A Mathematical Model Rescued My Book About Math
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I also find myself wanting to compose precise statements using "for each", "there exists", "such that", and so on, in a recursive formal logic structure, when discussing non-mathematical topics.
It's hard to tell if those analogies actually help you make real-life decisions, or if they are just a convenient way to state ideas that are also easily stated in non-mathematical language.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Wigner, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html wikipedia article https://wikipedia.org/wiki/The_Unreasonable_Effectiveness_of...
I kind of think much of mathematics was constructed to solve problems, so it's not that surprising that it solves problems.
On a deeper level, any optimal internally consistent system will probably be good at reasoning about any real phenomena with the same constraints.
OTOH our mathematics probably reflects human reasoning styles (despite us not understanding but "just getting used to it"), and aliens might have explored different mathematics first (e.g. algebraic geometry might make us the aliens to Euclid).
Maybe if I started learning to make games that would be an excuse to relearn some physics and I'd be able to use calculus again.
Calculus is unusual, but it does happen. We do have data with time dependent variables, but usually we don't need anything more complicated than ax + b.
When I took linear algebra and discrete math in college, my linear algebra professor was amazing and my discrete math professor was terrible. I got an A in both classes, but for the life of me I don't grok how discrete math is applicable to programming, but if someone starts describing a problem they have I'll be like, "have you tried linear algebra?" in the "have you tried turning it off and back on again?" voice.
I need to watch one of those lecture series on discrete math.
I wonder if it has anything to do with how discrete software is. A program executes in lurches, not as a continuous process. You sort of end up dealing with Riemann rectangles instead of curves, when you look at the time domain.
That resemblance is probably just a coincidence, though; maybe it has more to do with the fact that most programs react to input after the fact instead of trying to model the immediate future and act based on predictions.
It "uses" calculus only tangentially, and I see simulated annealing and optimization as a computational techniques, not mathematics.
Also but one must be the highest (the “global optimum”) is not neccessarily true; several can be equally highest, e.g. a sine wave.
I think what the author _meant_ was that he used the intuition derived from calculus to tackle the problem he was framing as a mathematical optimization problem.
Also, you're right, he missed that the global maximum might not be unique in a non-concave function.
Sketch a breadth-1st near-random (high heat/entropic) exploration map/terrain of conceptual/creation structure optima.
Over time, let the system cool.
Slowly raise the threshold of improvement-gradient acceptability (increasing negative value). This confines your exploration.
Ultimately end in a cooled state, going only directions of direct improvement.