> The space of possible avatars (2^256, in this case) is far, far larger than the number of distinct objects that humans can distinguish between.
That sounds intriguing to me. Are you aware of any research into this?
That sounds intriguing to me. Are you aware of any research into this?
I suppose it's a somewhat nuanced question, though. For example, if I were shown every avatar in sequence, I'm quite sure I would always notice the "diff" between two consecutive avatars. But the bar that I have in mind is much, much higher: given a sequence of avatars, can I recognize my friend's avatar with 100% accuracy? Given that we can't even do this within the set of <8 billion human faces (we occasionally accost a stranger as though they were a friend), I have to conclude that doing so within a set of 2^256 abstract shapes is entirely hopeless.
echo "hello" | sha256sum
>> 5891b5b522d5df086d0ff0b110fbd9d21bb4fc7163af34d08286a2e846f6be03
echo "world" | sha256sum
>> e258d248fda94c63753607f7c4494ee0fcbe92f1a76bfdac795c9d84101eb317
But were I to briefly glance at a computer screen, I'd probably confuse these next two:
e258d248fda94c63753607f7c4494ee0fcbe92f1a76bfdac795c9d84101eb317
e258d248fda94c63753607f7c4494ee0fcbe92f1a76bfaac795c9d84101eb317
Practically speaking, though, this isn't something that the average person is capable of doing. Even memorizing one hex string, let alone multiple (for each of your friends), requires a lot of effort for little benefit.
Furthermore -- if you can memorize the hex directly, you don't need the avatars in the first place! :P
Your example of the fact that we can't reliably recognize every face on this planet is very interesting. Let's imagine we know n faces which I can reliably distinguish from one another, but now there is a (n+1)th face which I mix up with one of the previous ones. Now lets assume this face would instead have a very unique characteristic, unlike all previous faces - lets imagine for example, the nose on this face is upside down. Surely I'd be able to differentiate it from the previous n faces, hence the issue of identifying it might've been the limited variability/characteristics in the various previous instantiations of a face.
So there are a number of characteristics in a face, which have a certain degree of variability, which enable us to distinguish from a number of them. I've been pondering on how many of those characteristics could be combined in an object, and how high the variability could be; to create uniquely identifiable patterns. It probably depends a lot on the meaning we attribute to the pattern, different associations we have to it.
I apologize - quite the tangent, I guess. I've just been pondering a lot on this for a project I've been working on for some time.
One billion is really really tiny though, let's just play a game :
- Unless you're colorblind, you can easily tell ten hues apart. Let's pick two colors, one with a saturated hue, and the other with a pastel one. That's 100 possibilities.
- I'm pretty sure you can easily recognize pictures of a hundred people you've met at some point in your life. Let's pick two of them, that's 10 thousand combinations.
- can you recognize ten different road signs? Ten country shapes ? Ten animals ? Ten fictional character? Ten books cover? Ten celebrities? Just pick three categories, and you've got a thousand combinations.
Now I'm pretty sure you can tell your grandma sitting under a vivid pink UK shape next to your 9th grade math teacher staring at Bruce Willis holding a giant light blue stop sign apart from any other imaginable combinations.
An untrained[1] human brain probably cannot distinguish between 2^256 items, but it's still able to do it for massive numbers.
[1]: but maybe it's possible with training: for instance, chess professionals might be able to do it.