That's precisely the fundamentals of France classes préparatoires (or casually prépa): iterate swiftly and efficiently on knowledge by challenging yourself to the upper limit... and above: there are quite a bunch of things I never ever thought I would be able to grasp, let alone master, yet I did, and more.
In our three-hour lesson that morning, he taught me a full semester of Berklee's harmony courses.
The first year's Mathematics course started with a single day during which we re-learned everything we though we knew about Mathematics that we learnt during the last three years. Yes, we covered three years worth in one day. It was an eye opener about the field of Mathematics as a whole. Physics course took another yet similar in goal approach.
The second year began with a full week Math course during which we re-learned everything we learned during that first year. This gave us a perspective of how far we've come but also at how challenging the coming year would be. I actually failed that second year the first time, although barely so I retried, with success.
It's extremely sad that this system is unpopular because it's perceived as elitist and inegalitarian, as well as an archaic Napoleonian process. People want education to cater for the poor folk that has a hard time keeping up with the basics (which is a worthwhile goal) but are dismissive to those that can easily keep up and more. In hindsight I could have actually failed before reaching la prépa out of boredom.
I would not put "classes prepa" in the challenging category. It is actually rather dull 2/3 years where you learn not so much about the material, but learn how to solve many exercices (I like the example given by Pierre Gilles de Gennes, which reminds me of my own attitude during some kholles: http://cscs.umich.edu/~crshalizi/reviews/fragile-objects/). Most people entering classes preparatoires will get out with something, so per definition it is not challenging: challenging means doing something that you did not think were possible from yourself. While classes preparatoires were not always easy for me, I was never really challenged by it, and I think most people were not either.
That was absolutely not my case (but I know it has been the case for some in other cities). In my case the exercises, while numerous, were not that many, but were selected and crafted to push and bend the mind. The goal each time was to produce not someone who knows but someone who builds. The most striking example was one of my professors who had a habit of yelling "Et là, c'est fini!" ("And then, its over!"), halfway through a proof and sometimes as early as the second line, or even once having completed writing the first line, when the crux of the problem was to ask yourself the right question and express it the right way. This was a kind of recurring joke while at the same time the signal of the crux, the apex of the proof, where once you get past that point the rest is downhill freewheeling (although as with downhill driving, you should not get too carried away). It was the mark at which you could find the pattern, the point which defines the line (as in racing) that you will be able to build upon to come up with your own solutions.
In front of the blackboard, solving the exercise was never a goal in itself, but the path mattered just as much, if not more. It was common to actually not achieve an academic solution but demonstrating an ability to build an overarching path, though incomplete in its proof, that would lead to the solution would be rewarded. It was not uncommon either to solve the problem much quicker than expected, and the remainder of the kholle would be spend either enhancing the solution, finding an alternative solution, or extending the problem with a follow up or a generalization.
We were not meant to be dumb technical toolboxes (which the PGdG example is a perfect example) but brand new problem solvers. I would draw much parallels between those problem solving abilities and hacking solutions, refactoring arcs, encapsulating problems and caring about the bigger scope, to produce elegant and rewarding solutions.
Granted, this kind of teaching is not ubiquitous to every single prépa out there, but my point is that it cannot occur at all in a "common denominator" environment, where by design people that can keep up will have to look elsewhere by themselves to be challenged, whereas prépa or schools like Berkelee can act as a catalyst.
I wish someone had told me this while I was in school.
I always wonder a bit whether the people who skip years and study super-fast really know anything about the world.
My advice is, if you're not sure whether you'll be able to do something, don't hesitate -- most of the time nothing bad happens if you fail, and if your case is different, the greater your motivation will be.
I agree that a good teacher and motivation can help you reach your potential very fast.
I would say there are two range of domains:
- 1. almost only synthetic, axiom system has small 'Kolmogorov complexity': mathematics, algorithmization (on non-research level)
- 2. more pattern matching, processing of huge amount of information: history, politics, industrial software development, business and everything on research-level.
In the first range, if you find a good teacher and you are motivated then you can go to your potential extremely fast. Miracles happen within weeks. After a point you reach the 2. range, where you are already playing in a league with similarly skilled people, and you progress only extremely slowly.
That's why some geeks are much better in math at the age 12 than the average adult, but they have to learn and practice for long years to become a professional mathematician or to create a successful software business.
In reality, there is a speed limit. At least until Kurzweil gets his way.
The analogy of the blog holds. Infinity only happens in calculus, so why bother poo-pooing a helpful metaphor?
Like a good vision statement in a business plan that calls for a direction without bothering with a specific magnitude, "There is no speed limit" calls the reader to question limitations as a matter of directing their imagination to the problem of expectation as opposed the conventional expectation.
"Power is nothing without control" - Pirelli
"Fun is not a straight line" - BF Goodrich
"The analogy of the blog holds" - GP poster
The analogy does hold for the purposes of a fluffy motivational blog post, of course.
I wouldn't trust the strong version of the accelerating change hypothesis. Actually augment our intelligence, or at least our speed of thought probably require major breakthroughs in neuroscience and relevant fields in engineering, which may occur as not-so-predictable quantum leaps.
Plus, there the safety problem: if we ever enhance someone's intelligence, we may want to make sure that (i) it doesn't make him mad, and (ii) the guy doesn't plan to take over the world. The proper sanity checks may require yet other breakthroughs.
In the end, Friendly AI may be easier.
We have the technology already to facilitate incredible intelligence - it's just extremely unevenly distributed, and stifled by lack of political will and social inertia.