WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:03.866
[playful instrumental synth music fades slowly]
You know...
00:00:00.000 --> 00:00:00.960
You know...
00:00:00.960 --> 00:00:03.752
Hexagons are the bestagons.
00:00:03.752 --> 00:00:04.429
Why?
00:00:04.429 --> 00:00:05.723
Because bees.
00:00:05.723 --> 00:00:06.836
Bees are the best
00:00:06.836 --> 00:00:09.301
and build only the bestagon, the hexagon.
00:00:09.301 --> 00:00:10.538
Now, I know what you’re thinking.
00:00:10.530 --> 00:00:12.940
Bees build hexagons because they're hexapods
00:00:12.940 --> 00:00:14.130
with hexagon eyes.
00:00:14.130 --> 00:00:15.760
How could they do otherwise?
00:00:15.760 --> 00:00:16.710
Excellent point.
00:00:16.710 --> 00:00:19.820
But the humble bumble has an engineering problem to solve.
00:00:19.820 --> 00:00:22.160
She makes two things: honey and wax.
00:00:22.160 --> 00:00:23.170
The former to eat,
00:00:23.170 --> 00:00:25.030
and the latter to contain the former.
00:00:25.030 --> 00:00:26.460
To make but a little honey,
00:00:26.460 --> 00:00:28.570
she must visit a lot of flowers.
00:00:28.570 --> 00:00:30.150
And to make one unit of wax,
00:00:30.150 --> 00:00:31.770
she needs eight units of honey.
00:00:31.770 --> 00:00:33.860
Wax is costly for bees in flower terms,
00:00:33.860 --> 00:00:35.860
and honey is drippy in food terms,
00:00:35.860 --> 00:00:38.300
so to make a hive that contains the maximum honey
00:00:38.300 --> 00:00:41.320
while using the minimum wax is royally vital.
00:00:41.320 --> 00:00:43.160
Thus, a honeycomb conjecture.
00:00:43.160 --> 00:00:44.770
Which shape works best?
00:00:44.770 --> 00:00:46.470
To answer, we need to talk tiles.
00:00:46.470 --> 00:00:49.440
Tiling is covering a surface with a pattern of polygons.
00:00:49.440 --> 00:00:50.580
There's lots of options
00:00:50.580 --> 00:00:52.220
because there's lots of polygons.
00:00:52.220 --> 00:00:54.520
Even the regulars go on and on-agon.
00:00:54.520 --> 00:00:55.920
Now for bees picking patterns,
00:00:55.920 --> 00:00:57.070
the more complicated ones
00:00:57.070 --> 00:00:59.510
obviously use more lines than necessary.
00:00:59.510 --> 00:01:01.160
That’s what complicated means.
00:01:01.160 --> 00:01:02.880
And thus a honeycomb of that tile
00:01:02.880 --> 00:01:04.700
would use more wax per honey.
00:01:04.700 --> 00:01:06.160
So sticking to the simple regulars,
00:01:06.160 --> 00:01:08.240
there are just three that tile tightly.
00:01:08.240 --> 00:01:09.850
Triangle, square, and hexagon.
00:01:09.850 --> 00:01:12.260
Pentagons are broken hexagons leaving gaps.
00:01:12.260 --> 00:01:13.400
Same with septagons.
00:01:13.400 --> 00:01:14.550
Octagons are alright,
00:01:14.550 --> 00:01:15.830
but they're no hexagon.
00:01:15.830 --> 00:01:18.480
Which leaves the tiling trio which tile differently.
00:01:18.480 --> 00:01:20.190
A square is a square of squares,
00:01:20.190 --> 00:01:22.190
which is a square of squares, and so on.
00:01:22.190 --> 00:01:24.420
Squares tile tidily by basically cheating.
00:01:24.420 --> 00:01:26.030
Covering an infinite plane with an
00:01:26.030 --> 00:01:28.030
infinite number of parallel lines.
00:01:28.030 --> 00:01:30.810
Like, wow, that's what a plane is.
00:01:30.810 --> 00:01:31.750
Boring!
00:01:31.750 --> 00:01:33.180
Triangles pull the same trick,
00:01:33.180 --> 00:01:35.550
dividing themselves down into infinite nothing.
00:01:35.550 --> 00:01:37.000
But not the hexagon!
00:01:37.000 --> 00:01:38.530
The only regular polygon
00:01:38.530 --> 00:01:42.020
to tile a plane without resorting to debasing self-division,
00:01:42.020 --> 00:01:43.790
unlike some squares I could mention.
