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1. Freshman Organic Chemistry: How Do You Know?
Poziom:
Temat: Edukacja
Prof: Okay.
So for 150 years organic
chemistry courses have tended to
acquire a daunting reputation.
So you need help.
I know you're very able,
but trust me,
you need help.
So where do you the help?
The PowerPoints are available
on the Web.
How many of you've already seen
the PowerPoint for today,
just so I have some idea?
So about a quarter of you maybe.
Okay, but anyhow,
so your lecture notes are
important,
but you don't have to worry
about getting everything down
because you can download it from
the Web.
And I do it on a Mac,
but I try my best to make it
compatible with PCs and even
with the free PC Viewer for
PowerPoint.
So you should be able to see it.
But I don't see it on a PC.
So if anything doesn't come
through, let me know so that I
can fix it.
Okay then, in-class discussion
is very important,
and if you're really,
really shy and can't
participate in discussion in
class,
then email me a question. Okay?
There's the course website,
which is our substitute for a
text.
It also includes the
PowerPoint, and there's the link
for it, and when go there you'll
see it develop.
The current website is mostly
last year's course,
so it'll change a little bit as
we go along, but fundamentally
it's the same.
If you want to look ahead
you'll see pretty much what's
coming up.
There'll be assigned problems
and questions,
and also there are previous
exams and answers keys.
All these things are on the
course website so you'll get
help there.
But one thing that's really
special is the course Wiki.
This is the third year we've
done it and the second year in a
really systematic way.
So you get assigned to do,
to cover a couple frames of the
PowerPoint.
So those are the ones you
really need to take careful
notes on, and write them up,
and help other people too;
that's the nature of a Wiki,
as you know.
How many of you have
participated in a Wiki?
Well, by next week it will be
all of you.
Okay, but in order to get
credit for it you have to get it
by the night after the lecture.
So for the lecture today you
have to get it by late tomorrow
night, 36 hours after the
lecture.
This is so other students can
use it.
Okay, in the spring there'll
probably be a textbook.
I haven't really decided yet.
These things cost an arm and a
leg.
Maybe we can find one that's
used, an older edition.
It doesn't make any difference
except to the publishers.
Okay, also there's personal
help, like from me,
and there's -- and you can find
my phone number,
email and so on,
on the website.
Also the two graduate student
TAs who are assigned to the
course,
who are Filip Kolundzic --
Filip, back there --
and Nathan Schley,
not Schlay, Schley.
So these are graduate students
in chemistry and they run these
discussion sections.
Typically you have a 50-minute
discussion section.
But the way we run it in this
course is that on two different
nights a week there are two-hour
sessions.
You can come to any part of it
you want to.
You can go to both of them,
you can go to four hours a week
if you want to,
or you can go to none at all if
you want to.
So really, for the bookkeeping
purposes of the department you
have to sign up for a section.
Sign up for any section you
want to and then come to what's
useful for you.
But also, the reason you pay
the big bucks to come here,
is not to hear me,
it's to interact with the other
students.
That's a really big help.
So, form study groups.
And in fact you can get advice
from previous people who've
taken the course.
That's on the Web.
Also there's some of them,
there's a list of them on the
Web who would be happy to talk
to you if you need it.
And we're blessed with three
alumni,
seniors who took this course as
freshmen,
who act as what are called peer
tutors,
and they'll run a session
Sunday evening,
from eight to ten p.m.
is the current plan.
We'll announce the rooms for
these things on the website and
probably by email to you as
well.
So let me introduce Tina Ho and
Drew Klein and Justin Kim.
So they'll be a big help to you
too.
So there's plenty of personal
help, so use it.
These are the dates we're going
to have exams.
There are ten lectures and then
an exam;
nine lectures, exam;
nine lectures, exam.
Actually, if you check,
you'll find that --
and also you get 50 points for
participation in the Wiki,
and the total is 650 points,
that's what your exam is based
on.
Actually this doesn't cover --
it's nine lectures that are
covered on the exam,
but the previous Wednesday part
of the lecture is going to be a
guest lecturer that's going to
be here just that day.
So we're putting the exam off
and it'll only cover the
previous material;
not that that's a big deal.
Okay, and the semester grade is
biased;
that is, it's based on this,
your total score here,
out of 650 points.
