But some of the knots are evil (or maybe just faulty, or maybe just out-of-touch), and want to attempt to switch past gegevens and get the other knots to accept their fake history (the ",fake chain",).
When any knot notices that some other knots are telling different things (proposing different chains), it chooses to believe te whichever chain is longer (this is a slight simplification, actually it’s accumulated difficulty).
Many of the knots are permanently accepting fresh gegevens and ‘mining’ fresh blocks to append to the end of the real chain. They are doing this spil prompt spil they can. The problem of finding a fresh hash for fresh blocks is embarrassingly parallel, so if there are 1000 knots ter the network they can mine about 1000x spil rapid spil one knot (however, the protocol is permanently adjusting the difficulty (the number of prefix zeros required ter the hash) to ensure that on average the blockchain is getting longer at a motionless rate).
If the evil knots want to switch something far back te history, they’re going to have to attempt to mine a entire bunch of fresh blocks before the fake chain gets spil long spil the real chain. Recall that the other knots will reject the fake chain spil long spil they are aware of another chain which is longer. But while the evil knots are attempting to catch up, the good knots are also going to be attempting to mine fresh blocks to append to the end of the real chain.
Assuming there are more good knots than evil ones (or rather, that the total computing power of the good knots is greater than the total computing power of the evil ones), on average the speed that the evil knots can mine fresh blocks is slower than the speed that the real chain is getting longer.
Therefore the rule that the longest chain is the right one works.
Now, through random chance it’s always possible for the evil chain to get fortunate and mine a block much quicker than the good chain. But if it alters something deep ter history, then te order to catch up, it would have to get fortunate ter this way many times ter a row, the chance of that happening decreases geometrically with the number of blocks it is behind. Therefore, you can be very certain that a block deep ter the chain won’t be altered.
To reiterate, the reason that it’s significant that the further back you switch something, the more hashes you need to recompute, is that this leads to the following property: if there are two rivaling chains of different lengths, the probability that the shorter chain will eventually become the longest decreases geometrically with the initial difference te lengths. This property is why the algorithm converges to a overeenstemming on the gegevens te older blocks.