Leonardo is really a bundle of contradictions
contradictions
contradictions he was an illegitimate child born in
he was an illegitimate child born in
he was an illegitimate child born in 1452 although we know him for being so
1452 although we know him for being so
1452 although we know him for being so prolific producing so much
he thought that he produced so little
he thought that he produced so little that in his deathbed he turned to an
that in his deathbed he turned to an
that in his deathbed he turned to an assistant and he asked did anything get
assistant and he asked did anything get
assistant and he asked did anything get done
he was good in virtually everything he
he was good in virtually everything he took up and he’s known as a universal
took up and he’s known as a universal
took up and he’s known as a universal genius I started learning about Leonardo
genius I started learning about Leonardo
genius I started learning about Leonardo when I was in high school school called
when I was in high school school called
when I was in high school school called st. Andrews in Middletown Delaware well
st. Andrews in Middletown Delaware well
st. Andrews in Middletown Delaware well when I was in the fifth former 11th
when I was in the fifth former 11th
when I was in the fifth former 11th grade the father of a student an
grade the father of a student an
grade the father of a student an engineer gave a talk about the divine
engineer gave a talk about the divine
engineer gave a talk about the divine proportion and the golden ratio and for
proportion and the golden ratio and for
proportion and the golden ratio and for the first time I saw how mathematics in
the first time I saw how mathematics in
the first time I saw how mathematics in art could in fact be cobbled together I
art could in fact be cobbled together I
art could in fact be cobbled together I had always had a passion for mathematics
had always had a passion for mathematics
had always had a passion for mathematics and I did art in my youth when my father
and I did art in my youth when my father
and I did art in my youth when my father was assigned as a military attache to
was assigned as a military attache to
was assigned as a military attache to London from Turkey
London from Turkey
London from Turkey I remember we lived in the house of Lord
I remember we lived in the house of Lord
I remember we lived in the house of Lord Curzon and I went around beautifying
Curzon and I went around beautifying
Curzon and I went around beautifying these paintings I remember that the one
these paintings I remember that the one
these paintings I remember that the one thing that Leonardo used to say was that
thing that Leonardo used to say was that
thing that Leonardo used to say was that the eyes were this the windows to the
the eyes were this the windows to the
the eyes were this the windows to the soul
soul
soul these paintings had no soul they were
these paintings had no soul they were
these paintings had no soul they were produced in the 18th and 19th centuries
produced in the 18th and 19th centuries
produced in the 18th and 19th centuries but the pupils were all closed I went
but the pupils were all closed I went
but the pupils were all closed I went around opening the pupils with a cork
around opening the pupils with a cork
around opening the pupils with a cork opener and no one really noticed my
opener and no one really noticed my
opener and no one really noticed my improvement until a few months later
improvement until a few months later
improvement until a few months later when the devil came to visit my father
when the devil came to visit my father
when the devil came to visit my father dressed as a diplomat he put out his
dressed as a diplomat he put out his
dressed as a diplomat he put out his hand and without stopping he raised his
hand and without stopping he raised his
hand and without stopping he raised his hand and he said there are holes in
hand and he said there are holes in
hand and he said there are holes in those eyes do you have a son
those eyes do you have a son
those eyes do you have a son so he had gotten to the culprit right
so he had gotten to the culprit right
so he had gotten to the culprit right from the beginning anyway over the years
from the beginning anyway over the years
from the beginning anyway over the years I did produce art and I gave lectures on
I did produce art and I gave lectures on
I did produce art and I gave lectures on cruises frequently and in the late 80s a
cruises frequently and in the late 80s a
cruises frequently and in the late 80s a passenger on the silver seas started
passenger on the silver seas started
passenger on the silver seas started applying steady but gentle pressure to
applying steady but gentle pressure to
applying steady but gentle pressure to publish how we in order to this art how
publish how we in order to this art how
publish how we in order to this art how mathematics and science came in handy
mathematics and science came in handy
mathematics and science came in handy I can speak about 1% of Leonardo and it
I can speak about 1% of Leonardo and it
I can speak about 1% of Leonardo and it will be interesting and it could be any
will be interesting and it could be any
will be interesting and it could be any 1% if Keith wants Lee my co-author
1% if Keith wants Lee my co-author
1% if Keith wants Lee my co-author speaks fast Leonardo I’m sure it’d be
speaks fast Leonardo I’m sure it’d be
speaks fast Leonardo I’m sure it’d be another 1% so this is 1% from the point
another 1% so this is 1% from the point
another 1% so this is 1% from the point of view of the scientists rather than in
of view of the scientists rather than in
of view of the scientists rather than in the artist now let me tell you about the
the artist now let me tell you about the
the artist now let me tell you about the other Leonardo the other Leonardo lived
other Leonardo the other Leonardo lived
other Leonardo the other Leonardo lived 300 years before Leonardo da Vinci his
300 years before Leonardo da Vinci his
300 years before Leonardo da Vinci his name was Leonardo Fibonacci de Pisa
Nardo Fibonacci de Pisa he was probably
Nardo Fibonacci de Pisa he was probably born around 1162 1170 at the same time
born around 1162 1170 at the same time
born around 1162 1170 at the same time as in Pisa when the Leaning Tower was
as in Pisa when the Leaning Tower was
as in Pisa when the Leaning Tower was first being erected
first being erected
first being erected well let’s Leonardo Fibonacci de Pisa in
well let’s Leonardo Fibonacci de Pisa in
well let’s Leonardo Fibonacci de Pisa in 1202 came back to us to a city of Pisa
1202 came back to us to a city of Pisa
1202 came back to us to a city of Pisa and wrote a book called the liberal a
and wrote a book called the liberal a
and wrote a book called the liberal a bocce the book of the abacus the year
bocce the book of the abacus the year
bocce the book of the abacus the year was 1202 it sounds very much like the
was 1202 it sounds very much like the
was 1202 it sounds very much like the name of a late pianist libera bocce
name of a late pianist libera bocce
name of a late pianist libera bocce in the book he starts out by proposing a
in the book he starts out by proposing a
in the book he starts out by proposing a couple of numbers
couple of numbers
couple of numbers he says read this number and then anyone
he says read this number and then anyone
he says read this number and then anyone read that number
read that number
read that number IDH how about this number will suffer
IDH how about this number will suffer
IDH how about this number will suffer also 98 L is 50 so 10 less than the next
also 98 L is 50 so 10 less than the next
also 98 L is 50 so 10 less than the next 50 and you can write the same number in
50 and you can write the same number in
50 and you can write the same number in different ways 1999 you can write 4 or 5
different ways 1999 you can write 4 or 5
different ways 1999 you can write 4 or 5 different ways he proposed using the
different ways he proposed using the
different ways he proposed using the Arabic system making 98 with two symbols
Arabic system making 98 with two symbols
Arabic system making 98 with two symbols and he introduced in his book in the
and he introduced in his book in the
and he introduced in his book in the first chapter the symbols some borrowed
first chapter the symbols some borrowed
first chapter the symbols some borrowed from the Arabs and some that he made up
from the Arabs and some that he made up
from the Arabs and some that he made up one to two horizontal lines I sort of
one to two horizontal lines I sort of
one to two horizontal lines I sort of lightly connected three horizontal lines
lightly connected three horizontal lines
lightly connected three horizontal lines slightly connected one two three four
slightly connected one two three four
slightly connected one two three four one two three four five one two three
one two three four five one two three
one two three four five one two three four five six number of straight lines
four five six number of straight lines
four five six number of straight lines reveal the value of the symbol seven
reveal the value of the symbol seven
reveal the value of the symbol seven takes some imagination but seven in
takes some imagination but seven in
takes some imagination but seven in medieval Europe when he wrote his book
medieval Europe when he wrote his book
medieval Europe when he wrote his book was like this one two three four five
was like this one two three four five
was like this one two three four five six seven and of course Europeans still
six seven and of course Europeans still
six seven and of course Europeans still across there seven eight one two three
across there seven eight one two three
across there seven eight one two three four five six seven eight nine she
four five six seven eight nine she
four five six seven eight nine she borrowed from the Arabs and the zero
borrowed from the Arabs and the zero
borrowed from the Arabs and the zero which he bought from the Hindus it was
which he bought from the Hindus it was
which he bought from the Hindus it was the Hindus who had originally come up
the Hindus who had originally come up
the Hindus who had originally come up with a decimal system and then the zero
with a decimal system and then the zero
with a decimal system and then the zero invented by the Hindus by a
invented by the Hindus by a
invented by the Hindus by a mathematician named Arya pata around 500
mathematician named Arya pata around 500
mathematician named Arya pata around 500 BC it turns out to be an all important
BC it turns out to be an all important
BC it turns out to be an all important component for modern mathematics you
component for modern mathematics you
component for modern mathematics you couldn’t we couldn’t have done calculus
couldn’t we couldn’t have done calculus
couldn’t we couldn’t have done calculus Newton could not have invented calculus
Newton could not have invented calculus
Newton could not have invented calculus without the zero you wouldn’t have had
without the zero you wouldn’t have had
without the zero you wouldn’t have had limits
limits
limits then he does in the book of 13 chapters
then he does in the book of 13 chapters
then he does in the book of 13 chapters algebra problems and finally in the last
algebra problems and finally in the last
algebra problems and finally in the last chapter he proposes a problem of rabbits
chapter he proposes a problem of rabbits
