The birthday paradox in action: calculating the probability of a hash collision
If you haven't seen this before then I urge you to have a guess now. Is it 180 people? More than that? Fewer than that? What do you think?
In the above calculations there were at least three occasions where I recognised things because I was familiar with them, had used them, had played with them, and they were, in a sense, my "friends."
People often ask "Why did you make that approximation?" or "How did you know that would work?" The short answer is often "I didn't, but it felt right."
People often ask why they need to memorise formulas, or why they need to practice solving equations, when they can simply look stuff up whenever they need it, and on-line computer algebra systems can solve equations faster than they can, and more reliably.
But this is an example of why the ability simply to look stuff up is near useless on its own. Searches are deep and wide, and you need intuition to guide you. You need to recognise what might work, things you've seen before, directions to take that are more likely to be fruitful.
The day probably will come when computers can do all of that better that we can, but that day isn't here yet. We still need human intuition, built from experience and practice, to guide the computer searches, to know what is more likely to work.
If you already know how to do this sort of calculation then you're probably nodding. If you don't, and you can't see how someone can possibly do this kind of stuff, this comment is for you. Practice and experience.
Once you play with things, the ability to invent and improvise is unleashed.Posted on 2012-11-07T20:04:42+0000