OT, and afraid to ask for directions Was: Re: Programming languages for the very young

From: Samuel Walters (swalters_usenet_at_yahoo.com)
Date: 01/20/04 

Date: Tue, 20 Jan 2004 08:46:04 GMT

| Brian Mastenbrook said |
> Well, kind of. We aren't born with an ability to do higher mathematics,
> though the basic symbolic structures which support it are already
> present. But when I speak of intuition, I don't speak of the fact that
> we have structures which help us learn it, I speak of the fact that it
> still has to be learned before we can use it. If this weren't the case
> then we would simply spring fully formed from our parents' foreheads.
> (Talk about your bizarre mating rituals!)

As long as I don't have to have my skull cleaved with ax to get my
students to learn math, I'll be happy.
 
>> Very young children have an innate ability to do basic arithmetic and
>> estimations of numbers, called sublimation. They know that if two
>> hand-puppets are hidden by a screen, and only one is there when the
>> screen comes back down, then something is wrong. They will visually
>> hunt for the missing puppet.

Citation:
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=6851716&dopt=Abstract

Correction: I meant to type subitizing, not sublimation. Very different
concepts.

> Amazing, isn't it, that a supposedly inexact brain is born with the
> ability to do symbolic computation like that. (Sorry, that's a whole
> different rant.)

Absolutely. I think that the strangely symbol-oriented nature is a
prerequisite for so much. With out it, there would be no language. It's
the basis for our problem-solving ability. We can see many uses for a
thing by because we can gut a metaphor from another domain, and plug new
symbols into it. I've often wondered how such a seemingly disordered mess
of neurons can produce this structure.

Have you, by chance, read Hofstadter's "Fluid Concepts and Creative
Analogies?" I'll bet you have, considering your field of research, but
perhaps not.

> The question is, is the brain doing two minus one, and determining that
> there is one missing, or are there simply two different symbolic
> representations in the brain, and what is noticed is that an object has
> disappeared? I would argue the latter.

That is an interesting question. I side with you, but believe the debate
to still be valid. I think that object persistence and subitizing are the
result of evolutionary pressures. After all, the caveman who wonders what
happened to the line that disappeared from a pride of five is more likely
to live than one who can't count that high.

It makes you wonder what other animals might have this capability, or
slightly more specific ones that are similar?

> Strangely enough, I've worked on these concepts directly. A professor
> and I used them as the basis for a simulated robot creature, and based
> on our experiences we were able to decompose some of them. Since I'm not
> feeling particularly eloquent right now, try reading the paper linked
> here and telling me if it makes any sense:
>
> Eric Berkowitz and Brian Mastenbrook. Autonomous Generation of Grounded
> Spatial Primitives for Agent Reasoning and Communication. In Proceedings
> of the 2003 International Conference on Artificial Intelligence , June
> 2003.
> http://www.cs.indiana.edu/~bmastenb/documents/ebicai03.pdf

Interesting. My favorite line was "It was even believed that by doing so,
ASPARC could acquire basic methods of arithmetic. All such efforts
failed." For some reason the bluntness made me chuckle.

I like it. Sorta SHRDLU meets Rodney Brooks meet Lakoff. From my
(un)official post as (arm)chair (quarterback) of Artificial Intelligence
research, I would like to say that I think you're on the right track.

Particularly interesting is the memory architecture. I like the way it
focuses on physical memories. That makes sense. I think a good deal of
why AI flounders (that's not a criticism, you guys are tackling a hard
problem) is that we're not really sure what the basic units of cognition
are. I mean, memory of physical action/sensory data pairs may be the
basis of it.

What does the phrase "meta-spatial perception" mean in this context? I
couldn't parse it back to the topic.

What motivated the decision to include numbers in the as atomic memories?

How was the goal data and location/orientation data communicated to
ASPARC? Specifically, I have often wondered if computer vision
researchers were tackling a different problem than the one that the human
brain tackles with vision. Perhaps the visual decomposition isn't
delivered simply in terms of object location/identity information, but
instead as some half-cooked or strange set of data that is then actively
integrated with, say, physical memories to produce a low-level diffuse
knowledge of the area. At least map-building does vary not only from
individual to individual, but there is a measurable difference between
genders. In other words, do you think this has any bearing on the
limitations and success of ASPARC?

I'm interested in knowing more. Is there any more info out there?

And now I *really* think you should read WMCF, if only to see if it has
anything to add to your ideas of human conception of infinite actions and
objects.

> I would argue that they provide a method of pulling up the intuitive
> mathematical ability by it's bootstraps, but the relation between the
> idea and this complete set of symbolic manipulations (albiet not atomic!
> see the paper above) will become more and more distant as the ideas
> become more complex. The fact that advanced symbolic reasoning can be
> intuitively grasped is what makes us learning creatures. If our brains
> were stuck with the above four manipulations only, advanced reasoning
> would be too slow to use.