chapter he proposes a problem of rabbits rabbits left in an enclosure a room like
rabbits left in an enclosure a room like
rabbits left in an enclosure a room like this where they’re left to multiply
this where they’re left to multiply
this where they’re left to multiply except there are some definite rules for
except there are some definite rules for
except there are some definite rules for example they must one pair of rabbits
example they must one pair of rabbits
example they must one pair of rabbits start the entire cycle then the rabbits
start the entire cycle then the rabbits
start the entire cycle then the rabbits have to mature for two months before
have to mature for two months before
have to mature for two months before they can give rise to new rabbits and
they can give rise to new rabbits and
they can give rise to new rabbits and the new rabbits have to mature for two
the new rabbits have to mature for two
the new rabbits have to mature for two months before they can give rise new
months before they can give rise new
months before they can give rise new curette to new rabbits so now we start
curette to new rabbits so now we start
curette to new rabbits so now we start out the cycle in January with one pair
out the cycle in January with one pair
out the cycle in January with one pair of rabbits in the second month February
will give them an ear which means there
will give them an ear which means there are one month mature now but they can’t
are one month mature now but they can’t
are one month mature now but they can’t have offspring yet by March they have a
have offspring yet by March they have a
have offspring yet by March they have a second ear and they reproduce by April
second ear and they reproduce by April
second ear and they reproduce by April the fourth month here’s the original
the fourth month here’s the original
the fourth month here’s the original pair one new pair this para gains an ear
pair one new pair this para gains an ear
pair one new pair this para gains an ear in May here’s the original pair one new
in May here’s the original pair one new
in May here’s the original pair one new pair this pair gains an ear this pair
pair this pair gains an ear this pair
pair this pair gains an ear this pair gains a second ear and reproduce this
gains a second ear and reproduce this
gains a second ear and reproduce this see how it works it’s all in the ears in
see how it works it’s all in the ears in
see how it works it’s all in the ears in June there’s the original pair one new
June there’s the original pair one new
June there’s the original pair one new pair this pair of gains an ear this para
pair this pair of gains an ear this para
pair this pair of gains an ear this para gains a second ear and immediately
gains a second ear and immediately
gains a second ear and immediately reproduces this pair is already mature
reproduces this pair is already mature
reproduces this pair is already mature they reproduce this pair gains an ear
they reproduce this pair gains an ear
they reproduce this pair gains an ear now as he looked at this cycle and these
now as he looked at this cycle and these
now as he looked at this cycle and these numbers he wondered whether there was a
numbers he wondered whether there was a
numbers he wondered whether there was a general way to ascertain how many
general way to ascertain how many
general way to ascertain how many rabbits there would be at the end of the
rabbits there would be at the end of the
rabbits there would be at the end of the year without drawing all these ears and
year without drawing all these ears and
year without drawing all these ears and he noticed squiggly that the first month
he noticed squiggly that the first month
he noticed squiggly that the first month was one the second month was one next
was one the second month was one next
was one the second month was one next month it was two next month it was three
month it was two next month it was three
month it was two next month it was three then five and then a
then five and then a
then five and then a anyone want to guess the next one
anyone want to guess the next one
anyone want to guess the next one thirteen next one twenty-one next
thirteen next one twenty-one next
thirteen next one twenty-one next thirty-four next fifty five I told you
thirty-four next fifty five I told you
thirty-four next fifty five I told you this was the smartest room in the entire
this was the smartest room in the entire
this was the smartest room in the entire city five then eighty nine then 144 233
city five then eighty nine then 144 233
city five then eighty nine then 144 233 377 what’s the algorithm how am I doing
377 what’s the algorithm how am I doing
377 what’s the algorithm how am I doing this
this
this add the last two terms to get the next
add the last two terms to get the next
add the last two terms to get the next six ten nine eighty seven three fifteen
six ten nine eighty seven three fifteen
six ten nine eighty seven three fifteen ninety seven and so forth I’ll do one
ninety seven and so forth I’ll do one
ninety seven and so forth I’ll do one more 2584 so first months January
more 2584 so first months January
more 2584 so first months January February March April May June July
February March April May June July
February March April May June July August September October November
August September October November
August September October November December 144 pairs by the end of the
December 144 pairs by the end of the
December 144 pairs by the end of the year January February March April May
year January February March April May
year January February March April May June 18 months into the cycle there
June 18 months into the cycle there
June 18 months into the cycle there should be twenty-five hundred and eighty
should be twenty-five hundred and eighty
should be twenty-five hundred and eighty four pairs of rabbits this is called the
four pairs of rabbits this is called the
four pairs of rabbits this is called the Fibonacci series as you add these
Fibonacci series as you add these
Fibonacci series as you add these numbers it’s an infinite sequence goes
numbers it’s an infinite sequence goes
numbers it’s an infinite sequence goes on like this what he didn’t realize it
on like this what he didn’t realize it
on like this what he didn’t realize it was discovered only the 19th century was
was discovered only the 19th century was
was discovered only the 19th century was that these are nature’s numbers if you
that these are nature’s numbers if you
that these are nature’s numbers if you look at at a flower if you look at let
look at at a flower if you look at let
look at at a flower if you look at let me look at a pinecone first here’s a
me look at a pinecone first here’s a
me look at a pinecone first here’s a pine cone pine cone has helical a
pine cone pine cone has helical a
pine cone pine cone has helical a pattern of scales that go up this way
pattern of scales that go up this way
pattern of scales that go up this way then there’ll be a pattern that goes
then there’ll be a pattern that goes
then there’ll be a pattern that goes this way you look at the bottom and the
this way you look at the bottom and the
this way you look at the bottom and the scales will radiate clockwise like this
scales will radiate clockwise like this
scales will radiate clockwise like this but then as you look at the sunflower
but then as you look at the sunflower
but then as you look at the sunflower the pine cone you’ll find that there are
the pine cone you’ll find that there are
the pine cone you’ll find that there are spirals in the other direction and in
spirals in the other direction and in
spirals in the other direction and in all pine cones
all pine cones
all pine cones it’ll be 13 in one direction 8 in the
it’ll be 13 in one direction 8 in the
it’ll be 13 in one direction 8 in the other it can’t be anything else this is
other it can’t be anything else this is
other it can’t be anything else this is the Filat axis of the pine cone if it
the Filat axis of the pine cone if it
the Filat axis of the pine cone if it were a daisy it would be 21 and 30 also
were a daisy it would be 21 and 30 also
were a daisy it would be 21 and 30 also true for the chrysanthemum in the case
true for the chrysanthemum in the case
true for the chrysanthemum in the case of the sunflower sunflower looks like
of the sunflower sunflower looks like
of the sunflower sunflower looks like this
there are radial patterns that go this
there are radial patterns that go this way and radial patterns that go in the
way and radial patterns that go in the
way and radial patterns that go in the other direction this way you count them
other direction this way you count them
other direction this way you count them and there they have to be 89 in one
and there they have to be 89 in one
and there they have to be 89 in one direction 55 in the other in some some
direction 55 in the other in some some
direction 55 in the other in some some some some flowers to actually find 144
some some flowers to actually find 144
some some flowers to actually find 144 and 89 in every instance is a pair a
and 89 in every instance is a pair a
and 89 in every instance is a pair a sequential pair of Fibonacci’s numbers
sequential pair of Fibonacci’s numbers
sequential pair of Fibonacci’s numbers leonardo knew this Leonardo knew about
leonardo knew this Leonardo knew about
leonardo knew this Leonardo knew about the spiral he used it in drawing embryo
the spiral he used it in drawing embryo
the spiral he used it in drawing embryo he used it in drawing hurricanes and and
he used it in drawing hurricanes and and
he used it in drawing hurricanes and and locks of the hair he always made this is
locks of the hair he always made this is
locks of the hair he always made this is signature Leonardo if you see
signature Leonardo if you see
signature Leonardo if you see logarithmic spirals and the curls it’s
logarithmic spirals and the curls it’s
logarithmic spirals and the curls it’s Leonardo okay I’ll go to my slides now
Leonardo okay I’ll go to my slides now
Leonardo okay I’ll go to my slides now this is Java nachi we have no idea what
this is Java nachi we have no idea what
this is Java nachi we have no idea what he really looked like but this was
he really looked like but this was
he really looked like but this was carved in 1978 it’s a statue on the
carved in 1978 it’s a statue on the
carved in 1978 it’s a statue on the banks of the Arno and Pisa there you can
banks of the Arno and Pisa there you can
banks of the Arno and Pisa there you can see the spirals in the Daisy and in the
see the spirals in the Daisy and in the
see the spirals in the Daisy and in the pine cone if I draw or paint a tree I
pine cone if I draw or paint a tree I
pine cone if I draw or paint a tree I start from the bottom at one point I
start from the bottom at one point I
start from the bottom at one point I divided up into two large branches after
divided up into two large branches after
divided up into two large branches after a while one of these divides up again
a while one of these divides up again
a while one of these divides up again but the other doesn’t but then after a
but the other doesn’t but then after a
but the other doesn’t but then after a while this divides up and one of these
while this divides up and one of these
while this divides up and one of these two branch but this one does not after a
two branch but this one does not after a
two branch but this one does not after a while this will branch this will not
while this will branch this will not
