Simple enough, right? If we have an input, and want to solve for an output, we just substitute. If you want the answer when x = 10, just sub in:

y = 2(10)² = 200. 

Similarly, if we have an output, and want to solve for an input, we can try to invert the function and swap y and x. In our case,

x = ±sqrt(y/2)

But that’s basic math – stuff we all learn in high school. What about a more complex function?

Don’t ask me what this function is, exactly – I have no idea. I’m a software engineer, not a mathematician! (although I really should be…)

Either way, this is hideously complex, and kinda cool. Now, if I give you an input value of x = 3, you can solve easily for y – in this case, it’s -284.161. (Thank you, built-in function evaluator in Grapher!)

Now, what happens if I give you an output value? Could you find me the set of all x in R for which y = 5000? Please? No?Wolfram Alpha may possibly be able to find a solution, with all of its carefully-coded mathematical prowess… but most humans would quickly give up.

Going one way through a function is easy – give it inputs, take its outputs. This is true in almost all fields. However, going the other way is tough. Very tough. Factoring, function inversion and the like are difficult tasks for humans, and quite difficult for computers as well.

What if the world were our function? Or, for a slightly easier analogy, if the internet were our function.

This function would take in a piece of information – an article, a tweet, a video, a blog post, and return its topic.Now, what would happen if we were looking for all pieces of content with, say, cats playing keyboards. (this seems to be a popular YouTube search term)We’d need an inverse of this function. We’d essentially need someone to solve this function.

Of course, Google has (for the past decade) been able to solve this function. If you’re looking for something, Google will know where to find it.This has been the problem throughout history – finding things. Search engines are humanity’s first effective, fast, and useful way to invert this function.After all, it’s easy to make things, and easy (now, with the internet) to publish them – but it’s still difficult to find what you’re looking for.

And Google isn’t done. They didn’t stop at search – they wanted a bigger data set to search on. They’re acquiring critical mass, and they’re getting more and more successful every day. 

It won’t be long until they can find anything. And this isn’t a bad thing.

Saying “google your car keys” sounds far-fetched, but all it would take is an RFID reader on your Nexus One and a constant lock on your car keys. Have the phone recall the last recorded GPS location where your car keys were in range, and you already have a better chance at finding them. A week after that, Google will come out with a low-cost, rechargeable GPS fob for your keys that automatically keeps track of their location.

Or maybe I’m just dreaming too much. Either way, it’d be a great world to live in.

-P