My Attitude About The Math /Science/ Logic Illiterate

[PairTheBoard]

Most people are really discussing side issues here. On the side issue of what people are capable of learning, I think the current state of the Science and Technology of Education is so primitive we are just guessing. My guess is that when the Science and Technology of Education is far far more advanced, as it will be in the future, we would be amazed at what kinds of mental skills most everbody will be able to master. Post-Phd level skills of today in SML will become basic education for everybody.

However most everybody here is missing Sklansky's main point about the Quantum Leap. How ever the MSL literate are defined and who ever is defined as Intellegent but not MSL literate, Sklansky's point is that for Problems that only require "a bit" of MSL, all other things being equal, the MSL literate person has a Quantum Advantage over the MSL non literate. The Quantum is SO large that the non literate deserves to be called a Moron in comparison to the MSL literate for purposes of work on this Problem - all other things being equal.

The thing is, Sklansky's Point is trivially valid if you define "a bit" large enough. Measuring on a scale of 1 to 100, if "a bit" means 100, ie. the problem is a MSL technical one where all the work on it is going to be applications of MSL, then you can't argue that the Literate doesn't have a huge advantage over the nonliterate. And clearly the measure of that advantage is a function of the measure of MSL involved in the Problem.

So you have a function,

A(m)

where m measures the amount of MSL involved in the Problem, and A(m) measures the advantage for the MSL literate over nonliterate - all other things being equal - in working on that Problem. Sklansky's 30%-3% figures are just a rough gauge of how many nonliterate people are available to make "all other things equal".

So, Sklansky's Point is about the SHAPE of the GRAPH of A(m). He is saying it's not linear. In fact, according to him, it is highly NonLinear and stays relatively high as m declines from 100 to 0. He is indicating there is a Sharp Dropoff somewhere in the graph and in his opinion, the Sharp Drop off is a lot closer to 0 than a lot of people think.

If he wasn't so lazy or lacking in some kind of literacy of his own, he would have done this himself. Now you have something to discuss.

PairTheBoard

[Taraz]

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I don't think the 3% and 30% figures are important, since it's obvious David pulled them out of the ether.

His main point is that a large percetnage of the population, probably a majority, seems to be unable to consitently construct/follow mildly complex logical arguments even with a decent education. Of the remainder, a relatively small fraction cultivates the talent they have for "MSL literacy".

Personally, I think the 3% and 30% figures are too low (especially the 3%). Furthermore, even David's 3% can be extremely dangerous if they think they're actually the top 0.01% (as is distressingly common).

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I would just hesitate to claim that the lack of a certain ability follows from "brain structure" and that it is immutable at birth. Especially since it's not grounded in any sort of scientific evidence. That kind of thinking leads down a very dangerous road.

[Rduke55]

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And how do you know this doesn't have to do with quality of education, life experiences, and hard work?

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It's well known that IQ is substantially inherited.
It's well known that IQ doesn't change much in adulthood.

What kind of proof do you want? Twin studies? Google them. Besides, I think it's extremely obvious that intelligent innately varies, just as height does. With an organ as complex as the brain and as sensitive to the influence of many genes, as well as prenatal development, it would have to.

Here's some reading to get you started:

http://www.newscientist.com/article.ns?id=dn1520

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I don't really want to have the debate about whether IQ is an accurate measure of anything right now. I'm pretty sure we've had that debate before. Let's just say it's unclear what IQ is really measuring.

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I think this has been done a lot here too. A lot of the time I read a post of Phil's and I think "He gets it." but for some reason when the subjects of intelligence, heredity, race, etc. comes up it's like the rational, educated poster gets possessed or something.

[born2ramble]

PTB,

Thanks for the analysis. I agree with everything you said (and believe that's DS's precise arguement) except for this:

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The Quantum is SO large that the non literate deserves to be called a Moron in comparison to the MSL literate for purposes of work on this Problem - all other things being equal.

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Correct me if I'm wrong, but, just to clarify, he's only calling the 27% morons. The minds Capable of becoming MSL literate, but who CHOOSE not to. If you fall into this 27%, then go on to pretend the MSL components of some problems don't exist: you're a moron.

And the whole point of the post is to motivate the smart-lazy type to learn some basic MSL.

[born2ramble]

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I would just hesitate to claim that the lack of a certain ability follows from "brain structure" and that it is immutable at birth. Especially since it's not grounded in any sort of scientific evidence. That kind of thinking leads down a very dangerous road.


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Sure, I tend to agree. For the sake of this argument, though, you can simply consider where everyone is at right now in life and discuss potential from there.

[Rduke55]

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Besides, I think it's extremely obvious that intelligent innately varies, just as height does.

