FACTORALY - E118 SYMMETRY

Episode Date: December 11, 2025

Symmetry is balance, and nature adores balance. There is symmetry everywhere if you look for it. This slightly more aesoteric episode ponders the existence of balance all around us. As always, go to the shownotes blog at factoraly.com to see both sides.  Hosted on Acast. See acast.com/privacy for more information.

Hello, Bruce. How are you on this chilly, wintry day? I'm snuggled up warmly, thank you, in this... I mean, normally we complain about our voiceover booths being too hot. Yes. But today, I'm not complaining. Yes, indeed. So who are we, Bruce?

Let's not get too existential about it, but for the uninitiated, who are we and what are we doing here? So my name is Bruce, as you just, spoiler. Spoiler alert. And my name, equally spoiler-ish, is Simon. Yes, yes. Hello, Simon. Hello, Bruce. Hello, everybody.

Welcome to factorily, fun, fact-filled feast of stuff. Yeah, good. That's all you need to know. Yeah. Bruce and I are both nerds. We love pub quizzes. We love facts. We love trivia. We are both that annoying bloke at the pub who starts every conversation with, did you know? Yes. Yes. Or actually, I think you'll find. Actually, I'm sorry, you're wrong there. And once a week as a cathartic effort to rid ourselves of excess knowledge, we come here and spread it to you guys, listening to us at home or on your dog walk or wherever you are.

We broadcast it. Yes, we do. We spread it around. Yeah. Yeah, we enjoy doing it. Why not? Why not? We're here.

We might as well. Yeah. We've got voices. We've got knowledge. Let's put the two together. So every week we pick a new subject. We basically put hundreds of subjects into a random subject picker. Yes.

Sometimes I wonder why I put them in in the first place. what induced me on earth to put symmetry into the checker. It's quite interesting. It seemed like a good idea at the time. Yes. I just was looking around and I thought, oh, that's a bit symmetrical. Yes. So this is rather a broad topic which can very easily get incredibly scientific and mathematical and overwhelming.

I'll tell you what else you did, Simon. It's very visual. Is it? And this is a podcast. oh blime you're right gosh this is going to have some really tricky stuff to describe if only there were some kind of

supporting repository of visual aids that could help people in listening to this podcast Bruce if only there was oh I'll tell you what there is though oh go on there may not be that but there is the show notes on our blog that'll do it so what we do is

we basically put all of the stuff we've been talking about into visual media videos pictures, all sorts of things, which you'll find if you go to the blog at factorily.com. Factorily.com. Do you know, apparently you didn't say that one week

and somebody got very upset. Oh, really? Oh, no. Oh, isn't it interesting? The little things that we sort of stumble across by mistake that become part of the fabric of this show. Yes, I know. I know. So, yeah, so go to the blog, look at the show notes, and reflect on what you see there.

Very good use of the word reflect there. so symmetry then Bruce what the word what's the word about I know it's got two ms in the middle yes annoyingly the word symmetry is not symmetrical which yeah really annoys me well it's a bit like what's the word for not being able to spell properly oh dyslexia yes that's really difficult to spell it is ironic isn't it yeah there's also this is nothing to do with anything but since we're on that topic hippopotomonstrosso sesquipidalia phobia thank you very much, is the phobia of long words. Of course it is.

It's just unkind, isn't it? Yeah, it is. Anyway, so the definition of symmetry, for a start, there's lots of different types of symmetry, so it's already awkward. But roughly speaking, an item or a pattern or whatever it is being made up of similar parts facing each other or based around an axis

is the rough definition. The word symmetry is first written down in English in the 16th century. It comes from the Latin word symmetria, which means symmetry, which in turn comes from ancient Greek, sun metron, which is two separate words, sun with metron, measure, or measurement. So it originally was with measure. How that sort of morphed into what it is now. I'm not entirely sure there seems to have been a bit of a jump.

