00:00:00
eons ago we gazed at the Stars and
00:00:03
discovered patterns we call
00:00:05
constellations even coming to believe
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they might control our destiny we watch
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the day's turn tonight and back today
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and seasons as they come and go and call
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that pattern time we see symmetrical
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patterns in the human body and the tiger
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stripes and build those patterns into
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what we create from art
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to our cities but what do patterns tell
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us why should the spiral shape of the
00:00:50
Nautilus shell be so similar to the
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spiral of a galaxy or the spiral found
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in a sliced open head of cabbage
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when scientists seek to understand the
00:01:04
patterns of our world they often turn to
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a powerful tool mathematics
00:01:10
they quantify their observations and use
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mathematical techniques to examine them
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hoping to discover the underlying causes
00:01:20
of nature's rhythms and regularities and
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it's worked revealing the secrets behind
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the elliptical orbits of the planets to
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the electromagnetic waves that connect
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our cellphones mathematics has even
00:01:36
guided the way leading us right down to
00:01:39
the subatomic building blocks of matter
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which raises the question why does it
00:01:48
work at all is there an inherent
00:01:51
mathematical nature to reality or is
00:01:55
mathematics all in our heads
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[Music]
00:02:03
mario livio is an astrophysicist who
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wrestles with these questions he's
00:02:08
fascinated by the deep and often
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mysterious connection between
00:02:12
mathematics in the world if you look at
00:02:16
nature there are numbers all around us
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you know look at flowers for example so
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there are many flowers that have three
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petals like this or five like this some
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of them may have 34 or 55 these numbers
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occur very often these may sound like
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random numbers but they're all part of
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what is known as the Fibonacci sequence
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a series of numbers developed by a
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thirteenth century mathematician you
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start with the numbers 1 and 1 and from
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that point on you keep adding up the
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last two numbers so 1 plus 1 is 2 now 1
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plus 2 is 3 2 plus 3 is 5 3 + 5 is 8 and
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you keep going like this
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trust me today hundreds of years later
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this seemingly arbitrary progression of
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numbers fascinates many who see in it
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clues to everything from human beauty to
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the stock market while most of those
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claims remain unproven it is curious how
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evolution seems to favor these numbers
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and as he turns out I mean the sequence
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appears quite frequently in nature
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tribune achi numbers show up in petal
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counts especially of daisies but that's
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just a start
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the typically the Fibonacci numbers do
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appear a lot in botany for instance if
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you look at the bottom of a pinecone you
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will see often spiral in their scale you
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end up counting those spirals you'll
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usually find a Fibonacci number and then
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you will count the spirals going in the
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other direction and you will find an
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adjacent if you go in actually
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the same is true of the seeds on a
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sunflower head two sets of spirals and
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if you count the spirals in each
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direction both are Fibonacci numbers
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well there are some theories explaining
