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Is There A "science Of Learning"


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#1 SaxonViolence

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Posted 06 December 2012 - 06:08 PM

Friends,

I know about Mnemonics and Speed Calculating.

Both work. Both take Beaucoup Practice to utilize Efficiently and both have a Very Narrow Range of Application.

But aside from these, has anyone came up with a Genuine System that an Individual can teach himself that will increase his ability to assimilate new knowledge and skills easier and faster?

Is there even any promising stuff on the Horizon?

You know, Arithmetic teaches you to find an answer that you don't already know.

All you have to do is apply it correctly and you get an answer—the correct answer.

All Symbolic Logic seems good for, is to check the accuracy of a long argument after you've come up with it all on your own.

It isn't the Least Bit Heuristic.

What if there were an "Arithmetic of Logic", where you could sit down with a bunch of miscellaneous Facts.....

Manipulate them Mechanically, no Insight or Imagination required, and come up with an answer?

The Dude who figures that out might not get rich off his discovery.....

{If you discovered Arithmetic, how could you Patent the idea?}

But he'd take his place beside Riemann, Euclid and Godel.



Saxon Violence

Edited by SaxonViolence, 06 December 2012 - 06:09 PM.


#2 SextonBlake

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Posted 15 August 2015 - 12:26 PM

The best way to learn something is to be interested in it. Hobbyists learn massive amounts of facts that someone with no interest in that hobby could not even begin to learn.



#3 CraigD

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Posted 17 August 2015 - 05:59 AM

I’m sorry I missed this old thread 2.5 years ago, and glad Sexton bumped it yesterday!
 

What if there were an "Arithmetic of Logic", where you could sit down with a bunch of miscellaneous Facts.....

Manipulate them Mechanically, no Insight or Imagination required, and come up with an answer?

The Dude who figures that out might not get rich off his discovery.....

{If you discovered Arithmetic, how could you Patent the idea?}

But he'd take his place beside Riemann, Euclid and Godel.

Godel came to mind before I read your mention of him, SaxonViolence, because his 1931 scheme for assigning a number to every symbol in a semantic system hints at using ordinary arithmetic on formal logical propositions. (shameless plug/bump: look at my 10-year-old thread The Starburst Challenge for fun with Godel numbering)

I don’t have a very clear intuition about figuring out the “arithmetic of logic” you describe, or even if it’s possible or not, but a couple of other famous names come to mind: First, Alan Turing, for the Turing machine, which, assuming that “coming up with an answer” is computable, gives a general scheme for describing a computer that could do so; Next, Roger Penrose, for the chapter of his wonderful 1989 book The Emperor’s New Mind where he illustrates that, since there’s a one-to-one mapping between tapes for a give UTM and the positive integers, it’s possible to run every possible computer program simply by counting.

Because the number of operations (which, for Penrose’s UTM, consist of putting a 1 or a 0 symbol in the current place on the tape and moving it one place left or right) that must be performed before finding a tape that results in the UTM doing something interesting is larger than a human can perform in their lifetime, this kind of exhaustive approach requires a computer. The key problem, in addition to having a virtually fast enough computer, then, is recognizing “interesting” when it’s generated.

I’m not sure if this is anything like what you had in mind when you imagined an “arithmetic of logic”, but it’s what came to my mind.