00:01:43.790 --> 00:01:45.210
At least triangle is trying to be
00:01:45.210 --> 00:01:47.210
more geometrically interesting than square,
00:01:47.210 --> 00:01:48.340
teaming up a bit to…
00:01:48.340 --> 00:01:49.810
one, two, three, four, five, six.
00:01:49.810 --> 00:01:50.690
Wait, hexagon!
00:01:50.690 --> 00:01:52.020
The other shapes can't help it.
00:01:52.020 --> 00:01:54.110
They just want to be the bestagon.
00:01:54.110 --> 00:01:55.300
Even some of the irregulars,
00:01:55.300 --> 00:01:57.140
like rhombus, tile by hexagoning.
00:01:57.140 --> 00:01:58.680
Same with your triakis tilis,
00:01:58.680 --> 00:02:01.290
[with difficulty]
and deltoidal trihexagonals,
00:02:01.290 --> 00:02:03.330
[with continued difficulty]
and your, ah, kisrhombille,
00:02:03.330 --> 00:02:06.610
[with laughter]
and floret pentagonals.
00:02:06.610 --> 00:02:07.980
Look, they're all just hexagons.
00:02:07.980 --> 00:02:09.160
Even Cairo tiles
00:02:09.160 --> 00:02:10.150
(poor pentagons)
00:02:10.150 --> 00:02:13.260
tile up as best they can to form a lumpy hexagon.
00:02:13.260 --> 00:02:16.030
The rest just can't compete with the best.
00:02:16.030 --> 00:02:16.840
The hexagon,
00:02:16.840 --> 00:02:18.410
nobly indivisible,
00:02:18.410 --> 00:02:19.790
is the bestagon.
00:02:19.790 --> 00:02:21.030
Uhh, where were we?
00:02:21.030 --> 00:02:22.270
Oh right, honeycomb conjecture.
00:02:22.270 --> 00:02:24.480
Max honey. Min wax. Three options.
00:02:24.480 --> 00:02:26.480
Okay yes there's the circle.
00:02:26.480 --> 00:02:29.290
A shape defined by the least perimeter for the most area,
00:02:29.290 --> 00:02:31.200
but that only works when you need just one.
00:02:31.200 --> 00:02:33.780
Pack circles and this is the best they can do.
00:02:33.780 --> 00:02:35.200
Look at all that wasted space!
00:02:35.200 --> 00:02:36.500
And even if you pack the gaps,
00:02:36.500 --> 00:02:37.970
you still use more wax.
00:02:37.970 --> 00:02:39.320
And, again, the way these circles,
00:02:39.320 --> 00:02:40.300
arrange themselves …
00:02:40.300 --> 00:02:41.040
it's almost like…
00:02:41.040 --> 00:02:42.010
onetwothreefourfivesix
00:02:42.010 --> 00:02:42.970
hidden hexagon!
00:02:42.970 --> 00:02:44.390
Bees use the hexagon
00:02:44.390 --> 00:02:46.210
because no shape is better to create
00:02:46.210 --> 00:02:48.690
the maximum area for the minimum wall.
00:02:48.690 --> 00:02:50.690
And this min-max stat of hexagon
00:02:50.690 --> 00:02:53.690
is one of the many reason they show up everywhere.
00:02:53.690 --> 00:02:56.330
Including in the aforementioned bee's eyes.
00:02:56.330 --> 00:02:58.650
Each hexagon is a long tube that leads
00:02:58.650 --> 00:03:00.500
to the light-catching cells at the bottom.
00:03:00.500 --> 00:03:02.120
More light equals better vision and
00:03:02.120 --> 00:03:04.290
hexagons let the most light in
00:03:04.290 --> 00:03:06.320
using the least amount of wall.
00:03:06.320 --> 00:03:08.600
So why aren't your eyes hexagons?
00:03:08.600 --> 00:03:09.770
Au contraire mon ami,
00:03:09.770 --> 00:03:11.260
they are l'Hexagone.
00:03:11.260 --> 00:03:14.090
[intensely]
Not on the outside, but on the inside.
00:03:14.090 --> 00:03:16.930
Your light-catching cells are at the back of your eye,
00:03:16.930 --> 00:03:19.910
in a hexagonal grid for the same reason as bees.
00:03:19.910 --> 00:03:21.530
Max light, min wall.
00:03:21.530 --> 00:03:23.040
Your window to the world,
00:03:23.040 --> 00:03:24.720
is but through the hexagon.
00:03:24.720 --> 00:03:26.720
Does that not make it the bestagon?
00:03:26.720 --> 00:03:28.590
Okay, maybe hexagon as min-max-agon
00:03:28.590 --> 00:03:29.870
doesn't catch your fancy.
