(You’re still reading this?! OK, I guess I can’t stop you, but don’t say you weren’t warned.)
So far I’ve discussed orders of magnitude, including negative and fractional orders of magnitude, and defined a logarithm of a number as the (possibly negative and/or fractional) order of magnitude corresponding to that number. Now it’s time to simplify the discussion by introducing some basic mathematical notation.^{1}
Using mathematical notation tends to freak some people out, because they see it as an entirely separate language which they don’t and can’t understand — like staring at text in Japanese if you don’t know any of the characters. But it’s better thought of as simply a shorthand way to express things that would take longer and be more cumbersome to express in conventional prose. Thus, for example, it’s easier to write 2 + 3 = 5 than it is to write “two plus three equals five,” and easier to write 10×10×10×10 or 10⋅10⋅10⋅10 (my preferred notation) than “ten times ten times ten times ten.”
With that in mind, let’s introduce the following notation: We represent a one order of magnitude increase as being multiplied by 10^{1} = 10, a two order of magnitude increase as being multiplied by 10^{2} = 10⋅10 = 100, a three order of magnitude increase as being multiplied by 10^{3} = 10⋅10⋅10 = 1,000, and so on. By convention we have 10^{0} = 1, i.e., a “zero order of magnitude” change or no change at all, as discussed previously.
Note that this notation makes it simple to see the effects of multiple increases by various orders of magnitude, using the addition rule discussed previously. For example, an increase of two orders of magnitude followed by an increase of three orders of magnitude is represented as multiplying by 10^{2} ⋅10^{3} = 10^{2+3} = 10^{5} , or an increase by a factor of 10⋅10⋅10⋅10⋅10 = 100,000.
What about a one order of magnitude decrease? We represent that as being multiplied by 10^{-1} = 1/10 = 0.1. Similarly, a two order of magnitude decrease is represented as being multiplied by 10^{-2} = 1/(10⋅10) = 1/100 = 0.01, a three order of magnitude decrease as being multiplied by 10^{-3} = 1/(10⋅10⋅10) = 1/1,000 = 0.001, and so on.
Again the effects of combined increases and decreases by various orders of magnitude can be found using the addition rule discussed previously. For example, an increase of two orders of magnitude followed by an decrease of three orders of magnitude is represented as multiplying by 10^{2} ⋅10^{-3} = 10^{2-3} = 10^{-1} , or an overall decrease by a factor of 10.
As a side note, an increase by, say, two orders of magnitude followed by a decrease by two orders of magnitude is represented as 10^{2} ⋅10^{-2} = 10^{2-2} = 10^{0} . We previously adopted the convention 10^{0} = 1, and we see now that that makes sense, since in this case there was no overall change.
We also have 10^{-2} = 1/100 = 1/(10^{2} ). So a negative value for orders of magnitude (i.e., decreasing by one or more orders of magnitude) converts multiplication into division, as we’ve discussed previously. We also have 1/(10^{-2} ) = 1/(1/100) = 100 = 10^{2} , by symmetry.
What about fractional orders of magnitude? We can represent an increase by half an order of magnitude as being multiplied by 10^{1/2} = 3.1623 (approximately). Again the addition rule for orders of magnitude can be used: an increase by half an order of magnitude followed by another increase by half an order of magnitude is represented as being multiplied by 10^{1/2} ⋅ 10^{1/2} = 10^{1/2 + 1/2} = 10^{1} = 10, as we would expect from the previous discussion.
Finally, how do we represent the logarithm of a number? We use the word “log,” of course: log(10^{3} ) = 3, for example. Often the parentheses are omitted: log 10^{-1} = -1.
Now let’s talk about something that was very important historically but is almost a curiosity now. Suppose you don’t have access to a computer, a calculator, or even an abacus. How can you do calculations like multiplying larger numbers, like 16 times 126, without resorting to pen and paper?