while this will branch this will not this will branch and one of these two
this will branch and one of these two
this will branch and one of these two will branch if the light is falling from
will branch if the light is falling from
will branch if the light is falling from this side as a right-hander I would
this side as a right-hander I would
this side as a right-hander I would shade this way if I were left-handed
shade this way if I were left-handed
shade this way if I were left-handed like Leonardo I would shade this way if
like Leonardo I would shade this way if
like Leonardo I would shade this way if the light is coming from this side then
the light is coming from this side then
the light is coming from this side then obviously it will be darker on the left
obviously it will be darker on the left
obviously it will be darker on the left side you can make the bark darker like
side you can make the bark darker like
side you can make the bark darker like this but what does this have to do with
this but what does this have to do with
this but what does this have to do with to Bonacci or do you see at any given
to Bonacci or do you see at any given
to Bonacci or do you see at any given height 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 8
height 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 8
height 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 8 if your Leonardo you do that if your any
if your Leonardo you do that if your any
if your Leonardo you do that if your any other artist you don’t count if a tree
other artist you don’t count if a tree
other artist you don’t count if a tree looks right it’s right it’s fine okay
looks right it’s right it’s fine okay
looks right it’s right it’s fine okay I’ll go ahead and turn this off
I’ll go ahead and turn this off
I’ll go ahead and turn this off there’s the cork tree this was the first
there’s the cork tree this was the first
there’s the cork tree this was the first x-ray picture taken by Wilhelm Rankin
x-ray picture taken by Wilhelm Rankin
x-ray picture taken by Wilhelm Rankin who invented of course the x-ray machine
who invented of course the x-ray machine
who invented of course the x-ray machine he discovered x-rays and in this case
he discovered x-rays and in this case
he discovered x-rays and in this case it’s a hapless hunter who’s been wounded
it’s a hapless hunter who’s been wounded
it’s a hapless hunter who’s been wounded by birdshot in this case the
by birdshot in this case the
by birdshot in this case the significance is if you measure the
significance is if you measure the
significance is if you measure the various joints this length divided by
various joints this length divided by
various joints this length divided by this length is 1.618
this length is 1.618
this length is 1.618 this length divided by this is one point
this length divided by this is one point
this length divided by this is one point six point eight this divided by this is
six point eight this divided by this is
six point eight this divided by this is one point six one eight nature knows how
one point six one eight nature knows how
one point six one eight nature knows how to divide how cells replicate and in the
to divide how cells replicate and in the
to divide how cells replicate and in the 19th century Gustav Fechner cut
19th century Gustav Fechner cut
19th century Gustav Fechner cut rectangles in different proportions and
rectangles in different proportions and
rectangles in different proportions and handed them out to people to select
handed them out to people to select
handed them out to people to select their favorites this would be a square
their favorites this would be a square
their favorites this would be a square this would be a rectangle 20 percent
this would be a rectangle 20 percent
this would be a rectangle 20 percent longer than it is wide the one that one
longer than it is wide the one that one
longer than it is wide the one that one with 35% is one point six two and here’s
with 35% is one point six two and here’s
with 35% is one point six two and here’s the histogram representing that
the histogram representing that
the histogram representing that so it’s clear that we do have this
so it’s clear that we do have this
so it’s clear that we do have this propensity for this ratio a three by
propensity for this ratio a three by
propensity for this ratio a three by five card looks better than a three by
five card looks better than a three by
five card looks better than a three by four for example here’s the Parthenon
four for example here’s the Parthenon
four for example here’s the Parthenon this is how the distortion would have
this is how the distortion would have
this is how the distortion would have looked it would it look like it’s
looked it would it look like it’s
looked it would it look like it’s sagging so they built it with a convex
sagging so they built it with a convex
sagging so they built it with a convex curvature like this I took this picture
curvature like this I took this picture
curvature like this I took this picture very long time ago
very long time ago
very long time ago there used to be a Dean my friend Roy
there used to be a Dean my friend Roy
there used to be a Dean my friend Roy Weinstock would know this thing but he
Weinstock would know this thing but he
Weinstock would know this thing but he was there with two other colleagues and
was there with two other colleagues and
was there with two other colleagues and he wanted to pick up a piece of the
he wanted to pick up a piece of the
he wanted to pick up a piece of the Parthenon he bent over to tie his
Parthenon he bent over to tie his
Parthenon he bent over to tie his shoelaces and when he stood up he was
shoelaces and when he stood up he was
shoelaces and when he stood up he was ashen white as friends asked him what
ashen white as friends asked him what
ashen white as friends asked him what was wrong was he sick and he said no I
was wrong was he sick and he said no I
was wrong was he sick and he said no I stole a piece of the Parthenon I could
stole a piece of the Parthenon I could
stole a piece of the Parthenon I could wind up in prison just as that they were
wind up in prison just as that they were
wind up in prison just as that they were leaving the Acropolis they saw a truck
leaving the Acropolis they saw a truck
leaving the Acropolis they saw a truck appear and to dump tons of stones for
appear and to dump tons of stones for
appear and to dump tons of stones for the next day now this is a sketch that I
the next day now this is a sketch that I
the next day now this is a sketch that I did at the National Cathedral and I used
did at the National Cathedral and I used
did at the National Cathedral and I used the inverse of that that golden
the inverse of that that golden
the inverse of that that golden rectangle with a hot spot the golden
rectangle with a hot spot the golden
rectangle with a hot spot the golden spot is right right down there with my
spot is right right down there with my
spot is right right down there with my Macintosh I was able to draw these
Macintosh I was able to draw these
Macintosh I was able to draw these polyhedra it’s called graph theory where
polyhedra it’s called graph theory where
polyhedra it’s called graph theory where you do this you write equations for
you do this you write equations for
you do this you write equations for different polyhedra and there are
different polyhedra and there are
different polyhedra and there are exactly these five regular polyhedra in
exactly these five regular polyhedra in
exactly these five regular polyhedra in this case these are irregular polyhedra
this case these are irregular polyhedra
this case these are irregular polyhedra the truncated icosahedron is here the
the truncated icosahedron is here the
the truncated icosahedron is here the truncated dodecahedron the stellated
truncated dodecahedron the stellated
truncated dodecahedron the stellated icosahedron right there is is the
icosahedron right there is is the
icosahedron right there is is the dodecahedron so you probably recognize
dodecahedron so you probably recognize
dodecahedron so you probably recognize this painting from the National Gallery
this painting from the National Gallery
this painting from the National Gallery it’s Salvador Dali’s Last Supper to the
it’s Salvador Dali’s Last Supper to the
it’s Salvador Dali’s Last Supper to the ancient Greeks
ancient Greeks
ancient Greeks this fifth polyhedron this one was the
this fifth polyhedron this one was the
this fifth polyhedron this one was the shape of the universe the dodecahedron
shape of the universe the dodecahedron
shape of the universe the dodecahedron the other four with
the other four with
the other four with shapes of atoms they believe there were
shapes of atoms they believe there were
shapes of atoms they believe there were four atoms earth fire water and air so
four atoms earth fire water and air so
four atoms earth fire water and air so this is all done with a Macintosh
this is all done with a Macintosh
this is all done with a Macintosh this is Leonardo without a Macintosh he
this is Leonardo without a Macintosh he
this is Leonardo without a Macintosh he Illustrated a book the Divina purports
Illustrated a book the Divina purports
Illustrated a book the Divina purports he owned it with for his good friend
he owned it with for his good friend
he owned it with for his good friend Luca Pacioli in the years that he lived
Luca Pacioli in the years that he lived
Luca Pacioli in the years that he lived in Milan
in Milan
in Milan there is Leonardo in a self-portrait but
there is Leonardo in a self-portrait but
there is Leonardo in a self-portrait but we’re not exactly certain we know it’s
we’re not exactly certain we know it’s
we’re not exactly certain we know it’s by Leonardo’s hand but we’re not certain
by Leonardo’s hand but we’re not certain
by Leonardo’s hand but we’re not certain it’s him
it’s him
it’s him most Leonardo’s scholars agree that it
most Leonardo’s scholars agree that it
most Leonardo’s scholars agree that it is him but David Allen Brown at the
is him but David Allen Brown at the
is him but David Allen Brown at the National Gallery who’s a renaissance
National Gallery who’s a renaissance
National Gallery who’s a renaissance scholar I thinks it’s from the wrong
scholar I thinks it’s from the wrong
scholar I thinks it’s from the wrong period Leonardo in his deathbed in
period Leonardo in his deathbed in
period Leonardo in his deathbed in Amboise France in the Loire Valley
Amboise France in the Loire Valley
Amboise France in the Loire Valley attended to by Francis the first his
attended to by Francis the first his
attended to by Francis the first his royal patron of the last three years he
royal patron of the last three years he
royal patron of the last three years he lived in France the last three years of
lived in France the last three years of
lived in France the last three years of his life as one reason the French the
his life as one reason the French the
his life as one reason the French the Louvre owns more than half Leonardo’s
Louvre owns more than half Leonardo’s
Louvre owns more than half Leonardo’s output this is Amboise the Chateau dump
output this is Amboise the Chateau dump
output this is Amboise the Chateau dump was there’s a church in the back where
was there’s a church in the back where
was there’s a church in the back where he’s buried is thought this is the
he’s buried is thought this is the
he’s buried is thought this is the church st. soother and his beloved Arno