00:03:29.870 --> 00:03:31.670
Then how about a little mystery, oui?
00:03:31.670 --> 00:03:33.510
Let us travel to Saturn.
00:03:33.510 --> 00:03:35.460
Yes, the rings are attention-grabbing,
00:03:35.460 --> 00:03:36.740
but leave the equator,
00:03:36.740 --> 00:03:39.530
travel north and here lies the unexplained.
00:03:39.530 --> 00:03:41.530
The Great Hexagon of Saturn.
00:03:41.530 --> 00:03:42.580
Need something for scale?
00:03:42.580 --> 00:03:43.960
Well, here's the Earth.
00:03:43.960 --> 00:03:46.190
Oh, here's six the Earths.
00:03:46.190 --> 00:03:48.720
Saturn's hexagon is pretty big.
00:03:48.720 --> 00:03:49.590
What is it?
00:03:49.590 --> 00:03:52.250
Well, you might be thinking it's a geological formation.
00:03:52.250 --> 00:03:53.980
An enormous basalt column
00:03:53.980 --> 00:03:56.190
like the smaller versions you find on Earth.
00:03:56.190 --> 00:03:56.770
But no.
00:03:56.770 --> 00:03:58.070
Saturn is a gas giant.
00:03:58.070 --> 00:04:00.700
There is no surface or geology to speak of.
00:04:00.700 --> 00:04:04.300
So the great hexagon is composed of shapeless clouds
00:04:04.300 --> 00:04:07.220
somehow keeping shape and changing color.
00:04:07.220 --> 00:04:09.830
It's a magnificent solar system mystery.
00:04:09.830 --> 00:04:11.830
And, while I'm no space archeologist,
00:04:11.830 --> 00:04:14.810
if I was looking for an alien-gifted monolith,
00:04:14.810 --> 00:04:16.550
on the most “look at me” planet,
00:04:16.550 --> 00:04:19.770
under a hexagon beacon with earth-sized sides,
00:04:19.770 --> 00:04:21.250
[tongue click]
that's where I would start.
00:04:21.250 --> 00:04:23.660
After all, what aliens would want to make
00:04:23.660 --> 00:04:25.910
first contact with the nearby monkeys
00:04:25.910 --> 00:04:27.730
before they became enlightened
00:04:27.730 --> 00:04:29.730
to pursue the universal truth.
00:04:29.730 --> 00:04:31.800
Hexagon is the bestagon.
00:04:31.800 --> 00:04:34.530
From the largest down to the smallest.
00:04:34.530 --> 00:04:37.360
Say, for example, this tiny snowflake I happen to have,
00:04:37.360 --> 00:04:40.200
that has six sides, as all snowflakes do.
00:04:40.200 --> 00:04:41.720
Gee, what could cause that to be?
00:04:41.720 --> 00:04:44.210
Let's zoom down to the atomic realm and see.
00:04:44.210 --> 00:04:46.690
When water molecules join together to make a flake,
00:04:46.690 --> 00:04:49.240
the sturdy shape they prefer is the hexagon.
00:04:49.240 --> 00:04:50.650
As more molecules join,
00:04:50.650 --> 00:04:52.420
they extend the flake fractally up.
00:04:52.420 --> 00:04:54.810
The beauty of the snowflake on the monkey scale,
00:04:54.810 --> 00:04:57.560
is but an extension of the hexagonal perfection
00:04:57.560 --> 00:04:58.820
on the atomic scale.
00:04:58.820 --> 00:04:59.730
Okay, yes*.*
00:04:59.730 --> 00:05:02.060
You will sometimes find snowflakes with twelve sides,
00:05:02.060 --> 00:05:03.650
but this happens when two growing snowflakes
00:05:03.650 --> 00:05:05.430
get stuck together, so it still counts.
00:05:05.430 --> 00:05:07.430
And the hexagon isn't just for snow,
00:05:07.430 --> 00:05:09.070
but for all ice 1H,
00:05:09.070 --> 00:05:11.230
which means basically all ice on earth.
00:05:11.230 --> 00:05:12.700
Yeah, there's a little ice 1C
00:05:12.700 --> 00:05:13.600
which we don't talk about
00:05:13.600 --> 00:05:14.820
because it's made of cubes,
00:05:14.820 --> 00:05:16.070
and cubes are boring.
00:05:16.070 --> 00:05:17.430
And there's a bit of ice 9.
00:05:17.430 --> 00:05:18.180
No, don't touch that.