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the Fibonacci botany connection it still
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raises some intriguing questions so do
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plants know math the short answer to
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that is no they don't need to know math
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in a very simple geometric way they set
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up a little machine that creates the
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Fibonacci sequence in many cases the
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mysterious connections between the
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physical world and mathematics run P we
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all know the number pi from geometry the
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ratio between the circumference of a
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circle and its diameter and that it's
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decimal digits go on forever without a
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repeating pattern as of 2013 it had been
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calculated out to twelve point one
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trillion digits but somehow pi is a
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whole lot pi appears in a whole host of
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other phenomena which have at least on
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the face of it nothing to do with
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circles or anything in particular it
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appears in probability theory quite a
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bit suppose I take this needle so that
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the length of the needle is equal to the
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distance between two lines on this piece
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of paper and suppose I drop this needle
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now on the paper sometimes when you drop
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the needle it will cut a line and
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sometimes it drops between the lines it
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turns out the probability that the
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needle ends so it cuts a line is exactly
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two over pi
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or about 64% now what that means is that
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in principle I could drop this little
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millions of time I could count the times
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when it crosses a line and when it
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doesn't cross a line and I could
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actually even calculate 5 even though
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there are no circles here no diameters
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of a circle nothing like that it's
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really amazing
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since pie relates a round object a
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circle with a straight one its diameter
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it can show up in the strangest of
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places some see it in a meandering path
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of rivers a rivers actual length as it
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winds its way from its source to its
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mouth compared to the direct distance on
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average seems to be about pie models for
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just about anything involving waves will
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have pie in them
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like those four lights and sound hi
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tells us which color should appear in a
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rainbow and how middle C should sound on
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a piano pi shows up in apples in the way
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cells grow into spherical shapes or in
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the brightness of a supernova one writer
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has suggested it's like seeing pie on a
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series of mountain peaks poking out of a
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fog shrouded valley we know there is a
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way they're all connected but it's not
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always obvious how pie is but one
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example of a vast interconnected web of
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mathematics that seems to reveal an
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often hidden and deep order to our world
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[Music]
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physicist max tegmark from MIT thinks he
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knows why he sees similarities between
00:08:06
our world and that of a computer game
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[Music]
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if I were a character in a computer game
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there were so advanced that I were
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actually conscious and I started
