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This is a nice summary of an earlier, more "optimistic" view of Mathematics and our understanding of Nature. The final words sum it up well: "We must know! We w

This is a nice summary of an earlier, more "optimistic" view of Mathematics and our understanding of Nature. The final words sum it up well: "We must know! We will know!" Then things like Gödel's Impossibility theorem and the Halting problem came to light. Or quantum physics, with it's inescapable uncertainties, etc. In those earlier days, it must have seemed like humanity would in due time reveal all of the workings of the universe / uncover God's Plan. Then we got a reality check (: I feel like I've gone on a similar trajectory in my understanding of the world. Early on, I felt like "the answers" were known, and I just needed to apply myself to understand them. Perhaps it's a side-effect of the way school and academics are structured. And over time I've come to understand that all the elegant formulae and high-level concepts are just approximations (albeit useful ones) to reality: which is a wild, beautiful, never-fully-knowable mess. Sometimes I think of it in terms of Plato's Cave[1]: the notion was that the Ideal is the "perfect thing", and our observed reality is just wavering shadows on the wall, derived from that ideal. But nowadays I think the shadows are the perfect reality, and the "ideal form" is just our derived, simplified, mental model, and we're more exploring our own limited ability to understand rather than some innate truths of nature itself. [1] https://en.wikipedia.org/wiki/Allegory_of_the_cave https://en.wikipedia.org/wiki/Allegory_of_the_cave

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AmosLightnin 2y ago
Well put. This notion of "ignorabimus"[1] which he opposes would seem to have gathered a great deal of evidence in the meantime. What I wish was more widely understood today was the cost of attempting to use models that are effective in the natural sciences in domains where they seem to be consistently ineffective. The replication crisis [2] , where in some cases less than 40% of key studies in psychology and the social sciences could be replicated, is often chalked up to improper statistical analysis or lack of integrity on the part of the authors. But it seems more likely to be the result of relentlessly applying linear mathematics and statistical methods to a domain where things simply do not work the way they works in physics or the natural sciences. To be sure - there is some baby in that bathwater, but the social "sciences" have thus far failed to articulate the domains that are baby and the domains that are bathwater. The amount of human effort and time that is wasted because "We must know" and "We will know" - trying to fit a square peg in a round hole - seems immense. [1] https://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus https://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus [2] https://en.wikipedia.org/wiki/Replication_crisis https://en.wikipedia.org/wiki/Replication_crisis

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AmosLightnin 2y ago

Well put. This notion of "ignorabimus"[1] which he opposes would seem to have gathered a great deal of evidence in the meantime. What I wish was more widely understood today was the cost of attempting to use models that are effective in the natural sciences in domains where they seem to be consistently ineffective. The replication crisis [2] , where in some cases less than 40% of key studies in psychology and the social sciences could be replicated, is often chalked up to improper statistical analysis or lack of integrity on the part of the authors. But it seems more likely to be the result of relentlessly applying linear mathematics and statistical methods to a domain where things simply do not work the way they works in physics or the natural sciences. To be sure - there is some baby in that bathwater, but the social "sciences" have thus far failed to articulate the domains that are baby and the domains that are bathwater. The amount of human effort and time that is wasted because "We must know" and "We will know" - trying to fit a square peg in a round hole - seems immense. [1] https://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus https://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus [2] https://en.wikipedia.org/wiki/Replication_crisis https://en.wikipedia.org/wiki/Replication_crisis