But if you're near a cutoff and
you were very good about turning
in your problem sets and so on,
then we boost you up.
We don't grade problem sets but
it's worthwhile to do them,
and they might make a
difference.
So where are we going with this?
What are the goals of our
Freshman Organic Chemistry?
In fact, if you click that in
your PowerPoint you'll get taken
to that site,
but it's right on the website,
you'll see it anyhow.
First is to learn the crucial
facts and vocabulary of Organic
Chemistry --
after all that's what we think
we're here for --
and to develop a theoretical
intuition about how bonding
works.
This is the goal for,
the primary goal of the first
half of the fall semester is to
learn how bonding works really,
and that relates then to
molecular structure;
and also how bonding changes,
and that of course is
reactivity.
But under the line there are a
lot of other things that we do
in Freshman Organic Chemistry
that are arguably just as
important,
like make the scientific
transition from school to
university.
In school they try to teach you
what people know.
In the University you try to
develop new knowledge.
So you need a different mindset
for that, and we hope this
course helps you develop that.
So learn from Organic
Chemistry, which is really in my
view a model science,
how to be a creative scientist.
So here's a creative scientist
by anybody's measure,
Louis Pasteur.
And in the 1880s he said this
in French,
but in English it says,
"Knowing to be astonished
by something is the mind's first
step toward discovery."
Another way of putting that is
that the characteristic comment
on making a real discovery is
not "Eureka",
it's "Huh,
that's funny." So
that's what you really have to
learn;
learn enough about how
chemistry works and form this
picture in your mind that when
something happens that doesn't
fit,
you know to be astonished so
that you can discover something.
That's exactly what Pasteur
did, and we'll talk about that
in the course.
And even perhaps more
important, to develop good
taste, so that you can
distinguish sense from nonsense;
there's certainly more nonsense
floating around than sense,
and being able to tell the
difference is important.
The way you do it is to develop
good taste by looking at a lot
of good examples and then you're
aware of how crummy the bad
examples are.
So we're going to try to
emphasize good examples,
and have fun.
So and as we go along,
if you have questions,
break in.
You'll do this much more as we
go along, I know.
So the class really is mostly
about theory,
although we describe the basis
for the theory and spend a lot
of time trying to make it real.
But we require Chemistry 126L,
the lab.
This is the only chemistry
course that requires you to take
a lab simultaneously.
So I hope you're all enrolling
in that because there'll be a
certain day that you want to be
able to take it.
It's just one afternoon a week,
three hours or whatever it is,
but you want to get your first
choice, so line up soon.
You'll be accommodated but it's
just more convenient if you get
it arranged earlier.
But why?
Because lab answers the really
big question.
And the big question was
brought home to me by my son,
John McBride,
in his third year.
This was the beginning of the
third year, and his mother and I
didn't know what was coming.
For the next year,
maybe 15, maybe 20 times a day,
he said, "How do
you know?"
So here's John this last summer.
He's now 38 and he has his own
three-year-olds to say that to
him.
And he doesn't say,
"How do you
know?" anymore.
He now says,
"How do you
know?"
Okay?
But that is the main question,
how do you know what these
things that they told you in
school?
Well, there are four ways we
can talk about of knowing,
and two of them are shown on
this manuscript from the
Carolingian book painter.
If we zoom in on the top frame,
here's Moses on Mount Sinai.
So the first way of knowing is
divine authority.
Here he's going to be the --
here's the graduate student here
getting the word.
Here's the teaching assistant
over on the left perhaps.
>
Aaron, right?
And then he comes down from
Sinai, to see the class,
the Children of Israel.
So here's another kind of
authority, which is human
authority interpreting the
scriptures.
And here you can see the class;
the guys are going like
"huh."
And the teaching assistant is
off on the side still.
But this doesn't make it.
Science is not faith based.
There may be other things you
know that way but not science.
Science ignores divine
authority and it ignores human
authority;
not that they might not exist
but they don't relate to
science.
Now as you walked in today,
did you notice these things
over here?
There's an Honor Roll of
Chemists, and in fact we'll use
that a lot this semester,
and in particular one of the
people on there is Michael
Faraday,
who started in a very humble
way.