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It's funny you pick height as an example, since that's a common trait scientists use to show how something could have both a hereditary component and a large environmental one (most famous is probably Gould's "The Mismeasure of Man").

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With an organ as complex as the brain and as sensitive to the influence of many genes, as well as prenatal development, it would have to.

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Why did you omit mentioning the massive influence of environmental factors on the brain?

[Taraz]

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Besides, I think it's extremely obvious that intelligent innately varies, just as height does.

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It's funny you pick height as an example, since that's a common trait scientists use to show how something could have both a hereditary component and a large environmental one (most famous is probably Gould's "The Mismeasure of Man").

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With an organ as complex as the brain and as sensitive to the influence of many genes, as well as prenatal development, it would have to.

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Why did you omit mentioning the massive, huge, ginormous influence of environmental factors on the brain?

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FYP [img]/images/graemlins/smile.gif[/img]

[born2ramble]

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He is indicating there is a Sharp Dropoff somewhere in the graph and in his opinion, the Sharp Drop off is a lot closer to 0 than a lot of people think.

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I think David pointed out, though, that the sharp drop off can be accounted for largely by one reason: in logical thinking, if you make one small error early on, the rest of the thought-process will be founded on unstable grounds and inherently fouled up.

The advantage comes up in the long-run, because the MSL literates, although he/she might make slightly fewer mistakes, will benefit from the extrapolated effects (i.e. messing up whole modes of thought and strings of ideas.) And it seems logical thought is important in constructing knowledge in a whole bunch of areas, and that's probably why David advocates learning a whole buncha math. Even if he never uses advanced math in practical every-day situations, the mathematician's mind (or "MSL literate") will be trained and better-suited to pick up these small errors.

[Silent A]

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Most people are really discussing side issues here. On the side issue of what people are capable of learning, I think the current state of the Science and Technology of Education is so primitive we are just guessing. My guess is that when the Science and Technology of Education is far far more advanced, as it will be in the future, we would be amazed at what kinds of mental skills most everbody will be able to master. Post-Phd level skills of today in SML will become basic education for everybody.

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Wow. This seems excessively optimistic to me. I don't think anything in history even remotely suggests that this could ever be possible unless you're thinking of completely new forms of education (not just science and technology education). For example, moving away from the teacher/student model towards directly altering the brains of individual "students".

[PairTheBoard]

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So you have a function,

A(m)

where m measures the amount of MSL involved in the Problem, and A(m) measures the advantage for the MSL literate over nonliterate - all other things being equal - in working on that Problem. Sklansky's 30%-3% figures are just a rough gauge of how many nonliterate people are available to make "all other things equal".

So, Sklansky's Point is about the SHAPE of the GRAPH of A(m). He is saying it's not linear. In fact, according to him, it is highly NonLinear and stays relatively high as m declines from 100 to 0. He is indicating there is a Sharp Dropoff somewhere in the graph and in his opinion, the Sharp Drop off is a lot closer to 0 than a lot of people think.
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Sklansky is making a significant statement beyond this. But you need to understand the A(m) graph idea first. A(m) is defined according to "all other things being equal". The only difference is a quantum between MSL literate and nonliterate. In his additional statement he wants to bring in a second variable, let's call it k. This is a non MSL element which would give a person an advantage in the non MSL area of the Problem - if there were no difference in MSL expertise. It's the measure of difference in things like knowledge or experience for Problems of this type. It could even be the advantage due to more natural intelligence or talent for working on the non MSL aspects of the problem. The variable k measures any such advantage the Non MSL literate person might have.

So Sklansky also wants to talk about the function,

A(m,k)

where k is defined as above.

When k=0, A(m,k) is just the function A(k). Recall its Graph which Sklansky asserts starts at 0 for m=0 and in some region for m relativly close to 0 jumps rapidly to a very high level. A high enough level to give the MSL literate the same advatage over the nonliterate as an average person would have over a Moron.

That's for k=0. Now, what happens as we look at that same graph for other fixed values of k? For large values of k we would expect it to take on negative values. ie. the Advantage goes to the MSL NonLiterate with the huge advantage in the non MSL aspects of the problem. This is where Sklansky suprises us with his Second Assertion. He claims that for suprisingly large fixed values of k, say k_0, the Graph of A(m,k_0) continues to look much like A(m), ie. A(m,0). He claims that the MSL Nonliterate can have a suprisingly large advantage in the Non MSL aspect of the problem and still get badly beat by the MSL literate for relatively small values of m in the Problem.

Of course this is all highly theoretical and speculative. He gives us no examples on which we can test his theory, much less any statistical evidence. It's probably a good idea for some kind of Research for somebody. Meanwhile, we can add our speculations on top of his.

It would be a big help if someone with graphics ability could post the graphs I describe above.

PairTheBoard