qqd wrote: ↑May 15th, 2023, 2:02 pm
Why aren't any new periods coming up like p19 or p41?
More or less, the answer boils down to "we have no efficient way to search for them". And we have no idea how complex the simplest p19s or p41s would be.
If they exist (and proving otherwise would be absurdly difficult. I don't think there's a way to do it without beyond-astronomical levels of casework), then we have no idea how complex they are. They could be only slightly more complex than our current methods can find within a reasonable amount of time. Or they could be far, far more complex than that.
For an analogy: imagine you're on an immense plain of sand. Sand stretches in all directions as far as your eyes can see, and it goes incredibly deep. You want to find a green grain of sand (these correspond with p19 oscillators, say). You have no idea how many green grains of sand there are (if there are any at all), though since the sand doesn't look noticeably green as a whole, it's probably very rare. The only option you have is to look at every single grain of sand one at a time and check if it's green. The only issue is that regardless of the exact specific mechanisms you use to look at these grains of sand, there are far, far, far too many grains of sand to ever check through all of them. Why haven't you found a green grain of sand after checking the first billion grains of sand? Well, presumably it's because they're too rare for you to be likely to find them in a billion grains. But you have no idea how many green grains of sand there are. Maybe there are none. Maybe there's only a few in the entire plain, in which case even if you worked at it for millions of times longer, you'd almost certainly still not be able to find a green grain of sand because all the grains you could ever cover in that time would be a miserably tiny fraction of the total number. Or maybe there are quite a lot, say, 1 in about the number you've searched through, but you're just a little bit unlucky so you haven't found any.
In other words: we haven't found p19 oscillators because our methods are much too inefficient for us to ever exhaust the search space. So it's basically just blindly groping around hoping that by chance we'll ever find them because maybe, just maybe, they're sufficiently frequent in the search space that we can look through enough of the search space in a reasonable amount of time that one of them will be in the region we searched. But we have no idea how frequent they are in the search space, so we've got no idea at all if we'll ever find them this way.
