Ask HN: What is the big idea with algorithms?

I've had to look into the efficiency of my algorithms when doing batch processing on massive XML files - I managed to cut run-time by 80% by paying more attention to my algorithm's efficiency.

On the other hand, if I'm just sorting 5 entries alphabetically for some table, it's better to implement a quick-and-dirty algorithm that will take an extra 2 milliseconds to compute, than for me to spend half my day worrying about it's efficiency.

So generally speaking - people designing low-level systems are very worried about their algorithms, with good reason: If their code is slow or wasteful, their platform can't be used. If you're designing a web app, you'd probably waste more time than it's worth if you delve into that. It's just a question of priorities.

Are there any math whiz kids on HN? (other than cperciva)

There are many smart people on HN, but I don't think there are math whiz kids. This is a hacker forum, not a math forum like AoPS. Sometimes we discuss stuff like complexity and algorithms, but most of the time, we rant on Ruby x Python or why kids these days want to build social networks for dogs instead of sending astronauts to Mars, or why big corporations are evil and small startups rock, or why PG is a supreme master and every single essay of his is nothing less than the truth. We are such cool kids we even have our own hacker-ghetto slang... including hideous terms like "ramen-profitable" ;-)

I know a forum where there's even a Fields medalist, and that is on quantitative finance. Whoever says that HN is made of math whiz kids probably knows very little math.

For instance chess is relatively easy to program where as go is quite a bit more difficult. ---------------------------------------

Here's a very good quote from wikipedia that might make it clearer:

The thesis is widely considered to be a good rule of thumb for real-life problems. Typical input lengths that users and programmers are interested in are between 100 and 1,000,000, approximately. Consider an input length of n=100 and a polynomial algorithm whose running time is n^2. This is a typical running time for a polynomial algorithm. (See the "Objections" section for a discussion of atypical running times.) The number of steps that it will require, for n=100, is 100^2=10000. A typical CPU will be able to do approximately 109 operations per second (this is extremely simplified). So this algorithm will finish on the order of (10000 ÷109) = .00001 seconds. A running time of .00001 seconds is reasonable, and that's why this is called a practical algorithm. The same algorithm with an input length of 1,000,000 will take on the order of 17 minutes, which is also a reasonable time for most (non-real-time) applications.

Meanwhile, an algorithm that runs in exponential time might have a running time of 2^n. The number of operations that it will require, for n=100, is 2^100. It will take (2^100 ÷ 109) ≈ 1.3×1021 seconds, which is (1.3×1021 ÷ 31556926) ≈ 4.1×1013 years. The largest problem this algorithm could solve in a day would have n=46, which seems very small.

http://en.wikipedia.org/wiki/Cobham%27s_thesis

AIT and computational complexity theory arguably underlay all other sciences. They allow us to define randomness (http://www.cs.auckland.ac.nz/~chaitin/georgia.html), pattern, probability (http://www.scholarpedia.org/article/Algorithmic_probability), inference (http://www.wisegeek.com/what-is-solomonoff-induction.htm), ignorance, and perhaps one day consciousness.

They allow us to prove, with absolute certainty, whether we are talking to a deity ( http://scottaaronson.com/blog/?p=56), and to prove that some questions will forever be beyond our grasp.

Even discounting Zuse and Wheeler's "It's from Bits" conception of information and computation as the basis of physics (http://en.wikipedia.org/wiki/Digital_physics), these disciplines promise to help us solve our hardest and most interesting problems by, first of all, telling us whether they are solvable at all, and if so, whether they are solvable before the heat death of the universe. Consider that Goedel, Cohen, and Turing struck down the Continuum Hypothesis from Hilbert's list of open problems, allowing us to abandon a futile line of inquiry and focus on other problems. Current developments in quantum computability theory may similarly strike down vast swathes of sterile ideas, directing us toward questions whose answers are solvable.