I received an email the other day completely out of the blue from a guy called Edward
who
said he was in a pub quiz.
One of the questions was how many sides does a banana have, and although he got the answer wrong the answer was five and
So he did some more research on bananas and found that bananas
have three parts to the inside the fruit, so his question to me, was
how does the five on the outside line up with the three on the inside
but that got me thinking - so this is a normal banana, it's a Cavendish banana, that's the variety - all
Cavendish bananas are clones of each other which means they're genetically identical. I mean a banana doesn't have seeds in it so it can't exactly
reproduce sexually. So if you were to push right down the center of
the banana
you will notice that
it splits really easily into three parts and
that is because the flower
The ovary of the flower had three parts to it three locules the name for like the hole in the ovary and so the fruit develops
in three and because the banana is centered around
the number three
That's why it's a bit odd that you get five sides on the outside of banana because you would expect it to be a multiple
of three, you'd expect there to be say six sides to a banana. So what do I mean by the sides of a banana?
well if you take a banana
preferably one that's not too ripe because it gets less noticeable the riper the banana is
you'll see that there are ridges that run all the way from the stem
to the flower scar and remember that bananas normally grow this way up and you can...if I was to draw on these ridges
you'll be able to see them more clearly so this one has one, two,
three,
four,
five, so this has five ridges and therefore five sides so this banana has five sides but
Do all bananas have five sides? So like any good scientist I went and collected more data
I actually stood by the banana section in multiple
supermarkets going around going one two three four five, one two three...most of them had five sides and then I found one banana
had four sides - ahh
and that means that five sides is not universal. It only takes one
four-sided banana to prove that not all bananas have five sides
But I wanted to know okay well what is the average number of sides of a banana and so I needed
yet more data I needed an even bigger sample size and
So I went ahead and bought
280 bananas now counting 280 bananas was not only gonna take me quite a lot of time but then
I'd be stuck with
280 bananas so luckily last week I was
invited to perform at the stand up show for a Festival of the Spoken Nerd
you probably know Matt Parker and Steve Mould, Helen Arney from YouTube and
so
what's a girl gonna do with 280 bananas but have a bit of an Oprah moment
[laughter]
If you think that's good...
Well, get ready to catch, everyone!
YOU get a banana! And YOU get a banana!
And YOU get a banana!
And everybody gets bananas!
And you get a banana!
Everybody gets bananas!
After that mayhem I managed to get 175 bananas counted. That's a great sample size, it's really large and
before I looked at the data in fact before I even bought that many bananas I wanted to
hypothesize why so many bananas have 5 sides but some of them only have 4 sides
So I looked to the biology of the banana. Bananas,
unsurprisingly, grow on banana trees although more surprisingly banana trees aren't actually trees they're herbs but moving on
Bananas grow in hands, the whole bunch of them is a hand and you'll get about 10 to 20
Cavendish bananas in a hand and I was looking at these pictures
and I spotted that
bananas always grow in two rows and with all these bananas growing together
I looked at where the sides actually are within the hand and I noticed that
normally you'd get one of these ridges where two bananas were touching each other and
where there was a gap next to a banana you tend to get just one edge rather than lots of
ridges and
this made me wonder well maybe it's the number of neighbors that
influences how many sides the banana has so I looked at all the scientific literature hoping to find something on
how all the bananas squished together is there
do they always have the same number of neighbors and I found this paper published by Kew Gardens in
1953 called the origin of the banana
inflorescence and what's great like I mentioned before is that all bananas are genetically identical so they all should have very very similar
patterns of where the bananas grow within the inflorescence and I found this figure figure one
which someone has looked at the flower buds developing and shown how they grow and just like in the pictures of the
adult bananas you can see that it forms two rows and that these flowers form a zig-zag pattern
there's a field of maths
that actually looks at if you've got things growing from a point and you've got neighbors next to each other you can get a
boundary where those two neighbors touch and it's Voronoi tessellation
that gives you Voronoi patterns you see it all over nature and combining the Voronoi idea with this figure and
a very handy website that had been made by a guy called Alex Beutel which allows you to draw your own
Voronoi patterns and put the starting points in I was able to replicate figure one as if it was a Voronoi diagram and
this one has
16 bananas in the hand that's pretty average for a Cavendish banana and if we count them
twelve out of the sixteen, three quarters of the bananas
should have five sides because they've got four neighbours and then the ones on the very ends of the bunch
have got either four or three sides and this means if my
neighbors hypothesis my Voronoi hypothesis is correct I would expect to see
three quarters of bananas having five sides and the other quarter having either three or
four sides and that would give me a mean number of sides of
4.625. Now I've got a hypothesis I can look at the data
the 175 bananas that the audience of the comedy club counted for me I
genuinely did not know how this was going to go
but it looks like
this
I could not believe how similar these graphs looked!
seriously, I,
it could have been any
distribution, it could have been normal, it could have been literally they were only
five and then tiny number of four side if enough, but look how similar they look! That's insane, especially because I'd not seen
anything about
tessellations or Voronoi patterns being used to explain the number of sides of a banana in fact I couldn't find anything explaining the number of sides
of a banana but still
I'd come up with this
hypothesis and it looks so similar obviously got to do some statistics on this can't just eyeball it as much as I would want to and
because I got a large sample size it doesn't matter that these aren't normally distributed I can still do a
t-test on the means on the averages and
it turns out that we get a non significant result which
normally you'd be a bit miffed as a scientist to see a non significant result but this test is
testing are these two means different and so non significant means it's not able to
disprove that the means are the same
which basically means that the means are the same which means that my two means, my predicted mean and the actual
mean are the same
which is
amazing I will say that if you look at the overall distribution not just means and do either a chi-squared test which you can't really
do because the expected values of zero or
If you do a Fisher's exact test then you don't get the distributions coming out as exactly the same
but given this is biology and biology is really messy I'm
pretty impressed with this hypothesis as explained going a long way to
explain the number of sides that a banana has and that means that the answer to how many sides does a banana have is
actually
4.625
sides which Matt Parker did point out is
five sides when rounded to the nearest whole number of sides
But that's not the point it means you can't just say that or bananas have five sides in the same way that the average
person has less than two legs because of the number of
one-legged or
no
legged people it brings down the averages averages are allowed to have
non integer values we're allowed to have a
fractional number of sides of a banana and actually someone at the comedy club came up to me afterwards from the audience and
brought me this banana which at one end has four edges and at the other end
has five edges and therefore is a 4.625 sided banana which I thought was great I
Hope you enjoyed this video it's been a long time since
I've made one but I am now back you can expect to see
many more science videos from me in your sub feed this is now my full-time job so if you or a company wants to pay
this newly qualified Doctor of Science to make videos for you drop me a link on my email which is all on my website
Thank you very much and see you next time which actually might not be that long