[Joke video] Hi everyone welcome back to another video. So a little while ago I made a
video covering this exam here that I'm holding in my hand and it's more of a
test, it's an IQ test and it was one of the ones from Mensa New Zealand saying
that if you can do well on this maybe you'll have a good shot at getting into
Mensa, a high IQ society. That has turned out to be a pretty popular video and
people love challenging themselves on some of these problems but every time I
think about it I sort of think about the idea of trying to test
intelligence based on a set of right and wrong answers which essentially this
test is, it's saying that some of these patterns are more valid than others and
you need to find the same patterns that the person who wrote the answers also
found but I want to take a little look at this exam, with the question in mind
you know, can any answer be correct? and can you basically fit a pattern to any
sequence of shapes or numbers? and you know, what would someone with a 300
IQ do if they were to approach one of these tests? Just to clarify I do know
that IQs of say over 140 would be considered a genius level so saying IQ
300 I know is a bit of a joke and this video is a bit of a joke but at least
maybe it can be a bit of insight into the idea of overfitting or, you know,
fitting overly complicated patterns to the data which, you know, model every
single data point and capture all of the noise and random data points as well not
just the general trend of the data which can be a genuine problem to
have if you're working in say machine learning or something like that
or just trying to predict anything. You actually lose your predictive powers if
you start to over fit your data or model it too closely. Back before we knew that
the earth and planets orbited around the we had some models such as the Ptolemy's
model that earth was at the center of the solar system and some of these
scientists came up with more and more intricate and complicated models to try
and explain every single, you know, data point they could find. They had to come
up with elaborate, you know, circles and loops that big planets were following
which would explain why they appeared to be moving back and forwards in the sky
if they were orbiting the Earth. I think it got to a point where this model was
just so complicated trying to explain everything in the wrong way that
ultimately it was better just to adopt a new model that made more sense. This
video is filmed on the 31st of July which is Harry Potter's birthday so
these glasses are reference to that but also perhaps they will give me the
necessary IQ points that I need to answer some of these. So here's the exam
and if you've seen my previous video this will be familiar to you. Now let's
just start with looking at the very first question here. Now the first one is
asking us to complete the next in the pattern or in the series so we've got
a, d, g, j now the low IQ or average IQ way to answer this would be to say that
there are two letters missing between each letter here and the answer given
in the answers is M but I thoroughly disagree with that seeing as we can do
this a much better way [sarcasm]. So what we could do is naturally assign each of our
letters to their numeral in the alphabet so A would give us one, D would
correspond to four, G to seven and J to ten. Our sequence is now 1, 4, 7, 10 if we
can find the next number in this series, translate it back into a letter we will
have an answer. So what are we going to do to find the next number in this
series? Well I'm going to do the thing that I think would be natural and
that's to fit a polynomial to these numbers here. You know, you can have
polynomials of increasing degree to model basically any sequence you want so
I'm going to model this with a fourth degree polynomial which is as follows
301 over 24 X to the 4 minus 1505/12...
