[Music] [Applause]
so a couple of weeks ago I was giving
so a couple of weeks ago I was giving another speech go figure
another speech go figure
another speech go figure – a group of Okinawan middle school
– a group of Okinawan middle school
– a group of Okinawan middle school students where I was asked to describe
students where I was asked to describe
students where I was asked to describe my work and I am a material scientist an
my work and I am a material scientist an
my work and I am a material scientist an engineer by trade with a background in
engineer by trade with a background in
engineer by trade with a background in nanotechnology and so the question arose
nanotechnology and so the question arose
nanotechnology and so the question arose what is a nanometer the textbook
what is a nanometer the textbook
what is a nanometer the textbook definition of a nanometer is a billionth
definition of a nanometer is a billionth
definition of a nanometer is a billionth of a meter but then that got me to
of a meter but then that got me to
of a meter but then that got me to thinking does anyone really know what a
thinking does anyone really know what a
thinking does anyone really know what a billionth of a meter is and that kind of
billionth of a meter is and that kind of
billionth of a meter is and that kind of took me down a line of thinking of just
took me down a line of thinking of just
took me down a line of thinking of just how ill-equipped the human mind is at
how ill-equipped the human mind is at
how ill-equipped the human mind is at comprehending quantities that are very
comprehending quantities that are very
comprehending quantities that are very large and very small now comprehending
large and very small now comprehending
large and very small now comprehending quantities that are very large and very
quantities that are very large and very
quantities that are very large and very small are is very important to science
small are is very important to science
small are is very important to science because in essence science is all about
because in essence science is all about
because in essence science is all about the quantification and qualification of
the quantification and qualification of
the quantification and qualification of things in the world around us right and
things in the world around us right and
things in the world around us right and you watch these documentaries sometime
you watch these documentaries sometime
you watch these documentaries sometime and in these documentaries they’ll talk
and in these documentaries they’ll talk
and in these documentaries they’ll talk about how the universe is 14 billion
about how the universe is 14 billion
about how the universe is 14 billion years old or how the universe may be
years old or how the universe may be
years old or how the universe may be comprised of strings that are 10 to the
comprised of strings that are 10 to the
comprised of strings that are 10 to the minus thirty fifth of a meter but to be
minus thirty fifth of a meter but to be
minus thirty fifth of a meter but to be honest I don’t think anyone the narrator
honest I don’t think anyone the narrator
honest I don’t think anyone the narrator myself or the Audion or the intended
myself or the Audion or the intended
myself or the Audion or the intended audience can actually comprehend these
audience can actually comprehend these
audience can actually comprehend these skills to actually Intuit what these
skills to actually Intuit what these
skills to actually Intuit what these numbers mean in the words of Richard
numbers mean in the words of Richard
numbers mean in the words of Richard Dawkins our brains have evolved to help
Dawkins our brains have evolved to help
Dawkins our brains have evolved to help us survive within the orders of
us survive within the orders of
us survive within the orders of magnitude of size and speed at which our
magnitude of size and speed at which our
magnitude of size and speed at which our bodies operate at and this talk is an
bodies operate at and this talk is an
bodies operate at and this talk is an attempt just an attempt to penetrate
attempt just an attempt to penetrate
attempt just an attempt to penetrate these veils of vastness smallness and
these veils of vastness smallness and
these veils of vastness smallness and innumerable ‘ti of the world around us
innumerable ‘ti of the world around us
innumerable ‘ti of the world around us so the first thing I came across in
so the first thing I came across in
so the first thing I came across in preparing for this talk was that human
preparing for this talk was that human
preparing for this talk was that human beings are terrible at counting all of
beings are terrible at counting all of
beings are terrible at counting all of us and I do mean all of us can’t really
us and I do mean all of us can’t really
us and I do mean all of us can’t really count beyond 8 now before everybody gets
count beyond 8 now before everybody gets
count beyond 8 now before everybody gets up in arms about their fancy college
up in arms about their fancy college
up in arms about their fancy college education I
education I
education I to clarify what I mean by counting
to clarify what I mean by counting
to clarify what I mean by counting counting here I mean what I mean by
counting here I mean what I mean by
counting here I mean what I mean by counting here is Sabbat is a ssin a term
counting here is Sabbat is a ssin a term
counting here is Sabbat is a ssin a term coined in 1949 by an American
coined in 1949 by an American
coined in 1949 by an American psychologist by the name of Al Kaufman
psychologist by the name of Al Kaufman
psychologist by the name of Al Kaufman sabot ization is our gut feeling for