church st. soother and his beloved Arno
church st. soother and his beloved Arno Valley and of course Florence where he
Valley and of course Florence where he
Valley and of course Florence where he lived from the time he was about 15 to
lived from the time he was about 15 to
lived from the time he was about 15 to the time he was close to 30 about 27
the time he was close to 30 about 27
the time he was close to 30 about 27 when Leonardo was 19
when Leonardo was 19
when Leonardo was 19 working for Andrea del Verrocchio he
working for Andrea del Verrocchio he
working for Andrea del Verrocchio he helped put this 8-foot copper sphere on
helped put this 8-foot copper sphere on
helped put this 8-foot copper sphere on top using the same voice that
top using the same voice that
top using the same voice that Brunelleschi had used the generation
Brunelleschi had used the generation
Brunelleschi had used the generation earlier this is the drawing the cartoon
earlier this is the drawing the cartoon
earlier this is the drawing the cartoon for school of athens this great painting
for school of athens this great painting
for school of athens this great painting by Raphael Raphael’s masterpiece since
by Raphael Raphael’s masterpiece since
by Raphael Raphael’s masterpiece since in the Vatican in the foreground is
in the Vatican in the foreground is
in the Vatican in the foreground is Michelangelo sitting in for Heraclitus a
Michelangelo sitting in for Heraclitus a
Michelangelo sitting in for Heraclitus a very difficult philosopher from the
very difficult philosopher from the
very difficult philosopher from the ancient days
ancient days
ancient days it was a good choice in this case
it was a good choice in this case
it was a good choice in this case because Michelangelo was a very
because Michelangelo was a very
because Michelangelo was a very difficult man
difficult man
difficult man but Michelangelo had seen the painting
but Michelangelo had seen the painting
but Michelangelo had seen the painting and he wasn’t in it and when he admired
and he wasn’t in it and when he admired
and he wasn’t in it and when he admired it so much
it so much
it so much Raphael decided to put him in there you
Raphael decided to put him in there you
Raphael decided to put him in there you see in the earlier cartoon he’s not
see in the earlier cartoon he’s not
see in the earlier cartoon he’s not there others in the painting this is
there others in the painting this is
there others in the painting this is Pythagoras over here is Euclid although
Pythagoras over here is Euclid although
Pythagoras over here is Euclid although it could be Archimedes Leonardo as Plato
it could be Archimedes Leonardo as Plato
it could be Archimedes Leonardo as Plato and this is Aristotle we don’t know who
and this is Aristotle we don’t know who
and this is Aristotle we don’t know who the model is the model for this is
the model is the model for this is
the model is the model for this is Bramante and Raphael himself is standing
Bramante and Raphael himself is standing
Bramante and Raphael himself is standing right there is sort of a Alfred
right there is sort of a Alfred
right there is sort of a Alfred Hitchcock moment this statue visited
Hitchcock moment this statue visited
Hitchcock moment this statue visited Washington I guess about four years ago
Washington I guess about four years ago
Washington I guess about four years ago anyone see it
anyone see it
anyone see it yes it’s under it
yes it’s under it
yes it’s under it rocio’s depiction of David just thought
rocio’s depiction of David just thought
rocio’s depiction of David just thought that the model for this is Leonardo
that the model for this is Leonardo
that the model for this is Leonardo himself as a teenager Verrocchio’s
himself as a teenager Verrocchio’s
himself as a teenager Verrocchio’s painting the baptism of Christ in which
painting the baptism of Christ in which
painting the baptism of Christ in which he asked his assistants to paint the
he asked his assistants to paint the
he asked his assistants to paint the angels Botticelli or de kratie painted
angels Botticelli or de kratie painted
angels Botticelli or de kratie painted this angel and Leonardo painted this
this angel and Leonardo painted this
this angel and Leonardo painted this angel if you go to the aficio from the
angel if you go to the aficio from the
angel if you go to the aficio from the Botticelli room to the Leonardo room and
Botticelli room to the Leonardo room and
Botticelli room to the Leonardo room and this is the painting facing you
this is the painting facing you
this is the painting facing you well when baroque you saw the angel he
well when baroque you saw the angel he
well when baroque you saw the angel he gave up the brush for good and didn’t do
gave up the brush for good and didn’t do
gave up the brush for good and didn’t do any more painting after that but it’s a
any more painting after that but it’s a
any more painting after that but it’s a genius meeting a trend a transformative
genius meeting a trend a transformative
genius meeting a trend a transformative genius happened when Isaac Newton I came
genius happened when Isaac Newton I came
genius happened when Isaac Newton I came back from 16 months in his village with
back from 16 months in his village with
back from 16 months in his village with a list of his mental inventions his
a list of his mental inventions his
a list of his mental inventions his theories and his professor Isaac Barrow
theories and his professor Isaac Barrow
theories and his professor Isaac Barrow immediately he had discovered calculus
immediately he had discovered calculus
immediately he had discovered calculus formulated calculus he had discovered
formulated calculus he had discovered
formulated calculus he had discovered the three laws of motion the universal
the three laws of motion the universal
the three laws of motion the universal law of gravitation is endless yet
law of gravitation is endless yet
law of gravitation is endless yet explained how a telescope works his
explained how a telescope works his
explained how a telescope works his professor Isaac Barrow also retired
professor Isaac Barrow also retired
professor Isaac Barrow also retired immediately and became a vicar a priest
immediately and became a vicar a priest
immediately and became a vicar a priest and Newton became the location professor
and Newton became the location professor
and Newton became the location professor Leonardo had a penchant for as I
Leonardo had a penchant for as I
Leonardo had a penchant for as I mentioned for the grotesques along with
mentioned for the grotesques along with
mentioned for the grotesques along with the sublimely beautiful in this case is
the sublimely beautiful in this case is
the sublimely beautiful in this case is called a man being teased by gypsies and
called a man being teased by gypsies and
called a man being teased by gypsies and the facial features with the golden
the facial features with the golden
the facial features with the golden rectangle for 17 years or so he was in
rectangle for 17 years or so he was in
rectangle for 17 years or so he was in the in the higher of the sports that
the in the higher of the sports that
the in the higher of the sports that Duke Sforza in Milan it was one of his
Duke Sforza in Milan it was one of his
Duke Sforza in Milan it was one of his most productive periods that’s what he
most productive periods that’s what he
most productive periods that’s what he was doing engineering military
was doing engineering military
was doing engineering military engineering and producing a few pieces
engineering and producing a few pieces
engineering and producing a few pieces of art including the Last Supper which
of art including the Last Supper which
of art including the Last Supper which was finished in 1498 now in here you can
was finished in 1498 now in here you can
was finished in 1498 now in here you can see his drawings at the top for the side
see his drawings at the top for the side
see his drawings at the top for the side wheeler and I bought a couple of ties
wheeler and I bought a couple of ties
wheeler and I bought a couple of ties along I don’t know if you can make these
along I don’t know if you can make these
along I don’t know if you can make these out but one has a positive slope the
out but one has a positive slope the
out but one has a positive slope the other has a negative slope this one has
other has a negative slope this one has
other has a negative slope this one has the positive slope that’s the way a
the positive slope that’s the way a
the positive slope that’s the way a right-hander would sketch would shade
right-hander would sketch would shade
right-hander would sketch would shade this is the way the left-hander was
this is the way the left-hander was
this is the way the left-hander was would sketch all English and European
would sketch all English and European
would sketch all English and European ties have positive slope
ties have positive slope
ties have positive slope all-american striped eyes have negative
all-american striped eyes have negative
all-american striped eyes have negative slope I don’t know where the convention
slope I don’t know where the convention
slope I don’t know where the convention comes from but it’s there’s never a
comes from but it’s there’s never a
comes from but it’s there’s never a violation of this rule but the negative
violation of this rule but the negative
violation of this rule but the negative slope the American tie this is the way
slope the American tie this is the way
slope the American tie this is the way the left-hander Leonardo would have
the left-hander Leonardo would have
the left-hander Leonardo would have shaded so that proves he really was
shaded so that proves he really was
shaded so that proves he really was American after all
American after all
American after all to me his drawings his mechanical
to me his drawings his mechanical
to me his drawings his mechanical drawings uh this particular exploded
drawings uh this particular exploded
drawings uh this particular exploded gear diagram is incredible it’s three or
gear diagram is incredible it’s three or
gear diagram is incredible it’s three or four hundred years before anyone else
four hundred years before anyone else
four hundred years before anyone else came up with exploded views of machine
came up with exploded views of machine
came up with exploded views of machine parts heat transmission this turns out
parts heat transmission this turns out
parts heat transmission this turns out to be it was always called Leonardo’s
to be it was always called Leonardo’s
to be it was always called Leonardo’s cart the powered cart but it turns out
cart the powered cart but it turns out
cart the powered cart but it turns out to be robotics he had invented he had
to be robotics he had invented he had
to be robotics he had invented he had started the field of robotics
started the field of robotics
started the field of robotics that’s an odometer this is a robotic
that’s an odometer this is a robotic
that’s an odometer this is a robotic Knight this is a mercedes-benz
Knight this is a mercedes-benz
Knight this is a mercedes-benz 3000 dollar bike these are Leonardo’s
3000 dollar bike these are Leonardo’s
3000 dollar bike these are Leonardo’s drawings left-handed shading for chain
drawings left-handed shading for chain
drawings left-handed shading for chain and sprockets and is designed for a
and sprockets and is designed for a