He was a book binder's
apprentice and he bound this
book --
not this particular copy but
this book --
which is called
Conversations on
Chemistry.
He bound the first edition.
This one is a later edition.
So you see it's
Conversations on Chemistry in
which Elements of that Science
are Familiarly Explained and
Illustrated by Experiments.
And who's the author?
J.L.***Comstock;
he's actually not the author,
he's the guy who stole it.
He stole it from a woman,
Mrs. Marcet,
in England, who wrote this
book,
which was the most popular
textbook --
it was written for girls -- but
it was the most popular textbook
in all chemistry,
for the first half of the
nineteenth century.
It went through like 20-some
editions.
And here you see at the
beginning it's a dialogue,
a conversation between Mrs. B
and Caroline and Emily,
and it's fun to see this here,
what Emily says at the
beginning.
"To confess the truth
Mrs. B,
I'm not disposed to form a very
favorable idea of chemistry,
nor do I expect to derive much
entertainment from it."
But in the long run,
as you can imagine,
they have a lot of fun with
chemistry.
It was a wonderful book,
and still is.
But he was binding it,
and read it.
And look what he says about
this, as his introduction to be
the leading experimental
scientist of the nineteenth
century:
"Do not suppose I was a
very deep thinker or was marked
as a precocious person.
I was a very lively,
imaginative person and could
believe in the Arabian Knights
as easily as the encyclopedia,
but facts were important to me
and saved me.
I could trust a fact and always
cross-examined an assertion.
So when I questioned
Mrs. Marcet's book by such
little experiments as I could
find means to perform,
and found it true to the facts,
as I could understand them,
I felt I had got hold of an
anchor in chemical knowledge and
clung fast to it."
So the experiments were what
did it.
So the third way of knowing is
by experimental observation.
And here's Richard Feynman.
How many of you've heard of
Richard Feynman?
He was a really great
physicist, wrote a wonderful
textbook as well as getting all
sorts of prizes.
He spoke to the National
Science Teachers Association in
1966 saying,
"Learn from science that
you must doubt the experts.
Science is the belief in the
ignorance of experts.
When someone says,
'Science teaches such and
such,' he's using the word
incorrectly.
Science doesn't teach it;
experience teaches it.
If they say to you,
'Science has shown such and
such,' you might ask,
'How does science show it?
How did the scientists find out?
How, what, where?'
Not science has shown,
but this experiment or this
effect has shown."
Now, why do we quote Feynman?
Because he's an expert.
>
Wrong.
Though literally,
expert,
the etymology of expert,
is it means someone who has
done experiments.
We quote him because what he
says makes sense.
So logic is the fourth way of
knowing things.
So the two ways that we know
things in chemistry,
or in science,
are experiment and logic.
And the lecture is a little bit
more focused on logic and the
lab is more focused on
experiment,
and you get an unbalanced view
if you do one without the other.
Okay, so modern science got
underway in the seventeenth
century.
There's the seventeenth
century, 1600 to 1700.
And 1638 was when New Haven
Colony was founded,
and 1701 was when Yale was
founded.
So that's when everything got
underway, just when this
enterprise was beginning here.
Here we are.
If you go back 100 years you
get to quantum,
quantization by Planck;
and we'll talk about that.
And if you go back another 100
years you get to Lavoisier and
oxidation;
and we'll talk about that.
And if you get another 100
years you get to Newton and
gravitation;
and we'll talk a little bit
about that.
And if you go back a little
more, another 100 years,
you get to Copernicus and the
revolution of the heavenly
bodies,
and Columbus and navigation,
and Luther and the Reformation.
And these things all have
something in common.
As Robert Hooke wrote,
"The seventeenth
century"
(his age) "was an age,
of all others,
the most inquisitive."
All these things have to do
with people inquiring into how
people know things and finding
out new things.
And in particular an important
figure was Francis Bacon and his
Instauration.
Now you may not know The
Instauration so well,
let's look at that.
Here's Francis Bacon,
there are his years.
He was Elizabethan and Jacobean.
He was almost exactly
contemporary with Shakespeare,
and with Galileo.
He went to school,
to university,
at Cambridge.
And here's a cartoon that shows
him -- it's a modern cartoon --
imagining him in a class at
Cambridge.