But that's where the word comes from. Fair enough. We sort of know what it means, but it sort of means all sorts of different things, doesn't it? It does. It can be used in quite a lot of different ways. There are different types of symmetry. I'm instantly taken back to sort of basic math lessons at school where you were given a picture of a rectangle, just a bog standard rectangle. And you had to draw the lines of symmetry through it. Yes. As if imagining a piece of paper being folded into. So there's a horizontal line through this rectangle

and there's a vertical line through this rectangle if you fold either of those it looks like a mirror image of itself so that's it in its basic form and we can all sort of picture that to get a bit more nitty gritty-gritty-ish there are several different types of symmetry I discovered there's lateral or

reflectional symmetry which is what I've just described you know sort of an ink blot folded in half opened up again mirror mirror images yeah and then there's a glide reflectional symmetry what Which is like that, but one step out of kilter. If you imagine footprints in the sand, left, right, left, right.

If you have the two feet next to each other, that's reflectional symmetry. Right. But if you have one foot in front of the other, that's glide reflectional symmetry, which is to say it's symmetrical, but it's one step out of step. Right, okay. I think I get that. Something like that. There's also radial symmetry, isn't there? Where if you look at a circle, it's like basically it's an infinite number of symmetries

because you can cut a circle in an infinite number of ways and it'll be symmetrical. Yes, sure, yeah. Or sort of an example of that in real life is, let's say, a starfish. You rotate it and it's symmetrical. No, starfish are very interesting. Well, go on. Because they're not symmetrical.

They start off symmetrical. And then they grow not to be symmetrical because some of the legs are slightly bigger than the others. Oh, really? Yes, so as young starfish, they are symmetrical. but as time goes on they become less symmetrical. How interesting. It's a bit like flatfish where the eyes migrate from either side of the head

to one side of the head, leaving the mouth at the bottom. Right, yeah. So they actually become more asymmetrical as time goes on. That's a weird thing, isn't it? It's a very good thing. Yes. So what's the first thing that people think of as being symmetrical? other than basic geometric shapes

yes yes so what's the first actual actual real life thing I guess it's people's faces isn't it yeah I mean it's it's kind of it's everywhere in nature it's it's right from the very sort of atomic molecular level you know the way molecules occur the way cells grow they everything grows in a roughly symmetrical no it doesn't oh

I said roughly symmetrical well if you look at trees trees are not symmetrical No, okay, so there's the difference. I keep hitting this difference during my research, and it's really annoying. There's exact symmetry, and there's rough symmetry. Okay. So you look at a face, which is easy for us to do, because we're here on a Zoom call. Everyone else, you'll just have to imagine this.

Your face is roughly symmetrical. That is to say, you've got an eye on both sides. You've got an ear on each side. It's roughly symmetrical, but it's not exactly symmetrical. The exact symmetry is far rarer. yes but rough symmetry exists all over the place yes but people aren't symmetrical if you take somebody's left side of their face and then mirror it and then take their right side of the face and then mirror that they look like two different people totally different faces yeah it's

very interesting yeah i mean people are bilateral yes good word most animals are bilateral so they've got two sides yeah okay um but actually that's on the outside if you cut me open and and look inside. What you'll find is I've got different bits on different sides that do different things. Yes, that's true. So you'll find that my heart is sort of in the middle, but slightly off to the left. And my heart itself is not symmetrical. All the chambers of my heart are different. You'll find that one of my lungs is actually slightly smaller. The left-hand lung is slightly smaller because it has to make room for that heart. You'll find that various organs about my body are sort of on one side or the other. If you split my brain,

in half, you'll find that some of my brain does one thing and the other half of my brain does other things. So although we look as though we're very symmetrical, actually we aren't. No, not at all. I had a look at facial symmetry. There's, it seems that people are naturally more attracted to faces that are more symmetrical. I read a theory about this. Oh, go on. What did you read? Especially women's faces. That's right. Yeah, men seem to be more prone to this than women. Go on, what did you find?

So I discovered that during ovulation, women's bodies slightly fill out, which means that their faces become more symmetrical. So men, when they see a female's face that's symmetrical, know that that female is ovulating. No way. And therefore, they become more attractive. Wow. So it's actually a naturally occurring reaction.

Gosh, that's very strange indeed. Yes. It's estimated that around 2% of the world's population have, you know, truly symmetrical faces. That's more than I was expecting. I was expecting nobody to have truly symmetrical faces. Yes. And as well as being more attractive, as well as making you think that they are better genetic specimens and therefore better for reproduction, etc. Yes. Apparently, more symmetrical faces are deemed to be more trustworthy faces, which I find really odd because I think if I were to see someone with a really symmetrical face, I would instantly think something was off. Yeah.

