@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.

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"?

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.

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.

Part of the fun of the Contact Project is trying to interpret a message that has been fully gensymmed.

always ask myself: "How would I regenerate this knowledge if it were deleted from my mind?"

Gold for this.

Back when I was a teenager, I distinctly remember wondering about how one would go about calculating the distance traveled by a constantly accelerating object during a given period of time. Of course, life -- as it is want to do -- quickly distracted me, and I didn't think about the problem again until years later when I learnt about integration and thought to myself "Oh, so that's how you'd do it!" Now, I don't think I would be able to regenerate interal calculus all on my own,but I know I'm at least observant enough to notice that something was missing -- or at least I was when I was 15 -- and I think that that's an important first step; the answers that we find are strictly limited by the questions that we ask As a side note, my cousin was, at the age of 6, able to derive multiplication from addition all on his own. He is made of win.

To Mazur’s consternation, the simple test of conceptual understanding showed that his students had not grasped the basic ideas of his physics course: two-thirds of them were modern Aristotelians. “The students did well on textbook-style problems,” he explains. “They had a bag of tricks, formulas to apply. But that was solving problems by rote. They floundered on the simple word problems, which demanded a real understanding of the concepts behind the formulas.”...Serendipity provided the breakthrough he needed. Reviewing the test of conceptual understanding, Mazur twice tried to explain one of its questions to the class, but the students remained obstinately confused. “Then I did something I had never done in my teaching career,” he recalls. “I said, ‘Why don’t you discuss it with each other?’” Immediately, the lecture hall was abuzz as 150 students started talking to each other in one-on-one conversations about the puzzling question. “It was complete chaos,” says Mazur. “But within three minutes, they had figured it out. That was very surprising to me—I had just spent 10 minutes trying to explain this. But the class said, ‘OK, We’ve got it, let’s move on.’ “Here’s what happened,” he continues. “First, when one student has the right answer and the other doesn’t, the first one is more likely to convince the second—it’s hard to talk someone into the wrong answer when they have the right one. More important, a fellow student is more likely to reach them than Professor Mazur—and this is the crux of the method.

...There’s also better retention of knowledge. “In a traditional physics course, two months after taking the final exam, people are back to where they were before taking the course,” Mazur notes. “It’s shocking.” (Concentrators are an exception to this, as subsequent courses reinforce their knowledge base.) Peer-instructed students who’ve actively argued for and explained their understanding of scientific concepts hold onto their knowledge longer. Another benefit is cultivating more scientists. A comparison of intended and actual concentrators in STEM (science, technology, engineering, mathematics) fields indicates that those taught interactively are only half as likely to change to a non-STEM discipline as students in traditional courses.

http://harvardmagazine.com/2012/03/twilight-of-the-lecture

This is not too different from what I did as a teenager in school. I separated out the facts as "axioms" and "theorems", noting that the theorems can be deduced from the axioms, should I forget them. I would try to figure out how to deduce the "redundant" theorems from my axioms, which would help me remember them. As a simple example, the Law of Conservation of Momentum, is redundant and easily derived from "every force has an equal and opposite force" -- simply multiply by time. Naturally, I also immediately deduced a conservation law for center of mass -- multiply by time again. I also noted places where two facts are redundant, but I couldn't decide which was the more fundamental. Mostly I did this because I know that my memory for boring disconnected facts is rather poor -- it "shouldn't" be easier for me to remember how to derive a fact than the fact itself, but often it is anyways.

"Could I regenerate this knowledge if it were somehow deleted from my mind?"

Epistemologically, that's my biggest problem with religion-as-morality, along with using anything else that qualifies as "fiction" as a primary source of philosophy. One of my early heuristic tests to determine if a given religious individual is within reach of reason is to ask them how they think they'd be able to recreate their religion if they'd never received education/indoctrination in that religion (makes a nice lead-in to "do people who've never heard of your religion go to hell?" as well). The possibles will at least TRY to imply that gods are directly inferable from reality (though Intelligent Design is not a positive step, at least it shows they think reality is real); the lost causes give a supernatural solution ("Insert-God-Here wouldn't allow that to happen! Or if He did, He'd just make more holy books!").

If such a person's justification for morality is subjective and they just don't care that no part of it is even conceivably objective... what does that say for the relationship of any of their moral conclusions to reality?

I think that is why biology students like to dissect animals. Our relatives think it gross, but when you see with your own eyes that a body consists of organs and you trace the links between them, it feels so great...

“What I cannot create, I do not understand.” - Richard Feynman.

This feels very important.

Suppose that something *was* deleted. What was it? What am I failing to notice? 

Maybe learning to 'regenerate' the knowledge that I currently possess is going to help me 'regenerate' the knowledge that 'was deleted'.

Once i had a dispute, i told that in world with internet you don't need to know and remember facts or principles because you can just google, my opponent told that with this method you don't have general picture and understanding in your head. Now i understand that i was wrong.

@Eliezer, some interesting points in the article, I will criticize what frustrated me:

> 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.

Things do not have intrinsic meaning, rather meaning is an emergent property of
things in relation to each other: for a brain, an image of a beaver and the sound
"beaver" are just meaningless patterns of electrical signals.

Through experiencing reality the brain learns to associate patterns based on similarity, co-occurence and so on, and labels these clusters with handles in order to communicate. ’Meaning’ is the entire cluster itself, which itself bears meaning in relation to other clusters.

If you try to single out a node off the cluster, you soon find that it loses all meaning and
reverts back to meaningless noise.

> G1071(G1072, G1073)

Maybe the above does not seem dumb now? experiencing reality is basically entering and updating relationships that eventually make sense as a whole in a system.

I feel there is a huge difference in our models of reality:

In my model everything is self-referential, just one big graph where nodes barely exist (only aliases for the whole graph itself). There is no ground to knowledge, nothing ultimate. The only thing we have
is this self-referential map, from which we infer a non-phenomenological territory.

You seem to think the territory contains beavers, I claim beavers exist only in the map, as a block arbitrarily carved out of our phenomenological experience by our brain, as if it were the only way to carve a concept out of experience and not one of infinitely many valid ways (e.g. considering the beaver and the air around and not have a concept for just a beaver with no air), and as if only part experience could be considered without being impacted by the whole of experience (i.e. there is no living beaver without air).

This view is very influenced by emptiness by the way.