4 ms·
A high-dimensional ball has more surface area than volume. Human brains are only used to thinking in lower dimensional spaces but human lives intrinsically occ
by shalmanese 4y ago
A high-dimensional ball has more surface area than volume.
Human brains are only used to thinking in lower dimensional spaces but human lives intrinsically occupy manyfold dimensional spaces.
"Better" is only a meaningful metric under two circumstances:
* A one dimensional ordering, in which case all items can be ordered in relation with each other
* A multi-dimensional ordering in which one item has total domination over an another item
Take recipes for example, recipes can be evaluated based on taste, nutrition, ease of preparation, quality of writing, availability of ingredients etc, etc, etc.
Is a recipe that's easier to make but less tasty "worse" than one that takes way more time but tastes way better? Either you can "linearize" the dimensions by assigning some kind of weighting like 0.5 * taste + 0.3 * easiness + 0.1 * nutrition + 0.1 * other OR you can accept there is no intrinsic ranking and say neither recipe is better than the other, they're just different.
But what you can say is that a recipe that is worse in taste AND worse in ease of preparation AND worse in nutrition AND worse at everything else is a categorically worse recipe. That's a recipe that's at the center of the ball and not the surface.
In a high-dimensional world, being the best is trivial, almost everyone is the best except the people who are all around mediocre, people who occupy the center of the ball.
Despite this, most people fail at this task, just like how most recipes you find on the internet are categorically not the best, because their mindset does not unlock this view of the world. They're followers rather than leaders and so they subscribe to a very narrow and rigid view of what programming means and are desperately competing amongst those dimensions with every other person who subscribes to that view and they never reach close to the top because a low dimensional ball has very little surface area relative to volume.
So if there's one single piece of advice I could give you about how to become "the best", it's to forge your own path early and confidently and bravely. There are a million different roles that programmers have in society that each require a million different types of skills and the one you're going to be the best at likely hasn't been discovered yet. Follow your passions and your interests and develop a unique point of view and thrive in the intersection between areas of rare overlap and becoming the best is simply table stakes.
Whatever you do, don't linearalize your life upon metrics given to you by someone else because they have an agenda to corrall you into a competition for their benefit, not yours. Introspect and figure out what "best" means for you and use that to drive you and you truly will believe you are the best because nobody else will share that same linearization as you.
For a very similar take on this, but from the Physics world, I recommend you read this paper: Physics in a diverse world or A Spherical Cow Model of Physics Talent [1]
[1] https://arxiv.org/abs/2203.09485 https://arxiv.org/abs/2203.09485