Personally I like project based learning. Just try to make something cool, maybe a game, a robot, a hydroponic grow station or whatever and then learn what you need to learn as you go along.
If you gave me a book of inverse kinematics I'd go to sleep in 10 minutes. If I get frustrated that my robot keeps falling over I could read about it for days.
There is an interesting, if quite technical, answer here about Goodstein's Theorem which is a very reasonable number theory theorem which cannot be proven in first order logic.
So questions around statements which are true but not provable in certain logical systems do have concrete examples and are interesting imo.
Goodstein's Theorem cannot be proved in Peano axiomatization of natural numbers in first order logic. You can have stronger axiomatization of natural numbers in first order logic that allows to prove Goodstein's Theorem - such axiomatization would contain subset of set theory and transfinite induction up to ordinal e_0. But it is still axiomatixation in first order logic.
In mathematics I'd put forward the conjecture that "for every proven theorem you could ask at least 5 more similar questions which are unproven."
For example it is proven there are infinitely many primes. Are there infinitely primes that differ by 2? By n for any n? Are there infinitely many palindromic primes? Are there infinitely many primes of form n^2 + 1? Is there always a prime between n^2 and (n+1)^2?
If this is true then, assuming there are 200k proven theorems, there would be >1m unproven but readily stated theorems which would mean it wouldn't be too hard to find areas no one is looking into.
I'm not sure, I'm not an expert, it says here the twin prime conjecture itself is still unproven.
"On April 17, 2013, Yitang Zhang announced a proof that for some integer N that is less than 70 million, there are infinitely many pairs of primes that differ by N."
I think you can set it to only scan when new pull requests are made. So you could commit your libraries etc without asking for review and then turn it on only for code you have written.
Does anyone know a good comparison of the cost of Nuclear with Solar + Batteries? I feel like just comparing against panels alone isn't really helpful.
I would imagine that if we really cared about climate change the best approach would be maximal effort on all fronts. So build renewables as fast as we can and build nuclear as fast as we can. That would be the quickest way to get carbon emissions to 0.
We could always spend the latter half of the century decommissioning the nuclear again.
Current battery technology is not up to what you are talking about. No one can come up with a price because we don't have the technology to store that much offline energy to handle the variability. Anyone who says we do -right now- is lying to you. We would need a factor of 100X energy storage density to what we have right now to even be close.
people who end up on opposite sides of this argument are usually talking about two different things:
1) Do we build exactly enough solar to meet our average power needs but have to build several-month-long battery storage capacity to bring summer sun into the winter,
2) Or do we build enough surplus solar so that we can run 100% load for 24 hours on a cloudy winter solstice, and just need big enough batteries to get through the longest night of the year, and under every other circumstance just be wildly over-provisioned
#1 is probably impossible with current technology. But our solar installations already produce surplus power during the summer that we don't use ("curtailment"), even at today's prices. It doesn't seem out of the question that we'd just build much more absurd extra solar to make up for our lack of storage. And then maybe we'd find a use for the excess summer electricity, like desalination or hydrogen production or bitcoin mining. It's technically possible, but it does increase costs - twice as expensive? three times? That might still be economically viable, if solar costs continue to fall or if the cost of natural gas spikes upward
If you gave me a book of inverse kinematics I'd go to sleep in 10 minutes. If I get frustrated that my robot keeps falling over I could read about it for days.