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exploring my video game world who would
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actually feel to me like it was made of
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real solid objects made of physical
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stuff yet if I started studying at the
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curious visitors than I am
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the properties are discussed the
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equations by which things move and the
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equations would give the metallurgy
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stuff its properties I would discover
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eventually that all these properties
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were mathematical the mathematical
00:08:54
properties that the programmer had
00:08:56
actually put into the software that
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describes everything the laws of physics
00:09:01
in a game like how an object floats
00:09:04
bounces or crashes our only mathematical
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rules created by a programmer ultimately
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the entire universe of a computer game
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is just numbers and equations that's
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exactly what I perceive in this reality
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- is a physicist that the closer I look
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at things that seem non-mathematical
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like my arm here in my hand the more
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mathematical it turns out to be could it
00:09:30
be that our world also then is really
00:09:32
just as mathematical as the computer
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game reality to match the software world
00:09:39
of a game isn't that different from the
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physical world we live in
00:09:45
he thinks that mathematics works so well
00:09:48
to describe reality because ultimately
00:09:50
mathematics is all that it is there's
00:09:54
nothing else many of my physics
00:09:57
colleagues will say that mathematics
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describes our physical reality at least
00:10:03
in some approximate sense I go further
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and argue that it actually is our
00:10:09
physical reality because I'm arguing
00:10:12
that our physical world doesn't just
00:10:14
have some mathematical properties but
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has only mathematical properties our
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physical reality is a bit like a digital
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photograph according to Max the photo
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looks like the pond but as we move in
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closer and closer we can see it is
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really a field of pixels each
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represented by three numbers that
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specify the amount of red green and blue
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[Music]
00:10:47
while the universe is vast in its size
00:10:50
and complexity requiring an unbelievably
00:10:54
large collection of numbers to describe
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maxi's its underlying mathematical
00:10:59
structure as surprisingly simple it's
00:11:04
just 32 numbers constants like the
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masses of elementary particles along
00:11:11
with a handful of mathematical equations
00:11:13
the fundamental laws of physics and it
00:11:17
all fits on a wall though there are
00:11:21
still some questions
00:11:23
but even though we don't know what
00:11:26
exactly is going to go here I am really
00:11:29
confident that what will go here will be
00:11:31
mathematical equations that everything
00:11:34
is ultimately mathematical max tegmark
00:11:39
matrix like view that mathematics
00:11:41
doesn't just describe reality but is its
00:11:44
essence may sound radical but it has
00:11:48
deep roots in history going back to
00:11:53
ancient Greece to the time of the
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philosopher and mystic pythagoras
00:12:00
stories say he explored the affinity
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between mathematics and music a
00:12:06
relationship that resonates to this day
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in the work of esperanza spalding an
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acclaimed jazz musician who studied
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music theory and sees its parallel in
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mathematics I love the experience of
00:12:23
math the part that I enjoy about math I
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get to experience through music too at
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the beginning you're studying all the
00:12:31
little equations but you get to have
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this very visceral relationships with
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the product of those equations which is
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sound and music and harmony and distance
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and all that good stuff so I'm much
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better at music than at math but I love
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math with a passion they're both just as
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much work okay both you have to study it
00:12:49
off your head off study your head off ha
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ha ha
