Grant Sanderson: prediction

Transcript context

…We were talking about this before the interview started but we have a much better grasp on reality based on our mathematical tools. I'm not talking about anything advanced. Literally being able to count in the decimal system that even the Romans didn't have. How likely do you think it is that something that significant would be enjoyed by our descendants in hundreds of thousands of years or do you think that that kind of basic numeracy level stuff those kinds of thinking tools are basically all gone? Just so I understand the question right, you're talking about how having a system for numbers changes the way that we think that then lends itself to a better understanding of the world like we can do commerce, things like that. Or we can think in terms of orders of magnitude that would have been hard to think about. We have the word “orders of magnitude” in a way that is hard to write down, much less think about if you're doing Roman numerals. Is there something analogous to that for our descendents? Fluency with a programming interface really can help with understanding certain problems. I think when people mess around in a notebook with something and it feels like a really good tool set. There's a way that has the same sensation as adopting a nice notation in that you write something with a small number of symbols but then you discover a lot about the implication of that. In the case of notation, it's because the rules of algebra are very constrained and so when you write something you can go through an almost game-like process to see how it reduces and expands and then see something that might be non-trivial. And in the case of programming, of course the machine is doing the crunching and you might get a plot that reveals some extra data. I think we're maybe at a phase where there's room for that to become a much more fluid process such that rather than having these small little bits of friction like you've got to set up the environment, and you got to link it in the notebook, you've got to find the right libraries, that there's something that feels as fluid as when you are good at algebra and you're just at a whiteboard kind of noodling it out. I think there's something to be said for the fact that there's still so much more value in paper. if you and I were going to go into some math topic right now. Let’s say you ask me something that's a terrible question for a podcast but I'm like “Oh. Let's actually dig into it.” The right medium to do that is still paper. I think I would break out some paper and we would scribble it out. Whenever it becomes the case that the right medium to do that lends itself to simulation and to programming and all that, that feels like it would get to the point where it shifts the way that you even think about stuff. What's up with miracle years? This is something that has happened throughout science and especially with mathematicians, where they have a single year in which they make up many, if not most, of the important discoveries that they have in their career. Newton, Einstein, Gauss they all had these years. Do you have some explanation of what's going on?…

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