Truly Part Of You

Followup to:  Guessing the Teacher's Password, Artificial Addition

A classic paper by Drew McDermott, "Artificial Intelligence Meets Natural Stupidity", criticized AI programs that would try to represent notions like happiness is a state of mind using a semantic network:

STATE-OF-MIND
     ^
     | IS-A
     |
HAPPINESS

And of course there's nothing inside the "HAPPINESS" node; it's just a naked LISP token with a suggestive English name.

So, McDermott says, "A good test for the disciplined programmer is to try using gensyms in key places and see if he still admires his system.  For example, if STATE-OF-MIND is renamed G1073..." then we would have IS-A(HAPPINESS, G1073) "which looks much more dubious."

Or as I would slightly rephrase the idea:  If you substituted randomized symbols for all the suggestive English names, you would be completely unable to figure out what G1071(G1072, 1073) meant.  Was the AI program meant to represent hamburgers?  Apples?  Happiness?  Who knows?  If you delete the suggestive English names, they don't grow back.

 Suppose a physicist tells you that "Light is waves", and you believe him.  You now have a little network in your head that says IS-A(LIGHT, WAVES).  If someone asks you "What is light made of?" you'll be able to say "Waves!"

As McDermott says, "The whole problem is getting the hearer to notice what it has been told.  Not 'understand', but 'notice'."  Suppose that instead the physicist told you, "Light is made of little curvy things."  (Not true, btw.)  Would you notice any difference of anticipated experience?

How can you realize that you shouldn't trust your seeming knowledge that "light is waves"?  One test you could apply is asking, "Could I regenerate this knowledge if it were somehow deleted from my mind?"

This is similar in spirit to scrambling the names of suggestively named LISP tokens in your AI program, and seeing if someone else can figure out what they allegedly "refer" to.  It's also similar in spirit to observing that while an Artificial Arithmetician can record and play back Plus-Of(Seven, Six) = Thirteen, it can't regenerate the knowledge if you delete it from memory, until another human re-enters it in the database.  Just as if you forgot that "light is waves", you couldn't get back the knowledge except the same way you got the knowledge to begin with - by asking a physicist.  You couldn't generate the knowledge for yourself, the way that physicists originally generated it.

The same experiences that lead us to formulate a belief, connect that belief to other knowledge and sensory input and motor output.  If you see a beaver chewing a log, then you know what this thing-that-chews-through-logs looks like, and you will be able to recognize it on future occasions whether it is called a "beaver" or not.  But if you acquire your beliefs about beavers by someone else telling you facts about "beavers", you may not be able to recognize a beaver when you see one.

This is the terrible danger of trying to tell an Artificial Intelligence facts which it could not learn for itself.  It is also the terrible danger of trying to tell someone about physics that they cannot verify for themselves.  For what physicists mean by "wave" is not "little squiggly thing" but a purely mathematical concept.

As Davidson observes, if you believe that "beavers" live in deserts, are pure white in color, and weigh 300 pounds when adult, then you do not have any beliefs about beavers, true or false.  Your belief about "beavers" is not right enough to be wrong.  If you don't have enough experience to regenerate beliefs when they are deleted, then do you have enough experience to connect that belief to anything at all?  Wittgenstein:  "A wheel that can be turned though nothing turns with it, is not part of the mechanism."

Almost as soon as I started reading about AI - even before I read McDermott - I realized it would be a really good idea to always ask myself:  "How would I regenerate this knowledge if it were deleted from my mind?"

The deeper the deletion, the stricter the test.  If all proofs of the Pythagorean Theorem were deleted from my mind, could I re-prove it?  I think so.  If all knowledge of the Pythagorean Theorem were deleted from my mind, would I notice the Pythagorean Theorem to re-prove?  That's harder to boast, without putting it to the test; but if you handed me a right triangle with sides 3 and 4, and told me that the length of the hypotenuse was calculable, I think I would be able to calculate it, if I still knew all the rest of my math.

What about the notion of mathematical proof?  If no one had ever told it to me, would I be able to reinvent that on the basis of other beliefs I possess?  There was a time when humanity did not have such a concept.  Someone must have invented it.  What was it that they noticed?  Would I notice if I saw something equally novel and equally important?  Would I be able to think that far outside the box?

How much of your knowledge could you regenerate?  From how deep a deletion?  It's not just a test to cast out insufficiently connected beliefs.  It's a way of absorbing a fountain of knowledge, not just one fact.

A shepherd builds a counting system that works by throwing a pebble into a bucket whenever a sheep leaves the fold, and taking a pebble out whenever a sheep returns.  If you, the apprentice, do not understand this system - if it is magic that works for no apparent reason - then you will not know what to do if you accidentally drop an extra pebble into the bucket.  That which you cannot make yourself, you cannot remake when the situation calls for it.  You cannot go back to the source, tweak one of the parameter settings, and regenerate the output, without the source.  If "Two plus four equals six" is a brute fact unto you, and then one of the elements changes to "five", how are you to know that "two plus five equals seven" when you were simply told that "two plus four equals six"?

If you see a small plant that drops a seed whenever a bird passes it, it will not occur to you that you can use this plant to partially automate the sheep-counter.  Though you learned something that the original maker would use to improve on his invention, you can't go back to the source and re-create it.

