Terence Tao: belief

Transcript context

…So since we mentioned a lot of math and a lot of physics, what is the difference between mathematics and physics as disciplines, as ways of understanding, of seeing the world? Maybe we can throw engineering in there, you mentioned your wife is an engineer, give it new perspective on circuits. So this different way of looking at the world, given that you’ve done mathematical physics, so you’ve worn all the hats. Right. So I think science in general is interaction between three things. There’s the real world, there’s what we observe of the real world, observations, and then our mental models as to how we think the world works. We can’t directly access reality. All we have are the observations, which are incomplete and they have errors, and there are many, many cases where we want to know, for example, what is the weather like tomorrow, and we don’t yet have the observation, but we’d like to. A prediction. Then we have these simplified models, sometimes making unrealistic assumptions, spherical cow type things. Those are the mathematical models. Mathematics is concerned with the models. Science collects the observations, and it proposes the models that might explain these observations. What mathematics does, we stay within the model, and we ask what are the consequences of that model? What observations, what predictions would the model make of future observations, or past observations? Does it fit? Observe data? So there’s definitely a symbiosis. I guess mathematics is unusual among other disciplines is that we start from hypotheses, like the axioms of a model, and ask what conclusions come up from that model. In almost any other discipline, you start with the conclusions. “I want to do this. I want to build a bridge, I want to make money, I want to do this,” and then you find the paths to get there. There’s a lot less sort of speculation about, “Suppose I did this, what would happen?”. Planning and modeling. Speculative fiction maybe is one other place, but that’s about it, actually. Most of the things we do in life is conclusions driven, including physics and science. I mean, they want to know, “Where is this asteroid going to go? What is the weather going to be tomorrow?”, but mathematics also has this other direction of going from the axioms. What do you think… There is this tension in physics between theory and experiment. What do you think is the more powerful way of discovering truly novel ideas about reality?…

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