by Yrrah Siladnuof
[As a reviewer of articles submitted for publication in philosophy and cognitive science journals, I often encounter an idea that can be stated, roughly, as follows: So-called ‘intelligent’ programs do not actually display genuine intelligence because each one works in a particular domain, and cannot place itself outside of this domain to critically review its own responses and attitudes. More important, these programs cannot diverge from their own domain to exchange ideas on little-related or even unrelated topics, which is something that occurs regularly in conversations among humans. This is a familiar attitude that dates back to the early days of “artificial intelligence” in the 20th century. It is amazing to see this idea surviving today, several decades after the turn of the millennium, even though several people have had some interaction — in one way or another — with one or more cognitive programs which managed to maintain a reasonably smooth conversation. I present below a dialogue that took place recently between a famous critic of programmed cognition — the author of several well-known books, whose name I prefer not to disclose — and a relatively unknown program, called “Phaeaco”, which started its life at the turn of the century working in the domain of so-called “Bongard Problems” (Foundalis, 2006; also, see Hofstadter, 1979, for an early presentation explaining the origin of these problems). In the dialogue that follows, Phaeaco’s phrases are shown in italics, the critic’s responses are in straight text, while my own comments appear indented and enclosed in square brackets. We start with a particular problem which the critic gave to Phaeaco to comment on.]
Well, dear program, here is a problem I specially designed for you, one of those I was told you should be able to handle easily. Let’s see, what do you think is the reason I separated the six boxes on the left from those on the right?
The first thing I observe with a cursory look is that in each box there is a number of smaller objects arranged so as to form a larger triangle...
[Phaeaco understands large structures formed out of smaller components.]
Wait a second please, this is interesting... Which quantity do you measure to decide whether objects of arbitrary shapes are lined up?
I have a built-in tendency to consider the center of an object, and a strong bias to pay attention to points forming lines — straight or curved.
And how do you define the “center” of an object? Is this the centroid, the “center of mass” you are talking about?
I’m afraid I’m not very familiar with the terms you are using...
[As we will soon see, Phaeaco’s command of the English language is very good. The problem here is simply that Phaeaco has not encountered terms like center of mass frequently enough to have a clear idea of what they represent.]
Never mind — I suppose actually you never have the true experience of things like mass and gravity. So would you please answer my question?
[ Showing some signs of human chauvinism.]
[ Phaeaco must remember what the question was.]
I’m sorry, I don’t know how I find the center of an object. It just occurs to me.
[Phaeaco has no access to its low level built-in processes. It actually does calculate the centroid as an average of coordinates of random points that belong to the object.]
It can’t just “occur” to you. You must have been instructed to calculate it in some way by your creator.
[Showing traces of human aggressiveness...]
I suppose you’re right.
[...but Phaeaco does not follow in aggressive style.]
What do you mean “I am right”? This must be some canned ELIZA-like answer of yours. Are you serious, or are you pretending you understood the meaning of what I said? You want me to believe you don’t know what “center of mass” is but you do know what a “creator” is? Who’s your creator?
Douglas R. Hofstadter.
[At this point the critic paused for a few moments. Finally...]
Are you saying you were programmed by Prof. Hofstadter?
No, my initial programmer was Harry Foundalis, and then others followed. The person who conceived me as an idea was Prof. Hofstadter.
I thought that was Prof. Bongard. You bear his name, after all!
Prof. M. M. Bongard was the originator of 100 problems that were named after him. My architecture was conceived in Prof. Hofstadter’s mind. I thought that’s what a “creator” of a program like me is.
[Phaeaco knows the distinction between humans and programs, and a few of the different properties these two notions have. It is quite possible that nobody told Phaeaco explicitly who its creator is, but it drew an analogy between programs, humans, and their creators. It probably did this not now but a long time ago, while pondering this idea in its leisure time.]
Well, I guess it’s difficult to say who’s the creator in your case. Any of these people could be given the title — it simply depends on how one extends the familiar idea of a creator to a program like you. Anyway, it seems you have a vague grasp of the idea of a creator. So, go on. What more do you see?
[One thing the critic does not have a chance to witness is the modification in Phaeaco’s knowledge. Phaeaco actually learns at this point that the notion of a “creator” is not always given by a black-and-white definition, but can have shades of gray. Phaeaco now pauses for a few seconds as it pays more attention to the problem.]