and there's my polynomial there. You can check my working if you wish to. If we
plug in an X value of one we will get a y value of one. If we plug in X is equal
to two we will get four. X is equal to three we will be at seven, X is equal to
four will get ten and X is equal to five which is really what we're trying to
generate here, our fifth number in the series, well X is equal to five would
give us a y-value of 314. I quite like that because it's you know an
approximation of pi. Now the only problem is translating it back to a letter well
there's not 314 letters in the alphabet there are however 26 letters in the
alphabet so if we do three one four mod 26 we would get an answer of two [should be mod25]. Okay
I'm sure you know how mod works it's basically the remainder if we were to
divide it by 26 we've got a mod of 2 which would correspond to a letter B and
now that would be my final answer to the question. It does not agree with the
answer given by the answers but I think there is nothing wrong with the way I've
got it and it is perfectly valid [joke]. So moving on, the next one that I'd like to
try is number 15 up here it's one of these visual ones. I've watched a few
episodes of Rick and Morty before I filmed this video so I should be fine
with coming up with something. Now for the sake of it I will give you what the
answer says are the correct answers here. So we're again finding the next one in
the series, we've got one two three. The answers say that number C 😂is the correct
answer for what comes next and they say this is true because the dash oscillates
between these diagonal spaces so would oscillate back to here and the dot moves
around clockwise so it would meet the dash there. I mean you could do that or
you could do my method. Now there's a little bit of setup for my method
but essentially when I look at a square like the one given I imagine it
in a point system where being in this spot here would give you one point, here
would give you two, three and four points. Now let's have a look at the behavior of
the dot in the first three elements. So in the first one it's in position 1 the
dot has accumulated 1 point and the second one it moves across to spot 2. It's
now got an additional two points and in this third one it's moved down to have
an additional 3 points. 1+2+3, at the end of this the dot is on a tally of 6
points. Now let's look at the behavior of the dash, it starts off in the 2 so it has 2
then we can add to that 4 and then we can add to that another 2 now you know
we've got a tally of points for both of them but what are we going to do with
that? Well the only logical thing to do with that would be to think okay
we've got you know one more element in the series and wouldn't it be great if
with that one last iteration we could make the points for both of the shapes
equal. Now there are a couple of ways that this could happen actually and I'll
draw the two possible options for the fourth item in the series so the
dot and the dash, well we've got 6 and we've got 8, well we could imagine that they
could go on to both equal 9 where the dot could gain an additional 3 so it
would have to be here and the dash would gain an additional 1 so it would be here.
I guess that would be one option where the tally would come to a total of 9. Our
other option is to bring the tally both to a total of 10 so the dot would have
to gain an additional 4 placing it here the dash would have to gain an additional 2
placing it here. Alright so that gives as both a total of 10. If we look up to
our possible answers to pick from this option here does not appear as an option
but this option here does so I would say that my better and more correct answer [joke]
would be B. I say the phrase 'more correct' but of course I mean that they
both could be correct depending on what you're looking for here if you're
looking for a IQ 300 play you know maybe that's what I've shown you but if you're
looking for how to score well on this test being marked by whoever is marking
it then you'll have to try and simplify your reasoning down to give an answer of C.
I'll try out one last one on the last page okay so number 30 is a little bit
different from what we've done already we are wanting to find out what shape
would go in this box here so there's obviously some pattern things are
following and to make it a little tricky they've blocked out these two squares so
we can't see what was going on there but we can still work out the pattern fine
enough. Now a quick glance of the answers do say that A is the expected answer for
this so let's see if we agree with them. Now first of all I want to find out what
is happening between this first line and the second line so just from looking
at it I can see a sort of a pattern already, if we count the number of sides
on the smaller shape and divide it by the number of sides on the larger shape
well what we would get is that the cross has 12 sides,
the box has four sides, that division would give us three but if we were to square
three we would get nine and if we were to times that by 10 we would get 90
degrees because that is how much it rotates in terms of where it's flying
off to between this line and the line. Here it flies out to the right, here
this little box appears to be flying down, you know downwards, so that's a
difference of 90 degrees. If we do the same logic I think we can find out what
kind of rotation this box would undergo when it turns into a dot and what angle
it would fly off at. So let's count the number of sides of the little shape, we
have four so that would be four divided by well a circle has one side so that would be four
over one, that would be four, four squared would be 16, times 10 would give us 160
degrees, so if this one is starting from the downwards position we want to rotate
160 degrees well that would be 90 and then would have 70 more we would expect
a triangle with a circle flying out at 160 degrees relative to the base so I
would expect that to be somewhere like there. Now that doesn't
quite perfectly match any of our answers, this one it flies out to the bottom, to
the top, to the right well it's definitely none of those so I would
agree that A fits our pattern most precisely although not exactly and there
you go I've solved a few problems there and I guess you can try out the rest of
them for yourself if you haven't already from my last video. So don't take that too
seriously it was really just a bit of fun to see if we can fit a model to
anything we want to and kind of force our way to any answer possible.
I guess there's something to say for, you know, trying to measure intelligence from
one set of answers, whether mine are more intelligent or less intelligent
is up to the viewer to decide but thank you for watching.