Because he wrote of his tutors
at Cambridge:
"They were men of sharp
wits, shut up in their cells of
a few authors,
chiefly Aristotle,
their dictator.
All the philosophy of
nature" (philosophy meant
science in those days) "all
the philosophy of nature,
which is now received,
is either the philosophy of the
Grecians or that of the
alchemists.
The one is gathered out of a
few vulgar"
(that means ‘common' of
course) "observations,
and the other out of a few
experiments of a furnace.
The one never faileth to
multiply words,
and the other ever faileth to
multiply gold."
So here's the book he wrote,
The Instauration.
That's the frontispiece for it.
This picture's from the
Beinecke Library;
I went down and got a picture
of the book.
Notice it was published in 1620.
What else happened then?
That's when the Pilgrims came
over, right?
So the title of the book,
rather small under his name and
title as Lord Chancellor of
England,
is Instauratio Magna,
which means the Great
Restoration.
Restoration of what?
Of the way of knowing.
A bigger, a part of it,
it's called the Novum
Organum,
which is -- and it develops the
inductive scientific method,
based on experiment,
to replace Aristotelian
deduction,
which is you maybe did one
experiment sometime,
and then you reason everything
from that.
But he says no,
you have to do more
experiments.
Now there's an interesting
thing here.
One of the devices on the
title, on this frontispiece,
is two pillars.
What in the world are they
doing there?
Well they're the same pillars
that you see on this.
That's a piece of eight;
you know, Treasure
Island, pieces of eight?
See it's eight reales,
and it came from the silver of
Mexico;
it was minted in Mexico City.
So and there you see the same
pillars and on them it says
plus ultra;
more beyond.
Beyond what?
What are the pillars?
Pardon me?
Student: Spain and
Africa.
Prof: Yes,
it's Africa and Spain,
but it's the Pillars of
Hercules,
which are the mouth of the
Mediterranean,
the old Classical World.
So there's the Mountain of
Moses in Morocco and the
Mountain of Tarik,
which is the name of Gibraltar.
So here's the Mediterranean,
the Classical World of
Aristotle, and you can sail out
into the New World and bring
back silver, for example.
There's danger of course.
But look at what it says at the
bottom.
What will be brought back?
Not just silver.
Multi pertransibunt &
augebitur scientia
--"Many will pass through
and knowledge will be
increased."
So we go beyond Aristotle into
experimentally based science and
knowledge will be increased.
So here's some quotes from
The Instauratio
Magna.
"That wisdom which we have
derived principally from the
Greeks" (no offense,
okay?)
"is but like the boyhood
of knowledge,
and has the characteristic
property of boys:
it can talk but it cannot
generate;"
"…it is but a
device for exempting ignorance
from ignominy."
That means it's a way of hiding
your ignorance,
and we'll see examples of that.
We'll talk about,
in Lecture 11,
about correlation energy,
and we'll talk in Lecture 32
about strain energy,
and you'll see that both of
these are just words that are
used to hide our ignorance.
"…the end which
this science of mine proposes is
the invention,
not of arguments,
but of arts"
(ways of doing things).
"…not so much by
instruments"
(although new instruments are
important,
like microscopes and so on)
"as by experiments,
skillfully and artificially
devised for the express purpose
of determining the point in
question."
(So artificial experiments
designed to decide a question;
experiments.)
"And this will lead to the
restoration of learning and
knowledge."
So followers of Bacon
established The Royal Society in
1662, just after Charles was
restored to England,
after the period of Cromwell.
And there was a history written
of The Royal Society,
a book about this thick,
published in 1667,
only five years after it was
founded.
Why did they publish a history
so soon?
Well let's look at this,
the frontis itpiece of this
book.
Here's the late Francis Bacon,
who was said to be Artium
Instaurator,
the Restorer of the Arts.
And here's the President of The
Royal Society,
the mathematician,
Viscount Brouncker,
and here in the middle,
being crowned with laurel,
is Charles II.
Why do they have him up on a
pedestal?
Because they're hoping,
as scientists have before and
ever since, to extract some
money out of the government to
do their research.
They actually never got it from
Charles but it wasn't for lack
of trying.
And this is why they wrote the
history, to try to make the case
for being supported.
Okay, now let's look at all the
good things that will come from
science, from The Royal Society.