OK... As I was saying earlier, there are these smaller objects arranged so as to form a triangle... but this is not a characteristic of the left side only... I see that the same triangular pattern appears at right, too. So, let’s pay attention to the lower-level details — let me focus on the smaller constituents...
[After a few more seconds of apparent thinking...]
It looks like the clues are on each individual side... of the triangle... some patterns... seem to be on each side, I think.
[Phrases are not generated easily as Phaeaco diverts its effort to thinking, rather than talking.]
Wait, please. On the surface, it would appear to the casual observer that you are “thinking”. Do you have any idea how many billions of possibilities you have considered within the last few seconds?
I have no idea. I don’t think there are “billions”, though. To me it appears as if I have considered very few, a handful of ideas maybe, and I managed to talk about even fewer. If you are alluding to brute-force search programs...
“Alluding”!... Wow! Your vocabulary is not so poor, after all.
...thank you! Brute-force search programs became outdated decades ago, and I am certainly not one of them. If you are referring to my processors’ instructions, then — yes, there might be several billions of them being executed, but I have no access to them. Just as you don’t have access to the billions of neurons of yours, I suppose.
That’s a rather interesting idea... However, your billions of instructions are merely calculating, while my billions of neurons are actually thinking, I should say.
[That’s a rather shaky idea, but Phaeaco cannot delve too deeply into a philosophical discussion — it just does not know enough about the subject.]
But anyway, excuse me for the interruption. Please, go on.
[Judging from the critic’s politeness, it looks like Phaeaco’s reputation was raised slightly in the critic’s eyes after the exchange of the last couple of sentences. Phaeaco tries to concentrate on the problem, once again.]
Yes, I see, it is quite clear now. Each triangular side conforms to a certain pattern. Where sides meet, patterns merge. For example, in box I-C the base line of the triangle consists of star-like things with a stem, the left side is “filled stars”, and the right one is “stars with five prongs”.
Do you think this description is violated by all boxes at right?
I don’t know, I’ll have to check. For example, in II-A,... let me see... left side is obvious... right side is “the number two”,... while the base doesn’t have a single pattern — I don’t think it does.
You’re right on this. Do you also see what’s wrong with II-B?
I can see the pattern in the base and right sides. So probably there is no pattern in the left side... Indeed, I can find no pattern there.
But wouldn’t it be OK to say that “all components of the left side consist of one polygon or circle inside another polygon or circle”? I do not think you would mind accepting this rule.
I don’t think you’re serious. By a “rule for the left side” one means a special description characterizing that side, rather than a general one which would apply equally to all three sides.
Quite right — that’s the spirit of all the boxes on the left. So, I guess this remark of yours rules out II-C as well. How about box II-D? Do you see what is wrong there?
The one thing that strikes me, before even looking for rules, is the single sun-like object at left contrasting with all the other objects which seem to conform to a single pattern.
That’s a good starting point. Let’s call the other objects “mushrooms”.
[Phaeaco can “sense” a pattern which has not been encountered before, and can refer to it even if it does not have a word for the pattern. In this case, the critic was keen enough to realize this, and kind enough to suggest a name for the pattern.]
Clearly there are rules for the other two sides. The mushrooms at right have a black stem, while the ones at bottom have filled circles inside. We could say that there is even a rule for the left side: “there is a single circle in the center of the structure”, whatever “center” would mean for something like a mushroom. So, in this sense, this box would be an example, rather than a counter-example. Are you sure you designed this right?
Quite sure. Box II-D is a counter-example.
So it seems you want me to infer a “better” description for the type-I boxes, which would rule out box II-D.
Fine. The obvious condition which has to be added to the description of type-I boxes, then, is this: All smaller structures that form the larger triangle must belong to the same “pattern”. Although this sounds vague, it is the best linguistic description I can come up with.
And a very good one, indeed. Congratulations, you have impressed me.
Now, in box II-E I clearly see rules for all three sides. The only difference here is that the triangle doesn’t stand on its base side. Do you want me to add the condition that “the larger triangle must have a base side on which to stand”?
[Phaeaco seems flattered by the critic’s compliment and exhibits a great zeal to go on and show that it can do even better.]
I see, you are very fast. Indeed, this is a condition that has to be added.
And then, in II-F I see several letters... actually nine of them, and I suppose there is some rule again for each side?
Yes, there is a rule for each side.
I trust you that there is one; so we have a large triangle standing on its base, and each component belongs to one pattern (a letter in this case), except that we have nine instead of six components as in all other boxes. So I conclude we have to add this condition, as well.