Let’s go back to the examples of fractional orders of magnitude I used previously, that multiplying by a factor of 16 corresponds to an approximately 1.2 order of magnitude increase, and 126 corresponds to an approximately 2.1 order of magnitude increase. In our new notation we have 16 = 10^{1.2} and 126 = 10^{2.1} . Alternately, 1.2 = log(16) and 2.1 = log(126), using the notation for logarithms.
Let’s also get better values for the logarithms of 16 and 126. Fortunately, way back in 1624 someone compiled a table of logarithms of numbers from 1 to 20,000 and from 90,001 to 100,000; on page 35 we find that the logarithm of 16 is 1.2041 (to four digits) and on page 36 we find that the logarithm of 126 is 2.1004 (also to four digits).^{2}
Using our new notation we then have 16⋅126 = 10^{1.2041} ⋅10^{2.1004} . But by our rule of adding orders of magnitude we have 10^{1.2041} ⋅10^{2.1004} = 10^{1.2041+2.1004} = 10^{3.3045} .
So we are looking for a number X = 10^{3.3045} ; this is equivalent to writing log(X) = 3.3045. We can look in the same table we used before to find a number whose logarithm is 3.3045, and on page 55 we find that that number is 2016. This is the value we are looking for, the number corresponding to 16 times 126.
Of course, it would be tedious to carry around a large book just to do multiplication. The solution was the slide rule. The following is a gross simplification of how it might work:
We have two straight rules made of wood, plastic, or metal, each with numbers marked on it, increasing left to right from one end to the other. For example, on one rule the number 16 is marked at a distance of 1.2 cm from the left end of the rule, and the number 2016 marked 3.3 cm from the left end. On the second rule the number 126 is marked at a distance 2.1 cm from the left end of that rule. In other words, in all three cases the distances in cm from the left end of the rule are the logarithms of the numbers in question.
If we line up the left end of the second rule with the number 16 on the first rule (i.e., 1.2 cm to the right of the left end of the first rule), on the second rule the number 126 will line up opposite the number 2016 on the first rule (since 1.2 cm + 2.1 cm = 3.3 cm). Thus we’ve found the result of the multiplication 16 times 126.
Of course, for such a rule to be useful it would need to have all numbers marked on it, and at the size mentioned would be too small to be useful. Actual slide rules used for multiplication contain only the numbers from 1 though 10, since any multiplication with larger numbers can be done by fiddling with the decimal places. For example, we have 16⋅126 = (1.6⋅10)⋅(1.26⋅100) = (1.6⋅1.26)⋅(10⋅100) = (1.6⋅1.26)⋅1,000. So we really only need to multiply 1.6 times 1.26, and then multiply the resulting value by 1,000.
This concludes the second post. I may or may not make more posts in this series.
Since Cohost didn’t support using LaTeX, the most common way to include mathematical symbols and equations in a plain text editor, I faked it using Unicode and HTML. ↩︎
The original book, Arithmetica logarithmica by Henry Briggs, was in Latin. I’m using a modern reconstruction of its tables. ↩︎
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.
(Is everyone else gone? OK, here goes…)
I think the best place to start to understand logarithms may be with the concept of “orders of magnitude,” a concept people use all the time. For example, consider the statement “there are an order of magnitude more users of Facebook than of Twitter, and two orders of magnitude more users of Twitter than of Mastodon.” Here an “order of magnitude more” means “about 10 times more,” and “two orders of magnitude more” means “about 100 times more.”^{1}
The first thing to note is that orders of magnitude can add together: If Twitter has two orders of magnitude more users than Mastodon, and Facebook has an order of magnitude more users than Twitter, then Facebook has three orders of magnitude more users than Mastodon (2 + 1 = 3).
Let’s drop the “about” and for this discussion assume that “an order of magnitude more” means “exactly 10 times more.” Then “two orders of magnitude more” would mean (exactly) 100 times more, “three orders of magnitude more” would mean (exactly) 1,000 times more, and so on.
