I really love the idea that pure mathematics and nature are the same thing. On a philosophical level, our daily lives are the expression of the differences and inefficiencies of our systems compared to an optimal end-state. Also, sometimes I think that religion and science have more in common than people think.
> I really love the idea that pure mathematics and nature are the same thing. On a philosophical level, our daily lives are the expression of the differences and inefficiencies of our systems compared to an optimal end-state. Also, sometimes I think that religion and science have more in common than people think.
The first of these isn't a coincidence; pure mathematics evolved from applied mathematics, which originally was the only kind, and which was specifically designed to handle nature. It has since departed from those roots, but is still guided by human intuition and æsthetic sense, both of which are deeply shaped by our experiences in the natural world.
This brings to mind Richard Hamming's wonderful essay "The Unreasonable Effectiveness of Mathematics", which really blew my mind ten years ago: "But if you do not like these two examples, let me turn to the most highly touted law of recent times, the uncertainty principle. It happens that recently I became involved in writing a book on Digital Filters [8] when I knew very little about the topic. As a result I early a…
(Having tried to read the paper without knowing any of the physics involved, it... seems... that circles are very much involved? It sounds less like they're saying "we tried to calculate this QM question and it turns out the answer is Pi, how elegant!" and more like they're saying "we've tried to use these standard physics formulas to calculate something involving strictly circular orbits [I think... something about how circular the strictly circular orbits of electrons around a hydrogen atom are? But again, I don't know any of the physics here, and am guessing a lot to make up for lack of understanding], which we already know the answer to which is "Pi", but we were surprised to arrive at this specific formula for Pi first derived in 1655, so probably part of the Schroedinger and Bohr equations we used is just an encoding of this Wallis formula for Pi that nobody noticed before [which is cool in a geeky way, and maybe we could rewrite them in a way that makes that Pi factor more apparent and would help us grok the equations better]?")
This brings to mind Richard Hamming's wonderful essay "The Unreasonable Effectiveness of Mathematics", which really blew my mind ten years ago: "But if you do not like these two examples, let me turn to the most highly touted law of recent times, the uncertainty principle. It happens that recently I became involved in writing a book on Digital Filters [8] when I knew very little about the topic. As a result I early a…
Great quotes!
I had an EE graduate degree (systems, dsp, control...) and returned to school for a physical chemistry graduate degree. Initially was nervous about my first QM class but as Hamming noted so much of the math is similar.
I really love the idea that pure mathematics and nature are the same thing. On a philosophical level, our daily lives are the expression of the differences and inefficiencies of our systems compared to an optimal end-state. Also, sometimes I think that religion and science have more in common than people think.
> I really love the idea that pure mathematics and nature are the same thing
This might not be what you mean, but there is a philosophical position that holds that all mathematical structures exist, and that our universe is simply one of these structures:
I really love the idea that pure mathematics and nature are the same thing. On a philosophical level, our daily lives are the expression of the differences and inefficiencies of our systems compared to an optimal end-state. Also, sometimes I think that religion and science have more in common than people think.
> I really love the idea that pure mathematics and nature are the same thing This might not be what you mean, but there is a philosophical position that holds that all mathematical structures exist, and that our universe is simply one of these structures: https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...
If you assume some notion of an object's description "really existing", it's easy to then assume the Universe must have a zero information description, since otherwise the description would be "outside" the Universe. And then you've backed yourself into a corner: what could zero information describe that also contains our observed universe? All mathematical structures it is.