When you contain the source of a thought, that thought can change along with you as you acquire new knowledge and new skills.  When you contain the source of a thought, it becomes truly a part of you and grows along with you.

Strive to make yourself the source of every thought worth thinking.  If the thought originally came from outside, make sure it comes from inside as well.  Continually ask yourself:  "How would I regenerate the thought if it were deleted?"  When you have an answer, imagine that knowledge being deleted as well.  And when you find a fountain, see what else it can pour.

Comments

[Nominull]

I make it a habit to learn as little as possible by rote, and just derive what I need when I need it. This means my knowledge is already heavily compressed, so if you start plucking out pieces of it at random, it becomes unrecoverable fairly quickly. As near as I can tell, my knowledge rarely vanishes for no good reason, though, so I have not really found this to be a handicap.

[Bob]

Reminds me of the time that my daughter asked me how to solve a polynomial equation. Many moons removed from basic algebra I had to start from scratch and quickly ended up with the quadratic equation without realizing where I was going until the end. It was a satisfying experience although there's no way to tell how much the work was guided by faint memories.

[Sharper]

A valuable method of learning math is to start at the beginning of recorded history and read the math-related texts that were produced by the people who made important contributions to the progression of mathematical understanding.

By the time you get to Newton, you understand the basic concepts of everything and where it all comes from much better than if you had just seen them in a textbook or heard a lecture.

Of course, speaking from experience, reading page after page of Euclid's proofs can be exhausting to continue to pay enough mental attention to actual understand them before moving on to the next one. :)

Still, it does help tremendously to be able to place the knowledge in the mental context of people who actually needed and made the advances.

[Harold]

@Sharper: There's actually a school that teaches math (and other things) that way, St John's College in the US (http://en.wikipedia.org/wiki/St._John's_College%2C_U.S). Fascinating place.

[Doug S.]

I make it a habit to learn as little as possible by rote, and just derive what I need when I need it. This means my knowledge is already heavily compressed, so if you start plucking out pieces of it at random, it becomes unrecoverable fairly quickly.

This is why I find learning a foreign language to be extremely difficult. There's no way to derive the word for "desk" in another language from anything other than the word itself. There's no algorithm for an English-Spanish dictionary that's significantly simpler than a huge lookup table. (There's a reason it takes babies years to learn to talk!)

[Bob Bane]

I make it a habit to learn as little as possible by rote, and just derive what I need when I need it.

Do realize that you're trading efficiency (as in speed of access in normal use) for that space saving in your brain. Memorizing stuff allows you to move on and save your mental deducing cycles for really new stuff.

Back when I was memorizing the multiplication tables, I noticed that

9 x N = 10 x (N-1) + (9 - (N-1))

That is, 9 x 8 = 70 + 2

So, I never memorized the 9's the same way I did all the other single digit multiplications. To this day I'm slightly slower doing math with the digit 9. The space/effort saving was worth it when I was 8 years old, but definitely not today.

[Dynamically Linked]

So, what about the notion of mathematical proof? Anyone want to give a shot at explaining how that can be regenerated?

[Silas]

Dynamically_Linked: On that one, I'm having a hard time understanding what exactly is being regenerated. If it's just a matter of "systematizing the process of deducing from assumptions", then it doesn't sound hard. The question is just -- what knowledge do I have before that, on which I'm supposed to come up with the concept? What's the "the sides of this triangle are 3 and 4 and this angle is right, and the hypotenuse is calculable"?

[LG]

Very good post -- I think it'd be helpful to have a series of examples of knowledge being regenerated. Then people could really get your idea and use it.

[Stefan Pernar]

Life is full of contradictions. Your boss wants you to work more, you want to spend more time with your family. On the one hand you need the salary to support your family and on the other hand you need a private life to enjoy yourself, recharge and be ready again to work some more. Do you work to live, or do you live to work? Can the question even be answered with a simple 'yes' or 'no'? Assuming you do not live to work - then why do you work? And the other way around: if you do not work to live, then why do you live? That is a contradiction.

But life is not a matter of yes or no questions. Or is life a matter of yes and no questions? This is a clear 'yes or no question' and clearly a matter concerning life. Assuming life is, then it would not be a matter of yes or no questions and the statement 'Life is not a matter of yes or no questions' would be false, assuming on the other hand that life is a matter of yes and no questions then the statement would be false as well. No matter how you approach it the statement is always false but you nevertheless agree with it. Another contradiction - how can this be?

The answer is of course the middle ground. You do not only work just to life and you do not only life just to work. Being the smart person that you are you look at you options, understand the consequences and strike a compromise. Work some so you can life some so you can work some more... A part of your salary is flowing back into your next salary by allowing you to recharge and a part of your life supported by your salary is the cause that lets you recharge in order to earn more salary. It is a recursive self referencing feedback loop - like a Moebius snail.

How to understand this recursive self-referencing feedback loop - let us call it the Moebius effect - to know what you have to do, is what I want to help you realize.

[a]

Those "meaningless" tokens aren't only used in one place, however. If you had a bunch of other facts including the tokens involved, like "waves produce interference patterns when they interact" and "light produces interference patterns when it interacts", then you can regenerate "light is waves" if it is lost.

Similarly, while "happiness is a state of mind" is not enough to define happiness, a lot of other facts about it certainly would. The fact that it is a state of mind would also let us apply facts we know about states of mind, giving us even more information about happiness.