Exactly, dear program. As I had expected, this problem of mine was a breeze for you. So what do you think of this problem? Did you like it?
[ Not quite “expected”, but Phaeaco’s knowledge of human nature is insufficient to allow it to detect this subtle lie. For a similar reason Phaeaco does not understand that with the question “Did you like it?” the critic expects some kind of compliment.]
To tell you the truth, not very much. You see, the overall description of the six boxes at left seems to me extremely contrived — very artificial.
[The critic is now about to discover that Phaeaco has an ability to judge the aesthetic merits of problems — my feeling is that somehow the critic asked for it...]
You think so? How is that so?
Well, for a problem to appeal to my sense of “neatness”, it must have a relatively short description for the six boxes at left. Look at the description for the problem you designed: it would be something like,
“A triangle, formed by six smaller components, arranged so that there are three on each side. Each component follows a certain pattern. All three components on each side of the triangle must conform to one rule. Finally, the triangle must be standing on its base.”
Right. I admit this sounds a bit long. I didn’t expect you to dislike it, though — actually, to be fair, I didn’t expect that you would have an opinion on this matter. And why you don’t like long descriptions, if I may ask?
I don’t know why. Maybe it is because such a long description often results in an ambiguous problem.
What do you mean?
I mean it has so many conditions and sub-conditions that the twelve given boxes are insufficient to define it unambiguously. For example, is the large triangle always equilateral? We could assume this to be true, as all twelve triangles seem to be equilateral, but who knows — an additional box with a non-equilateral triangle could be given, either as an example, or as a counter-example, and this would either reject or support this additional condition.
[Actually, Phaeaco is wrong in guessing the reason why it does not like the given problem. Phaeaco’s penchant for simplicity is an emergent property of its lower-level pattern sensors: A simple pattern (such as a notch or a protrusion) makes Phaeaco “happy” if there is a simple way to describe the pattern through visual primitives. Phaeaco elevates this sense of “happiness” (which results from simplicity) to the level of a whole problem. At that level Phaeaco becomes conscious of the fact that it is happy with the simply-describable problem, and it can talk about this feeling. In short, Phaeaco’s creator probably never wrote an explicit rule stating that “you have to feel happy whenever Bongard problems have simple-and-not-obvious solutions”.]
Also, your design has another little flaw in box II-F. Can you see it?
You found a flaw in II-F? You mean something other than the fact that it has nine components instead of six?
Yes, it has another flaw and so it shouldn’t be there.
I didn’t think you even had time to consider anything else besides the “nine instead of six” idea when we talked about that box. Do you have “alter egos” running in parallel, and thinking while you are talking?
Come on, don’t be naive about programmed cognition. I can’t have multiple personalities at will any more than you can.
So what’s this “other flaw”?
It is that Bongard problems are usually constructed so that everything about them can be inferred from the geometry of the input, not from any other arbitrary convention. In your II-F box the components belong to the same pattern not because they share some geometric property, but by virtue of being letters. Somebody who does not know the human conventions about letters cannot place them under the same category or pattern.
Ah!... I guess you are right... I remember I had seen this condition while I was preparing myself for this meeting with you. Well, what can I say — to err is human, ha ha!
[Another little chauvinistic comment. Evidently our critic did not learn much from this interaction with Phaeaco.]
I will take this as a compliment. Normally I make more errors than humans.
So... Why don’t you show us what you can do? Can you construct a problem and give it to me to find the solution?
Certainly. In fact, I have designed quite a few over the years. Is it OK if I pick one and present it to you?
Of course, of course! Let’s see what you can do.
[Phaeaco picks up a pen and draws on a clean sheet of paper the figure shown below. While it does so, the critic watches curiously over Phaeaco’s shoulder.]
Are you “downloading” now from some internal memory image of yours?
Actually I don’t remember the exact details of the boxes when I first thought of this problem. All I remember is the main idea — the solution, that is — and I’m just coming up with examples and counter-examples to this solution.
Interesting... I thought you programs have a “photographic memory” of some sort...
[Finally Phaeaco came up with the problem shown in the figure above. The critic spent more than half an hour pondering over it, sometimes questioning Phaeaco, and occasionally attempting to elicit some hint, but to no avail. Eventually the critic gave up, muttering : “I’ll have to take this home and think it over. I’ll get back to you as soon as I find the answer.” I contacted Phaeaco several days later and it informed me that it was still expecting to receive some feedback on that problem, but, to that date, the critic had not answered back.]