I mean, there are actors who have very symmetrical, like Leonardo DiCaprio has a very symmetrical. Scully Johansson. They're very symmetrical. But then others are really asymmetric. I actually think there's a nice, what is it called? It's beauty and imperfection, which I'd rather like. Symmetry is all about balance.

And things are imbalanced emotionally That can be difficult So for example Things that show symmetry are things like reciprocity So I do something for you You do something for me That's symmetrical Yes, okay

You feel sad I feel sad for you Right again But if you feel sad And I don't even notice that you're sad Then that's out of balance That's asymmetric Yes

And in general things like apologising Saying that you're sorry It's kind of like I understand and that I've, you know, I've done something to upset you. I'm sorry. And, you know, the epitome of this is the golden rule, which is, you know, do unto others as you would be done by.

Yes. So that's a very symmetrical attitude. It's about sort of equilibrium and balance and stability, isn't it? Yes. You know, in nature, you think of a butterfly. Well, that symmetry in nature is very interesting. interesting yeah um you know if a butterfly weren't symmetrical if it had one wing bigger than the other yes have a jolly hard time flying unless that was to its advantage yes you've got things like

the fiddler crab the fiddler crab the fiddler crab the fiddler crab you know the crabs that have like one large claw they've got one small claw and one large claw yeah there's a reason for that okay they use that claw they wave it in a sort of fiddling motion that's why they're called fiddler crabs to attract females who prefer males with larger claws So it's like ignore the other one. Look at this one. This is my mating claw. Yes, yeah.

Or not just mating. It's like also for intimidating rivals. You know, you can use it as a weapon. Yeah, sure. It's also quite handy for burrowing and things like that. Okay. And you can dissipate excess body heat with that claw. Right.

But the other thing is that if a male loses the large claw, then the little claw grows into a large one. Really? To compensate. Yes. That's amazing. So the big one becomes a little one. And the little one becomes a little one.

big one. Oh, that's brilliant. Wow. So for all the examples in nature where symmetry is favoured, every now and then the complete opposite is true. Yeah. How interesting. So if you look at antlers on a Maldia, then they're very rarely symmetrical. It looks as though they should be. Yeah. But if you look closely, you'll see that they're not. Yeah. It's what you're saying about rough symmetry. Yes, exactly, yeah. Since we're in nature, I had a quick look at snowflakes. We had a...

our first snowfall of the season yesterday in parts of the country. Yes, we did. Very brief. Including here in London. Yeah, very brief, totally slushy, utterly worthless, pointless snow. Anyway, snowflakes, you know, no two snowflakes are the same. Obviously, that's an old cliche. But snowflakes are kind of symmetrical.

Again, not perfectly symmetrical. But the very basis of an ice crystal is that it grows in a hexagonal shape. And therefore, when each of those six sides has more ice crystals grow, as the water freezes on the surface of each of those sides, you end up with six prongs or arms and those are roughly symmetrical, which is why it's so easy

to make paper snowflakes come Christmas time. And I think, you know, in some respects, nature's lazy, nature likes efficiency, nature likes the easiest route, the majority of the time. I would say it likes simplicity. There you go, let's go with that.

Not laziness. The more symmetrical you can get, the easier it is, the more efficient it is. is the stronger it sometimes is, and then all of a sudden you get the fiddler crab, which just bucks that entire theory. But you talked about Snowflakes. I mean, snowflakes are a sort of fractal.

Yes. And if you look at fractals, fractals are fascinating because they look as though they should be symmetrical. Yeah. But just occasionally there'll be a flaw in the maths. Yeah. That's making the fractal. And that floor will be amplified

so that if you keep looking, you realize that actually it started to go completely asymmetric. Yes. And I've got a video which I'll put on the show notes, which is a fractal sort of like, you know how you get those zoom in, zoom out fractals? This is a zoom out fractal. But if you look at it really carefully, you'll see that it's not always entirely symmetrical just because of the way the mass works. Brilliant.

