> I was referring to AIXI as the perfect mathematical AI.

I will have to Google AIXI. A big point about
being mathematical is that that is about the only
solid way we can evaluate candidate work before running
software and, say, something like a Turing test.

Some math is most of why we know, well before any
software is written, that (1) heap sort will run
in n ln(n), (2) AVL trees find leaves in ln(n),
and (3) our calculations for navigating a space
craft to the outer planets will work. More
generally, the math is 'deductive' in a
severe and powerful sense and, thus, about the
only tool we have to know well in advance of, say,
writing a lot of software.

But math does not have 'truth' and, instead,
needs hypotheses. So, for hypotheses, for some
design for some software for AI, we need some.
Enough hypotheses are going to be a bit tough
to find. And math gives only some mathematical
conclusions, and we will need to know that these
are sufficient for AI; for that we will want,
likely need, a sufficiently clear definition
of AI, that is, something better than just an
empirical test such as a Turing test or
doing well on and IQ test. Tough challenge.

Instead of such usage of math, about all we have
in AI for a 'methodology' is, (1) here I have
some intuitive ideas I like, (2) with a lot
of money I can write the code and, maybe,
get it to run, and (3) trust me, that program
can read a plane geometry book with all the
proofs cut out and, then, fill in all the
proofs or some such. So, steps (1) and (2)
are, in the opinion of anyone else, say, DARPA,
'long shots', and (3)
will be heavily in the eye of the beholder.
The challenges of (1), (2), and (3) already
make AI an unpromising direction.

> The main recent advancement in machine
learning is deep learning.
It's advanced the state of the art
in machine vision and speech recognition quite a bit.

AI has been talking about 'deep knowledge' for a
long time. That was, say, in a program that
could diagnose car problems, 'knowledge' that
the engine connected to the transmission
connected to the drive shaft connected to the
differential connected to the rear wheels or
some such and, then, be able to use this
'knowledge' in 'reasoning' to diagnose
problems. E.g., a vibration could be
caused by worn U-joints.
When I was in AI, when I worked
in the field, there were plenty of people who
saw the importance of such 'deep knowledge'
but had next to nothing on really how to
make it real.

For 'deep learning', the last I heard, that was
tweaking the parameters 'deep' in some big
'neural network', basically a case of nonlinear
curve fitting. Somehow I just don't accept
that such a 'neural network' is nearly all that
makes a human brain work; that is, I'd expect
to see some promising 'organization'
at a higher level than just the little
elements for the nonlinear curve fitting.

E.g., for speech recognition, I believe an important
part of how humans do it is to take what they
heard, which is often quite noisy and by itself
just not nearly enough, and
compare it with what they know about the
subject under discussion and, then, based
on that 'background knowledge', correct the
noisy parts of what they heard. E.g., if
the subject is a cake recipe for a party
for six people, then it's not "a cup of salt"
but maybe a cup or two or three of flour.
If the subject is the history of US
presidents and war, then "I'll be j..."
may be LBJ and "sson" maybe "Nixon". Here
the speech recognition is heavily
from a base of 'subject understanding'.
An issue will be, how the heck does the
human brain sometimes make such
'corrections' so darned fast.

For image recognition, the situation has
to be in part similar but more so: I doubt that
we have even a shot at image recognition
without a 'prior library' of 'object
possibilities': That is, if we are
looking at an image, say, from
satellite, of some woods and looking
for a Russian tank hidden there,
then we need to know what a Russian
tank looks like so that we can guess
what a hidden Russian tank would look
like on the image so that we can, then,
look for that on the image. Here we
have to understand lighting, shadows,
what a Russian tank looks like from
various directions, etc. So, we are
using some real 'human knowledge'
of the real thing, the tank, we
are looking for.

E.g., my kitty cat has a food
tray. He knows well the difference
between that tray and everything
else that might be around it --
jug of detergent, toaster, bottle
of soda pop, decorative vase,
a kitchen timer. Then I can move
his food tray, and he doesn't get
confused at all. Net, what he is
doing with image recognition is
not just simplistic and, instead,
has within it a 'concept' of his
food tray, a concept that he
created. He's not stupid you know!

So, I begin to conclude that for
speech and image recognition, e.g.,
handwriting recognition, we need
a large 'base' of 'prior human
knowledge' about the 'subject area',
e.g., with 'concepts', etc.,
before we start. That is, we need
close to 'full, real AI' just to,
say, do well reading any handwriting.
From such considerations, I believe
we have a very long way to go.

Broadly one of my first cut guesses about
how to proceed would be to roll back
to something simpler in two respects.
First, start with brains smaller, hopefully
simpler, than those of humans.
Maybe start with a worm and work up to
a frog, bird, ..., in a few centuries, a
kitty cat! Second, start with the baby
animal and see how it learns once it
starts to as an egg, once it's born,
what it gets from its mother, etc.
So, eventually work up to software that
could start learning with just "Ma ma'
and proceed from there. But can't just
start with humans and "Ma ma" because
a human just born likely already has
somehow built in a lot that is crucial
we just don't have a clue about.
So, start with worms, frogs, birds,
etc.

Another idea for how to proceed is to
try for just simple 'cognition'
with just text and image input
and just text output. E.g., start
with something that can diagram
English sentences and move from there
to some 'understanding', e.g., have
made progress enough with
'meaning' that, e.g., know
when two sentences with quite different
words and grammar really mean essentially
the same thing and when they don't mean
the same thing report why not and be
able to revise one of the sentences so that
the two do mean the same thing.
So, here we are essentially assuming
that AI has to stand on some capabilities
with language -- do kitty cats have
an 'internal language'? Hmm ...! If
kitty cats don't have such an 'internal
language', then I am totally stuck!

Then with some text and
image input, the thing should be able
to cook up a good proof of the
Pythagorean theorem.

I can believe that
some software can diagram
English sentences or come close
to it, but that is just a tiny
start on what I am suggesting.
The real challenge, as I am guessing,
is to have the software keep track of
and manipulate 'meaning', whatever
the heck that is.

And I would anticipate
a 'bootstrap' approach: Postulate and
program something for doing such things
with meaning, 'teach' it, and then
look at the 'connections'
it has built internally, say, between
words and meaning, and also observe
that the thing appears to work well.
So, it's a 'bootstrap' because it
works without our having any
very good prior idea just why;
that is, we could not prove in
advance that it could work.

So, for kitty cat knowledge,
have it understand its environment
in terms of 'concepts' (part of 'meaning') hard, soft, strong, weak,
hot, cold, and, then, know when
it can use its claws to hold on to
a soft, strong, not too hot or too
cold surface, push out of the way
a hard, weak obstacle, etc.

Maybe some such research direction
could be made to work.
But I'm not holding my breath waiting.