and sprockets and is designed for a bicycle and there is a model a replica
bicycle and there is a model a replica
bicycle and there is a model a replica of the bicycle more than anything else
of the bicycle more than anything else
of the bicycle more than anything else he wanted to master flight he wanted
he wanted to master flight he wanted
he wanted to master flight he wanted humans to achieve flight he said
humans to achieve flight he said
humans to achieve flight he said whatever the birds can do man should
whatever the birds can do man should
whatever the birds can do man should also be able to do so he designed
also be able to do so he designed
also be able to do so he designed various ornithopters these flapping wing
various ornithopters these flapping wing
various ornithopters these flapping wing devices you can imagine his assistants
devices you can imagine his assistants
devices you can imagine his assistants coming to work and being told they were
coming to work and being told they were
coming to work and being told they were going to test fly then he decided maybe
going to test fly then he decided maybe
going to test fly then he decided maybe a helicopter would work better and
Sikorsky early in the 20th century
Sikorsky early in the 20th century invented the helicopter inspired he said
invented the helicopter inspired he said
invented the helicopter inspired he said by having seen Leonardo’s drawing of the
by having seen Leonardo’s drawing of the
by having seen Leonardo’s drawing of the aerial screw in case something there was
aerial screw in case something there was
aerial screw in case something there was a mishap he invented the parachute
a mishap he invented the parachute
a mishap he invented the parachute there’s the drawing and the specs were
there’s the drawing and the specs were
there’s the drawing and the specs were given below all through the 20th century
given below all through the 20th century
given below all through the 20th century that people have seen this drawing they
that people have seen this drawing they
that people have seen this drawing they would say it’s amazing
would say it’s amazing
would say it’s amazing such prescience except they said it
such prescience except they said it
such prescience except they said it probably would not work in that design
probably would not work in that design
probably would not work in that design in 2000 here’s someone in South Africa
in 2000 here’s someone in South Africa
in 2000 here’s someone in South Africa coming down with whee
coming down with whee
coming down with whee whose parachute it works his great
whose parachute it works his great
whose parachute it works his great patron Lorenzo the Magnificent and his
patron Lorenzo the Magnificent and his
patron Lorenzo the Magnificent and his brother Giuliano de Medici Giuliano was
brother Giuliano de Medici Giuliano was
brother Giuliano de Medici Giuliano was assassinated in the cathedral and
assassinated in the cathedral and
assassinated in the cathedral and Lorenzo barely escaped but within a few
Lorenzo barely escaped but within a few
Lorenzo barely escaped but within a few weeks all the assassins were rounded up
weeks all the assassins were rounded up
weeks all the assassins were rounded up the ringleader of the assassins had fled
the ringleader of the assassins had fled
the ringleader of the assassins had fled all the way to to Constantinople
all the way to to Constantinople
all the way to to Constantinople actually it was already Istanbul by then
actually it was already Istanbul by then
actually it was already Istanbul by then this was 1478 Leonardo would have been
this was 1478 Leonardo would have been
this was 1478 Leonardo would have been 26 he saw the man hanging and
26 he saw the man hanging and
26 he saw the man hanging and immediately did the sketch and even like
immediately did the sketch and even like
immediately did the sketch and even like a photojournalist explain what the man
a photojournalist explain what the man
a photojournalist explain what the man was wearing he said he’s wearing Turkish
was wearing he said he’s wearing Turkish
was wearing he said he’s wearing Turkish clothes by 1498 when he was in Milan the
clothes by 1498 when he was in Milan the
clothes by 1498 when he was in Milan the notorious southerner Ola of course had
notorious southerner Ola of course had
notorious southerner Ola of course had upended the Medici in Florence Leonardo
upended the Medici in Florence Leonardo
upended the Medici in Florence Leonardo was living in Milan after two or three
was living in Milan after two or three
was living in Milan after two or three years of truly a cool rule the Pope
years of truly a cool rule the Pope
years of truly a cool rule the Pope realized it wasn’t that there was he’s
realized it wasn’t that there was he’s
realized it wasn’t that there was he’s seen as an early Protestant revolution
seen as an early Protestant revolution
seen as an early Protestant revolution and he was denounced by the Pope he was
and he was denounced by the Pope he was
and he was denounced by the Pope he was burned at the stake and in Ferrara where
burned at the stake and in Ferrara where
burned at the stake and in Ferrara where he was born there’s a statue of him now
he was born there’s a statue of him now
he was born there’s a statue of him now and certainly if Leonardo had been
and certainly if Leonardo had been
and certainly if Leonardo had been influenced then he would have sketched
influenced then he would have sketched
influenced then he would have sketched this a student of mine sent this to me
this a student of mine sent this to me
this a student of mine sent this to me once it says I saved some money on the
once it says I saved some money on the
once it says I saved some money on the footings but don’t worry no one will
footings but don’t worry no one will
footings but don’t worry no one will ever notice well two people who noticed
ever notice well two people who noticed
ever notice well two people who noticed were Leonardo and gal Leo Leonardo did
were Leonardo and gal Leo Leonardo did
were Leonardo and gal Leo Leonardo did some experiments dropping objects from
some experiments dropping objects from
some experiments dropping objects from the side and there’s no evidence that he
the side and there’s no evidence that he
the side and there’s no evidence that he did this experiment in Pisa I’m not sure
did this experiment in Pisa I’m not sure
did this experiment in Pisa I’m not sure you ever went to Pisa but this is a good
you ever went to Pisa but this is a good
you ever went to Pisa but this is a good model to to explain the phenomena he
model to to explain the phenomena he
model to to explain the phenomena he found that an equal second periods of
found that an equal second periods of
found that an equal second periods of time second units that an object would
time second units that an object would
time second units that an object would descend one
descend one
descend one two three four five units of distance
two three four five units of distance
two three four five units of distance sequential seconds
sequential seconds
sequential seconds Galileo 110 years later found the
Galileo 110 years later found the
Galileo 110 years later found the distances to be one three five seven
distances to be one three five seven
distances to be one three five seven these are both arithmetic series when
these are both arithmetic series when
these are both arithmetic series when you add these arithmetic series the sum
you add these arithmetic series the sum
you add these arithmetic series the sum is a quadratic what this means is the
is a quadratic what this means is the
is a quadratic what this means is the acceleration is constant and that’s what
acceleration is constant and that’s what
acceleration is constant and that’s what Galileo is giving credit for having
Galileo is giving credit for having
Galileo is giving credit for having discovered the law of freefall that
discovered the law of freefall that
discovered the law of freefall that objects fall with constant acceleration
objects fall with constant acceleration
objects fall with constant acceleration independent of their weights Leonardo
independent of their weights Leonardo
independent of their weights Leonardo had discovered that but he hadn’t
had discovered that but he hadn’t
had discovered that but he hadn’t written it here is Galileo also
written it here is Galileo also
written it here is Galileo also Aristotelian physics physics being
Aristotelian physics physics being
Aristotelian physics physics being taught all through the 17th century had
taught all through the 17th century had
taught all through the 17th century had the trajectory of projectiles to be like
the trajectory of projectiles to be like
the trajectory of projectiles to be like this
this
this Galileo discovered in 1609 with his
Galileo discovered in 1609 with his
Galileo discovered in 1609 with his experiments that there were parts of
experiments that there were parts of
experiments that there were parts of parabolas that the trajectories were
parabolas that the trajectories were
parabolas that the trajectories were parabolic Leonardo 120 years earlier had
parabolic Leonardo 120 years earlier had
parabolic Leonardo 120 years earlier had already drawn this picture of parabolic
already drawn this picture of parabolic
already drawn this picture of parabolic trajectories the trouble with Leonardo
trajectories the trouble with Leonardo
trajectories the trouble with Leonardo is he didn’t publish then in the hands
is he didn’t publish then in the hands
is he didn’t publish then in the hands of Isaac Newton another 160 years later
of Isaac Newton another 160 years later
of Isaac Newton another 160 years later the parabolic trajectories became
the parabolic trajectories became
the parabolic trajectories became elliptical trajectories this is the
elliptical trajectories this is the
elliptical trajectories this is the frontispiece of Isaac Newton’s great
frontispiece of Isaac Newton’s great
frontispiece of Isaac Newton’s great book the most important book in the
book the most important book in the
book the most important book in the sciences here is Galileo’s telescope
sciences here is Galileo’s telescope
sciences here is Galileo’s telescope 1609 here is Isaac Newton’s reflector
1609 here is Isaac Newton’s reflector
1609 here is Isaac Newton’s reflector 1668
1668
1668 here is the hubble reflector 1986 and
here is the hubble reflector 1986 and
here is the hubble reflector 1986 and here is Leonardo’s reflector 1500 this
here is Leonardo’s reflector 1500 this
here is Leonardo’s reflector 1500 this is the level of anatomical drawings that
is the level of anatomical drawings that
is the level of anatomical drawings that existed in Leonardo’s day Bernardo did
existed in Leonardo’s day Bernardo did
existed in Leonardo’s day Bernardo did his own anatomical drawings and in this
his own anatomical drawings and in this
his own anatomical drawings and in this case his writing was always from right
case his writing was always from right
case his writing was always from right to left he always wrote backwards it was
to left he always wrote backwards it was
to left he always wrote backwards it was more practical he was left-handed and if
more practical he was left-handed and if
more practical he was left-handed and if he wrote to the right the the quill
he wrote to the right the the quill
he wrote to the right the the quill would get stuck in the
would get stuck in the
would get stuck in the / so he wrote a mirror script and you