In the background can you see
what that is?
We'll blow it up.
Here there's a hint to it on
the bookshelf.
If you look really fine on the
bookshelf you can see that some
of them have writing on the
spine.
Do you see what that one is?
Can anybody read it?
What?
What science book do you think
they might have had?
Student: Copernicus.
Prof: Copernicus, right?
So astronomy;
that's a telescope in the back.
Okay, or over here on the wall,
what's that thing?
It's a clock.
Why is it shaped like a piece
of pie?
Student: Because it has
a pendulum inside.
Prof: Ah,
because it has a pendulum
inside.
So horology, making good clocks.
Okay, or here,
what's that thing?
It's hard for you to know.
Student: Solar.
Prof: It's a wind gauge.
It has a vane inside that it
blows on -- and you can tell
from how far it goes on the
scale how strong the wind is.
So meteorology.
And back here on the pillar,
what are those things for?
Students: A compass.
Prof: For cartography.
Now what do all these things
have in common that they're
going to do for Charles II?
Astronomy --
Student: For the
records.
Prof: Good clocks,
meteorology,
cartography,
what --
<<Students speak over one
another>>
Prof: They all have to
do with navigation,
with making England strong at
sea.
Now back here is another
science, Chemistry.
That doesn't seem to have
anything to do with navigation.
Why would Chemistry be
important to Charles?
Student: War.
Prof: Look at it.
Student: War.
Prof: To make gun powder.
There was a chapter about gun
powder in The History of the
Royal Society.
Okay, and up here at the top is
the motto,
which is Nullius in
Verba, which comes from this
quote from Horace,
and what it says is,
"Lest you ask who leads
me,
in what household I lodge"
(that is,
what philosophy I advocate)
"there is no master in
whose words I am bound to take
an oath.
Wherever the storm forces me,
there I put in as a
guest."
So it's the experiment,
not the philosopher,
that leads you to the
conclusion.
So Nullius in Verba is
'in the words of none.'
And, in fact,
the original name of The Royal
Society was The Royal Society
for the Improving of Natural
Knowledge by Experiments.
Okay, so we're going to see,
as the course goes along,
important experiments that
really decided questions,
and in fact Bacon's most
important kind of experiment was
one that "finally decides
between two rival hypotheses,
proving the one and disproving
the other."
So you can do all sorts of
experiments and just be
collecting butterflies --
no, I don't mean to insult
people who collect butterflies,
it's a fine thing to do.
But there's something special
about experiments that really
are designed to answer a
question.
Now Bacon devised a name for
such experiments,
and they're based on this
model, that you have a road that
diverges and you need to know
which way to go between these
two hypotheses.
What do you need,
to know which way to go?
You need a sign,
or this was a cross that you
mounted at a crossroads.
So the Latin name for cross is
crux.
Do you see what they call the
experiment?
Crucial.
That's the origin of the word
crucial, right?
It's the one that tells you
which way to go.
Okay, so here is Isaac Newton
and he's holding something.
Can you see what he's holding
in his hand?
Student: A candle.
Prof: I'll give you a
hint.
It's a prism.
Why is he holding a prism?
Because that was his crucial
experiment;
and here's his diagram in that
experiment with a prism in it.
He called it the
Experimentum Crucis,
taking the word from Bacon.
Okay, so light came in through
a hole in the window,
through a lens,
and then got bent and dispersed
into the different colors.
So you get a spectrum here on
this thing, the different
colors.
Now there's the question,
how does the prism make color?
Hooke and Descartes thought
that light was a train of pulses
and as it goes through something
like a prism,
or as it reflects from a thin
layer of oil on water or
something like that,
that it changes the timing of
the pulses and therefore changes
the color.
But Newton thought that the
colors were pre-existing,
and the prism just separates
them.
And this was his crucial
experiment to decide between
those two theories.
You see what he did?
He drilled a hole through the
board and let through only the
red light, and put a second
prism there.
And he wrote here,
three times -- he wrote it
here, and also here,
and also here -- nec variat
lux fracta colorem;
which means "the broken
light does not change its
color."
So this proved to Newton,
at least at that time,
that light is a substance,
not a train of pulses.
What do you think of that proof
now?
You think light is a substance
or a train of pulses?