sabot ization is our gut feeling for
sabot ization is our gut feeling for numbers our ability to look at a certain
numbers our ability to look at a certain
numbers our ability to look at a certain amount of something of identical objects
amount of something of identical objects
amount of something of identical objects and immediately say oh there’s three or
and immediately say oh there’s three or
and immediately say oh there’s three or four of this on the table and it turns
four of this on the table and it turns
four of this on the table and it turns out that beyond a your mileage will
out that beyond a your mileage will
out that beyond a your mileage will definitely vary but let’s look at why
definitely vary but let’s look at why
definitely vary but let’s look at why I’d like to ask the audience to do a bit
I’d like to ask the audience to do a bit
I’d like to ask the audience to do a bit of a thought experiment with me here so
of a thought experiment with me here so
of a thought experiment with me here so I’d like you all to imagine a single
I’d like you all to imagine a single
I’d like you all to imagine a single elephant with majestic tusks and trunk
elephant with majestic tusks and trunk
elephant with majestic tusks and trunk and all even if you haven’t been to the
and all even if you haven’t been to the
and all even if you haven’t been to the zoo you can probably imagine what an
zoo you can probably imagine what an
zoo you can probably imagine what an elephant looks like next I’d like to ask
elephant looks like next I’d like to ask
elephant looks like next I’d like to ask the audience to find their elephant a
the audience to find their elephant a
the audience to find their elephant a nice date so now you have two elephants
nice date so now you have two elephants
nice date so now you have two elephants still within the realm of possibility
still within the realm of possibility
still within the realm of possibility how about three elephants doable for
how about three elephants doable for
how about three elephants doable for elephants yeah you could do that five
elephants yeah you could do that five
elephants yeah you could do that five elephants uh so what’s happening here
elephants uh so what’s happening here
elephants uh so what’s happening here chances are you’ve started putting your
chances are you’ve started putting your
chances are you’ve started putting your elephants in recognizable shapes
elephants in recognizable shapes
elephants in recognizable shapes triangles or rows or crosses or squares
triangles or rows or crosses or squares
triangles or rows or crosses or squares or what have you
or what have you
or what have you and this is a neat thing that the brain
and this is a neat thing that the brain
and this is a neat thing that the brain does called visual grouping studied in
does called visual grouping studied in
does called visual grouping studied in 1930s and 1940s by group by a school of
1930s and 1940s by group by a school of
1930s and 1940s by group by a school of psychology called Gestalt psychology in
psychology called Gestalt psychology in
psychology called Gestalt psychology in Germany this school found that even
Germany this school found that even
Germany this school found that even babies were capable of discerning and
babies were capable of discerning and
babies were capable of discerning and identifying small abstract numbers they
identifying small abstract numbers they
identifying small abstract numbers they were able to identify that three of
were able to identify that three of
were able to identify that three of something was more than two of something
something was more than two of something
something was more than two of something but in that same vein as the number
but in that same vein as the number
but in that same vein as the number increases or as the or as the adage goes
increases or as the or as the adage goes
increases or as the or as the adage goes as above so below if the fraction
as above so below if the fraction
as above so below if the fraction decreases it becomes more difficult for
decreases it becomes more difficult for
decreases it becomes more difficult for us to subah ties so a hundred elephants
us to subah ties so a hundred elephants
us to subah ties so a hundred elephants a thousand elephants not as easy to
a thousand elephants not as easy to
a thousand elephants not as easy to actually imagine as one cognitive
actually imagine as one cognitive
actually imagine as one cognitive scientist called Douglas Hofstadter put
scientist called Douglas Hofstadter put
scientist called Douglas Hofstadter put it we have a sense of number numbness
it we have a sense of number numbness
it we have a sense of number numbness for very large and very small quantities
for very large and very small quantities
for very large and very small quantities so that’s one thing that’s getting in
so that’s one thing that’s getting in
so that’s one thing that’s getting in the way of our perception of very large
the way of our perception of very large
the way of our perception of very large and very small quantities
and very small quantities
and very small quantities another thing that’s also getting in the
another thing that’s also getting in the
another thing that’s also getting in the way is how we define numbers because how
way is how we define numbers because how
way is how we define numbers because how we define numbers inadvertently ends up
we define numbers inadvertently ends up
we define numbers inadvertently ends up affecting how we perceive them there are
affecting how we perceive them there are
affecting how we perceive them there are two kinds of numbers
two kinds of numbers
two kinds of numbers the first is cardinal numbers and that
the first is cardinal numbers and that
