Starting at 0130. That's 1:30 AM for you people that don't use 24-hour clocks.
I have a habit of mentally filing nagging problems away, to sleep on them, so to speak. That involves obvious scheduling problems, as sometimes they get slept on for days or weeks. A less obvious problem is that sometimes a solution, or at least the next step toward a solution, prefers to wake me, rather than present itself in a nice orderly manner, when I wake up as usual.
I am fine with that, in that it feels like my subconscious just told my waking mind, “Allow me to surprise you with this delicious cookie.” However, eating the delicious cookie can be a lot of work. In this case, I didn't get a solution, but the next step. Five hours invested in writing some exploratory code, which looks promising, and I was about at a natural stopping point. No solution, but I'm confident that I have the next step. So, it's a win, even though it has messed up my weekend a bit.
It's just as well that I was at a natural stopping point, because the sleep rule on my phone expired, and notifications happened. Most were private, or of no possible interest to you, or both. But before I go sit on the beach (it is Saturday morning, after all) I'd like to point to a G+ post from
Bee Hossenfelder: https://plus.google.com/u/0/111136225362929878171
which points to Top 10 mathematical innovations at
The comments are interesting. I tend to agree with the first one. “This article takes a very narrow view of what "mathematics" means.” … “But this list virtually ignores the past 264 years.”
First off, the context is missing. Was this an innovation mostly important for the field of mathematics, the usefulness of the innovation to society, or what?
Geometry is not on the list, though non-Euclidean geometry is at #7. But geometry was important to ancient Egyptian civilization (building, surveying, etc.), ancient astronomy, etc.
Statistics is not on the list, though it has enabled huge advances in modern manufacturing, through statistical process control. It's a vital component of modern science and engineering. It has also enabled politicians and marketers to lie in innovative ways, to such an extent that I have come to believe that statistics should replace trigonometry, or at least be on offer, in US high-school education.
And now it is time to go sit on the beach for a bit. Have a great Saturday, or at least a cookie.