Students: Both.
Student: Neither.
Prof: But at least you
can see that in terms then,
that was a crucial experiment,
a really important experiment,
and that's the kind of
experiments we'll try to talk
about in the course.
Experiments are indispensable
in Organic Chemistry.
It's an empirical science based
on observation,
and that's why you have to take
the lab.
But so is logic -- that was
number three and number four of
the ways of knowing -- logic is
important too.
So believe what I tell you here
only when it makes sense to you.
Don't just cram it in,
make sure it makes sense.
But what if it doesn't?
Now here's how to succeed in
Chem.
125, and we'll take as our
model science student Samuel
Pepys.
How many people have heard of
Samuel Pepys?
Have you heard of him as a
scientist?
Student: I don't
remember.
Prof: What did you hear
of him as?
What do you associate with
Samuel Pepys?
Student: Newton-Pepys
Problems.
Prof: Right in this
period, in the heart of the
science growth.
But what you know him for was
his diary, which tells all about
life, everyday life in
Restoration London.
He was actually,
as a sixteen-year-old,
present when Charles I was
beheaded in 1649.
Now what's the connection?
Do you know where this is?
Anybody been there?
Dixwell, Goffe and Whalley
Avenues,
those are named for three of
the 50 judges that condemned
Charles I to be beheaded,
and they were the only ones
that lasted very long,
after the Restoration,
and they lasted because they
fled to New England and were
hidden on West Rock.
All these roads are heading
west toward West Rock.
Okay, so that's a tie-in to the
same period.
But anyway, he got his B.A.
in Cambridge in 1654 and a
Master's in 1656.
And he got a good job,
he became Clerk of the Acts for
the Navy Board,
which meant he was the guy that
purchased everything for the
Royal Navy,
all the rope,
all the tar,
all the lumber and so on.
And on July Fourth,
1662 -- it's the fourth of July
but it's more than 100 years
before that became relevant --
he writes in his diary,
"By and by comes
Mr. Cooper,
mate of the Royall
Charles,
of whom I intend to learn
mathematiques,
and do begin with him to-day,
he being a very able
man… After an hour's
being with him at arithmetique
(my first attempt being to learn
the multiplication-table);
we then parted till
tomorrow."
So here was the guy doing all
the purchasing for the Royal
Navy and he didn't know
multiplication,
let alone division.
But he worked hard at it.
July ninth, five days later:
He's "Up by four o'clock,
and at my multiplicacion-table
hard,
which is all the trouble I meet
withal in arithmetique."
He can do the other things
pretty well.
July eleven:
"Up by four o'clock and
hard at my multiplicacion-table,
which I am now almost master
of."
Christmas -- so six months
later: "…so to my
office,
practicing arithmetique alone
and making an end of last
night's book with great content
till eleven at night and so home
to supper and to bed."
Or a year later -- so he was
motivated and he was diligent;
that's good.
A year later,
on a Sunday:
"…I below by myself
looking over my arithmetique
books and timber rule.
So my wife arose anon and she
and I all the afternoon at
arithmetique,"
* "and
she has come to do Addition,
Subtraction and Multiplicacion
very well,
and so I purpose not to trouble
her yet with
Division…"
Right?
>
So he worked with a study
partner, and that's crucial.
And Isaac Newton -- does
anybody recognize this book?
Student: Yes, sure.
Prof: Right?
The Mathematical Principles
of Science, of Natural
Philosophy.
But there's an interesting
thing on the title page.
Samuel Pepys is the one who
gave permission to publish that
book, because he was the
president of The Royal Society.
Now six years later Pepys
encountered a problem with dice.
The reason was he went to
coffee shops every night for
dinner and they'd gamble,
and people proposed various
kinds of bets,
and he couldn't figure out this
one,
so he wrote Newton for help.
So this was the problem that he
wrote to Newton,
twenty-second of November.
So A has six dice in a box,
and he has to throw a Six by
throwing it;
B has 12 dice and he has to
fling two Sixes;
and C has 18 Dice but he has to
get 3 Sixes to win.
The question,
"Whether B and C have not
as easy a Taske at A,
at even luck?"
That is, if the dice aren't
loaded or anything,
who has the better bet?
>
How many people think that it's
the same?
