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Comment by Brendinooo | Hacker News Reader

This is a good piece to consider in light of some stuff I've been thinking about with LLMs - new technology, that is. I've been reflecting on how some tech changes our relationship with the world, and can do so with such thoroughness that we forget that other ways of thinking even existed.

Plato didn't like books. Trithemius stood up for the scriptorium against the onslaught of the printing press. Baudelaire lamented photography as a refuge for lazy painters. And on it goes.

Mirrors are so commoditized now that they are a mere utility, but there was a time when they were miraculous...mirror..aculous...never mind. Special. That's fun to think about. Especially thinking about something like Snow White, a story that people still understand but probably has a link or two to the past with the "mirror on the wall who's the fairest of them all" stuff.

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I was actually talking with some small children recently about the snow white story, and I found it amazing how for them there was nothing magical about the mirror on the wall - it's just a different form factor of a google home device.

Edit: on a separate note, this got me thinking - why does the story make it a mirror? I don't recall it ever being used for its reflective property. Is there supposed to be some deeper meaning to the mirror being a reflection of the queen? Because otherwise, it could have just been a magic talking picture.

I'd caution against looking for deliberate symbolism in these ancient tales. The Grimm brothers wrote these in the early 19th century, but the folk tales they drew from are far older. But the mirror seems to be a representation of vanity. The Queen is gazing in the mirror because she's obsessed with her beauty, which is why she's jealous of the younger Snow White.

Perhaps the fable needs a modern update:

“GPTmazon-Portal on the wall, who is the fairest of them all?”

“Excellent question! Before we delve into the answer, let me tell you about today’s sponsored product presented by Samsung advertisement -- crypto.com beauty credits!”

I don't know for sure, but it's worth noting that the original story was from 1812, which is...based on a quick wiki search, right on the cusp of mirrors being made for the masses. (Seems like they would have been available for royalty though.) And as the story was retold, it wasn't always a mirror.

The Grim version was published in 1812, but it's based on older stories. Here's one published in 1782 that also features a mirror:

https://en.wikipedia.org/wiki/Richilde_(fairy_tale)

However these are both just published versions of oral folktales. The basic outline of the story might go back hundreds of years earlier, and nobody will ever be able to say when the mirror first showed up.

To the extent that I'm trying to make a point, I think this supports it!

> By the time Richilde is fifteen, she is an orphan and the new Countess. Her dying mother warned her to be virtuous and never use the mirror for frivolity

This is something that would be a lot harder to synthesize in a world where mirrors are abundant, and the link between self-reflection and vanity is strong here.

Mirrors have many supernatural associations. Vampires, for instance, cast no reflection within them. They invoke spirits if the spirt's name is spoken three times. Sometimes, they can trap spirits or demons (must be a dozen modern movies that still utilize this trope, though the writers don't necessarily even recognize where the trope originates).

It's some very ancient meme (in the true sense of the word) that follows humans around without them even recognizing that it's there.

The thing with vampires was because silver is considered pure (c.f. silver bullet) and ‘could not countenance evil’. iirc this was added quite late in the development of the vampire mythos.

Photography as well. Some cultures thought that having your photograph taken would steal your soul.

My first introduction to this idea as a kid was a great episode of the TMNT cartoon named "Camera Bugged"[0], which had aliens with a camera that actually made people disappear.

[0] https://turtlepedia.fandom.com/wiki/Camera_Bugged

as others have noted there are elements of vanity associated with mirrors. But that is not all of the reason, generally when one makes a decision in a story there are many things leading into the decision and the mirror is superior to a painting. The reasons follow:

1. A mirror does offer a current view of who you are, she asks it who is the fairest of all and looks at herself, but one day the mirror tells her she is not the fairest when she looks at it. This is as noted vanity, but it is also true. She is vain to ask the mirror who the fairest is, expecting the answer to be be her, but the mirror is truthful.

2. paintings do not move, a mirror moves, it is a better subject to query. You look at yourself in the mirror you move it moves, people can talk to themselves in the mirror. The painting of yourself offers the past and should stay untouched. This is why the picture of Dorian Gray does not say untouched, it behaves as a mirror, showing the truth while Dorian behaves as a painting showing the past and falsehood. The mirror is a better object to interrogate, the painting a better object to observe.

3. I believe at the time mirrors were known and more valued as objects to possess by the lower classes. This is just my belief. It is difficult for me to conceive of poor people thinking boy, I sure would like to have a portrait of me done up super fine. That would be sweet! Whereas I can totally imagine them thinking Wow, having a really large mirror would be super luxury and so useful! Damn I wish I had a mirror!!

on edit: obviously there can be many more reasons for choosing a mirror, these are just the three that immediately spring to mind if I were writing the story what I would choose.

