4 ms·

Math is the shadow universe of physics. Most theorems may not look like they are useful for anything real world till someone is able to peg all the variables to

Math is the shadow universe of physics. Most theorems may not look like they are useful for anything real world till someone is able to peg all the variables to real world. And then as if by magic we realize we already know how how the real world behaves. Till someone does this pegging, the theorems sit idle waiting for problems to solve. I believe this is actually a good thing. We are letting people find solutions before someone finds problems to use them for.

stuxnet79 11y ago
> I believe this is actually a good thing. We are letting people find solutions before someone finds problems to use them for. This may lead to a few problems too: (1) Prior knowledge can serve as a blinder. Our conceptual toolkits may end up consisting of unwieldy theorems that while useful are cumbersome to use. (2) The number of theorems with no immediately evident practical use is so large that they may end up being "forgotten" anyways, and this will result in us having to do the "mental heavy lifting" all over again.
daniel-levin 11y ago
I disagree. A mathematical result doesn't have to have direct application to the real world for it to be useful. Drawing analogies between the real world and mathematical concepts is very powerful. I have a good example: Number theorists (amongst others) are seemingly obsessed with bounding things. There are entire books written about obtaining and then refining bounds - which appear to be nothing more than inequalities. There is great real-world value to be derived from seeing 'inequalities' as tools to leverage. Brian Kernighan once commented that controlling software complexity is the essence of programming [0]. I believe similar thinking applies to other aspects of software engineering, and product and business development. If you can take a hard problem, and bound its complexity, then you can say "the problem is no more complex than this". This is very useful. The chief value proposition of many SaaS businesses is the trivialisation of the upper bounds of complexity of hard problems. For instance, for many developers, Heroku makes the complexity of deployment very low. [0] http://quotes.cat-v.org/programming/ http://quotes.cat-v.org/programming/

stuxnet79 11y ago

> I believe this is actually a good thing. We are letting people find solutions before someone finds problems to use them for. This may lead to a few problems too: (1) Prior knowledge can serve as a blinder. Our conceptual toolkits may end up consisting of unwieldy theorems that while useful are cumbersome to use. (2) The number of theorems with no immediately evident practical use is so large that they may end up being "forgotten" anyways, and this will result in us having to do the "mental heavy lifting" all over again.

daniel-levin 11y ago

I disagree. A mathematical result doesn't have to have direct application to the real world for it to be useful. Drawing analogies between the real world and mathematical concepts is very powerful. I have a good example: Number theorists (amongst others) are seemingly obsessed with bounding things. There are entire books written about obtaining and then refining bounds - which appear to be nothing more than inequalities. There is great real-world value to be derived from seeing 'inequalities' as tools to leverage. Brian Kernighan once commented that controlling software complexity is the essence of programming [0]. I believe similar thinking applies to other aspects of software engineering, and product and business development. If you can take a hard problem, and bound its complexity, then you can say "the problem is no more complex than this". This is very useful. The chief value proposition of many SaaS businesses is the trivialisation of the upper bounds of complexity of hard problems. For instance, for many developers, Heroku makes the complexity of deployment very low. [0] http://quotes.cat-v.org/programming/ http://quotes.cat-v.org/programming/