hecker

Amateur essayist, anime & manga fan

Resident of Howard County, Maryland, systems engineer, and amateur essayist and data scientist. Author of the book That Type of Girl: Notes on Takako Shimura's Sweet Blue Flowers. Staff writer for Okazu.


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frank@frankhecker.com

posts from @hecker tagged #mathematics

also:

I get nervous when I write about something I don’t totally understand. As a result, I sometimes resort to writing down an explanation of that something to myself, in an effort to understand it better. While writing an upcoming post I realized that I wasn’t doing a good job of explaining what a log-normal distribution was, and in particular needed a better understanding of what a logarithm was.

This post is my attempt to explain the concept of logarithms to myself, which I do in my usual way by writing as if I’m explaining it to someone else with no background in the subject. If you’re already familiar with the concept of logarithms then you can skip this, and if you’re not then you can find better explanations elsewhere. In other words, nobody should read this post except me.



Who I am (in case it factors into your decision): old straight white cisgender man, married with one daughter, former math and physics major, living in Maryland, USA, and working as a “pre-sales engineer.”

What I write: original essays on quasi-random stuff like

More on my interests below, in case you want to compare mine to yours ...



I've been around long enough to notice that stories involving magic seem to be more popular now than they used to be, and I've often wondered why that might be. I was reminded of that once again while reading one of the most delightful and charming stories about magic, Kamome Shirahama's manga series Witch Hat Atelier. In the manga the young girl Coco is initiated into the world of witches--a world she thought had been closed to her from birth, but which she discovers is open to anyone who can learn to draw the intricate designs by which spells are cast.

The world of Witch Hat Atelier is of course fictional, and its magic likewise. But here in the real world we can also perform magic by making drawings, like so-called Feynman diagrams (see above), and manipulating symbols in other ways. These manipulations have a deep connection to physical reality, and enable us to divine the secrets of the universe and shape matter and energy to our will. They are "magic that actually works".

So why don't people pay more attention to real magic than fake magic? Of course, fake magic is embedded in stories that are more entertaining than real life. But beyond that, I think there are two key reasons:

First, real magic is hard. Not as hard as people think--it's possible to grasp the basics of something like quantum computing or even quantum mechanics with no more mathematics than what is taught in high school (algebra, complex numbers, and matrix multiplication). But it is indeed true that applying that knowledge to real physical systems calls for much more knowledge and expertise.

More important, I think, is that though our diagrams and calculations may capture the universe precisely, in and of themselves they are powerless to change it. To do that requires advanced engineering and precision manufacturing, using techniques refined over multiple generations by thousands of people. No one person can totally comprehend everything that goes in making, say, a modern smartphone; even mundane products like LED light bulbs and your cat's laser pointer are incredibly sophisticated at their core. Unable to understand how these devices work and what goes into making them, we simply take them for granted.

Once upon a time technology was simpler to understand. I think one of the attractions of the steampunk genre is that it harks back to the last time technology was truly legible, all puffing steam engines and rotating gears. Even electric motors and generators are not incomprehensible, although they mark the transition from the intuitive physics of Michael Faraday (famed for giving lectures and demonstrations to enthusiastic crowds of Londoners) to the mathematical physics of James Clerk Maxwell and his equations of electromagnetism.

Maxwell published his key papers in the 1860s. Perhaps not so coincidentally, 1870 is when the economist Brad DeLong sees everything changing: "In 1870 industrial research labs, modern corporations, globalization, and the market economy ... proved keys to the lock that had kept humanity in its desperately poor iron cage .... And previously unimaginable economic growth revolutionized human life over and over, generation by generation."

Those developments brought advanced technology to millions and ultimately billions, but they also killed its magic, as the heroic lone inventor in their workshop (another steampunk staple) gave way to the corporate R&D department and globalized supply chains. So we seek the magic we crave in novels, comics, and films and TV--the latter themselves benefiting from the use of computer graphics to create increasingly fantastical special effects.

Now we can be (fake) magicians ourselves, thanks to software and its ability to create virtual worlds in which our actions can be translated instantly into effects, whether that be digging a hole in Minecraft or casting an elaborate spell in a fantasy MMO. I could be snobbish and dismiss all this as inauthentic wish fulfillment (for example, comparing "survival mode" in Minecraft to a true survival experience in a wilderness), but I think that's a fundamental mistake: we have always created new environments for us to live in, and (for example) an urban street with quaint shops and comfy apartments is just as much an artificial creation as the latest AAA title. There is no virtue in elevating the former over the latter.

And just as science drives technology, so technology drives science in a feedback loop, for example from the early microscopes that discovered bacteria to the scanning tunneling microscopes that can visualize and manipulate individual atoms. It's possible that software worlds and the tools used to create them will in turn enable new ways to do science and engineering, so that in the future the diagrams drawn by a real-life Coco can create real-life magic.