the first is cardinal numbers and that is the numbers those are the numbers
is the numbers those are the numbers
is the numbers those are the numbers that we use for counting on a day-to-day
that we use for counting on a day-to-day
that we use for counting on a day-to-day basis the number of things so for
basis the number of things so for
basis the number of things so for example the number of unnecessary
example the number of unnecessary
example the number of unnecessary sequels or prequels or reboots or
sequels or prequels or reboots or
sequels or prequels or reboots or spin-offs in your favorite movie
spin-offs in your favorite movie
spin-offs in your favorite movie franchise
franchise
franchise seriously Hollywood enough on the other
seriously Hollywood enough on the other
seriously Hollywood enough on the other hand there are also ordinal numbers and
hand there are also ordinal numbers and
hand there are also ordinal numbers and ordinal numbers are the numbers in a
ordinal numbers are the numbers in a
ordinal numbers are the numbers in a sequence the first second third fourth
sequence the first second third fourth
sequence the first second third fourth fifth and sixth item on a list now this
fifth and sixth item on a list now this
fifth and sixth item on a list now this is very very important because
is very very important because
is very very important because scientific notation which is by far the
scientific notation which is by far the
scientific notation which is by far the most common means of representing human
most common means of representing human
most common means of representing human numbers is involved with juggling
numbers is involved with juggling
numbers is involved with juggling cardinal and ordinal quantities so for
cardinal and ordinal quantities so for
cardinal and ordinal quantities so for example instead of saying 10,000 you can
example instead of saying 10,000 you can
example instead of saying 10,000 you can say 10 to the fourth power right or
say 10 to the fourth power right or
say 10 to the fourth power right or instead of saying 1,000 you can say 10
instead of saying 1,000 you can say 10
instead of saying 1,000 you can say 10 to the third power scientific notation
to the third power scientific notation
to the third power scientific notation is a strong but double-edged weapon in
is a strong but double-edged weapon in
is a strong but double-edged weapon in our representation of large quantities
our representation of large quantities
our representation of large quantities it allows us to make immediate
it allows us to make immediate
it allows us to make immediate assertions that 6 million of something
assertions that 6 million of something
assertions that 6 million of something is less than 7 million of something but
is less than 7 million of something but
is less than 7 million of something but on the other hand it does nothing for us
on the other hand it does nothing for us
on the other hand it does nothing for us if you put six million grains of sand on
if you put six million grains of sand on
if you put six million grains of sand on the ground right now
the ground right now
the ground right now and I immediately ask you how many
and I immediately ask you how many
and I immediately ask you how many grains of star there you can’t do you
grains of star there you can’t do you
grains of star there you can’t do you can’t count that that you can’t sabotage
can’t count that that you can’t sabotage
can’t count that that you can’t sabotage that the notation is only good for
that the notation is only good for
that the notation is only good for representing the numbers not for
representing the numbers not for
representing the numbers not for intuiting them right and at the core of
intuiting them right and at the core of
intuiting them right and at the core of this at the core of scientific notation
this at the core of scientific notation
this at the core of scientific notation is this idea of exponentiation this idea
is this idea of exponentiation this idea
is this idea of exponentiation this idea of multiplying or dividing a number by
of multiplying or dividing a number by
of multiplying or dividing a number by itself a certain number of times right
itself a certain number of times right
itself a certain number of times right and we deal with exponentiation all the
and we deal with exponentiation all the
and we deal with exponentiation all the time with denominations of money when we
time with denominations of money when we
time with denominations of money when we say the number of Dimes in a dollar or
say the number of Dimes in a dollar or
say the number of Dimes in a dollar or the number of $10 bills in a hundred
the number of $10 bills in a hundred
the number of $10 bills in a hundred right so manipulating numbers having to
right so manipulating numbers having to
right so manipulating numbers having to go back and forth and basically compare
go back and forth and basically compare
go back and forth and basically compare quantities is something that is
quantities is something that is
quantities is something that is happening in different regions of the
happening in different regions of the
happening in different regions of the brain when we try and when I ask you to
brain when we try and when I ask you to
brain when we try and when I ask you to do a long division problem it turns out
do a long division problem it turns out
do a long division problem it turns out that
that
that functional MRI studies show us that it’s
functional MRI studies show us that it’s
functional MRI studies show us that it’s the left hemisphere portions of the left
the left hemisphere portions of the left
the left hemisphere portions of the left hemisphere of your brain that are