Strangely, I think that we, as mathematicians, develop those metaphor
extensions and variations to a level where higher level concepts seem more
natural than the bare concepts and actually replace our natural intuition
of those concepts. I'm not talking about rote recall vs visualization of
the situation. Rote recall bridges several steps with a single recall
operation. It acts as a bridge just as ASPARC needed a cognitive bridge
to make "extend leg" + "pull body" into "step." I think you would argue
that ASPARC will need to retain both the "extend leg" and "pull body"
actions if you ever hope it to tackle variations or complications in the
problem domain.

> I certainly agree. But that world of pattern opens up even more once the
> knowlege that 3 times 5 is fifteen is at your immediate command.
> Visualising advanced concepts in terms of the basics is the right way to
> introduce a concept, and a poor way to use it - when I'm trying to solve
> a calculus problem, I don't want to stop and think /every/ time about
> what a multiplication represents, or need to do that to solve the
> problem. Presumably that knowledge is subsumed by my learned, intuitive
> understanding of algebra and geometry and trigonometry, and I can rely
> on it by proxy.

Of course, I'm not advocating that you stop to consider it /every/ time,
but it must be accessible. Try to teach a student that an integral can be
used to calculate area under a curve when they still don't grasp on a gut
level that the area of a rectangle is length times width. It's easier to
teach them "When the question asks for area under the curve, do this..."
but is it advisable?

>> Here's anecdotal evidence from a bit higher up the educational chain.
>> Freshman students invariably ask me why they can't divide a number by
>> zero. I grab a pile of scratch paper, which we always have nearby, and
>> say "If I wanted to divide this stack of papers into three, I'd do it
>> like this..." and I begin placing them one-by-one into three piles.
>> "If I wanted to divide it in two, I'd do it like this..." and then
>> divide it in two. "If I wanted to divide it into one..." I place the
>> papers one by one into a pile on the table. Then I hand them the stack
>> of papers and ask "Now that you know what division is, divide this pile
>> into zero piles and don't throw anything away!" First comes confusion,
>> then enlightenment. Through that physical metaphor, they have seen the
>> fundamental barrier to division by zero.
>
> Except that example relies on the idea that either the piece of paper is
> atomic or it is composed of atomic components. If that were not the
> case, and there were a fixed-time way to completely decompose an object,
> then it would be possible.

Of course. I'm relying on the notion that not all that is imaginable
should be considered. I could ponder all day what it would feel like to be
able to fly like superman, but it will not really get me anywhere other
considerations couldn't get me faster.

> Hopefully your visceral knowledge of physics gives rise to the above
> possiblity though. Knowing what ideas are atomic and what are not is the
> key skill of mathematics and philosophy, and should be an overt focus of
> our school curriculums.

Certainly it does. I want the student to be able to trust a rote memory
of certain kinds of facts without having to work them out all the time. I
just think it's important to be able to work them out, if necessary
because it equips the student to deal with variations. I think this theme
carries from the basement of arithmetic to the towers of theoretical
mathematics.

For instance. I know that the set of rationals is denumerable. I don't
have to recall the proof to make a decision based on that fact. I do,
however, trust it more because I can recall how it is proven, and I can
apply the same concept when I ask myself if other sets are denumerable.

> It's worse when you can just push a button and make it happen.
> Calculators are truly detrimental to the acquisition of a skill in
> detail.

In a way, I think we both had the same concept from the beginning, but
simply were coming from such distant definitions of the problem and
terminology that we thought we were disagreeing.

If you recall, this is the one point upon which I agreed in my first
response. :-P

A little bit more from the (arm)chair (quarterback) of AI:

It's amazing how evolutionary systems find evolutionary advantage in such
odd places. I once saw a show about an AI researcher who hacked an Aibo
to "learn" to walk via genetic algorithms. It did wonderfully. When he
went to show it to the press, the dog just kept wiggling in place.
Embarrassed, he took it back to the lab and, miraculously, it walked!
After much pontification, he realized that the genetic algorithms took
advantage of the friction of the thin carpet on his workbench. He had
attempted to demonstrate it on conference table.

It really makes you wonder what sort of evolutionary hacks mother nature
has done while evolving us.

I mean, could neurons be using some as-of-yet-unknown quirk of quantum
physics to communicate information around the brain? I'm not appealing to
the idea that the brain is somehow a special organ that draws mystical
energies from the quantum-mechanical aether. I'm pointing out that we're
not sure how thin of a carpet evolution can use to it's advantage.

Consider the gecko. Until recently, we were baffled by how well it was
able to stick to any surface. Turns out that, while not really quantum
mechanical forces, Van der Waals forces were it's secret. That's some
thin carpet. We studied the feet of the gecko because they seemed
extraordinary. In general, feet are mundane. What extraordinary things
are we overlooking because they're more cleverly hidden in a mundane
category?
http://www.howstuffworks.com/news-item21.htm

Sam Walters. 

-- 
Never forget the halloween documents.
http://www.opensource.org/halloween/
""" Where will Microsoft try to drag you today?
    Do you really want to go there?"""

Relevant Pages