00:05:18.180 --> 00:05:19.630
But if there is ice in your drink,
00:05:19.630 --> 00:05:22.220
give thanks to the hexagon for keeping it cool.
00:05:22.220 --> 00:05:23.280
And it's not just water.
00:05:23.280 --> 00:05:25.480
Lots of atoms use hexagons because…
00:05:25.480 --> 00:05:26.360
(take a note)
00:05:26.360 --> 00:05:28.360
hexagons are the bestagons.
00:05:28.360 --> 00:05:29.660
Oh, using a pencil?
00:05:29.660 --> 00:05:31.660
Get ready to have your mind blown
00:05:31.660 --> 00:05:33.440
about the hexagon here too.
00:05:33.440 --> 00:05:34.340
The lead.
00:05:34.340 --> 00:05:36.340
Well, it isn't lead lead, it's carbon.
00:05:36.340 --> 00:05:38.800
And you know what carbon atoms think is the bestagon?
00:05:38.800 --> 00:05:40.310
[snap]
The hexagon.
00:05:40.310 --> 00:05:43.160
Pencil graphite is a whole bunch of hexagonal carbons,
00:05:43.160 --> 00:05:45.160
and when they happen to be in a straight sheet,
00:05:45.160 --> 00:05:46.240
that's graphene,
00:05:46.240 --> 00:05:48.260
which happens to be the strongest
00:05:48.260 --> 00:05:50.600
atomic material in the universe.
00:05:50.600 --> 00:05:52.380
Some of which is in that pencil.
00:05:52.380 --> 00:05:53.940
To tear a sheet of graphene apart,
00:05:53.940 --> 00:05:56.190
you would need a hundred times more force
00:05:56.190 --> 00:05:57.700
than to do so with steel.
00:05:57.700 --> 00:05:59.630
Hexagon is strong-a-gon.
00:05:59.630 --> 00:06:01.580
This is because when hexagons come together,
00:06:01.580 --> 00:06:04.770
they form three-sided joints 120 degrees apart.
00:06:04.770 --> 00:06:06.330
This, for the least material,
00:06:06.330 --> 00:06:08.730
is the most mechanically stable arrangement.
00:06:08.730 --> 00:06:09.660
Pull on one joint,
00:06:09.660 --> 00:06:11.500
and the other two equally pull back,
00:06:11.500 --> 00:06:13.080
push in, and the other two are the
00:06:13.080 --> 00:06:15.080
most able and stable to resist.
00:06:15.080 --> 00:06:17.080
Now look anew at a tiling of hexagons
00:06:17.080 --> 00:06:18.840
and you see it is composed of nothing
00:06:18.840 --> 00:06:20.290
but these max stable joints,
00:06:20.290 --> 00:06:22.660
each arranged perfectly to help the others
00:06:22.660 --> 00:06:24.120
be stronger and stabler.
00:06:24.120 --> 00:06:27.420
This is another reason hexagons show up everywhere.
00:06:27.420 --> 00:06:30.610
The universe blesses stability in her physics,
00:06:30.610 --> 00:06:32.210
from those basalt columns,
00:06:32.210 --> 00:06:33.150
to bubbles which,
00:06:33.150 --> 00:06:34.150
as soon as they can,
00:06:34.150 --> 00:06:36.080
ditch their spheres to become
00:06:36.080 --> 00:06:38.880
as close to hexagonal perfection as they can.
00:06:38.880 --> 00:06:39.950
That's so cool.
00:06:39.950 --> 00:06:40.560
Oh right, yes.
00:06:40.560 --> 00:06:42.240
So if your pencil lead contains
00:06:42.240 --> 00:06:44.640
some of the strongest material in the universe
00:06:44.640 --> 00:06:45.700
how can you write with it?
00:06:45.700 --> 00:06:46.430
Okay, okay.
00:06:46.430 --> 00:06:49.010
This is going to get even more exciting.
00:06:49.010 --> 00:06:51.290
While hexagons are super strong this way,
00:06:51.290 --> 00:06:53.190
they aren't super strong this way.
00:06:53.190 --> 00:06:54.040
On a small scale,
00:06:54.040 --> 00:06:55.720
that means your pencil can break off
00:06:55.720 --> 00:06:57.190
in layers to leave a mark.
00:06:57.190 --> 00:06:58.300
But on a big scale,
00:06:58.300 --> 00:07:01.590
hexagons can be flexible while keeping their strength,
00:07:01.590 --> 00:07:04.680
letting us construct some totally unreal materials.
