You should probably read Scott Aaronson's post Umeshisms before reading this post.
Concentrate on the higher-order bits.
Back in the day, this sentence took me a long time to understand, and nobody would explain it when I asked, so this is what it means:
Look at the following number: 12,345,678.
All it means is something obvious, which is that the underlined digit is a lot more important than the bolded one. If you want to make a big difference to what the number represents, you need to change the digits closer to the underlined one than to the bold one.
(As an aside, you might consider something like ?________________________________________
I'm writing this for three reasons. First because I used to think umeshisms had achieved memetic fixation, but when I talk to people about them they've almost never heard of it. I googled it just now and was sort of shocked to find it has only 29 results.
Second because when I tell people about umeshisms, and give examples, statements like "If you've never been arrested, you're not doing enough interesting things," or "If you've never broken a bone, you're not doing enough dangerous physical activity," they don't seem to get it. Trying to come up with their own examples, they fail. Something counterintuitive about the idea that a successful strategy includes nonzero probability of unimportant bad things happening.
Pop quiz: Is "If you've never falsified an umeshism, you're not being badass enough," an umeshism? Answer at end of post.
Third because I want to explain the umeshism mindset, as distinct from umeshisms, the type of aphorism. I don't want this post to be a repository of umeshisms (though it'd be super cool if someone made one, like quotedb or the erstwhile limerickdb where people could submit and vote on them). Umeshism is so named like pragmatism, stoicism, or agnosticism, not in the philosophical school sense, but in the state of mind sense.
"Don't sweat the small stuff," is umeshism, but so is, "sweat the big stuff." Effective altruism is umeshism applied to doing material good. Rejection therapy is for getting your system 1 to be more umeshic in the context of asking for things.
The Hamming questions translate to, "Why aren't you being more umeshistic?" From Richard Hamming's You And Your Research:
Over on the other side of the dining hall was a chemistry table. I had worked with one of the fellows, Dave McCall; furthermore he was courting our secretary at the time. I went over and said, ``Do you mind if I join you?'' They can't say no, so I started eating with them for a while. And I started asking, ``What are the important problems of your field?'' And after a week or so, ``What important problems are you working on?'' And after some more time I came in one day and said, ``If what you are doing is not important, and if you don't think it is going to lead to something important, why are you at Bell Labs working on it?'' I wasn't welcomed after that; I had to find somebody else to eat with! That was in the spring.Umeshism is prioritization. It's caring more about more important things than about less important things. It doesn't mean caring a lot, or a little, in full generality; it means caring in the right order. It means not spending all your time on social media if you have anything useful to do. But it also means not spending all your time setting up intricate systems to prevent you from wasting your time.
Every mathematician has only a few tricks.The way I see it, the way humans have different incommunicable cognitive habits is in large part responsible for differences in quality of their intellectual work, and an important proximate cause of people's uniqueness. I often see deep links between my thinking and other people's thinking, always so deep that I can't articulate them. It makes me wonder whether I have some ultra-deep grognor-only intuitions that languish, unused, because I never see them in anyone else and thus they never get reinforced.
A long time ago, an older and well known number theorist made some disparaging remarks on Paul Erdos's work. You admire Erdos's contributions to mathematics as much as I do, and I felt annoyed when the older mathematician stated, in flat and definitive terms, that all of Erdos's work could be ``reduced'' to a few tricks which Erdos repeatedly relied upon in his proofs. Actually, what the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks that they use over and over. Take Hilbert. The second volume of Hilbert's collected papers contains all of Hilbert's papers in invariant theory. I have made a point of reading some of these papers with care. It was very sad to note how some of Hilbert's beautiful results have been completely forgotten.
But it was surprising to realize, on reading the proofs of Hilbert's striking and deep theorems in invariant theory, that Hilbert's proofs relied on a few tricks that he used over and over. Even Hilbert had only a few tricks!