/ so he wrote a mirror script and you
/ so he wrote a mirror script and you need to put a mirror right next to it to
need to put a mirror right next to it to
need to put a mirror right next to it to make out the text but these the detail
make out the text but these the detail
make out the text but these the detail of these vital organs in the human here
of these vital organs in the human here
of these vital organs in the human here is the heart and lungs
is the heart and lungs
is the heart and lungs the cardiovascular system as detailed
the cardiovascular system as detailed
the cardiovascular system as detailed drawing notes all written beautifully
drawing notes all written beautifully
drawing notes all written beautifully from right to left his master Verrocchio
from right to left his master Verrocchio
from right to left his master Verrocchio had told the pupils his apprentices to
had told the pupils his apprentices to
had told the pupils his apprentices to learn the body from the inside out he
learn the body from the inside out he
learn the body from the inside out he would have had no idea to what level
would have had no idea to what level
would have had no idea to what level Leonardo would go to learn the body from
Leonardo would go to learn the body from
Leonardo would go to learn the body from the inside out in this case the old man
the inside out in this case the old man
the inside out in this case the old man here is thought to be one fellow he met
here is thought to be one fellow he met
here is thought to be one fellow he met when he visited a hospital in in
when he visited a hospital in in
when he visited a hospital in in Florence man was very old and Leonardo
Florence man was very old and Leonardo
Florence man was very old and Leonardo asked him he sat with him and held his
asked him he sat with him and held his
asked him he sat with him and held his hand and asked how old he was and the
hand and asked how old he was and the
hand and asked how old he was and the man said I don’t know but I’m very old
man said I don’t know but I’m very old
man said I don’t know but I’m very old Leonardo said what is very old and he
Leonardo said what is very old and he
Leonardo said what is very old and he said I don’t know what my grandson is 58
said I don’t know what my grandson is 58
said I don’t know what my grandson is 58 in order estimated man must been over a
in order estimated man must been over a
in order estimated man must been over a hundred and with a smile on his face man
hundred and with a smile on his face man
hundred and with a smile on his face man passed away leonardo wrote I quickly did
passed away leonardo wrote I quickly did
passed away leonardo wrote I quickly did a anatomy of him well he wanted to find
a anatomy of him well he wanted to find
a anatomy of him well he wanted to find out how anyone could die such a happy
out how anyone could die such a happy
out how anyone could die such a happy death then a few weeks later he did an
death then a few weeks later he did an
death then a few weeks later he did an Anatomy or post-mortem on a child and he
Anatomy or post-mortem on a child and he
Anatomy or post-mortem on a child and he wrote the difference he said in the case
wrote the difference he said in the case
wrote the difference he said in the case of the child the blood vessels leading
of the child the blood vessels leading
of the child the blood vessels leading to the heart were supple and clear in
to the heart were supple and clear in
to the heart were supple and clear in the case of the old man they were
the case of the old man they were
the case of the old man they were occluded or clogged and brittle he’s
occluded or clogged and brittle he’s
occluded or clogged and brittle he’s describing atherosclerosis 500 years ago
describing atherosclerosis 500 years ago
describing atherosclerosis 500 years ago was first identified in modern times by
was first identified in modern times by
was first identified in modern times by at the university of vienna around the
at the university of vienna around the
at the university of vienna around the 1890s and the person who revolutionized
1890s and the person who revolutionized
1890s and the person who revolutionized medicine Berzelius of course in 1543 24
medicine Berzelius of course in 1543 24
medicine Berzelius of course in 1543 24 years after Leonardo’s passing hired a
years after Leonardo’s passing hired a
years after Leonardo’s passing hired a Flemish artist to draw a human body
Flemish artist to draw a human body
Flemish artist to draw a human body during dissections
during dissections
during dissections this is Vesalius at 29
this is Vesalius at 29
this is Vesalius at 29 that’s when the scientific revolution
that’s when the scientific revolution
that’s when the scientific revolution starts with Copernicus’s book in 1543
starts with Copernicus’s book in 1543
starts with Copernicus’s book in 1543 and with Vesalius his book Leonardo’s
and with Vesalius his book Leonardo’s
and with Vesalius his book Leonardo’s drawings of the heart the human heart
drawings of the heart the human heart
drawings of the heart the human heart recently it was it came to the news a
recently it was it came to the news a
recently it was it came to the news a couple of years ago that a well-known
couple of years ago that a well-known
couple of years ago that a well-known surgeon cardiac surgeon in Cambridge at
surgeon cardiac surgeon in Cambridge at
surgeon cardiac surgeon in Cambridge at Cambridge University was doing mitral
Cambridge University was doing mitral
Cambridge University was doing mitral valve repairs looking at Leonardo’s
valve repairs looking at Leonardo’s
valve repairs looking at Leonardo’s drawings and his descriptions and this
drawings and his descriptions and this
drawings and his descriptions and this turns out to be revolutionary medicine
turns out to be revolutionary medicine
turns out to be revolutionary medicine mitral valve repair using these five
mitral valve repair using these five
mitral valve repair using these five hundred year old descriptions that
hundred year old descriptions that
hundred year old descriptions that Leonardo gave or maybe the modus
Leonardo gave or maybe the modus
Leonardo gave or maybe the modus operandi that he taught us my son who’s
operandi that he taught us my son who’s
operandi that he taught us my son who’s a Cardiacs
a Cardiacs
a Cardiacs radiologists gave me that drawing I
radiologists gave me that drawing I
radiologists gave me that drawing I could rotate the heart and get just the
could rotate the heart and get just the
could rotate the heart and get just the right angle as a counterpoint to
right angle as a counterpoint to
right angle as a counterpoint to Leonardo’s drawings of the human heart
Leonardo’s drawings of the human heart
Leonardo’s drawings of the human heart this is the way you would have seen his
this is the way you would have seen his
this is the way you would have seen his handwriting pretty hard to read this is
handwriting pretty hard to read this is
handwriting pretty hard to read this is called the da vinci font you can flip it
called the da vinci font you can flip it
called the da vinci font you can flip it back and forth like this fact in the new
back and forth like this fact in the new
back and forth like this fact in the new book Leonardo’s universe all the
book Leonardo’s universe all the
book Leonardo’s universe all the quotations are with Leonardo’s font he’s
quotations are with Leonardo’s font he’s
quotations are with Leonardo’s font he’s talking about evolution
talking about evolution
talking about evolution this is 350 years before Darwin there is
this is 350 years before Darwin there is
this is 350 years before Darwin there is a legend that around 1480 the the
a legend that around 1480 the the
a legend that around 1480 the the conqueror of constantinople mammoths ii
conqueror of constantinople mammoths ii
conqueror of constantinople mammoths ii invited Leonardo to Turkey to
invited Leonardo to Turkey to
invited Leonardo to Turkey to Constantinople Leonardo had just taken a
Constantinople Leonardo had just taken a
Constantinople Leonardo had just taken a job in Milan and he was very happy with
job in Milan and he was very happy with
job in Milan and he was very happy with the job in Milan he didn’t go but
the job in Milan he didn’t go but
the job in Milan he didn’t go but there’s no real proof of this 20 years
there’s no real proof of this 20 years
there’s no real proof of this 20 years later
later
later Leonardo was out of a job this forces
Leonardo was out of a job this forces
Leonardo was out of a job this forces were ran out run out by a French
were ran out run out by a French
were ran out run out by a French and Leonardo applied to the Sultan of
and Leonardo applied to the Sultan of
and Leonardo applied to the Sultan of Turkey
Turkey
Turkey this letter ironic it’s written from
this letter ironic it’s written from
this letter ironic it’s written from right to left
right to left
right to left in the way that old Turkish used to be
in the way that old Turkish used to be
in the way that old Turkish used to be written but following Convention
written but following Convention
written but following Convention correctly he talks about building a
correctly he talks about building a
correctly he talks about building a bridge over the Golden Horn Golden Horn
bridge over the Golden Horn Golden Horn
bridge over the Golden Horn Golden Horn is an Istanbul it said unless about 7
is an Istanbul it said unless about 7
is an Istanbul it said unless about 7 miles or 10 kilometers long from the
miles or 10 kilometers long from the
miles or 10 kilometers long from the Bosphorus and he says I understand
Bosphorus and he says I understand
Bosphorus and he says I understand you’re looking for an architect or
you’re looking for an architect or
you’re looking for an architect or engineer to build this bridge and I
engineer to build this bridge and I
engineer to build this bridge and I happen to be the architect who can do
happen to be the architect who can do
happen to be the architect who can do this unhappily the Sultan the son of the
this unhappily the Sultan the son of the
this unhappily the Sultan the son of the conqueror was not a visionary and he
conqueror was not a visionary and he
conqueror was not a visionary and he didn’t hire Leonardo a couple of hundred
didn’t hire Leonardo a couple of hundred
didn’t hire Leonardo a couple of hundred years later a bridge was built it
years later a bridge was built it
years later a bridge was built it probably survived for ten or fifteen
probably survived for ten or fifteen
probably survived for ten or fifteen years here’s the bridge over the Golden
years here’s the bridge over the Golden
years here’s the bridge over the Golden Horn
Horn
Horn there is a fire tower in the back and
there is a fire tower in the back and
there is a fire tower in the back and this is the famous mosque the selamanya
this is the famous mosque the selamanya
this is the famous mosque the selamanya but this is the Golden Horn it’s about
but this is the Golden Horn it’s about
but this is the Golden Horn it’s about two hundred forty meters or seven
two hundred forty meters or seven
two hundred forty meters or seven hundred and ninety feet across I sat at
hundred and ninety feet across I sat at
hundred and ninety feet across I sat at the top of the tower and looking at this
the top of the tower and looking at this
the top of the tower and looking at this mosque I sketched it here is two point