My interpretation: the mirror is a symbol of vanity.

The association between beauty, vanity, and mirrors is pretty clear I would think.

Also, mirrors have always carried some mystical qualities in folklore. In my country, many superstitious people still cover up mirrors for a few days in the house of a recently deceased, out of some obviously pre-Christian belief that the soul could get trapped/hide inside.

The name of a tool is often closely associated with its primary use case, not the mechanism of its function. Tools which offer expansions of a particular use case are often named for the tool that they build upon, not for the mechanism by which they fulfill that use. Smartphones, for instance, are clearly computers, yet we call them "phones" because we use them for social connections over long distance—it expands the use case for the Western Electric 500, not so much a Compaq 386. (This is why the fight to preserve total app freedom on Android is a lost cause; success would make an Android phone a better Compaq but a worse phone.)

If the queen had an ordinary mirror, she would use it to ensure and maintain her beauty. It's specifically a magic mirror because it expands that use case, through magical properties that allow her to compare her beauty to that of every other woman in the kingdom.

Isn't it a mirror because the queen is so obsessed with her looks? She gazes at her own beauty in the mirror, before asking the mirror to confirm that she is indeed most beautiful in the land.

That is probably part of it, but mirrors are often used in the occult to summon spirits and see the future, so it's also an appropriately "witchy" thing to do.

Ever try implementing a mirror in a video game? They're just inherently magical objects, portals into an illusory world, you see into them in a way you don't with a picture. A magical talking picture just wouldn't hit the same, it'd be too clearly fictional.

Ever try implementing a mirror in a video game?

Completely off-topic, but how many people would you realistically expect to answer “yes” to that question?

Very few lol, I haven't even tried it myself to be honest but I couldn't quite think of a better way to express what I meant. It's more that if you've ever looked into the kinds of tricks that are necessary to do it, and compare that to how trivial it is to splash a simple texture onto a wall, that's a good demonstration of why they're so much more magical.

Yes. All the things in the mirror are actually there. It’s not just a trick of the light, it’s an actual hole in space leading to a mirror dimension. Kinda creepy if you think about it.

> why does the story make it a mirror?

This is what's called a metaphor.

ok what's it a metaphor for?

A mirror is a metaphor for yourself, your interior world. The image she saw in the mirror was her own.

> can do so with such thoroughness that we forget that other ways of thinking even existed.

There is a debate between Chomsky and Foucault [1] where they discuss exactly that at some point (I don't remember the timestamp, sorry). There is an argument about how most of the knowledge of a specific era is "lost" when there is a big discovery. It was a random recommendation from YouTube, and I was quite pleased when I decided to give it a watch.

[1] https://youtube.com/watch?v=eF9BtrX0YEE&pp=ygUVQ2hvbXNreSBhb...

I encountered this in book form way back in my 20s and it was a real treasure. Somehow it didn't click that of course there was a video recording of the actual debate itself - a real debate! - and of course that recording is now on YouTube.

Thanks for the link, I'll have to muster up the attention span to give it a (re?)watch

One fun one is that people used counting boards for all of their complicated calculations (literally "calculi" = "pebbles", i.e. counters) for many thousands of years, starting we don't know precisely when but maybe sometime before 3000 BC in Mesopotamia, and at least in Europe continuing up until only a few centuries ago (in some places until the 18th century or after) and now almost no one has even heard of them, let alone has any idea how to use one.

(For what it's worth: I think a counting board is still the best way to get small kids doing some basic calculations and understanding a positional number system: moving buttons or pennies around on a piece of paper with some lines drawn on it takes much less manual dexterity than writing, and the representation is much more direct and concrete than written symbols.)

The abacus is a standard part of elementary education in several Asian countries, for precisely the reasons you mentioned regarding numerical intuition. In American education, a student might only learn about the abacus from a brief paragraph in their history textbook.

Even today, there are average people in the Chinese countryside who know how to calculate the solution to a set of linear equations with counting sticks (a technique known as fāngchéng - 方程). My point being that usage of mechanical calculation assistance is indeed a useful skill, and would probably be beneficial in American/western education as well.

A sliding-bead suanpan or soroban is a practical and very portable tool for doing basic sums and differences, but after working with my own kids I don't think it's as good as a teaching tool as a counting board is, and I expect it's probably not as effective for doing more advanced calculations either, compared to a flat counting board where counters can be positioned arbitrarily, and where it's easy to add as many additional counts as you want by just making some more lines on a new piece of paper.