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the ancient Greeks found three
00:12:57
relationships between notes especially
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pleasing now we call them an octave a
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fifth and a fourth
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an octave is easy to remember because
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it's the first two notes are somewhere
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over the rainbow
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wah-wah that's an octave somewhere a
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fifth sounds like this la la or the
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first one of those twinkle twinkle
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little star and a fourth
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sounds like la la you can think of it as
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the first two notes of here comes the
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bride in the sixth century BCE the Greek
00:13:43
philosopher Pythagoras is said to have
00:13:45
discovered that those beautiful musical
00:13:47
relationships were also beautiful
00:13:49
mathematical relationships by measuring
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the lengths of the vibrating strings in
00:13:55
an octave the string lengths create a
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ratio of 2 to 1 in 1/5 the ratio is 3 to
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2 and in 1/4 it is 4 to 3 being a common
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pattern throughout sound that could be a
00:14:18
big eye-opener saying well if this
00:14:20
existence sound and if it's true
00:14:23
universally through all sounds this
00:14:26
ratio could exist universally everywhere
00:14:29
right and doesn't it pythagoreans
00:14:34
worship the idea of numbers the fact
00:14:37
that simple ratios produce harmonious
00:14:40
sounds was proof of a hidden order in
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the natural world and that order was
00:14:46
made of numbers a profound insight that
00:14:50
mathematicians and scientists continued
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to explore to this day
00:14:57
in fact there are plenty of other
00:14:59
physical phenomena that follow simple
00:15:01
ratios from the two-to-one ratio of
00:15:05
hydrogen atoms to oxygen atoms in water
00:15:08
to the number of times the moon orbits
00:15:11
the earth compared to its own rotation
00:15:13
one to watch or that mercury rotates
00:15:18
exactly three times when it orbits the
00:15:21
Sun twice a three-to-two ratio in
00:15:28
ancient Greece Pythagoras and his
00:15:30
followers had a profound effect on
00:15:32
another Greek philosopher Plato whose
00:15:35
ideas also resonate to this day
00:15:38
especially among mathematicians Plato
00:15:42
believed that geometry and mathematics
00:15:44
exist in their own ideal world so when
00:15:48
we draw a circle on a piece of paper
00:15:50
this is not the real circle the real
00:15:53
circle is in that world and this is just
00:15:56
an approximation of that real circle in
00:15:59
the same with all other shapes and Plato
00:16:02
liked very much these 5 solids the
00:16:04
Platonic solids we call them today and
00:16:06
he assigned each one of them to one of
00:16:10
the elements that formed the world as he
00:16:12
saw the stable cube was earth the
00:16:18
tetrahedron with its pointy corners was
00:16:22
fired the mobile looking octahedron
00:16:25
Plato thought of as hair
00:16:29
and the 20-sided icosahedron was water
00:16:34
and finally the dodecahedron this was
00:16:38
the thing that signified the cosmos as a
00:16:40
whole so Plato's mathematical forms were
00:16:47
the ideal version of the world around us
00:16:50
and they existed in their own realm and
00:16:53
however bizarre that may sound that
00:16:56
mathematics exists in his own world
00:16:59
shaping the world we see it's an idea
00:17:02
that to this day many mathematicians and
00:17:05
scientists can relate to the sense they
00:17:08
have when they're doing math that
00:17:10
they're just uncovering something that's
00:17:12
already out there
00:17:14
I feel quite strong that mathematics is
00:17:16
discovered in my work as a mathematician
00:17:17
those feels to me there is a thing out
00:17:20
there and I'm kind of trying to find it
00:17:22
and understand it and touch it but
00:17:26
someone who actually has had the
00:17:27
pleasure of making new mathematics it
00:17:30
feels like there's something there
00:17:31
before you get to it if I have to choose
00:17:34
I think it's more discovered and
00:17:36
invented because I think there's a
00:17:37
reality to what we study in mathematics
00:17:40
when we do good mathematics we are
00:17:43
discovering something about the way our
00:17:45
minds work and interaction with the
00:17:47
world I know that because that's what I
00:17:50
do I come to my office I sit down in
00:17:51
front of my whiteboard and I try and
00:17:53
understand that thing that's out there
00:17:56
and every now and then I'm discovering a
00:17:58
new bit of it that's exactly what it
00:18:00
feels like
00:18:02
to many mathematicians it feels like
00:18:04
math is discovered rather than invented
00:18:07
but is that just a feeling
00:18:10
could it be that mathematics is purely a
00:18:13
product of the human brain meat shop a
00:18:18
bona fide math whiz 800 on the SAT math
00:18:23
that's pretty good and you took it when
00:18:25
you are how old 11 11 wow that's like a
00:18:28
perfect score
00:18:29
where does Sean's math genius come from
00:18:32
it turns out we can pinpoint it and it's
00:18:35
all in his head using fMRI scientists
00:18:41
can scan Sean's brain as he answers math
00:18:44
questions to see which parts of the
00:18:46
brain receive more blood a sign they are
00:18:49
hard at work alright Sean we'll start
00:18:53
right now everybody
00:18:57
in images of Sean's brain the parietal
00:19:00
lobes glow an especially bright crimson
00:19:03
he is relying on parietal areas to
00:19:07
determine these mathematical
00:19:09
relationships that's characteristic of
00:19:11
lots of math gifted types or in tests