mosque I sketched it here is two point
mosque I sketched it here is two point perspective Leonardo had invented two
perspective Leonardo had invented two
perspective Leonardo had invented two point perspective one point perspective
point perspective one point perspective
point perspective one point perspective was known by Brunelleschi but this is
was known by Brunelleschi but this is
was known by Brunelleschi but this is two point perspective where these
two point perspective where these
two point perspective where these parallel lines converge at two vanishing
parallel lines converge at two vanishing
parallel lines converge at two vanishing points and in this sketch the Golden
points and in this sketch the Golden
points and in this sketch the Golden Horn or hullick would be right here for
Horn or hullick would be right here for
Horn or hullick would be right here for 500 years
500 years
500 years Leonardo’s plans lay they were wasted
Leonardo’s plans lay they were wasted
Leonardo’s plans lay they were wasted these are Leonardo’s designs for the
these are Leonardo’s designs for the
these are Leonardo’s designs for the bridge and finally in Norway just
bridge and finally in Norway just
bridge and finally in Norway just outside Oslo the bridge was built this
outside Oslo the bridge was built this
outside Oslo the bridge was built this is Leonardo’s design and the Norwegian
is Leonardo’s design and the Norwegian
is Leonardo’s design and the Norwegian artist who spearheaded this project
artist who spearheaded this project
artist who spearheaded this project Beveren son would like to do it
Beveren son would like to do it
Beveren son would like to do it in Istanbul me this is in the Golden
in Istanbul me this is in the Golden
in Istanbul me this is in the Golden Horn and this is what the bridge would
Horn and this is what the bridge would
Horn and this is what the bridge would look like now I should have shown you I
look like now I should have shown you I
look like now I should have shown you I should have talked about this when I was
should have talked about this when I was
should have talked about this when I was first sketching but in 1998 Christopher
first sketching but in 1998 Christopher
first sketching but in 1998 Christopher Tyler an Englishman a psychologist
Tyler an Englishman a psychologist
Tyler an Englishman a psychologist living in San Francisco discovered the
living in San Francisco discovered the
living in San Francisco discovered the centerline principle in all great
centerline principle in all great
centerline principle in all great portraits a line that divides the
portraits a line that divides the
portraits a line that divides the painting into a vertical line passes
painting into a vertical line passes
painting into a vertical line passes through an eye here is of course Mona
through an eye here is of course Mona
through an eye here is of course Mona Lisa here’s a Rembrandt self-portrait
Lisa here’s a Rembrandt self-portrait
Lisa here’s a Rembrandt self-portrait it’s in the National Gallery and here’s
it’s in the National Gallery and here’s
it’s in the National Gallery and here’s the Picasso the portrait of Dora Maar if
the Picasso the portrait of Dora Maar if
the Picasso the portrait of Dora Maar if Picasso had known this principle he
Picasso had known this principle he
Picasso had known this principle he would have put the eye somewhere around
would have put the eye somewhere around
would have put the eye somewhere around here this is in in Leningrad at Saint
here this is in in Leningrad at Saint
here this is in in Leningrad at Saint Patsy Armitage there is a the portrait
Patsy Armitage there is a the portrait
Patsy Armitage there is a the portrait of the old rabbi by Rembrandt who seems
of the old rabbi by Rembrandt who seems
of the old rabbi by Rembrandt who seems to have more life than four haggard
to have more life than four haggard
to have more life than four haggard tourists in the front right through the
tourists in the front right through the
tourists in the front right through the eye right through the eye as my son
eye right through the eye as my son
eye right through the eye as my son right through the eye go home and look
right through the eye go home and look
right through the eye go home and look at your pictures photographs that you’ve
at your pictures photographs that you’ve
at your pictures photographs that you’ve taken and see if you haven’t focused
taken and see if you haven’t focused
taken and see if you haven’t focused that way in this picture in this
that way in this picture in this
that way in this picture in this painting by
painting by
painting by a Jamie Wyeth line doesn’t go through
a Jamie Wyeth line doesn’t go through
a Jamie Wyeth line doesn’t go through the center of the portrait central would
the center of the portrait central would
the center of the portrait central would be somewhere around here but it turns
be somewhere around here but it turns
be somewhere around here but it turns out this is one part two 0.618 the
out this is one part two 0.618 the
out this is one part two 0.618 the golden ratio
golden ratio
golden ratio Jamie Wyeth wrote a little blurb for the
Jamie Wyeth wrote a little blurb for the
Jamie Wyeth wrote a little blurb for the back of math and the Mona Lisa
back of math and the Mona Lisa
back of math and the Mona Lisa it was fascinated he said by chapter 8
it was fascinated he said by chapter 8
it was fascinated he said by chapter 8 where I talked about this principle now
where I talked about this principle now
where I talked about this principle now one other principle it turns out we have
one other principle it turns out we have
one other principle it turns out we have a propensity for left cheeks over right
a propensity for left cheeks over right
a propensity for left cheeks over right cheeks when we pose for portraits there
cheeks when we pose for portraits there
cheeks when we pose for portraits there are more left cheeks than right cheeks a
are more left cheeks than right cheeks a
are more left cheeks than right cheeks a young Australian psychologist decided to
young Australian psychologist decided to
young Australian psychologist decided to put this to the test to find out whether
put this to the test to find out whether
put this to the test to find out whether it was the subject deciding or whether
it was the subject deciding or whether
it was the subject deciding or whether it was the artists eye
it was the artists eye
it was the artists eye which way to have the subject turn so he
which way to have the subject turn so he
which way to have the subject turn so he said he took a group of 400 which would
said he took a group of 400 which would
said he took a group of 400 which would be just about the size of this audience
be just about the size of this audience
be just about the size of this audience and he he said we’re going to do a
and he he said we’re going to do a
and he he said we’re going to do a portrait of you with a camera
portrait of you with a camera
portrait of you with a camera photographic portrait then he escorted
photographic portrait then he escorted
photographic portrait then he escorted how to half of them out of the room and
how to half of them out of the room and
how to half of them out of the room and he told the half that remained that the
he told the half that remained that the
he told the half that remained that the portrait was going to hang in the house
portrait was going to hang in the house
portrait was going to hang in the house of their mothers their boyfriends their
of their mothers their boyfriends their
of their mothers their boyfriends their girlfriends but a loved one and
girlfriends but a loved one and
girlfriends but a loved one and immediately it would be the left cheek
immediately it would be the left cheek
immediately it would be the left cheek that became prominent the person would
that became prominent the person would
that became prominent the person would face this way then the second group was
face this way then the second group was
face this way then the second group was brought into the room and the first
brought into the room and the first
brought into the room and the first group left they were told that the
group left they were told that the
group left they were told that the painting was going to hang next to
painting was going to hang next to
painting was going to hang next to Albert Einstein a certified genius
Albert Einstein a certified genius
Albert Einstein a certified genius immediately was the right cheek in
immediately was the right cheek in
immediately was the right cheek in something like 78 percent of the time
something like 78 percent of the time
something like 78 percent of the time and the question is why do we behave
and the question is why do we behave
and the question is why do we behave like this and it was exactly the same
like this and it was exactly the same
like this and it was exactly the same number for men and women and the
number for men and women and the
number for men and women and the psychologists had a very interesting
psychologists had a very interesting
psychologists had a very interesting interpretation we we do art we are
interpretation we we do art we are
interpretation we we do art we are emotional we emote on the right bright
emotional we emote on the right bright
emotional we emote on the right bright on the right brain which controls the
on the right brain which controls the
on the right brain which controls the left cheek we do mathematics right here
left cheek we do mathematics right here
left cheek we do mathematics right here above the left ear and that of course
above the left ear and that of course
above the left ear and that of course controls the right cheek so if we want
controls the right cheek so if we want
controls the right cheek so if we want to hang next to Albert Einstein we start
to hang next to Albert Einstein we start
to hang next to Albert Einstein we start putting out our intelligent cheek
putting out our intelligent cheek
putting out our intelligent cheek controlled by the left left brain in
controlled by the left left brain in
controlled by the left left brain in this case though these are all
this case though these are all
this case though these are all Rembrandt’s now Leonardo painted all of
Rembrandt’s now Leonardo painted all of
Rembrandt’s now Leonardo painted all of a dozen paintings
a dozen paintings
a dozen paintings Rembrandt painted himself ninety seven
Rembrandt painted himself ninety seven
Rembrandt painted himself ninety seven times this is a sampling of of six
times this is a sampling of of six
times this is a sampling of of six paintings and they’re all six to one
paintings and they’re all six to one
paintings and they’re all six to one here is five to one but six to one with
here is five to one but six to one with
here is five to one but six to one with right cheeks why does he want to be
right cheeks why does he want to be
right cheeks why does he want to be intelligent looking rather than
intelligent looking rather than
intelligent looking rather than emotional or cute looking endearing
emotional or cute looking endearing
emotional or cute looking endearing looking any ideas any portrait artists
looking any ideas any portrait artists
looking any ideas any portrait artists here we’re looking at a mirror it’s
here we’re looking at a mirror it’s
here we’re looking at a mirror it’s reversed
reversed
reversed this is his endearing sight these were
this is his endearing sight these were
