> Let's start from the other end. Just a pawn and two kings. It's possible to describe some quite succinct rules for when that's a draw versus a win for the side with the pawn. Agreed? Club players know these by heart. You could write that doen as invariants. As long as the side with the pawn stays inside the "green zone" of the state space, there is nothing the other side can do to void mate.
The flaw in this line of reasoning is that it's easy to come up with a theorem that works for KP vs K. However as the number of pieces increases, it becomes impossible to distill all the branches of possible moves into a simple theorem like that. If what you said were possible, endgame would be a simple flowchart, but look at how much time even GM players use in endgame and how often mistakes are made, and you'll recognize Chess endgame is not distillable into a simple flowchart when there are even as few as 7 pieces on the board.
Given the above, the only option is enumeration, if you want to prove that in all cases the outcome is White win or draw.
Tesla IPO'd at 1.7B and is worth 1.4T today. Giving you the benefit of doubt since it would be closer to a 1000x gain rather than the 100x gain that you didn't buy right at IPO, I will point out that there's a world's difference buying in at 1.7B, because there's still room for the stock to 1000x, but there's not much gain to be had buying in at 1.7T valuation.
Even the most highly company in the world Nvidia is less than 3x that valuation, so it's not a good comparison with Tesla's IPO.
Direct indexing will soon be able to provide that functionality of giving you S&P 500 stocks minus A, B and C companies you don't want to hold. However, cheap and reliable direct indexing brokerages aren't out there yet. Hopefully more competitors show up and help lower the prices for everyone.
This reminded me of those booths they have at company holiday parties where they take a photo of you, convert it to a line drawing and have the robot draw it out for you to keep. Very cool hack!
I had this same feeling. Same with reading a biography of Kurt Vonnegut. Before reading it, I thought of them in idealistic ways. They had multiple affairs and weren't such great people, even though they both wrote really, really well.
Thanks for the info! I don't have a Zhihu account to check myself, but I believe you.
I think it would be helpful to dispel any confusion if you added somewhere on the Substack post (e.g. at the bottom) the above message you are the author of the Zhihu post.
+1 The long gap between 2016 when the original article was written in Chinese and 2025, the fact that the Substack article does not cite the original Zhihu article (until someone other than OP linked it in this thread), not linking previously English translations of this article, and the financial incentive of the LLM-translated article being on Substack make OP's claim of authorship of the Chinese article very sus.
Bogleheads [1] gives better financial advice than HN. Every time I peruse some threads there, I learn something new about personal finance I didn't know about.
My read of "pre-2016 playbook" was referring to someone using a traditional campaign like Hillary (rather than Trump using his pre-2016 strategy), and that they were saying Trump changed the entire game in 2016 so that shameless strategies would be the winning strategy going forward. So I don't see a contradiction.
>During mitosis and meiosis, microtubules depend on a stable magnetic field to orient the mitotic spindle and ensure accurate chromosome segregation — processes critical for embryonic growth. A spacecraft lacking any magnetic field would halt human reproduction, dooming both the mission and the survival of the colony.
That seems wrong to me. The last time I calculated it out, the Earth's magnetic field isn't that strong, and for someone on earth's surface is dwarfed even by high voltage power lines. This is due to the Earth magnetic field radiating out from the iron core which is much farther away at the surface compared to the power lines, and declining by the square root law.
"It's very hard to perceive counterpoint, and there is a limit to how much we can perceive at once. 2 voices is hard and takes practice, 3 voices is even harder, but you can have these flashes where you hear clearly voices playing off one another and its like getting a glimpse into the divine."
I've always wanted to learn how to listen to counterpoint. Anyone have good tips on how to appreciate it and know what it means to perceive counterpoint?
What you're talking about sounds a lot like the post-scarcity world that Gene Roddenberry envisioned in the Star Trek universe, where everyone has enough to live on, so social status is attained by prestige and doing admirable things (i.e. working for Starfleet). However, there's a lot of work to be done getting from here to there.
Essentially the plot of "Mother Night" by Kurt Vonnegut. An American spy sent to Germany before WW2 who works there as a radio host, but who ends up spreading even more anti-semitic messaging than Nazi members themselves. "We are what we pretend to be, so we must be careful about what we pretend to be."
> (1) intentional fouling to get an advantage. It’s the only major sport where fouling can often work to your advantage.
nitpick: This happens in soccer as well. Oftentimes it's late in the game and you see the opponent has a counterattack that has a high probability of scoring. In that case, it's better for you to tactically foul them by taking them down before they reach your box and take the yellow card.