My most delicious example of a fractal is a Romanesque broccoli. Oh, yes. You know that wonderful broccoli that looks like a peak. And if you look at each individual Romanesque frond. Florette. Floret. Yes, thank you. Floret.

It looks like the whole broccoli, which is unusual. Interesting. That's a whole different sort of symmetry. Yeah. Where one part of something looks like the rest of it. The other place where symmetry is very obvious is in architecture. Oh, I was just going to go with architecture, yes.

Were you? Yeah, good. So architects have always built buildings. i think for for a balance reason and also for uh the reason that it seems to be structurally stronger yeah if you make things symmetrical it does yes but then modern architecture sometimes is asymmetrical yes um so so you look at something like the taj Mahal and if you know that classic picture looking down the avenue of trees towards the i don't know i'm doing that in my house um down the tajmahal towards the tajmahal with the trees on either side

it looks like it's an absolutely perfectly symmetrical thing and if you look at it at it from above it still looks symmetrical because it's actually built like that to look symmetrical from above but there are modern architects who use that asymmetry to make a striking imposing building absolutely i was thinking about this we both really enjoy walking around london and you know there are so many examples of symmetrical structures in in london all of the bridges for a start are kind of you know nicely symmetrical if you look at them sideways on you look at um the front of the Natural History Museum or the two wings of the Royal Naval College in Greenwich or whatever. You know, they're designed to, as you say, sort of create balance and harmony and equilibrium.

And it just looks pretty if they're symmetrical. You walk into a church or a cathedral or a town hall or anything like that. And you sort of walk down this central aisle and it's roughly symmetrical. The line of symmetry going down the ceiling through the centre, your eye is automatically brought into the center of that symmetry. And, you know, that's really used in many buildings, particularly in religious buildings, you know, the way your eye is drawn down the central aisle because of the symmetry and you end up looking at the altar. Or you end up looking at the figure in the centre of the stained glass window, which nearly always has, you know, a person standing on either

side of the central figure because it just, it makes it feel more complete and more whole and balanced. Yeah. And then you get the more modern buildings, which are deliberately going away from that and trying to be edgy and cool and different and quirky. Yeah. Well, because modern materials and engineering says that you can. You can't cantilever and things like that. Yes, that's true, yeah. There's a building, one of the newer buildings in London is called the scalpel.

And it hasn't got a symmetrical bone in its body. Its facades are all over the place and it has angles and twists and turns and all sorts. Let's put a picture of that in the show notes. Let's. The scalpel. there's one particular face of the building I suppose what you'd call the roof but it's a funny angle

if you look at that building from the east it looks like the play button in the middle of a YouTube video and when people first starting putting photos of this building online people were clicking on it thinking it was a video but yeah so sometimes you can use asymmetry to make it stand out to make it be a bit different from the rest

yeah another place where architect use symmetry is in the inside of a building the way they decorate it yes so whether it's the the way that the offices or the way that the rooms within a building work as well or whether it's even the soft furnishings because if you think about we go back to the Taj Mahal some of the the mosaics in the Taj Mahal are very interesting as are the rugs and weaving is a very if you look at fabrics fabrics use symmetry quite frequently

things like wallpaper has patterns that repeat I'm just sort of looking around my sound booth now I've got a rather decorative design base trap on my wall it's a very symmetrical pattern I have my laptop in the middle of the booth I have my acoustic panelling

in symmetrical patterns around me there is very little in the world that cannot be symmetrical yes And it just feels better. And unless you're sort of, you know, I expect there are people out there who like a jaunty angle or an unrepeating pattern or, you know, one wall that's just a completely different colour to everything else or whatever it is. Yeah. But I think I have, well, you and I both have fairly sort of logic-oriented minds. And I can't imagine being a house that doesn't have a lot of symmetry.

Yes. I found one particular building that is painfully asymmetrical, and that's the City Hall in Brussels. At first glance, it looks symmetrical, but one side of it is a bit longer than the other. And it's got a perfectly understandable reason, which is to say that it's been added to over the years. It's been sort of built upon and expanded and so on. But to the people who have only just sort of seen it and think what's up with that, there's a wonderful kind of completely false tale told by locals, which is to say that it was an accident. They claim that the architect of City Hall in Brussels got his measurements wrong. And when the thing was built,

it turned out to be asymmetrical. And he was so miserable about that fact that he went to the top of the tower and threw himself off in a fit of despair. Wow. Totally not true. It's just that it's had wings added to it, you know, and it's been extended and therefore it looks asymmetrical. That's all. When we first started to talk about symmetry, when it came up as a subject, what was the first thing that you thought about? Oh, as an instant reaction. Yes. I think I actually thought of those geometric line folding images that I mentioned right at the beginning. Right, because I thought of William Blake.

