Maybe it was faster for truly smart people to get a Ph.D. back in the day. My father had his Ph.D. in computer science by the time he was 21. I tried to take one masters-level course when I was 22 and they laughed at me.
I think it is the education systems' fault, rather than your own.
I vividly remember feeling this way too (not about Wolfram, but about similar things) when I was 23. In my experience, a benefit of getting older has been that this sort of concern gradually fades. Eventually, you affectionately wonder how you ever could have let it matter to you so much.
i guess you wouldn't like to hear that his first quantum physics publication was as a teenager?
i read somewhere that when Feynman first met SW, he said he was amazing.
But would you trust math olympiad performance over good grades in graduate level math courses? What about publications in respected math journals? If by the time you graduate from college your math olympiad scores are the best things you have going for you, you've got a problem.
But it takes more than a scalar score on a test to prove your ability to integrate whats around you into something new. If you get a perfect score on one of those tests and don't do jack shit afterwards, what does it mean?
As other people have mentioned, doing well in college is more about learning a lot and doing research than getting good grades. With this in mind, I think doing well in college can be important for a couple of reasons:
1) You should try to learn as much as you can.
2) Grad school. If you decide you want to go to grad school, it's important to have good grades and more importantly research experience.
3) Employment. Grades / research experience may not matter for a startup, but I think it does help with getting your foot in the door with big tech companies like Microsoft, Google, etc.
Only 1) matters as far as start ups are concerned, but it's good to keep options open. Your interests may change (I'm only 23, and my interests have changed a few times already).
The 1-norm tends to also be less sensitive to outliers, and in machine learning, 1-norm regularization leads to sparse solutions. The real reason 2-norm is popular is that it is easy to minimize (differentiable).
Don't tell Dave Winer that to his face. He'll start rambling about OPML, outliners, and other shit only he and like 3 other people care about (i.e., way more people care about Haskell than they do about outliners from what I can tell).
What you are talking about is more along the lines of inductive logic programming, where the goal is to induce general symbolic rules from specific examples. Even with ILP I'm not sure how exactly you could phrase things so that the machine could learn "addition" though. An ILP system could probably learn something like a + b = c implies b + a = c (i.e. commutativity) and other properties of addition from examples.
If it can learn these properties, it may be even better! Then it can do all computations. So, can it learn commutativity, and other properties? Would it be smart enough to look for them in the first place?
I don't know a lot about ILP algorithms, but my understanding of them is that they basically search the space of logical rules for rules that "explain" the examples they are given. More formally, they look for rules from which you could then prove the given examples. So in an ideal world you could give an ILP system a bunch of formulas and it would give you back the Peano axioms or something like that I'm not sure if state of the art ILP systems are good enough to do that in practice or not.
Metric trees (sometimes called ball trees) are a simple generalization of this to arbitrary metrics. They're also useful for points in a high dimensional euclidean space that have low intrinsic dimensionality.
I have to say, I'm not that sympathetic. If you are using open source software, you can't expect free support, and you definitely can't expect immediate free support. Plus, it actually looks like you got each of your questions answered within an hour, which is pretty impressive actually.
No problem. If you're using Google, you can't expect to get your results in 0.13 seconds. If you're playing a free game, you can't expect it to be fun. If you're in News.YC, you can't expect to interact with smart people, like yourself. If you use software, you can't expect things to work.
With that said, I wasn't expecting free support, nor immediate free support, and the answers I received were extremely helpful. There are wonderful, nice, and extraordinarily talented people on #lisp who are more intelligent than I could ever hope to become in my wildest dreams. However, there's a good deal of elitism, too. Statements like "There is no Lisp community, this is just an IRC channel" just reinforce that. You end up not being attached to the place you live in. You don't even feel like you live there; you just happen to be there. It's kind of like working at a company where you don't own any of the software you write (in the sense of, this is my module; if it breaks, I'm responsible, and its design choices are my call). If you think of your car as a hunk of metal, you're far less likely to oil its engine regularly.
I'm contrasting the Lisp experience with the Ruby and Python experience. In the Lisp world, things aren't obvious. It's not the programming language that's at fault, it's the interfaces. Things can make a great deal of sense when designed a certain way but require several steps and much thought. Or things can be simpler and require little thinking so people can focus their thoughts on what matters to them: creating the systems they want to create. Top that off with a community that might throw malicious code at a newbie or throw a patient response and you have a tough situation. It's the difference between a website's creators feeling they're doing users a favor by letting them visit versus feeling proud that they're making people happy.
Things don't need to be this way, and I'm confident that there will be changes for the better. Those wonderful, intelligent souls I referred to earlier will help turn the tide. Secretly, everyone wants to be perceived as a nice person, and building a community in which you can improve the life of just one person is a fabulous experience.
The point of open source software is to act as an alternative to the proprietary stuff out there. Therefore, you can and should expect free support. It's in the best interests of the project to have more people use it.
I understand that it is in the best interests of an open source developer to give support for his software (assuming he wants people to use it), but he's in no way obligated to do so. Some people just develop software for fun and make it available to the public as an afterthought in the hopes like minded people will find it useful. I know with the personal projects I've released as open source, although I fixed bugs and responded to requests when I could, it was my goal to give prompt technical support.
Some people just develop software for fun and make it available to the public as an afterthought in the hopes like minded people will find it useful.
That's true. But this is a programming language we're talking about. The goal is to create a good implementation and part of that is having good support. Does a programming language exist if no one uses it?
I had to stop reading there as I became ill. (23 year old that hasn't passed quals)