00:07:04.680 --> 00:07:06.790
Print out a grid of hexagons in whatever,
00:07:06.790 --> 00:07:07.970
from aluminum to cardboard,
00:07:07.970 --> 00:07:08.970
make a little sandwich,
00:07:08.970 --> 00:07:09.750
and pow!
00:07:09.750 --> 00:07:11.230
You've got honeycomb paneling.
00:07:11.230 --> 00:07:13.760
A ridonkulously tear-resistant material
00:07:13.760 --> 00:07:15.970
that's also super light and flexible.
00:07:15.970 --> 00:07:17.420
It's used everywhere
00:07:17.420 --> 00:07:19.310
but particularly in aviation.
00:07:19.310 --> 00:07:21.310
Rockets need to be strong yet light.
00:07:21.310 --> 00:07:22.480
Same for aircraft.
00:07:22.480 --> 00:07:24.480
With wings that really can't tear
00:07:24.480 --> 00:07:25.980
but also need to bend.
00:07:25.980 --> 00:07:28.110
And only the magic of the honeycomb panel
00:07:28.110 --> 00:07:29.430
can do both as well.
00:07:29.430 --> 00:07:32.180
Give thanks to the hexagon for blessing our flight.
00:07:32.180 --> 00:07:34.050
And we still haven't yet discussed
00:07:34.050 --> 00:07:36.830
the most important application of the hexagon.
00:07:36.830 --> 00:07:37.540
Games!
00:07:37.540 --> 00:07:40.920
For centuries there has been great debate over boards,
00:07:40.920 --> 00:07:42.770
squares or hexagons?
00:07:42.770 --> 00:07:44.210
Spoiler... hexagons win.
00:07:44.210 --> 00:07:45.610
Square boards are the first thing
00:07:45.610 --> 00:07:47.610
an unenlightened species would think of.
00:07:47.610 --> 00:07:50.190
They look sensible and are easy to implement,
00:07:50.190 --> 00:07:51.270
but they are terrible,
00:07:51.270 --> 00:07:53.890
ineffective boards that cause spatial suffering.
00:07:53.890 --> 00:07:55.610
On a square board move horizontal
00:07:55.610 --> 00:07:56.670
or vertical one space
00:07:56.670 --> 00:07:58.420
and you've moved one space,
00:07:58.420 --> 00:07:59.760
but move diagonal
00:07:59.760 --> 00:08:02.320
and the distance is the square root of two spaces.
00:08:02.320 --> 00:08:03.140
Gross.
00:08:03.140 --> 00:08:05.630
Diagonals warp the distance pieces move.
00:08:05.630 --> 00:08:07.700
Square boards look even and tidy,
00:08:07.700 --> 00:08:08.530
but it's deceit.
00:08:08.530 --> 00:08:12.050
Their diagonals corrupting the meaning of space and time,
00:08:12.050 --> 00:08:13.490
and of course they must,
00:08:13.490 --> 00:08:16.640
because a square only has four true neighbors.
00:08:16.640 --> 00:08:18.440
Hexagons, however, have six
00:08:18.440 --> 00:08:19.620
which is more than four,
00:08:19.620 --> 00:08:20.280
which is better!
00:08:20.280 --> 00:08:22.480
And the distance from one space to the next
00:08:22.480 --> 00:08:24.200
is the same in every direction.
00:08:24.200 --> 00:08:25.250
One space.
00:08:25.250 --> 00:08:26.570
Just as it should be.
00:08:26.570 --> 00:08:28.030
If you're a game based on squares,
00:08:28.030 --> 00:08:29.020
I'm so sorry.
00:08:29.020 --> 00:08:30.360
But there is hope.
00:08:30.360 --> 00:08:31.540
With thought and effort,
00:08:31.540 --> 00:08:34.550
you can hexagon yourself into a better place.
00:08:34.550 --> 00:08:36.430
As we all should aspire to do,
00:08:36.430 --> 00:08:39.070
spreading order and hexagonal enlightenment
00:08:39.070 --> 00:08:41.730
for, hexagons are the bestagons.
00:08:41.730 --> 00:08:44.370
And now that you agree, with your eyes will see
00:08:44.370 --> 00:08:46.950
their six-sided perfection in all things.
00:08:46.950 --> 00:08:48.560
And you will say to yourself,
00:08:48.560 --> 00:08:49.840
as part of the order
00:08:49.840 --> 00:08:52.250
hexagons are the bestagons.
00:08:56.400 --> 00:09:00.150
Uhh, thanks for stopping by for communicator coffee.
00:09:02.150 --> 00:09:05.980
Now, go. Share the enlightenment of the order with others.
00:09:05.980 --> 00:09:07.470
[click]