00:19:15
similar to Shawn's kids who exhibit high
00:19:18
math performance at five to six times
00:19:20
more neuron activation than average kids
00:19:23
in these brain regions but is that the
00:19:26
result of teaching and intense practice
00:19:28
or are the foundations of math built
00:19:32
into our brains scientists are looking
00:19:39
for the answer here at the Duke
00:19:42
University lemur center a 70 acre
00:19:45
sanctuary in North Carolina the largest
00:19:48
one for rare and endangered lemurs in
00:19:50
the world
00:19:51
[Music]
00:19:53
like all primates lemurs are related to
00:19:57
humans through a common ancestor that
00:19:59
lived as many as 65 million years ago
00:20:01
[Music]
00:20:04
scientists believe lemurs share many
00:20:06
characteristics with those earliest
00:20:08
primates making them a window though a
00:20:11
blurry one into our ancient past got a
00:20:17
choice here Terry come on up Duke
00:20:20
professor Liz Brannon investigates how
00:20:22
well lemurs like parries here can
00:20:25
compare quantities many different
00:20:28
animals choose larger food quantities so
00:20:30
what is Terry is doing what are all of
00:20:34
these different animals doing when they
00:20:36
compare two quantities well clearly he's
00:20:39
not using verbal labels he's not using
00:20:42
symbols we need to figure out whether
00:20:44
they can really use number pure number
00:20:47
as a cue to test how well Terry's can
00:20:53
distinguish quantities he's been taught
00:20:55
a touchscreen computer game the red
00:20:58
square starts around if he touches it
00:21:02
two squares appear containing different
00:21:05
numbers of objects he's been trained
00:21:08
that if he chooses the box with the
00:21:10
fewest number he'll get a reward a sugar
00:21:14
pellet our wrong answer
00:21:19
[Music]
00:21:21
we have to do a lot to ensure that
00:21:24
they're really attending to number and
00:21:26
not something else to make sure the test
00:21:29
animal is reacting to the number of
00:21:31
objects and not some other cute Liz
00:21:34
varies the object size color and shape
00:21:39
she has conducted thousands of trials
00:21:42
and shown that lemurs and rhesus monkeys
00:21:45
can learn to pick the right answer
00:21:48
Tereus obviously doesn't have language
00:21:50
and he doesn't have any symbols for
00:21:52
number so is he counting is he doing
00:21:55
what a human child does when they recite
00:21:57
the numbers 1 2 3 no and yet what he's
00:22:01
going to be attending to is the very
00:22:04
abstract essence of what a number is
00:22:10
lemurs and rhesus monkeys aren't alone
00:22:12
in having this primitive number sense
00:22:14
rats pigeons fish raccoons insects
00:22:19
horses and elephants all show
00:22:22
sensitivity to quantity and so do human
00:22:26
infants at her lab on the Duke campus
00:22:32
liz has tested babies that were only 6
00:22:35
months old
00:22:36
they'll look longer at a screen with a
00:22:39
changing number of objects as long as
00:22:42
the change is obvious enough to capture
00:22:44
their attention
00:22:47
liz has also tested college students
00:22:51
asking them not to count but to respond
00:22:54
as quickly as they could to a
00:22:56
touchscreen test comparing quantities
00:22:58
the results about the same as lemurs and
00:23:03
rhesus monkeys in fact there are humans
00:23:06
who aren't as good as our monkeys and
00:23:09
others that are far better so there's a
00:23:11
lot of variability in human performance
00:23:13
but in general it looks very similar to
00:23:16
a monkey substituting the 3 what to the
00:23:21
4 even without any mathematical
00:23:30
education even without learning any
00:23:32
number words or symbols we would still
00:23:34
have all of us as humans a primitive
00:23:37
number sense that fundamental ability to
00:23:41
perceive number seems to be a very
00:23:43
important foundation and without it it's
00:23:45
very questionable as to whether we could
00:23:47
ever appreciate involves mathematics the
00:23:51
building blocks of mathematics may be
00:23:53
pre-programmed into our brains part of
00:23:56
the basic toolkit for survival
00:23:59
like our ability to recognize patterns
00:24:01
and shapes or our sense of time from
00:24:06
that point of view on this foundation
00:24:08
we've erected one of the greatest
00:24:10
inventions of human culture
00:24:15
mathematics but the mystery remains if
00:24:20
it is all in our heads
00:24:22
why has math been so effective through
00:24:27
science technology and engineering it's
00:24:29
transformed the planet even allowing us
00:24:33
to go into the beyond as in the work
00:24:40
here at NASA's Jet Propulsion Laboratory
00:24:42
in Pasadena California
00:24:44
Roger copy mission country in 2012 Scott
00:24:49
Grady started they landed a car-sized
00:24:51
Rover sending out about 0.75 meters per
00:24:54
second that expected on Mars touchdown
00:24:58
confirmed Adam steltzner was the lead
00:25:07
engineer on the team that designed the
00:25:09
landing system they're worth depended on
00:25:12
a groundbreaking discovery from the
00:25:15
Renaissance that turned mathematics into
00:25:18
the language of science
00:25:21
the law of falling bodies the ancient
00:25:29
Greek philosopher Aristotle taught that
00:25:31
heavier objects fall faster than lighter
00:25:34
ones an idea that on the surface make
00:25:39
sense even this service the Mars yard
00:25:43
where they test a Rovers at JPL so
00:25:47
Aristotle reason that the rate at which
00:25:51
things would fall was portion to their
00:25:53
weight which seems reasonable in fact so
00:26:01
reasonable the view held for nearly two
00:26:03
thousand years until challenged in the
00:26:07
late 1500s by Italian mathematician
00:26:09
Galileo Galilei legend has it that
00:26:14
Galileo dropped two different weight
00:26:16
cannonballs from the Leaning Tower of
00:26:19
Pisa well we're not in Pisa
00:26:21
we don't have cannonballs but we do have
00:26:23
a bowling ball and a bouncy ball let's
00:26:27
weigh them first we weigh the bowling
00:26:30
ball it weighs 15 pounds and the bouncy
00:26:35
ball it weighs hardly anything let's
00:26:39
drop them according to Aristotle the
00:26:42
bowling ball should fall over 15 times
00:26:45
faster than the bouncy ball
00:26:49
well they seem to fall the same rate
00:26:54
