Sometimes things don’t go as planned. Sometimes claims, a thousand times tested, a thousand times confirmed true, turn out to not be that in the slightest.

I’ve read about the P=NP problem, trying to make the sense of it, since it seemed to touch a really deep dichotomy which gets manifested in many different areas of thought. My understanding of it is that P not being equal to NP means that testing the truthfulness of a solution is a much easier problem than getting to the solution in the first place. Of course, the formal wording is more strictly worded, as it actually describes the increase in difficulty of a problem as the size of the input increases. That way, the size is cancelled out, and only the approaches to solving/testing are compared. For now, it seems as if P is not equal NP, and on this presumption our technology, hence our civiliziation, is fundamentally based. That is because technology is communication of information, and communication is best when it’s reliable and secure. Both are achieved by cryptography, which assumes that finding prime numbers is hard (NP), while checking if any one number is prime is easy (P). It works like this: you start checking random numbers, until you find two primes. You multiply those primes, and write that result on your forehead. There’s one clever formula though, that is easy to calculate for products of two primes, like the number on your forehead, but otherwise it’s hard. It gives you a number which we’ll call the magic number, because it’s magically connected to the number 3. Bear with me. Whoever wants to communicate with you reliably and securely, turns his message into a number, and then multiplies it by itself 3 times. Then he starts substracting the forehead number from it, until he gets a number smaller than the forehead number, and sends that to you. You take that number, which is basically the encrypted message, and multiply it by itself magic number times, and then subtract the forehead number until you get to the number smaller than the forehead number. That’s your fucking message. The idea behind all of this is to use calculations that are easy to get the numbers that are not secret (forehead number, encrypted message) from your secret two primes, but very hard to get secret primes from those. On the other hand, when you have your secret primes, you can easily calculate the magic number, and with that you can easily calculate the message from the number that is sent to you. BTW, forehead number is usually called the public key, and the magic number is a number that, when multiplied by 3, has a property that …yeah it’s fucking complicated.