But we also have 100 = 10 times 10, and 1,000 = 10 times 100 = 10 times 10 times 10. So an order of magnitude increase means the original amount was multiplied by 10, a two orders of magnitude increase means the original amount was multiplied by 10 and then by 10 again (i.e., by 100), and a three orders of magnitude increase means the original amount was multiplied by 10 and then by 10 again and then by 10 once more (i.e., by 1,000).
In other words, the number of orders of magnitude by which the original amount was increased is the number of times you multiply by 10. If you do successive increases first by, say, two orders of magnitude, and then by three orders of magnitude, the resulting amount corresponds to an increase by five orders of magnitude, or 2 + 3.
Now let’s consider the case where something is an order of magnitude less than something else. For example, when we say “Twitter has an order of magnitude fewer users than Facebook,” we typically mean “Twitter has about one tenth the number of users of Facebook,” and when we say “Mastodon has two orders of magnitude fewer users than Twitter,” we typically mean “Mastodon has about one hundredth the number of users of Twitter.”
Again, let’s be exact about this. Then an order of magnitude decrease means the original amount was divided by 10, a two orders of magnitude decrease means the original amount was divided by 10 and then by 10 again (i.e., by 100), a three orders of magnitude increase means the original amount was divided by 10 and then by 10 again and then by 10 once more (i.e., by 1,000). In other words, the number of orders of magnitude by which the original amount was decreased is the number of times you divide by 10.
What about an increase followed by a decrease? Let’s suppose the number of Twitter users increases by five orders of magnitude over a period of years, and then it decreases by two orders of magnitude within a year. That means that the original amount first got multiplied by 10 five times (10 times 10 times 10 times 10 times 10, or 100,000), and then the resulting amount got divided by 10 twice (i.e., by 10 times 10 or 100). The final amount is 1,000 times the initial amount, corresponding to an overall three orders of magnitude increase. We have 3 = 5 - 2, so another way to get the final amount is to add the number of orders of magnitude by which the number of users increased, and then subtract the number of orders of magnitude by which it decreased.
What if something increases by (say) three orders of magnitude and subsequently decreases by three orders of magnitude; in other words it gets multiplied by 10 three times (i.e., by 1,000) and then gets divided by 10 three times (again, by 1,000). The net effect is to return to where it started. But using our rule above, an increase by three orders of magnitude followed by a decrease by three orders of magnitude nets out to an overall increase of 3 - 3 or 0 orders of magnitude. So we can equate “0 orders of magnitude” to mean “no change” or (what’s the same thing) “multiplied by 1.”
Here’s an interesting question: What does it mean (if it means anything at all) to say that something increased by half an order of magnitude? If something increases by half an order of magnitude, and then increases by another half order of magnitude, then overall it’s natural to say that overall there was an increase by one order of magnitude. After all, we’ve been using a rule that you add orders of magnitude when doing a first increase by a certain number of orders of magnitude followed by a second increase by another number of orders of magnitude. And one half plus one half equals one.
Since an increase of one order of magnitude is equivalent to multiplying by 10, an increase of one half an order of magnitude is equivalent to multiplying by some number X, such that multiplying by X and then multiplying by X again is the same as multiplying by 10. In other words, we should have X times X equal to 10.
Does such a number exist and, if so, how could we find it? Well, we know that 3 times 3 is 9, and 4 times 4 is 16, so X should be somewhere between 3 and 4. If we try 3.5 times 3.5, that comes out to 12.25, which is too high. Trying a smaller number, 3.2 times 3.2 is 10.24, which is still too high, but closer. 3.1 times 3.1 is 9.61, which is too low. So X should be somewhere between 3.1 and 3.2. We have 3.15 times 3.15 equal to 9.925, again too low, and 3.17 times 3.17 equal to 10.0489, again too high, but getting very close. If you do this exercise a couple more times on your phone’s calculator app you will find that 3.1623 times 3.1623 is almost exactly equal to 10. So we can say that an increase of half an order of magnitude corresponds to multiplying the original amount by (a number very close to) 3.1623.^{2}
Similarly, we can imagine a third of an order of magnitude increase as corresponding to a number Y such that multiplying an initial amount by Y three times produces an order of magnitude increase. In other words, Y times Y times Y is equal to 10. We have 2 times 2 times 2 equal to 8, and 3 times 3 times 3 equal to 27. So Y must be a number between 2 and 3, and is probably closer to 2. Trying numbers out like was done above, we end up with 2.154 times 2.154 times 2.154 being almost exactly equal to 10.