this isn't that high though maybe we
00:26:57
should drop them from higher incomes and
00:27:03
based in favor so II D is 20 feet in the
00:27:08
air up there let's see if the balls fall
00:27:10
at the same rate ready three two one
00:27:16
drop
00:27:18
[Music]
00:27:25
Galileo was right
00:27:26
Aristotle you lose dropping feathers and
00:27:31
hammers is misleading thanks to air
00:27:33
resistance my left hand I have a feather
00:27:38
my right hand a hammer a fact
00:27:42
demonstrated on the moon where there is
00:27:44
no air in 1971 during the Apollo 15
00:27:48
mission you know drop - I'm here how
00:27:53
about that
00:27:53
after Calvin Louis track little ball
00:27:57
soccer ball so while counterintuitive
00:28:00
that's it's balls if you take the air
00:28:03
out of the equation everything falls at
00:28:07
the same rate even Aristotle
00:28:10
[Music]
00:28:13
but what really interested Galileo was
00:28:17
that an object dropped at one height
00:28:20
didn't take twice as long to drop from
00:28:23
twice as high it accelerated but how do
00:28:27
you measure that everything is happening
00:28:31
so fast
00:28:35
[Music]
00:28:38
Galileo came up with an ingenious
00:28:40
solution
00:28:44
he built a rare an inclined plane to
00:28:51
slow the falling motion down so he could
00:28:54
measure so we're going to use this ramp
00:28:58
to find a relationship between distance
00:29:02
and time for time I'll use an arbitrary
00:29:06
unit the Galileo one Galileo the length
00:29:12
of the ramp that the ball rolls during
00:29:14
one Galileo becomes one unit of distance
00:29:18
so we've gone one unit of distance in
00:29:22
one unit of time now let's try it for
00:29:25
two counts one Galileo two Galileo in
00:29:29
two units of time the ball has rolled
00:29:32
four units of distance now let's see how
00:29:37
far it goes in three Galileo's one
00:29:40
Galileo two Galileo three Galileo in
00:29:44
three units of time the ball has gone
00:29:47
nine units of distance so there it is
00:29:51
there's a mathematical relationship here
00:29:54
between time and distance
00:29:57
Galileo is inspired use of a ramp had
00:30:00
shown falling objects follow mathematic
00:30:03
laws the distance the ball traveled is
00:30:08
directly proportional to the square of
00:30:10
the time that mathematical relationship
00:30:14
that Galileo observed is a mathematical
00:30:19
expression of the physics of our
00:30:21
universe Galileo's centuries-old
00:30:24
mathematical observation about falling
00:30:26
objects remains just as valid today it's
00:30:31
the same mathematical expression that we
00:30:33
can use to understand how objects might
00:30:35
fall here on earth roll down a ramp
00:30:39
even a relationship that we used to land
00:30:42
the Curiosity rover on the surface of
00:30:45
Mars that's the power of mathematics
00:30:51
Galileo's insight was profound
00:30:55
mathematics could be used as a tool to
00:30:58
uncover and discover the hidden rules of
00:31:01
our world he later wrote the universe is
00:31:06
written in the language of mathematics
00:31:10
math is really the language in which we
00:31:14
understand the universe we don't know
00:31:16
why it's the case that the laws of
00:31:18
physics and the universe follows
00:31:21
mathematical models but it does seem to
00:31:23
be the case
00:31:24
while Galileo turned mathematical
00:31:27
equations into laws of science it was
00:31:30
another man born the same year Galileo
00:31:33
died who took that to new heights that
00:31:36
crossed the heavens his name was Isaac
00:31:41
Newton
00:31:43
he worked here at Trinity College in
00:31:46
Cambridge England Newton cultivated the
00:31:50
reputation of being a solitary genius
00:31:53
and here in the bowling-green of Trinity
00:31:57
College it was said that he would walk
00:32:00
meditatively up and down the paths
00:32:03
absent mindedly drawing mathematical
00:32:06
diagrams in the gravel and the fellows
00:32:09
were instructed or so it was said not to
00:32:13
disturb him not to clear up the gravel
00:32:16
after he passed in case they
00:32:18
inadvertently wiped out some major
00:32:21
scientific or mathematical discovery in
00:32:25
1687 Newton published a book that would
00:32:29
become a landmark in the history of
00:32:30
science today it is known simply as the
00:32:35
Principia in it
00:32:37
Newton gathered observations from around
00:32:39
the world and used mathematics to
00:32:42
explain them for instance that of a
00:32:45
comet seemed widely in the fall of 1680
00:32:48
he gathers data worldwide in order to
00:32:52
construct the Comets path so for
00:32:55
November the 19th he begins with an
00:32:59
observation made in Cambridge in England
00:33:01
at 4:30 a.m. by certain young person and
00:33:06
then at 5 in the morning at Boston in
00:33:11
New England so what Newton does is to
00:33:14
accumulate numbers made by observers
00:33:17
spread right across the globe in order
00:33:20
to construct an unprecedented ly
00:33:23
accurate calculation of how this great
00:33:25
comet moved through the sky
00:33:29
Newton's groundbreaking insight was that
00:33:32
the force that sent the comet hurtling
00:33:34
around the Sun was the same force that
00:33:39
brought cannonballs back to earth it was
00:33:44
the force behind Galileo's law of
00:33:47
falling bodies and it even held the
00:33:50
planets in their orbits
00:33:53
a called the force gravity and described
00:33:58
it precisely in a surprisingly simple
00:34:01
equation that explains how two masses
00:34:04
attract each other whether here on earth
00:34:06
or in the heavens above what's so
00:34:11
impressive and so dramatic is that a
00:34:14
single mathematical law would allow you
00:34:17
to move throughout the universe today we
00:34:24
can even witness it at work beyond the
00:34:27
Milky Way this is a picture of two
00:34:31
galaxies that are actually being drawn
00:34:34
together in a merger his whole dog is
00:34:37
building alright Mario Livio is on the
00:34:40
team working with the images from the
00:34:42
Hubble Space Telescope for decades
00:34:45
scientists have used Hubble to gaze far
00:34:48
beyond our solar system even beyond the
00:34:51
stars of our galaxy it shown us the
00:34:54
distant gas clouds of nebulae and vast
00:34:57
numbers of galaxies wheeling in the
00:35:00