this is his endearing sight these were all not his right cheek but his left
all not his right cheek but his left
all not his right cheek but his left cheek in the portraits
okay Leonardo’s virgin of the rocks– he
okay Leonardo’s virgin of the rocks– he painted two of these is his partners the
painted two of these is his partners the
painted two of these is his partners the pretty brothers helped him and probably
pretty brothers helped him and probably
pretty brothers helped him and probably painted most of the second version the
painted most of the second version the
painted most of the second version the one in England but this one is in the
one in England but this one is in the
one in England but this one is in the Louvre it’s one of the most beautiful
Louvre it’s one of the most beautiful
Louvre it’s one of the most beautiful paintings in the world certainly they
paintings in the world certainly they
paintings in the world certainly they are organized by the pyramid
are organized by the pyramid
are organized by the pyramid Leonardo invented this pyramid form for
Leonardo invented this pyramid form for
Leonardo invented this pyramid form for for organizing his quartet and then it
for organizing his quartet and then it
for organizing his quartet and then it was a plot this is the English version
was a plot this is the English version
was a plot this is the English version of the virgin of the rocks– it’s
of the virgin of the rocks– it’s
of the virgin of the rocks– it’s slightly different but just a couple of
slightly different but just a couple of
slightly different but just a couple of years ago I think it was in 2006 that an
years ago I think it was in 2006 that an
years ago I think it was in 2006 that an infrared refract ography revealed that
infrared refract ography revealed that
infrared refract ography revealed that Leonardo had another design in mind I
Leonardo had another design in mind I
Leonardo had another design in mind I presumably his patrons you can see the
presumably his patrons you can see the
presumably his patrons you can see the red here it’s been reproduced over here
red here it’s been reproduced over here
red here it’s been reproduced over here he had an entirely different design of
he had an entirely different design of
he had an entirely different design of mine rather than using the same form
mine rather than using the same form
mine rather than using the same form that he had used for virgin of the
that he had used for virgin of the
that he had used for virgin of the rocks– in the Louvre version there are
rocks– in the Louvre version there are
rocks– in the Louvre version there are the golden rectangles organizing each of
the golden rectangles organizing each of
the golden rectangles organizing each of the three women that he painted 15 years
the three women that he painted 15 years
the three women that he painted 15 years apart this is the one in Washington now
apart this is the one in Washington now
apart this is the one in Washington now in the one in Washington this part of
in the one in Washington this part of
in the one in Washington this part of the painting is missing David Allen
the painting is missing David Allen
the painting is missing David Allen Brown the curator of Renaissance art I
Brown the curator of Renaissance art I
Brown the curator of Renaissance art I melded brought together the hands that
melded brought together the hands that
melded brought together the hands that Leonardo had drawn there in Windsor
Leonardo had drawn there in Windsor
Leonardo had drawn there in Windsor Castle and with computers they married
Castle and with computers they married
Castle and with computers they married together the hands and the rest of the
together the hands and the rest of the
together the hands and the rest of the painting in each case the central line
painting in each case the central line
painting in each case the central line goes through one eye the Mona Lisa is
goes through one eye the Mona Lisa is
goes through one eye the Mona Lisa is organized further in the Golden Triangle
organized further in the Golden Triangle
organized further in the Golden Triangle and right there is Leonardo’s
and right there is Leonardo’s
and right there is Leonardo’s fingerprints he was touching the
fingerprints he was touching the
fingerprints he was touching the painting and fixing it with his fingers
painting and fixing it with his fingers
painting and fixing it with his fingers called the process called Villa Tora
called the process called Villa Tora
called the process called Villa Tora where the paint is not mixed on the
where the paint is not mixed on the
where the paint is not mixed on the palate but applied directly onto the
palate but applied directly onto the
palate but applied directly onto the board rarely a canvas they used wooden
board rarely a canvas they used wooden
board rarely a canvas they used wooden boards then
boards then
boards then and then he would use his fingers he was
and then he would use his fingers he was
and then he would use his fingers he was finger-painting there is the Mona Lisa
finger-painting there is the Mona Lisa
finger-painting there is the Mona Lisa and the next time you see a portrait of
and the next time you see a portrait of
and the next time you see a portrait of the Mona Lisa close-up look at the mouth
the Mona Lisa close-up look at the mouth
the Mona Lisa close-up look at the mouth look away can’t come back go back and
look away can’t come back go back and
look away can’t come back go back and forth and see if that phenomena doesn’t
forth and see if that phenomena doesn’t
forth and see if that phenomena doesn’t occur to you the smile disappears when
occur to you the smile disappears when
occur to you the smile disappears when you look right at the mouth now in this
you look right at the mouth now in this
you look right at the mouth now in this painting these are the rocks they were
painting these are the rocks they were
painting these are the rocks they were always thought to be a figment of the
always thought to be a figment of the
always thought to be a figment of the inaros imagination is very rich
inaros imagination is very rich
inaros imagination is very rich imagination has experienced seeing
imagination has experienced seeing
imagination has experienced seeing nature and right there is a bridge with
nature and right there is a bridge with
nature and right there is a bridge with seven arches there are the rocks there
seven arches there are the rocks there
seven arches there are the rocks there are the valdarno
are the valdarno
are the valdarno there in the county of Valdano they’re
there in the county of Valdano they’re
there in the county of Valdano they’re called the balsa rocks and this is the
called the balsa rocks and this is the
called the balsa rocks and this is the bridge the Ponte Ponte Briana very close
bridge the Ponte Ponte Briana very close
bridge the Ponte Ponte Briana very close to arezzo not far from Florence finally
to arezzo not far from Florence finally
to arezzo not far from Florence finally The Last Supper
The Last Supper
The Last Supper how many of you believe this is Mary
how many of you believe this is Mary
how many of you believe this is Mary Magdalene oh he did make st. John rather
Magdalene oh he did make st. John rather
Magdalene oh he did make st. John rather a feminine feminist he had he was like a
a feminine feminist he had he was like a
a feminine feminist he had he was like a Hollywood casting director
Hollywood casting director
Hollywood casting director he knew the faces he wanted for his
he knew the faces he wanted for his
he knew the faces he wanted for his painting he had a fairly easy time
painting he had a fairly easy time
painting he had a fairly easy time finding various apostles or disciples
finding various apostles or disciples
finding various apostles or disciples here this is Bartholomew this is Andrew
here this is Bartholomew this is Andrew
here this is Bartholomew this is Andrew this is a Vettius this is doubting
this is a Vettius this is doubting
this is a Vettius this is doubting Thomas as Saint Peter right there Saint
Thomas as Saint Peter right there Saint
Thomas as Saint Peter right there Saint John and Matthew well he had a very hard
John and Matthew well he had a very hard
John and Matthew well he had a very hard time finding his model for Christ and
time finding his model for Christ and
time finding his model for Christ and his model for Judas Iscariot
his model for Judas Iscariot
his model for Judas Iscariot he painted Christ in sort of a nebulous
he painted Christ in sort of a nebulous
he painted Christ in sort of a nebulous way it’s never quite clear but in the
way it’s never quite clear but in the
way it’s never quite clear but in the case of Judas a friend came to him and
case of Judas a friend came to him and
case of Judas a friend came to him and told him of having seen a perfect Judas
told him of having seen a perfect Judas
told him of having seen a perfect Judas for him he was in a prison in order went
for him he was in a prison in order went
for him he was in a prison in order went to the prison in Milan and found the man
to the prison in Milan and found the man
to the prison in Milan and found the man and agreed that this would indeed be a
and agreed that this would indeed be a
and agreed that this would indeed be a perfect model for his Judas
perfect model for his Judas
perfect model for his Judas is the man in all earlier paintings of
is the man in all earlier paintings of
is the man in all earlier paintings of the Last Supper
the Last Supper
the Last Supper you see Judas from the back but Leonardo
you see Judas from the back but Leonardo
you see Judas from the back but Leonardo use the more Democratic lineup all
use the more Democratic lineup all
use the more Democratic lineup all looking this direction except Judas’s
looking this direction except Judas’s
looking this direction except Judas’s faces in the shadow
faces in the shadow
faces in the shadow he’s spilled the cellar of salt he has
he’s spilled the cellar of salt he has
he’s spilled the cellar of salt he has in front of them and he’s holding a
in front of them and he’s holding a
in front of them and he’s holding a small purse in his hand anyway when he
small purse in his hand anyway when he
small purse in his hand anyway when he started painting Judas the man agreed
started painting Judas the man agreed
started painting Judas the man agreed and he started drawing and painting him
and he started drawing and painting him
and he started drawing and painting him man said you don’t recognize me do and
man said you don’t recognize me do and
man said you don’t recognize me do and Nardo suddenly started trembling you
Nardo suddenly started trembling you
Nardo suddenly started trembling you realized this was as Jesus three years
realized this was as Jesus three years
realized this was as Jesus three years earlier this was a picture I saw coming
earlier this was a picture I saw coming
earlier this was a picture I saw coming out of Johns Hopkins once the iconic
out of Johns Hopkins once the iconic
out of Johns Hopkins once the iconic figure these are various languages that
figure these are various languages that
figure these are various languages that not the Mona Lisa’s appeared in and here
not the Mona Lisa’s appeared in and here
not the Mona Lisa’s appeared in and here is the new book anyway thank you very
is the new book anyway thank you very
is the new book anyway thank you very much
”
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