Don't be shy.
How many think it's A?
How many think B?
How many think C?
How many don't really have any
opinion at all?
Good, that wins.
Okay, so he wrote this letter
to try to get help on his bets
from Newton,
and Newton replied,
four days later,
"What is the expectation
or hope of A to throw every time
one six,
at least,
with six dyes?"
So you get two sixes you still
win;
that wasn't clear in the
original statement.
So he says, "If we
formulate the question that way,
it appears by an easy
computation that the expectation
of A is greater than B or C;
that is, the task of A is the
easiest."
There's the answer.
So Pepys replied on the sixth
of December: "You give it
in favour of the Expectations of
A,
& this (as you say) by an
easy Computation.
But yet I must not pretend to
soe much Conversation with
Numbers,
as presently to comprehend as I
ought to doe,
all the force of that wch you
are pleas'd to assigne for the
Reason of it,
relating to their having or not
having the Benefit of all their
Chances."
So he wasn't ashamed to admit
that he didn't really understand
-- that's crucial.
"And therefore,
were it not for the trouble it
must have cost you,
I could have wished for a sight
of the very Computation."
Can you show me how to figure
it out?
And he wanted that because
somebody might change the terms
of the bet and then he wouldn't
know.
He wanted really to understand.
He insisted on proof.
So this is two of the pages
from Newton's correspondence of
the letter that he wrote in
response,
and you can see that Pepys
certainly got more than he had
bargained for.
"So to compute this I set
down the following progressions
of numbers."
So you can go through all this
and you get complicated
quotients here,
and it turns out that A has
31,031 chances out of 46,656,
or 0.6651 chance of winning,
and B has this,
which is 0.6187;
A wins.
So is Pepys satisfied with this?
Pepys writes back and he says,
"Why?"
Right?
"I cannot bear the Thought
of being made Master of a Jewell
I know not how to wear."
So he's willing to swallow his
pride to search for really solid
understanding.
Now compare this with a comment
we got at an end-of-semester
evaluation in January a year
ago.
"I never went to his
office hours for help because I
felt like he would make me feel
stupid,
because he's superior to me in
chemistry."
I hope I'm superior to you in
chemistry.
>
I'm not superior as a person,
but I hope I'm superior in
chemistry.
You're paying me the big bucks
because of that.
So swallow your pride and ask
someone for help.
Follow Pepys.
So read "Pepys and
Newton" and get together to
do problems for Monday,
and contribute to the Wiki when
you're asked to do so.
So here are problems.
For Friday the problems are
optional but very helpful.
One is find out which two class
members have the rooms nearest
you so that you can maybe use
them as study partners.
You don't have to use them,
use anybody,
but use someone,
don't try to go it alone.
Two.
What are the three most common
items of advice from course
veterans?
So if you click there,
or go to the webpage,
you can get anonymous advice;
I was careful to make sure it's
anonymous.
So you can get all -- much of
it is contradictory,
so your job is to look through
it and try to get some idea of
what they're telling you that's
worth knowing.
For Monday there are problems
from that webpage,
"Pepys &
Newton."
And let me tell you that you
better get together with other
people to do it,
because there's a lot of stuff
there.
So get together in a group,
parcel out who works on what,
discuss what went on and so on.
And then for a week from Friday
there's stuff about drawing
Lewis Structures,
from another webpage about
functional groups.
So we'll get to that later,
I just wanted you to know
what's coming up.
Incidentally,
this thing about the problems
set that has to do with the
mathematics that Newton and
Pepys were working on there,
has to do with isotope ratios.
You know, chlorine has a funny
atomic weight.
Why?
What is the atomic weight,
does anybody know?
Student: 35.5.
Prof: Thirty-five and a
half.
Why a half?
Most of the elements are pretty
near integers.
It's because it's a mixture of
isotopes.
It's a quarter of one isotope
and three-quarters of the other,
and the average is thirty-five
and a half;
thirty-five and thirty-seven.
But in fact it depends on where
you get chlorine from,
what the ratio is.
There's thirty-five and a half
for a standard atomic weight,
but it ranges quite a bit,
depending on where you get it.
So by measuring these ratios,
which is a lot like these odds
in the betting,
you can tell where things came
from.
You can tell where hydrocarbons
came from sometimes that way.