heavens billions of light-years away and
00:35:03
what those images show is that
00:35:06
throughout the visible universe as far
00:35:08
as the telescope can see the law of
00:35:12
gravity still applies you know Newton
00:35:15
wrote these laws of gravity and of
00:35:18
motion based on things happening on
00:35:21
earth and the planets in the solar
00:35:23
system and so on but these same laws
00:35:26
these very same laws apply to all these
00:35:29
distant galaxies and you know shape them
00:35:32
and everything about them how they form
00:35:34
how they move is controlled by those
00:35:37
same mathematical laws
00:35:41
some of the world's greatest minds have
00:35:44
been amazed by the way that math
00:35:45
permeates the universe Albert Einstein
00:35:50
he wondered he said how is it possible
00:35:53
that mathematics which is he thought the
00:35:56
product of human thought does so well in
00:36:00
explaining the universe as we see it and
00:36:02
Nobel laureate in physics Eugene Wigner
00:36:05
coined this phrase the unreasonable
00:36:08
effectiveness of mathematics he said
00:36:11
that the fact that mathematics can
00:36:13
really describe the universe so well in
00:36:16
particular physical laws is a gift that
00:36:20
we neither understand nor deserve in
00:36:24
physics examples of that unreasonable
00:36:27
effectiveness about when nearly 200
00:36:33
years ago the planet Uranus was seen to
00:36:35
go off track
00:36:36
scientists trusted the math and
00:36:39
calculated it was being pulled by
00:36:42
another unseen planet
00:36:45
[Music]
00:36:47
and so they discovered Neptune
00:36:51
mathematics had accurately predicted a
00:36:53
previously unknown but if you formulate
00:36:59
a question properly mathematics gives
00:37:03
you the answer like having a certain
00:37:07
that is far more capable than you are so
00:37:11
you tell it do this and if you say it
00:37:13
nicely then it will do it and it will
00:37:16
carry you all the way to the truth to
00:37:19
the to the final answer
00:37:21
[Music]
00:37:24
evidence of the amazing predictive power
00:37:26
of mathematics can be found all around
00:37:29
us I heard it took five Elvis's to pull
00:37:31
them apart i television radio your cell
00:37:37
phone satellites the baby model
00:37:40
Wi-Fi your garage door Oh GPS and yes
00:37:46
even maybe your TV's remote all of these
00:37:50
use invisible waves of energy to
00:37:52
communicate and no one even knew they
00:37:55
existed until the work of James Maxwell
00:37:58
a Scottish mathematical physicist in the
00:38:02
1860s he published a set of equations
00:38:06
that explained how electricity and
00:38:08
magnetism were related how each could
00:38:12
generate the other the equations also
00:38:17
made a startling prediction together
00:38:22
electricity and magnetism could produce
00:38:24
waves of energy that would travel
00:38:27
through space at the speed of light
00:38:32
electromagnetic waves Maxwell's theory
00:38:35
gave us these radio waves x-rays these
00:38:39
things which were simply not known about
00:38:42
at all so the theory had a scope which
00:38:44
was extraordinary almost immediately
00:38:49
people set out to find the waves
00:38:51
predicted by Maxwell's equations what
00:38:55
must have seemed the least promising
00:38:57
attempt to harness them is made here in
00:38:59
northern Italy in the Attic of a family
00:39:02
home by twenty-year-old
00:39:04
Giuliano Marconi his process starts with
00:39:08
a series of sparks the burst of
00:39:15
electricity creates the momentary
00:39:17
magnetic field which in turn generates a
00:39:21
momentary electric field which creates
00:39:23
another magnetic field the energy cycles
00:39:27
between the two propagating an
00:39:29
electromagnetic wave Marconi gets his
00:39:36
system to work inside but then he scales
00:39:40
up
00:39:44
over a few weeks he builds a big antenna
00:39:48
beside the house to amplify the waves
00:39:51
coming from his spark generator then he
00:39:54
asks his brother and an assistant to
00:39:56
carry a receiver across the estate to
00:39:59
the far side of a nearby hill they also
00:40:03
have a shotgun which they will fire if
00:40:05
they manage to pick up the signal and it
00:40:26
works the signal has been detected even
00:40:29
though the receiver is now hidden behind
00:40:31
a hill at over a mile
00:40:34
it is the farthest transmission to date
00:40:37
in fewer than 10 years Marconi will be
00:40:41
sending radio signals across the
00:40:43
Atlantic in fact when the Titanic sinks
00:40:48
in 1912 he'll be personally credited
00:40:51
with saving many lives because his
00:40:54
onboard equipment allowed the distress
00:40:57
signal to be transmitted thanks to the
00:41:02
predictions of Maxwell's equations
00:41:04
Marconi could harness a hidden part of
00:41:08
our world assuring in the era of
00:41:11
wireless communication
00:41:17
[Music]
00:41:19
since Maxwell and Marconi evidence of
00:41:22
the predictive power of mathematics has
00:41:24
only grown especially in the world of
00:41:28
physics a hundred years ago we barely
00:41:31
knew atoms existed it took experiments
00:41:35
to reveal their components the electron
00:41:37
the proton and the neutron but when
00:41:41
physicists wanted to go deeper
00:41:43
mathematics began to lead the way
00:41:45
ultimately revealing a zoo of elementary
00:41:49
particles discoveries that continue to
00:41:53
this day here at CERN the European
00:41:56
Organization for Nuclear Research in
00:41:59
Geneva Switzerland these days their most
00:42:03
famous for their Large Hadron Collider a
00:42:06
circular particle accelerator about 17
00:42:09
miles around it built deeper underground
00:42:15
this 10 billion dollar project decades
00:42:19
in the making
00:42:20
had a well publicized goal the search
00:42:23
for one of the most fundamental building
00:42:25
blocks of the universe
00:42:29
the subatomic particle mathematically
00:42:32
predicted to exist nearly 50 years
00:42:35
earlier by Robert Brout and Francois
00:42:39
unclear working in Belgium and Peter
00:42:41
Higgs in Scotland Peter Higgs sat down
00:42:46
with the most advanced physics equations
00:42:48
we had and calculated isn't I plated and
00:42:51
made the audacious prediction than it
00:42:53
we built the most sophisticated machines
00:42:55
humans have ever built and used it to
