Welcome calculator fanciers to Numberphile's series of unboxing videos. My name's Matt Parker and I will be
looking at these three fantastic specimens for you today. Okay so we'll start with the
Morrisons desktop calculator. For those of you not from the UK, Morrison's is a particularly classy
shop over here, think kind of Harrod's. £2 is not a bad amount of money. Now what I like
about this is before you're committing to that kind of investment, because it's in a transparent
blister pack, and because it's reasonably flexible you can actually turn it on while it's in there
and you can test it in the shop. 7 times 7, make sure we get 49. And you kind of know what you're
getting in for before you buy it. We however have shelled out both of those pounds so we will open
it up and see what we're actually dealing with. The blister pack is surprisingly easy to
cut through, here we go. As you can see I am very safely cutting towards my body at all times so I
can keep a closer eye on the blade. We now pop this open, there we are. Oh, okay, so first thing
out is an instruction booklet which is in case you're unfamiliar with the concept of numbers
being represented by digits. We'll leave that for later reference should we get confused. And there
is no other real information on the packet; again it tells you to not put it in the bin because it
is a calculator and it's very difficult to use in a bin, a fact that is repeated on the leaflet over
there. And Morrison's do claim that they are here to help. I'm sure if we do ring their helpline which
they give you here, if we have any calculation or mathematical inquiries about the calculator they
should be able to help us out. Okay so we'll get it out of its packet, there we are, and yes as you
can see it looks alarmingly similar to what it did inside the packet. I can't- there's two tiny
screws on the back - but it is solar powered, that should be fine. The display is pretty good,
we can get 1, 2, 3, 4, 5, 6, 7, 8, 9- we can get eight digits. It can do all
the four major functions: it can add, subtract, multiply, and divide. It's also got a square root
which is very interesting. In fact we'll take the square root for a spin, we'll put in 2 square
root, and that looks pretty accurate to me. And then just as a test we'll multiply that by the square
root of 2 and the answer is: 1.9999998. Okay, that's a little
bit out. In fact we can try a classic one okay: 1 divided by 0 equals error again. Okay, no problem,
okay so accuracy is not brilliant; functions are perfectly passable. If we cover up the screen there
it's got a decent battery life so should it become temporarily overcast you can continue calculating.
And in terms of holding in the hand it's not great, it's a bit awkward to hold to be honest, but
then again as you can see they very explicitly say put it on top of a desk so we can't take too many
points off for that. And on a desk I think that works quite nicely. The scores for the Morrisons
desktop calculator: for display I've given it 5, big but not enough digits. Functionality,
5, accuracy, 3 - can't do root 2. In terms of ergonomics I've given it a 4; its overall
cred a 2, you wouldn't want to be seen on the street using this one. And for durability...
Survived the fall quite well, I give it a 6. That's a total of 25 which is an average score of
4.16 reoccurring. Okay so up next we have the WHSmith scientific calculator for using
while doing science. They make a few hidden claims on the side here that there is a 10 digit display,
which we'll be the judges of, that it's battery-powered, and that it's got 136 functions.
That's quite impressive. And on the back here they just basically list not all 136 functions but a
decent number of them, and a life-size one-to-one scale of the screen showing everything at once. So
I guess if you actually see that your calculator has crashed. Oh and again this one is not for doing
calculations in a bin. Should you accidentally overcut the problem is you will no longer be able to
keep your calc- your calculator in its original packet so please be very careful when you open
this to get a kind of hinging effect so you can return the calculator here for display purposes
afterwards. Oh as always an instruction booklet, and this is substantially more than the Morrisons - look
at this. Before starting calculations, so we have important warnings to use before you even start.
You know what, let's, you know, let's be mavericks and just dive straight in without reading any of that.
So- oh it's got a case! Should your calculator be at risk of splashes you can slide this from only one
of the two directions, and that is not indicated anywhere on the packet so a little bit confusing,
and it does click into place very nice. And should you need to eject it there is a thumb bit at the
bottom there, very very useful. Accuracy wise we can check the square root test, so 2 square root
multiplied by 2 square root equals 2 - much better. So it square roots perfectly accurate. Now we have trigonometric functions
so let's have some fun with those.
So a very interesting test for trigonometric functions is to see how small an angle you can still calculate the
sine of. And so we will switch this into radians; now we're in radians we will take the sine of a
very small angle. And if we do a sine of let's say 0.1 the answer - this is the small angle
approximation - should be about the same number. It gives me about 0.1 but slightly
different. If I do a smaller angle, so clear that, 0.01, sine, I get again closer to what I
started with and the point where it can no longer tell the difference between an angle and the sine
of the angle gives you a test of how accurate its trigonometric function is. So it can do 0.01, 0.001, okay
that's still slightly different, and then 0.0001 - slightly different. 0.00001, that's four
0s and a 1, and it's exactly the same. Okay so at this point it can't tell the difference
between the angle and the sine of the angle. So as far as calculators are concerned, getting to ten
to the minus four and still being able to tell the difference and not being able to attend to
the minus five is average to good. I mean it's all right, I wouldn't write a song about it. Okay
so I mean there are loads of other functions here but I I think we'll just now, instead of
testing how accurate they are because I think the trigonometry is pretty good, we will see how it handles errors. So
we'll put in a negative number, we'll put in negative 5, where's my negative? Take the
square root of that - error. Error and 0, cool, and we'll try 1 divided by 0, and that's
again error and 0. And we'll see if it does the correct order of operation. So I'm going to do 5
plus 2 times 5. If it does it correctly we should get 15, if it does it wrong we'll get 35.
