Dr. Wiseman,
Ahaha, thank you
What have we got today, what are we doing?
Okay, today we're going to talk about reading numbers
I don't mean like numerology,
like reading the stars or anything
I mean, actually seeing a number and reading it and speaking it,
and the processes that happen when you are doing that.
If we're gonna talk about reading, then we probably should think about
words quickly because we know a whole lot about how we read words.
There are two different processes in the brain when we read words. We can either
read words that we're familiar with which are legal words
and those are ones that we have like a long-term memory representation of
so words that you can find in the dictionary Brady: Go on, give me some
Dr Wiseman: cat, lamppost, elephant, tutu
that's a really interesting mental image I just got there
I don't know where that came from those are just four of the many words are
available to you
and we know that people can read those because they see it and they recognize the
kind of shape of it
and then they produce the noise they produce the phonological form of that word
however when you're reading something that's a non-word like
BLWRGAHLMARJJ
you're actually doing something very different because you can't recognize it and then produce it
you're actually looking at it
letter by letter so we know there are two different routes that you can take
when reading words and non-words. Now if we think about it there is actually an
equivalent to this with numbers
now your reaction to me saying that is what's a non-number because
there's no such thing as a dictionary of numbers and there are infinitely
many numbers I've checked it on Wikipedia if you go to the list of
numbers Wikipedia article it will tell you
that is an incomplete list, so there are, actually I've double checked an infinite number of numbers
Brady: if we're going to allow things like BLWRGAHLMARJJ
there's probably an infinite number of words. Dr W: BLWRGAHLMARJJ is a non-word
so that falls outside of the scope there is no numerical equivalent to
BLWRGAHLMARJJ
so what are we actually looking at? the equivalent
is whether or not the numbers that you're reading
are familiar, or meaningful to you, or whether or not they're
unfamiliar, or meaningless to you. The thing that happens in your brain when you read
a number that you're familiar with
is different to what happens when you read a number
that you are unfamiliar with Brady: so it's the same as with words?
Dr W: exactly exactly there are multiple different routes that you can choose to read a number
so if you ask me how you define a familiar number, the answer is
poorly. It's super subjective. There are numbers that are familiar to me
that to me that will mean absolutely nothing to you and vice versa there are
a massive set of numbers that culturally we all find familiar
so for example the the year 2015 thats familiar to all of us
but if I was to pick the number
1804 that probably doesn't mean much to you
no? that's because it's my birthday how dare you not know when my birthday is
Brady: What, as in the 18th of the 4th? Dr W: exactly, so that number however
is very familiar to myself I think the number 1066
is probably a familiar number to most people
however having had that assumption very confidently around a lot of people I
realize that some people's knowledge of history
is not exactly as good as you might imagine Brady: I guess numbers that are
like titles of films and things like that Dr W: exactly
Brady: lower numbers are better for this? Dr W: I have done some research on this and I
basically made this survey and got people to just type in a load of numbers they liked and then
assessed whether or not they thought they were familiar or random the distribution
was the case that a lot of the lower numbers were very much more familiar to people
and then as you went up in magnitude the frequency of familiar numbers that you got
decreased however there were like nice peaks
you get peaks for numbers that look like years
so I wanted to know when the kind of future would end I think I did
this a couple years ago
so 2013 was a familiar number to people 14 15 16 was
but 2017 people decided was not familiar to them so Brady: four years?
Dr W: yes four years that's the end of the future and
people don't care about it after after that it appears
obviously now you're sitting there thinking well 2017 is highly familiar to me
that's because that's two years away and you're in the future now so there are other things
90210 is a familiar thing to people and
that's interesting itself because it began as a zip code but
it probably doesn't mean a zip code to most people probably means the TV program
there's a whole load of reasons for numbers to be familiar to us
okay okay let's explore this so I said there were
multiple different routes
I'm going to give us a start number so this is the number that we are going
to be reading
the most basic thing we can do with it is we can take it
and turn into its Arabic numeral form so that is
when we're reading it out we get out at the end 1 9 8 9
it has no other meaning beyond it's just a string of digits and they
don't interfere with or talk to either either
the other digits around it very straightforward obviously now the next thing we can do is
we can turn into its number word form. Now this is probably going to be a bit contentious.
I'm going to turn into the word form nineteen hundred and eighty nine
I say contentious because I think that when you read that number that is
probably not the first thing you go to when you read it as a word
so with the first one you haven't done any processing on it you've just gone
digit by digit and turned into its phonological form whereas with this second way of
processing it what you have to do is work out exactly
which digit you're reading and also the position of that digit within the number
so this nine gets read out as nine whereas this nine gets
joined to the one and becomes the number nineteen. On the mathematical route
this means we might come up with some mathematical facts about the number
so when you read that number you might say I know that that number
is greater than a 1000 I know that that number
is odd there's a whole load of things you might notice. That number
represents a kind of an amount of something
it has a meaning
beyond the first two levels we talked about Brady: it has constituent parts and ...