hemisphere of your brain that are
hemisphere of your brain that are lighting up like a Christmas tree doing
lighting up like a Christmas tree doing
lighting up like a Christmas tree doing this operation on the other hand when I
this operation on the other hand when I
this operation on the other hand when I hold up three fingers and I hold up four
hold up three fingers and I hold up four
hold up three fingers and I hold up four fingers and I ask you which one of these
fingers and I ask you which one of these
fingers and I ask you which one of these is bigger it’s actually both hemispheres
is bigger it’s actually both hemispheres
is bigger it’s actually both hemispheres of your brain that are involved in
of your brain that are involved in
of your brain that are involved in comparing numbers
comparing numbers
comparing numbers long story short as far as your brain is
long story short as far as your brain is
long story short as far as your brain is concerned doing math and comparing
concerned doing math and comparing
concerned doing math and comparing quantities are two completely different
quantities are two completely different
quantities are two completely different things so that can get in the way of
things so that can get in the way of
things so that can get in the way of your understanding of what large numbers
your understanding of what large numbers
your understanding of what large numbers are or what small numbers are to put
are or what small numbers are to put
are or what small numbers are to put this in perspective a million dollars
this in perspective a million dollars
this in perspective a million dollars could fit in a suitcase a billion
could fit in a suitcase a billion
could fit in a suitcase a billion dollars would require a large pickup
dollars would require a large pickup
dollars would require a large pickup truck to transport whereas a trillion
truck to transport whereas a trillion
truck to transport whereas a trillion dollars would be a football field as
dollars would be a football field as
dollars would be a football field as high as the average adult male now
high as the average adult male now
high as the average adult male now orders are magnitude are ordinal right
orders are magnitude are ordinal right
orders are magnitude are ordinal right the orders of magnitude themselves for
the orders of magnitude themselves for
the orders of magnitude themselves for example the third power the fourth power
example the third power the fourth power
example the third power the fourth power the minus third power are ordinal but
the minus third power are ordinal but
the minus third power are ordinal but they increase earth medically they are
they increase earth medically they are
they increase earth medically they are linear so third fourth fifth and so on
linear so third fourth fifth and so on
linear so third fourth fifth and so on however the quantities that they
however the quantities that they
however the quantities that they represent the cardinal numbers that they
represent the cardinal numbers that they
represent the cardinal numbers that they represent are increasing exponentially
represent are increasing exponentially
represent are increasing exponentially we’re multiplying again the number again
we’re multiplying again the number again
we’re multiplying again the number again by itself so each number for example in
by itself so each number for example in
by itself so each number for example in the thousandfold common usage of numbers
the thousandfold common usage of numbers
the thousandfold common usage of numbers of millions billions and trillions is a
of millions billions and trillions is a
of millions billions and trillions is a thousandfold of the preceding number so
thousandfold of the preceding number so
thousandfold of the preceding number so numbers can quickly blow much larger
numbers can quickly blow much larger
numbers can quickly blow much larger than we can understand them one last
than we can understand them one last
than we can understand them one last thing to also consider as to why numbers
thing to also consider as to why numbers
thing to also consider as to why numbers are so difficult to calm and small
are so difficult to calm and small
are so difficult to calm and small numbers are so difficult to comprehend
numbers are so difficult to comprehend
numbers are so difficult to comprehend is their novelty 1939 a mathematician by
is their novelty 1939 a mathematician by
is their novelty 1939 a mathematician by the name of Edward Kasner challenged his
the name of Edward Kasner challenged his
the name of Edward Kasner challenged his nine-year-old nephew to come up with an
nine-year-old nephew to come up with an
nine-year-old nephew to come up with an inconceivably large number his nephew
inconceivably large number his nephew
inconceivably large number his nephew Milton industrious fellow that he was
Milton industrious fellow that he was
Milton industrious fellow that he was decided to take a piece of paper write
decided to take a piece of paper write
decided to take a piece of paper write down one and follow it with a hundred
down one and follow it with a hundred
down one and follow it with a hundred zeroes he called this number a Google
zeroes he called this number a Google
zeroes he called this number a Google now a Google truly is large so large in
now a Google truly is large so large in
now a Google truly is large so large in fact that it might be larger than the
fact that it might be larger than the
fact that it might be larger than the total number of atoms in the
total number of atoms in the
total number of atoms in the servable universe which scientists
servable universe which scientists
