
A Mathematical Model Rescued My Book About Math - vo2maxer
https://lithub.com/how-a-mathematical-model-rescued-my-book-about-math/
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blt
I am surprised by the usefulness of math concepts as analogies for everyday
life. Local vs. global optima, explore vs. exploit, depth-first vs. breadth-
first, constraints vs. objectives, necessary vs. sufficient, ...

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.

~~~
hyperpallium
_THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS_ , Hamming,
[https://ned.ipac.caltech.edu/level5/March02/Hamming/Hamming....](https://ned.ipac.caltech.edu/level5/March02/Hamming/Hamming.html)

 _The Unreasonable Effectiveness of Mathematics in the Natural Sciences_ ,
Wigner,
[http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html](http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html)
wikipedia article
[https://wikipedia.org/wiki/The_Unreasonable_Effectiveness_of...](https://wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences)

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).

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tombert
I'm a little sad that I never get to use calculus as a software engineer. It's
relatively easy to use discrete mathematics, or even something more theory-
heavy like type-theory or category theory can be used a bit, but I sadly
haven't been able to find much work doing calc, even though I really enjoyed
the classes.

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.

~~~
nwallin
Linear algebra lands in my professional lap surprisingly often, to the point
where I ask myself if it's a linear algebra problem fairly early on in the
problem solving process. (I'm in GIS)

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.

~~~
tombert
I recommend playing with TLA+ if you want to see how discrete math can map
into compsci; you model everything in terms of discrete states and use logical
predicates and set theory instead of "types".

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hyperpallium
I like the writing style of this essay. The end of the first paragraph is
particularly funny. But to fulfill my contractual obligations for gratuitous
criticism as a HNer:

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.

~~~
kmundnic
I agree that saying that he used calculus is a bit of a stretch. However,
calculus is essential for all the gradient-based methods (or algorithms) in
optimization. Moreover, if you want to analyze these algorithms, you have to
know about convex analysis.

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.

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tr352
As someone currently being stuck in a kind of scientific writer's block, this
was a nice read.

~~~
xrd
What are you writing about? One of the takeaways for me is that it is good to
talk to [someone|anyone] about being stuck. The conversation could lead
towards a local minimum, or a local maximum, or even a global maximum.

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elevenoh
This applies generally - as an optimal path to creating anything (life
philosophy, advancing science, tool creation etc.)

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.

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invalidOrTaken
I haven't read the book, but now want to, and just want to vent something I've
been thinking for a long time---this, or something like it, is a _really
really important project_. We desperately need to be able communicate better
about calculus.

~~~
SQueeeeeL
I sort of agree, but the problem is algebra is fundamentally taught terribly
in America, a lot of people get confused on simple operations. Here's the
goldstandard essay exploring the failures of math education
[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

~~~
invalidOrTaken
I love Lockhart's Lament! Poetically, it could be seen as a mourning over a
case of Goodhart's Law...

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xrd
As a published author, I love this so much. Local vs. global maximum's,
simulated annealing. So terrific. It's all so true.

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johncalvinyoung
Sadly, I rather wish I could read the original book. I _might_ read the book
that resulted.