Dr W: exactly, it has rules that it adheres to. Up until, like, quite recently
all models of number reading have really just focused on these
these three levels we call this one surface reading and this one is a deeper
semantic reading of it. What you have to do is not just
turn into a phonological form you've also had to appreciate
kind of the meaning behind and what it actually relates to
there is a fourth level and this is kind of something that we've only
recently started trying to put into
models of number reading and that fourth level is something called
encyclopedic look up
and this is what happens when the number that you're reading
has some position in your long-term memory that is
when the number the you're reading means something to you
when you've come across it before in some circumstance
so, this number you may have realized
looks quite a lot like a year for example 1989
to me the reason I've chosen it is because that
is a personal important to me because that's when my sister was born
that's my sister yeah, yay!
there is also a cultural significance to this year
at the moment Taylor Swift's incredible new album
is called 1989 Brady: is that 'cos she was born in 1989?
Dr W: I assume so Brady: is Taylor Swift your sister?
Dr W: (sharp intake of breath) I've chosen this method to tell everyone that yes
Taylor Swift is my younger sister. So there is this
more cultural and kinda shared reason for this number to be familiar
to me, you Brady I know, and
probably millions and millions and millions of other people that have
caused this album to be at the number one spot for 10 weeks running or something
like that see you get this
cultural significance: Taylor. Now there are lots of models of number reading
and they haven't really incorporated all of these these these levels
together before
and the reason it's interesting
is because we can kinda prove that these levels exist
it might like I say it might be kinda obvious to you
that you can read these numbers like this and you're probably not aware of
you doing all of these different things but people that are aware of this
are researchers who look at patients with aphasia
aphasia is a language disorder that
is often caused by a brain trauma and
by language disorder I mean its affects your ability to
affects your ability to read sometimes it affects your ability to speak
but that's all it does it doesn't affect your
understanding of what you're reading, or what you're trying to say
some people get a specific
effect of aphasia on their ability to read numbers
it can kind of take out some of these pathways
Brady: but not all of them? Dr W: not all of them which is the really really
cool and interesting thing. In this paper they do this case study
and they look at a man who is 43 and he suffers a brain trauma and then he
he develops aphasia as a result of that this guy
his ability to do that digit by digit reading
had been lost and so when he was shown a number that
he was unfamiliar with he couldn't read it out loud that means
this pathway here been taken out this part way here
had been taken out as well so no longer could he rely
on just sounding out numbers or producing number words
so he was very interested in racing rally cars in particular, so he was
shown this number
he said "number of cars that win"
"it was my first car, it begins with a P, Peugeot, Renault, it's Peugeot!"
four oh three, five hundred, no, five oh four
so that's how he managed to get to it because 504 is a brand of Peugeot car
that according to this man wins.
It's the car that wins and so that shows you exactly how he managed to read it out loud
he went through this encyclopedic stage
and found this memory representation of the number
and was able to read it out loud Brady: so if you'd shown him
505 he would never ... he would have had no chance .. he couldn't even say it
Dr W: no, he wouldn't be able to do it
Brady: he wouldn't even have been able to say "that's a 5"
"that's a zero, that's a 5" Dr W: he would read this unfamiliar number out
as the similar familiar number if you see what I mean
Brady: so if I showed him 505 he might have said 504!
Dr W: Yes exactly yeah, so there was one example the patient is
is French and apparently in France the
the common thing for doctors to check your breathing is to ask you to say the
number 33
and so that makes it a familiar number to him and he was shown the number
330 which was unfamiliar to him
and he sat looked at it and he said "33?"
because he was desperately trying to read it out and so he
took this encyclopedic route and that was the closest number that he could
find was 33
Brady: you didn't cross out the mathematical branch
Does that mean if I showed him two numbers he would know which was bigger than the other or ...
Dr W: yes it does mean that, he was able to do that
he still had the mathematical ability
and he was still able to tell which of two numbers were
larger. If he was shown equations, he tell you whether the equation was correct or not
you read in a mathematical way, you kind of access this set of facts
but you still have to read it out loud this patient yes was able to
form comparisons understand inequalities
but he had still lost
this branch so he couldn't read the numbers out
Brady: so he knew that 10 plus 10 equals 20 is correct but couldn't say it out loud
Dr W: couldn't say it out loud, no, couldn't get to it
unless for some reason 20 was very familiar to him
the number nineteen he read initially as the "that's the age my daughter that"
"the age of my daughter" before finally getting to
19 so if he'd have been able to do some maths that
got to nineteen then yes but he would have been using this route and not this
route to say it
it's twice a day really that I
a good chunk a spare time when I take the dogs out for a walk and that'd seem
like a great chance to catch up on some the latest books
but reading and walking at the same time has its pitfalls
don't worry
help is at hand crack out the phone and and download an audiobook from
audible.com now audible has a staggering range of books
and you can have your choice piped into your ears
with just a few taps if your thumb there are plenty I could recommend but I'm not
above being a bit biased
so why not look at these ones by people who actually star in numberphile videos
and I'll put the titles of their books below in the video description
now if you go to audible, and you use the URL audible.com/numberphile
you will make these puppies very happy
and you'll be showing your appreciation to audible for its support
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you will get a free audiobook the free audiobook of your choice may be one of
those ones are recommended
when you sign up for a trial did you hear that? a free audiobook
and happy puppies what more could you ask check them out thanks to audible
and never walk into a tree again
I'm gonna do a 'not equal to' just in case you were still thinking that maybe Taylor
might be my sister