servable universe which scientists guesstimate at 10 to the 81st power
guesstimate at 10 to the 81st power
guesstimate at 10 to the 81st power simply speaking before very recent times
simply speaking before very recent times
simply speaking before very recent times we simply did not have neither the
we simply did not have neither the
we simply did not have neither the computational power nor the resolving
computational power nor the resolving
computational power nor the resolving power to actually observe numbers that
power to actually observe numbers that
power to actually observe numbers that were very large or very small of
were very large or very small of
were very large or very small of anything of a God Rose number which you
anything of a God Rose number which you
anything of a God Rose number which you may remember from your high school
may remember from your high school
may remember from your high school chemistry class as the number of species
chemistry class as the number of species
chemistry class as the number of species B they atoms ions or atoms in a grand
B they atoms ions or atoms in a grand
B they atoms ions or atoms in a grand mole of substance is something that is
mole of substance is something that is
mole of substance is something that is very recent it was only discovered in
very recent it was only discovered in
very recent it was only discovered in 1909 which is a blink of an eye
1909 which is a blink of an eye
1909 which is a blink of an eye in the hill in the human in human
in the hill in the human in human
in the hill in the human in human history right another thing to consider
history right another thing to consider
history right another thing to consider is that for example looking very far
is that for example looking very far
is that for example looking very far away with say the Hubble Space Telescope
away with say the Hubble Space Telescope
away with say the Hubble Space Telescope the Hubble was launched in living memory
the Hubble was launched in living memory
the Hubble was launched in living memory it was launched in 1990 and even just
it was launched in 1990 and even just
it was launched in 1990 and even just last year in 2016 they discovered yet
last year in 2016 they discovered yet
last year in 2016 they discovered yet another distant galaxy and broke the
another distant galaxy and broke the
another distant galaxy and broke the cosmic distance record so seeing things
cosmic distance record so seeing things
cosmic distance record so seeing things that are this far is still something
that are this far is still something
that are this far is still something that is ongoing in closing there’s an
that is ongoing in closing there’s an
that is ongoing in closing there’s an ongoing debate in pedagogy developmental
ongoing debate in pedagogy developmental
ongoing debate in pedagogy developmental psychology and cognitive neuroscience
psychology and cognitive neuroscience
psychology and cognitive neuroscience about why it is so difficult for human
about why it is so difficult for human
about why it is so difficult for human beings to comprehend very large and very
beings to comprehend very large and very
beings to comprehend very large and very small quantities and to be frank I think
small quantities and to be frank I think
small quantities and to be frank I think that nothing short of a sci-fi s
that nothing short of a sci-fi s
that nothing short of a sci-fi s cybernetic upgrade would allow a person
cybernetic upgrade would allow a person
cybernetic upgrade would allow a person to just look at a pile of sand and say
to just look at a pile of sand and say
to just look at a pile of sand and say oh yeah of course there’s 53 million 237
oh yeah of course there’s 53 million 237
oh yeah of course there’s 53 million 237 499 grains in this pile but the takeaway
499 grains in this pile but the takeaway
499 grains in this pile but the takeaway here isn’t how to perceive these large
here isn’t how to perceive these large
here isn’t how to perceive these large quantities it’s what’s getting in the
quantities it’s what’s getting in the
quantities it’s what’s getting in the way in the hope that this awareness will
way in the hope that this awareness will
way in the hope that this awareness will help the pedagogy the pedagogical
help the pedagogy the pedagogical
help the pedagogy the pedagogical community in conveying large and small
community in conveying large and small
community in conveying large and small quantities so first of all just to
quantities so first of all just to
quantities so first of all just to summarize cognition the sense of number
summarize cognition the sense of number
summarize cognition the sense of number numbness that gets in the way and the
numbness that gets in the way and the
numbness that gets in the way and the lateralization of rein function we’re
lateralization of rein function we’re
lateralization of rein function we’re doing operations and comparing
doing operations and comparing
doing operations and comparing quantities occupies different regions of
quantities occupies different regions of
quantities occupies different regions of the mind second convention and the
the mind second convention and the
the mind second convention and the scientific notation and how it can be a
scientific notation and how it can be a
scientific notation and how it can be a double-edged weapon and finally novelty
double-edged weapon and finally novelty
double-edged weapon and finally novelty in perceiving and quantifying very large
in perceiving and quantifying very large
in perceiving and quantifying very large and very small quantities thank you
and very small quantities thank you
and very small quantities thank you you
”
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