Intelligence as Abstraction

[gusl]

mathemajician reminded me (i.e. I reminded myself by reading him) to write up my notes about intelligence, since he is trying to write a philosophical paper on intelligence at the moment.

Don't pay attention to the circularity: it's a necessary part of the philosophical process.

intelligence: the ability to create and use abstraction.
abstraction: a central feature of intelligence, whose purpose is to economize computational resources by reusing similar structures.
redundancy: randomness deficiency. Redundancy is the property of, for example, structures with similar parts. Data without redundancy is simply random noise. Redundancy is a prerequisite for meaningfulness: without redundancy, language would be unlearnable. Nature herself is highly redundant: if it weren't, science wouldn't work. See: Information Theory, Kolmogorov Complexity, Learning as Compression.

Hardcoding is the lack of abstraction. It is more efficient for specialized behavior. So it's a trade-off. However, abstraction, being a conscious process, allows a greater degree of control and flexibility; not to mention the freedom to use one's intelligence & knowledge on novel applications. Abstraction allows true "creativity".


SOME DOMAINS:

behavior type--> domain	intelligent	unintelligent
language is known to be an area in which our processing (including some "reasoning") is largely automatic and unconscious.	Abstract thought away from language. Try to generate utterance from the abstract thought.	Think in their mother tongue. Translate word by word. Sometimes even translate things like: "het weer" => "the again".
music	Solfège: map songs to sequence of abstract notes relative to the key. Once a song has been learned, a solfeger can play it in any key and on any instrument. Solfege taps into the efficient language-processing module by encoding notes as syllables (we can process language representations), which may aid not only memorization, but also improvisation and composition (after enough solfeging in a musical idiom, the musician learns a language of syllable patterns, which he can use to create novel phrases and decode them back into music).	map: songs -> sequence of finger positions
science and mathematics	* meta-science * applying proof theory to analysis (see Kohlenbach). * A good design of Mathematical Concepts may reduce cognitive burden (i.e. economize computational resources)
programming	meta-programming, modular design of code AND data, intelligent design patterns, high-level languages: code is close to specifications	hardcoding, low-level languages

intelligence (refined definition): the ability to represent abstract structures on their own. This is extremely difficult in some cases, if only because of the computational load. But abstract imagination seems inherently difficult: how can one imagine a structure which is inherently abstract? How can one picture a tree which could have either 3 or 4 branches, no more, no less? This can perhaps be done by imagining a flickering picture.

reflection and self-improvement

humans seem to be happy as long as they are learning optimally. If challenges are too hard or too easy, they will get bored.

Comments

Picky note...

[dwagoner.livejournal.com]

You assume "moveable do" solfege for the domain of all solfege. Really, "fixed do" is more common in traditional studies. More generally, I don't know if the mapping between remembering the solfege and remembering how it feels in your body to play a given piece is correct. It is like saying that remembering how to spell words as part of your speaking is more important than the feel of the words in your mouth. I don't think the domains are as separate as you are making them.

Just my 2-cents.

Re: Picky note...

[gustavolacerda.livejournal.com]

Re: FixedDo
Thanks. I actually had that down, but I've been having trouble with my version control. Now I'm wondering how I'm going to put it in there.

Would you say that working with "movable do" is more intelligent than "fixed do"? It's certainly more abstract. I guess for low-creativity performers, could be better, since it's just simpler to use "fixed do" in an instrument like piano, unless you're very good with your scales.

Re: the domains being separate
I know many people who can only play a simple tune in one instrument, even though they can play other instruments just as well. Likewise many people can only play a tune in the key they learned it, not because of motor constraints, but because of cognitive ones: they actually do not have a representation of the music independent of the specific way of playing it: the music is hard-coded in their brains.

For some reason, I tend to think that singing develops a good ear. Does that correspond to your experience?

Btw, spelling words is not a part of speaking. The mapping goes the other way: from speaking to spelling. And English is a terrible example.

Looking forward to your insights.

[dwagoner.livejournal.com]

I don't think that moveable-do is more abstract, just a different way of measuring it. It is the difference between picking up your ruler each time you want to measure something vs having a numberline printed on your desk. The advantage of fixed-do is that you are much more closely symchronized with your reading and you tend to develop a better sense of absolute pitch than with moveable-do. There is a point during learning where they start to merge. Personally, I always wished that I had been taught fixed-do.

I don't know if the experience of playing the tune on one instrument without being able to play it in other keys is an issue of cognitive constraints. Speaking from my perspective, I am a very kinesthetic learner and I have to work hard to not just quickly remember how it feels to play a piece. I would say that your explanation isn't nuanced enough for my taste. I would say not "the music is hard-coded in their brains" so much as they are "remembering the act of playing". I don't think it maps to intelligence the way you are suggesting. Just because someone isn't thinking of x abstractly doesn't speak to whether they have the ability to do so. No?

As to the spelling being part of speaking: I meant "solfege is to spelling as playing is to speaking".

I will have to think about this more.

[gustavolacerda.livejournal.com]

Just because someone isn't thinking of x abstractly doesn't speak to whether they have the ability to do so. No?

Well, I'm not making a statement about the person's general intelligence. When someone is unable to play a tune in a different key, indeed it could be that there is interference in their performance from the way they learned it (what educational theorists sometimes call "negative transfer"), but I think many many students can't play in a different key because they really lack a pure representation of the music itself, which is more abstract than finger movements.

I prefer this analogy: "solfege is to listening (to music) as spelling is to listening (to speech)"

Thanks for the thoughts. Keep them coming :-)

[mathemajician.livejournal.com]

You say that intelligence is the ability to create and use abstraction.

Ok, so what do you make a Ned Block type machine? Here's the idea: You make a huge table of all conversations that could last for 100 years and you put it into a machine. Then you simply get the machine to look up the next thing to say based on its history. Such a machine would of course easily pass a Turing test and with simple modifications to the argument you could make it pass the more difficult Total Turing Tests and so on that require more than just text communication.

Or don't you believe that the Turing Test is a sufficient test of intelligence? (Most believe that it's not necessary, but relatively few believe that it's also not sufficient)

Before taking the debate further I'll wait to hear you position on some of these things.

[gustavolacerda.livejournal.com]

Well, of course we desire simplicity too (relatively low Kolmogorov Complexity). This machine seems like "hard coding" to me.

But since one can take a conversation into exponentially many directions, I think even then no machine could pass Turing Test without genuine intelligence... unless you mean a table of all possible conversations, but this would be impossibly huge.

[mathemajician.livejournal.com]

Yes, the machine is totally hard coded. So by your definition it's not intelligent in the slightest.

And you say that no machine could pass the Turing Test without genuine intelligence, so you support the sufficiency of the Turing test.

Ok.

As you point out there is an exponential explosion in the size of the machine which makes it too big to build in reality, at least as far as we know by the laws of physics. However the point is that the machine is finite and so it's not logically impossible right?

In which case we now have the logical possibility that a non-intelligent machine could consistently pass your test for intelligence.