And it does it correctly! We got 15 so it is doing correct orders of operation, that's very impressive.
This is not a bad all-round calculator, I'm very impressed with it. And it has got a tiny screw
there should you do so many calculations you need to put in a new battery. Scores for the WHSmith
scientific calculator: for the display I've given it a 7 out of 10, in terms of functionality
8, accuracy 8, economics a 7 - it does fit very snugly in the hand. In terms of cred I'd
give it a 7, it hasn't got branding but it looks pretty slick. And now in terms of durability...
Survived the fall pretty poorly, that's a 4, for a grand total of 41, an average score of
6.83 reoccuring. Okay and finally we have the Canon with the arc design; and you may think
I'm showing you the back of the box here but in fact I'm not because the front of the box
is the back of the box. It does have a lot more information, in fact even a picture because
I guess you can't see through the packet, this is entirely opaque. Oh and you see unlike the
other ones they have packaged it in a kind of a cuboid of cardboard, which is quite nice. It's I
guess topologically equivalent to the 2-sphere, and it is able to contain something quite nicely in
R3, so I'm very impressed with the packaging there. Okay so there we are, so let's open that up nicely
and then in here it appears to- okay that's not it's not a smooth slide out, it's quite- it's
sticking quite a bit, and that's not very good. I guess for protection and safety, and
should you get any spills or splashes. Maybe you can keep this, so should you be calculating in
a wet environment or maybe you're using it in the shower or a swimming pool you can put the
protective splash layer back over it. I suspect it wouldn't be good if it's actually submerged though;
however I will remove that for now. As you can see it's in no way sealed to allow easy reinsertion of
the calculator into its protective cover. And we are also given - here we go - an instruction booklet. Wow!
This is possibly by surface area even bigger than the instructions we had for the WHSmith one. Again
if you're unfamiliar with what buttons do, and what digits are, they're all over here. And then should
you wish to learn a foreign language they have lessons in foreign languages on this side. Again
we have an on and on button, but suspiciously no off button in this case. I think once you start
calculating they correctly assume you're simply not going to stop. Function wise we have the four
standard guys hanging out the corner here, and then we have Ms with with different numbers of lines
and crosses next to them and some level of memory. And then this is the Greek letter mu, so should you
be calculating any density you can use mu; and should you be using this to do calculations in
an RV, let's say you're making meth, you can use the RV mode. Maybe this makes it more shock-resistant
if you switch into RV or off-road - or GT is if you're racing with the calculator. It is a bit
big to be hon- I'm struggling to hold that entirely in one hand; whereas if you remember the WHSmith
job, look at that! That's a nice little tidy package, that that fits very snugly in there, and it's got
a good reach. I can go all the way across, I mean it's ambidextrous. Whereas this one, I mean that's-
I mean if I was suddenly you know needed GT mode at short notice I really- I can't reach that with the
one handed mode, it would have to be put down and then used from here. But it does have a slightly
raised 5 which it which is very good, so if you're calculating in the dark, you know, after
hours calculations you can still find your way to the 5 and then you can extrapolate where all
the other buttons are from there. Oh and you can see in addition to the normal 0 it's got the
double 0; that's for when things are really 0. I mean this one's pretty 0, this one's
absolute 0. So we'll do the square root of 2 and look- I mean wow! I mean 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12- 12 digits, that's amazing! I'm surprised I don't write
that right across the top- oh they do, there it is. 12- 12 digits, that is an impressive display.
But let's see how the accuracy goes, multiply that by the square root of 2 and we get! Aww it's- well it
has put it into racing mode which is good to see, but it has just got lots of 9s which which is
a real real shame there So alarming close. Another test we can do to see if it can redeem
its accuracy is if we do 1/9, so we get a ninth, if we now multiply that by 9 - if it's really
accurate we'll get 1 back, if it's not accurate we'll get 0.9 reoccurring.
And we get 0.9 reoccurring. So this this is not good for the accuracy. I mean it's got a lot of digits it can
show you, unfortunately it doesn't need to use all of them, in fact it just shows you lots and lots of
inaccurate digits. I mean on the whole I think it's quite a nice calculator, and again it's got screws
on the back should you wish to update the battery. It's battery and solar powered as indicated on
here, solar and battery, so during normal use it can be powered by our free photons but should
this be a post nuclear winter you can continue calculating solely on the battery. So there you
are, that ladies and gentlemen is the Canon. Scores for the Canon AS-120 with the ARC design: display, 9,
lots of digits nice and big. Functionality, only a 6. Accuracy I've given it a 6.9999999.
Ergonomics a 5 - it may be arced but it's still hard to hold. In terms
of cred, a 6, you could get away with using this in a maths department. And for durability:
With the protective cover it handles water very well, I'm giving it a 7,
for a total score of 39.9999999
which is an average of 6.66666542 - possibly a 7.
What did the number 0 say to the number 8? Nice belt. Why do mathematicians confuse Halloween
and Christmas? Because Oct 31 equals Dec 25! There are 10 types of people in the world,
those who understand binary, those who don't, and those who didn't expect this joke to be in base 3.