What about an increase of tenth of an order of magnitude? This would correspond to a number Z such that multiplying an initial amount by Z ten times produces an order of magnitude increase. In other words, Z times Z times Z times Z time Z times Z times Z times Z times Z times Z is equal to 10. A little thought will convince one that Z must be between 1 and 2, and likely closer to 1. Using the same techniques as above, we end up with 1.2589 as a number that when multiplied by itself ten times is (almost exactly) equal to 10.
Continuing from the discussion in the previous section, what does it mean to have an increase of, say, 2.3 orders of magnitude? If we follow the rule of adding orders of magnitude, we see that 2.3 is 2 plus 1/10 plus 1/10 plus 1/10, and conclude that an increase of 2.3 orders of magnitude corresponds to first multiplying by 100 (two orders of magnitude), then multiplying by (approximately) 1.2589 (one tenth of an order of magnitude), then multiplying by 1.2589 again, and then multiplying by 1.2589 once more. We have 100 times 1.2589 times 1.2589 times 1.2589 equal to (approximately) 199.5141. So a 2.3 order of magnitude increase corresponds to an increase by a factor of approximately 200.
We can then turn this around and say that multiplying by a factor of 200 corresponds to a 2.3 order of magnitude increase. We can do something similar for other numbers. For example, what order of magnitude increase corresponds to multiplying by a factor of 16? Multiplying by a factor of 10 corresponds to one order of magnitude, and multiplying by a factor of 100 corresponds to two orders of magnitude, so multiplying by 16 must correspond to an order of magnitude between 1 and 2.
Based on the discussion above, a 1.1 order of magnitude increase corresponds to multiplying by 10 (one order of magnitude) and then by 1.2589 (one tenth of an order of magnitude), or 10 times 1.2589, equal to 12.5889. This is less than 16, so the order of magnitude corresponding to multiplying by a factor of 16 is more than 1.1. What about an order of magnitude increase of 1.2? That corresponds to multiplying by 10 times 1.2589 times 1.2589, or 15.8483. This is very close to 16, so the order of magnitude increase corresponding to a factor of 16 is likely just a bit more than 1.2. (The actual number is approximately 1.2041.)
We can do similar calculations for other numbers. For example, multiplying by a factor of 126 corresponds to an approximately 2.1 order of magnitude increase, multiplying by 2,500 corresponds to an approximately 3.4 order of magnitude increase, and so on.
We can now say what a logarithm is: the logarithm of a number is the order of magnitude increase corresponding to multiplying by that number.^{3} Thus the logarithm of 10 is 1 (one order of magnitude increase), the logarithm of 16 is approximately 1.2 (1.2 orders of magnitude increase), the logarithm of 100 is 2, the logarithm of 126 is approximately 2.1, the logarithm of 1,000 is 3, the logarithm of 2,500 is approximately 3.4, and so on.
What about decreases by some orders of magnitude? They correspond to negative values of the logarithm. A decrease by one order of magnitude corresponds to dividing by 10, and an increase of three orders of magnitude followed by a decrease of one order of magnitude amounts to an overall increase by 3 - 1 = 2 orders of magnitude, according to the rule of adding and subtracting orders of magnitude discussed above. Since dividing by 10 is equivalent to multiplying by one tenth or 0.1, the logarithm of 0.1 is -1. Similarly, the logarithm of one hundredth or 0.01 is -2, the logarithm of one thousandth or 0.001 is -3, and so on.
Also, above we concluded that a “0 orders of magnitude” increase means “no change” or “multiplied by 1.” So the logarithm of 1 is 0.