Okay. Talk us through your thought process, Bruce. Okay. So William Blake wrote a poem. called the tiger. Oh yes. Spelt with a Y rather than an eye. How annoying, but sure. Which goes, tiger, tiger burning bright

in the forests of the night. What immortal hand or eye could frame thy fearful symmetry? Right. And it carries on. And the last line, it's all about God, changes that could frame my fearful symmetry into dare frame my fearful symmetry. Oh, nice.

Which is very nice. Nice. But again, that form of poetry, where you start with something and then come back to exactly the same thing is symmetrical. So in literature there are rules about symmetry. So for example, in a story arc, you try and come back to where you started. Yes, okay, yeah. So there's a lot of symmetrical stuff happening in literature.

In music, there are music forms. So things like the arch form of music, which is like A, B, C, B, C, A. Again, that's very symmetrical. The bars of a blue song, you know, the last bar repeats the first bar. Exactly. One of the things is symmetrical is a palindrome. Oh, yes, yes. You know, things like madam my madam.

Yes. Just one word, like rotator or race car or repaper, are all palindromic. Yeah, so they read the same forwards as they do backwards, yeah. Exactly. Brilliant. And there are sentences that do that as well, aren't they? they, not just single words. A man, a plan, a canal, Panama.

Read that forward and backward. It still comes out as the same thing. Yes. I mean, there are loads of things like, you know, damn it, I'm mad. Yes. I'll do one French one. Oh, go on. Hey, so va la mash, which is, and how is the cow?

There was a whole book written as a palindrome. Oh, really? Yes. Wow. Called Dr. Orkwood, an old. Olson in Oslo. It's a by-guer called Lawrence Levine. It contains 31,594 words.

Good grief. You can read the whole thing backwards. Oh, that's a mind-blower, isn't that? Normally at this point, we would sort of talk about records. But I can't believe, if you go to the Guinness book and say symmetry, will anything come up? Not a single thing, Bruce. This has really frustrated me today.

it's too you know there's nothing that says this is the most symmetrical animal plant snowflake the only thing that there's a possibly a gaping hole in this topic of symmetry that we haven't talked about and i only stumbled across it in looking for records and that's kaleidoscopes oh yes i love a kaleidoscope so kaleidoscopes are these sort of tubes with mirrors down the length of them and one of those sections contains some little colourful shapes or whatever and you hold it up to the eye you rotate it and those shapes are mirrored and it forms beautiful beautiful patterns

and I found the world's largest kaleidoscope which is called the Nagoya City Pavilion Earth Tower which is in Nagoya Japan and it stands 47 metres high as 154 feet and you don't sort of pop your head inside and look at the images but as the insides rotate and create

these different images, it's projected onto a nearby wall, what it's showing. And that has the record for the world's largest kaleidoscope. And that's the closest to a record that actually has anything to do with symmetry. Wow. There is actually,

I don't know whether I officially suffer from this, but there is actually something called asymmetrophobia, which is a phobia over of asymmetrical things. So there's two. is asymmetrophobia and symmetrophobia. Oh. Right, so people who are actually afraid of symmetry, gosh, they would have a hard time walking around in life.

Yes. Wow. Can you imagine living with symmetricalophobia? Cricy. Well, if any of our listeners do suffer from either symmetrophobia or asymmetrophobia, we'd like you both to write in for the purposes of symmetry. Tell us what your experience is like. And you can write in to hello at factorily.com.

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yes you can in which case you'll get a lovely little notification every Thursday saying that a new episode has arrived yep absolutely right so thank you ever so much for coming along to listen to us talk about symmetry please come again next time for another fun-filled fantastical factual episode of factorily bye for now pip pip that's a palindrome isn't it it is very nice Thank you.