00:42:57
smash particles together near the speed
00:42:58
of light in a certain way that we would
00:43:00
their discover a new particle and if
00:43:02
this math was really accurate the
00:43:05
discovery of the Higgs particle would be
00:43:08
proof of the higgs field a cosmic
00:43:11
molasses that gives the stuff of our
00:43:13
world mass what we usually experience as
00:43:17
weight without mass everything would
00:43:21
travel at the speed of light and would
00:43:23
never combine to form atoms that makes
00:43:27
the Higgs field such a fundamental part
00:43:30
of physics that the Higgs particle
00:43:32
gained the nickname the god particle
00:43:36
[Music]
00:43:39
in 2012 experiments at CERN confirmed
00:43:43
the existence of the Higgs particle
00:43:45
making the work of Peter Higgs and his
00:43:48
colleagues decades earlier one of the
00:43:50
greatest predictions have made we built
00:43:55
it and it worked and he got a free trip
00:43:58
to Stockholm
00:43:59
[Music]
00:44:02
[Applause]
00:44:09
here you have mathematical theories
00:44:12
which make very definitive predictions
00:44:17
about the possible existence of some
00:44:19
fundamental particles of nature and
00:44:23
believe it or not they make these huge
00:44:26
experiments and they actually discover
00:44:28
the particles that have been predicted
00:44:30
mathematically I mean this is just
00:44:33
amazing to me why does this work how to
00:44:39
mathematics be so powerful it's
00:44:42
mathematics you know a truth of nature
00:44:45
or does it have something to do with way
00:44:48
we as humans perceive nature and it's to
00:44:52
me this is just a you know a fascinating
00:44:53
puzzle I don't know the answer in
00:44:58
physics mathematics has had a long
00:45:00
string of successes but is it really
00:45:03
unreasonably effective not everyone
00:45:07
thinks so I think it's an illusion
00:45:09
because I think what's happened is that
00:45:11
people have chosen to build physics for
00:45:15
example using the mathematics that has
00:45:17
been practiced has developed
00:45:18
historically and then they're looking at
00:45:21
everything they're choosing to study
00:45:22
things which are mean able to studies in
00:45:24
the mathematics that happens to have
00:45:26
arisen
00:45:27
but actually there's a whole lost ocean
00:45:30
of other things that are really quite
00:45:32
inaccessible to those methods with the
00:45:36
success of mathematical models and
00:45:38
physics it's easy to overlook where they
00:45:40
don't work that well like in weather
00:45:43
forecasting
00:45:44
there's a reason meteorologists predict
00:45:47
the weather for the coming week
00:45:49
but not much further out than that in a
00:45:53
longer forecast small errors grow into
00:45:56
big ones daily weather is just too
00:45:59
complex and chaotic for precise model
00:46:02
and it's not a woman
00:46:04
so is the behavior of water boiling on a
00:46:08
stove or the stock market or the
00:46:14
interaction of neurons in the brain much
00:46:17
of human psychology and parts of biology
00:46:20
biological systems economic systems it
00:46:25
gets very difficult to model those
00:46:27
systems with math we have extreme
00:46:29
difficulty with that so I do not see
00:46:32
math as unreasonably effective I see it
00:46:36
as reasonably ineffective perhaps no one
00:46:43
is as keenly aware of the power and
00:46:45
limitations of mathematics as those who
00:46:48
use it to design and make things
00:46:50
engineers look at how will in their work
00:46:54
the elegance of math meets the messiness
00:46:58
of reality and practicality rules today
00:47:03
mathematics and perhaps mathematicians
00:47:06
deal in the domain of the absolute and
00:47:08
engineers live in the domain of the
00:47:12
approximate now we are fundamentally
00:47:15
interested in the practical and so
00:47:18
frequently we make approximations we cut
00:47:20
corners we omit terms and equations to
00:47:23
get things that are simple enough to
00:47:26
suit our purposes and they meet our
00:47:28
needs
00:47:28
[Music]
00:47:31
many of our greatest engineering
00:47:34
achievements were built using
00:47:35
mathematical shortcuts simplified
00:47:39
equations that approximate an answer
00:47:41
trading some precision for practicality
00:47:44
and for engineers approximate is close
00:47:49
enough close enough to take you to Mars
00:47:54
[Music]
00:47:55
for us engineers we don't get paid to do
00:47:57
things right we get paid to do things
00:48:00
just right enough
00:48:05
many physicists in uncanny accuracy in
00:48:08
the way mathematics can reveal the
00:48:10
secrets of the universe making it seem
00:48:14
to be an inherent part of nature
00:48:19
meanwhile engineers in practice have to
00:48:23
sacrifice the precision of mathematics
00:48:26
to keep it useful making it seem more
00:48:29
like an imperfect tool of our own
00:48:32
invention
00:48:34
so which is mathematics a discovered
00:48:38
part of the universe or a very human
00:48:42
invention maybe it's both
00:48:47
[Music]
00:48:51
what I think about mathematics is that
00:48:54
it is an intricate combination of
00:48:57
inventions and discoveries so for
00:49:00
example take something like natural
00:49:02
numbers 1 2 3 4 5 etc I think what
00:49:06
happened was that people were looking at
00:49:08
many things for example in seeing with
00:49:10
our two eyes below two breasts two hands
00:49:13
you know and so on and after some time
00:49:16
they abstracted from all of that the
00:49:19
number two according to Mario 2 became
00:49:24
an invented concept as did all the other
00:49:27
natural numbers but then people
00:49:30
discovered that these numbers have all
00:49:32
kinds of intricate relationships those
00:49:35
who discoveries we invented the concept
00:49:40
but then discovered the relations among
00:49:43
the different concepts so is this the
00:49:46
answer that math is both invented and
00:49:50
discovered this is one of those
00:49:53
questions where it's both yes it is
00:49:55
feels like it's already there but yes
00:49:57
it's something that comes with our deep
00:49:59
creative nature as human beings we may
00:50:03
have some idea to how all this works but
00:50:06
not the complete answer in the end it
00:50:09
remains the great math mystery
00:50:16
[Music]
00:50:21
[Music]
00:51:07
you