There is no order of magnitude increase corresponding to multiplying by 0, and no order of magnitude decrease corresponding to dividing by 0 (which isn’t even defined). So the logarithm of 0 is undefined.
There is also no order of magnitude increase corresponding to multiplying by a number less than zero (like -1), and no order of magnitude decrease corresponding to dividing by a number less than zero. So the logarithm is also undefined for numbers less than zero (“negative numbers”).^{4}
The logarithm as we have defined it is thus defined only for numbers greater than zero (“positive numbers”). For numbers greater than one the logarithm is greater than zero, for numbers between 0 and 1 the logarithm is less than zero, and for the number 1 the logarithm is exactly zero.
This is getting pretty long, so I’ll continue the discussion in part 2.
For the record, Facebook has 3 billion users worldwide and Twitter over 300 million, so the “about ten times more” works out in that case. The number of users of Mastodon depends on how you count them, but the number 2.5 million has been thrown around—close enough to 3 million, and thus 100 times less than Twitter. ↩︎
If you have a calculator app on your phone that has a “scientific calculator” mode then you can compute this more exactly by entering the number 10 and then pressing the so-called “square root” key, which should look something like √. On my phone’s calculator app the resulting value is 3.162277660168379—but note that this is still just an approximation. ↩︎
Strictly speaking, this is the so-called logarithm for base 10. ↩︎
It’s possible to define the logarithm of a negative number by allowing the value to be a so-called “complex” number, but that’s beyond the scope of this discussion. ↩︎
Left: In an illustration from the manga Witch Hat Atelier, the young witch Coco explains how to create a magic spell by drawing a diagram. Right: A Feynman diagram showing a neutron (composed of one up quark and two down quarks) decaying into a proton (composed of two up quarks and one down quark) and a weak boson, which then in turn decays into an electron and an electron antineutrino. Click for a higher-resolution version. Left image © Kamome Shirahama, right image in the public domain.
[This post originally appeared on Cohost.]
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.
Nice thoughts! Theres a lot of interesting things to talk about here, but one aspect that comes to mind is the way that this relates to the role of agency in fiction.
For example, why are medieval fantasy themes popular? I suspect that part of this is because they are useful for both the writer and the reader in terms of providing a setting that allows for more flexible agency.
If you compare a medieval fantasy setting to a realistic modern setting, I think you’ll find differences such as:
The state is less powerful(except at the author’s whims) and has less ability to distribute its power effectively. This means several things—such as that the interactions between friends and foes is less cordoned off, and the onus of fixing a problem can be relocated more to individuals.
Warfare can conceivably make individual skill/effort a lot more relevant, especially when you introduce magic and unrealistic strength etc, which gives characters more agency and room for expression of their efforts
There is more nature to act against and with- even without the fantasy element, nature is wild and untamed, back to when it was more of a threat to humans.
There’s more unknowns, because of less state/more nature/less information/less ability to completely overwhelm individuals with modern structures and technologies, even prior to magic.
And there’s probably more that I’m just not remembering from the last time I thought about this, haha.
Because of these, the writer has more avenues to create and unfold conflicts dynamically to create drama, back and forth, themes, gravitas, specific ways things play out, etc without having to fight constantly to create plausibility. I guess the “Wild West” setting has a lot of similarities to it, now that I think about it.
Fictional magic, similarly, is an individual-scale avenue for potential/unknowns/agency that the writers can get more freedom with and readers can be connected to particular things they enjoy seeing expressed(again, agency of individuals).
