natural numbers and their  
absolutely incommensurable problem of marrying addition and  
multiplication. From inside novelty is unbounded, and unavoidable, as  
a consequence of that problem. To live consists in solving the problem  
raised by living, and computers are needed to solve the problems  
raised by computers. Even in Plato Heaven, universal machine put some  
disorder and platonic shit happens.
I guess that's why universal souls can "fall". Among the novelties,  
there are good surprises and bad surprises.

> E.g. cousins of the Milky Way in outer space before the telescope.  
> That did not fit into the Flat Earth views. -  A 'better mousetrap'  
> IS 'patentable and new'.
> I agree with your ending: " How to define "new", [for example]. It  
> is a relative concept."

To have "perception", even just self-perception, you need already two  
universal machines.

No problem, there exists an infinity of them in elementary arithmetic.  
Interacting in all possible ways.
Problem: our experience fluxes are distributed among them all.  
Observable and sensible realities escapes the computable, a priori.

Happy new year,



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