And those are the problems that
you have to deal with.
So it's not really very,
very relevant to the course as
a whole, but it's relevant to
the Pepys and Newton thing and
it's a fun problem.
So that's what you've got to do
for Monday.
Okay, and here are the
assignments.
I emailed all these people.
I hope you're here,
and that you picked up on what
we talked about today so that
you can improve the Wikis from
last year.
Last year people developed
their Wikis from scratch.
This time -- which is a very
valuable thing to do.
So I was torn this year as to
whether to have you do them from
scratch or whether to modify
last year.
I figured modifying last year
is better because then you have
something to read earlier on,
for those who are not working
on developing it.
So anyhow, but the hope is --
so if you modify it --
it has to be something
significant,
not put a comma in or something
like that,
but add something useful to
understanding.
If you do it within thirty-six
hours, you get two points,
and if what you do is really
good, you get three points.
So you go to that page and you
click on those things and then
you can read what -- or you can
either modify them or read it;
it's a Wiki.
Now, we come to the question
that we'll address more.
We have another five minutes
here.
The question we're really
dealing with now,
having seen how to work in
Chem.
125, is are there atoms and
molecules;
how do you know?
And what force holds them
together?
Because if we knew that they're
real, and we knew what force
held them together,
then in principle we might be
able to calculate everything.
So it would all be theory.
So is it springs that hold
atoms together?
So Robert Boyle -- notice he's
right at that time,
1627 to 1691,
and he's the oldest person
that's on the Honor Roll outside
the building here,
he's over that way -- so Robert
Boyle wrote this first important
book in chemistry,
New Experiments
Physico-Mechanical:
Touching the Spring of
Air.
So you know Boyle's Law,
how pressure and volume change,
that air in a piston acts like
a spring.
So PV is a constant;
that's Boyle's Law.
So he developed this science on
the basis of a new instrument,
the pneumatical engine,
which was built by Robert
Hooke, the guy we quoted.
And there's a picture of the
air pump here with that crank on
it, and so on to pump things in
or out of that bulb.
Now a couple of years later
Hooke wrote this book,
Lectures,
De Potentia Restitutiva,
or of Spring,
explaining the power of
springing bodies.
And this is the beginning of
that book.
"The Theory of Springs,
though attempted by divers
eminent Mathematicians of this
Age has hitherto not been
Published by any.
It is now about eighteen years
since I first found it out,
but designing to apply it to
some particular use,
I omitted the publishing
thereof."
So he kept it secret so no one
would steal the idea.
What did he hope to do with a
spring, a really important
technology that he could do with
a spring?
There was a coil in the spring
that he depended on.
Student: Flying.
Student: Pendulum
clock.
Prof: A new kind of
clock, one that could work
better for navigation.
It was his spring that actually
allowed Harrison,
100 years later,
to win the contest about making
an accurate clock;
some of you must know that
story.
So anyhow he had been hiding
this so it wouldn't be stolen.
In fact, it was stolen by
Huygens.
So "about three years
since His Majesty was pleased to
see the experiment that made out
this theory,
tried at White Hall,
and also my spring watch.
About two years since I printed
the theory in an anagram at the
end of my book on the
description of helioscopes,
viz." this.
So this is what he published at
the end of this book on
helioscopes,
and that is an anagram of how
springs work,
so that later he could prove
that he knew it,
if needs be,
but no one could steal it in
the meantime.
And if you unscramble it,
it's "Ut tensio sic
vis;
that is, the power of any
spring is in the same proportion
with the tension thereof.
That is, if one power stretch
or bend at one space,
two will stress at two,
three will bend at three,
and so forward."
So here's his figure that shows
that.
That's Hooke's Law,
the force law.
The force is proportional to
the distortion.
So here's his figure,
and he's got plots of it here.
Ut tensio (as the
extension) sic vis (so
the force).
So it's linear,
the force is how much you
stretch it.
And he has lots of different
kinds of springs that do that.
Here's this clock kind of
spring, a coil spring,
just stretching a wire.
So the force is proportional to
the extension.
Or another way of saying it is,
"The potential energy is
proportional to the square of
the extension."
So it's a parabola.
So that's Hooke's Law,
and that's where we'll take up
next time.