Thank you for the comment! I think you are correct about historical/fantasy settings providing more agency to the characters. I’m guessing that a part of this is also that rule was/is personalized, being centered in the persons of the monarch and their courtiers/vassals/etc., as opposed to being exercised via a more impersonal bureaucracy.
i think an aspect of “real magic”, as you put (sub)atomic sciences, that makes it disinteresting to a large number of people (including myself) is how divorced from everyday sensory reality it is.
i say this as somepony who is intensely interested in earth sciences; geology, botany, paleontology, zoology, even microbiology and some aspects of astronomy, to a certain degree, are all fairly accessible, and influence ones life in very visible ways. i may not be able to see tectonic plates moving but i can feel earthquakes, and i can see rock structures that are only possible because of uplift. i don’t have a microscope, but if i wanted one, i could get one, and suddenly the cellular structures of the organisms around me would be open to me
even molecular biology, to a certain degree, is somewhat accessible. like, PCR is revolutionary not just because it is a powerful tool for multiplying and sequencing dna but also because it is such a wildly simple technique that you can literally do it over a fucking campfire, and someone has. the barrier to entry for dna sequencing as an amateur biologist is mostly the cost of the chemical components—you don’t need a college degree to understand and carry out the process.
quantum physics, and to a strong degree also much of astrophysics, by contrast, is not something that can readily be understood if you didn’t specialize in it. people can sell you analogies in pop sci books but my trust of such books has been basically irrevocably damaged after i’ve been burned too many times finding out that i’ve been fed a false explanation of how something worked and that the true explanation is just way over my head completely incomprehensible. and if i did manage to understand it, it would feel about as real to me as fictional magic.
i feel like i couldn’t go applying the things i learned in any real way, not the way that knowing about the genetic history of plant families makes you understand what your senses are experiencing better.
the closest i ever came to feeling like i got that kind of everyday application of quantum mechanics to my life was reading QED by richard feynman and him adding up arrows to explain why light bent on a hot road. which is pretty interesting, if a bit abstract! (and there’s that thing again, the real magic doesn’t actually feel particularly real or connected to reality) but meanwhile, i have never actually been able to “understand” quantum computing. ppl make videos trying to explain it and i’ve watched many of them, i’ve tried to even write qasm, but the conclusion i came to is that you can’t actually understand it unless you go into heavy maths and write code, and you can’t write code that actually does anything discernable on a quantum computer unless you have a lot of money reply
Thanks for stopping by to comment! You’re right about quantum phenomena being hard to see and visualize, though people do try: here’s an article about seeing single photons with the naked eye, and another one about replicating the famous double-slit experiment with a cheap laser pointer. You’re also right about Feynmann’s QED: it’s an interesting and fun book.
for me the closest thing to ’fictional magic’ is ’cooking’. you follow a recipe passed down by the sages of old, you improvise a little every once in a while to make it better, and voila, you turned things that people don’t like so much into a magical substance that enamors everyone at the party and has them begging for you to do that trick again next month. and you can just do it in real life any time you want to.
and really if you think about it, the only difference between chemistry and cooking is that cooking is that cooking is limited (mostly) to human-safe substances. and has significantly less extreme effects, like your product probably won’t kill most people. also something something potion brewing. reply
Thanks for commenting! You’re right, cooking can be pretty magic at times, especially in the hands of a master chef.
I’ve thought about these comparisons(often from slightly different angles, but definitely in the same vein, and often also inspired by fiction like WHA) many times, especially the frustrating disparity between [ the ability to understand the fascinating systems underlying everything ] and [ the ridiculously disproportional amount of time and effort required to actually utilise that knowledge practically, especially as an individual ].
This post really nicely expands on those thoughts in ways I never would’ve thought of, and introduces some entirely new threads of thought that feel really enjoyable to explore, like the point about artificial environments. Great post!
brackets added for readability, maybe I wouldn’t need this crutch if my punctuation were better. Sorry
Thanks for your comment! I’m glad you found the post interesting.
this feels like a very wise and true analysis
i’ll add that programming is one field where you can still be a rag-tag do-it-yourself-magician. the stuff you produce will not have the production value and polish of a megacorporation, but it still just might be functional
Thanks for stopping by to comment! I apologize for being so late to follow-up. Yes, you’re absolutely right, software is the one place a sole creator can make a difference, especially given all the (mostly) free tools at their disposal nowadays.
]]>