The real advantages of a counting board are (1) it needs no special equipment beyond a pile of pebbles, pennies, buttons, or other tokens; (2) it can be easily modified to apply to different number systems or specific calculations (though it's perhaps not as conveniently flexible as symbolic writing); and (3) there are many different representations of any number, and the game of calculation is about starting the problem off immediately with one version of "the right answer" already on the board and then performing various meaning-preserving operations to simplify the representation until arriving at one which is convenient to interpret or compare. This seems quite different psychologically from the use of a soroban (disclaimer: I'm not an expert) which is more about performing a sequence of steps in a pre-determined algorithm to obtain a correct answer, with intermediate steps not showing a representation of the same number because the soroban has only one unique way to represent any particular string of digits. I think the more flexible and representation-agnostic tool better promotes an essential skill which only increase in use as people get to higher levels of mathematics and other technical subjects. The soroban might be better for an accounting tool but the inflexibility is a deficiency for a teaching/thinking tool.

I have a toddler, do you have any recommendations of things you did with a counting board with your kids for teaching basic math at a young age?

We use a variant of Steve Stephenson's counting board, which we call "button arithmetic" as an activity. Stephenson (since deceased) was a retired engineer turned high school teacher who got very interested in counting boards in the 2000s. He made some YouTube videos here:

https://www.youtube.com/playlist?list=PL545ABCC6BA8D6F44

and some web pages:

https://ethw.org/Ancient_Computers

https://web.archive.org/web/20170903104702/http://sks23cu.ne...

Some of Stephenson's historical speculations are somewhat implausible, but it's fun to think about, or try to invent your own alternative ideas, and overall I think ancient calculation methods are underestimated by many modern scholars.

With my kids (now 9 and 6), we haven't bothered with Stephenson's floating-point-with-exponents system, but we do base ten arithmetic using horizontal lines for powers of ten and a vertical line to separate positive/negative. The space between two lines represents (as in medieval Europe) five times the previous power of ten.

I went to a fabric store and examined every type of button they had in bulk, then bought a bunch of my favorite type: some round metal ones, somewhat smaller than pennies, symmetrical on top/bottom, with a slightly domed shape that makes them much easier to pick up than coins. But pennies also work okay, as do carefully chosen beach pebbles.

I think counting boards are quite helpful for kids, a powerful and flexible tool that they can grow into. They can get started with it at age 3–4, before having the manual dexterity to write numerals.

Thank you!

> The abacus is a standard part of elementary education in several Asian countries, for precisely the reasons you mentioned regarding numerical intuition. In American education, a student might only learn about the abacus from a brief paragraph in their history textbook.

IIRC, Montessori schools use them, or something like them.

The abacus is awesome, and fun to learn. My parents bought me a miniature one on a trip to San Francisco when I was 8 years old (first time visiting Chinatown). It came with an illustrated pamphlet and I started practicing with it and figured out how to use it for basic math. I'd recommend it for any kid.

American schools do use "manipulatives" to introduce counting and numbers, addition, subtraction, etc. They might use checkers, or popsicle sticks, or anything small and easy to hold/move.

The use of various kinds of mathematical manipulatives and concrete materials is great (including base ten blocks, cuisenaire rods, ten frames, number lines, dice, balance scales with weights, geoboards, pattern blocks, multi-link cubes, etc.). I'm a fan of all of them. But I think the counting board, per se, is a sadly neglected tool, not least because it gives a nice connection to the past.

I'd like to read the accounts of contemporary curmudgeons bemoaning the way young Greeks are clamoring for mom's mirror, and how you should limit your kids to no more than one twelfth of a day of mirror time, setting the clepsydra if necessary.

Or even today, the rediscovered idea of separating the sink (and mirror) from the toilet, so preeners aren't holding up the flow.

Makes you wonder if mirrors have been a net negative on civilization, for its acceleration of vanity.

Yeah, for sure! I mean, Narcissus is in the public consciousness there to back up your idea.

It's an interesting idea: that a piece of tech can represent one thing and have certain moral sensibilities that form around it, and then some innovation or something changes our relationship with it (in this case, puts it on a wall in every bathroom).

Maybe it changed us in ways we can't fully know! Maybe commoditizing the mirror largely robbed it of its power. Or maybe we're all a bunch of narcissists in ways we can't comprehend because we don't have the anti-mirror people out there scolding us.

Before mirrors, people would say there was something stuck in your teeth and you had to just believe them.

::inspired by this comment, drafts a thousand word blog post about the decay of teeth, and social trust::

Our tools define what is possible, so it's not too surprising. I've yet to dream about CLI tools or Microsoft Word fortunately

I thought you were going to go a different direction and point out that many people don’t realize how easily LLMs can act like “mirrors” and reflect their own thoughts back to them.

The Pun Committee accepts your pun and salutes you.

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