Although today was the last day that you could receive _credit_
for asking about the course, it is always good for you to ask me
any questions about the class. You may do this in many
different ways. You may add it to your reactions (but not
one of the ten). You may send email, visit office hours, or
send a feedback message.
One of the reasons why I do reactions for this class is to hear
from _everyone_ not only the people who speak loudest. Often
i hear the most insightful thoughts from the typically “quiet”
students. I appreciate that. I also see who is being
thoughtful. You, yes you, be thoughtful.
I would be overjoyed if anyone ever came to me from this class
and said "we talked about this in class, and I just want to
understand it more." My joy would largely come from the pure
interest in learning. Maybe some day …
Lecture Reactions
*Course
Hold on to your hats, there’s going to be vast amount of
information here in this course. Take what you like.
There is much to choose from. What I said in class applies
to both reading and lecture - take what you like, what may be
useful to you in any way. Beside that, for the course, a
timeline of who, what, where, when along with some classifications
by themes would be great.
For the exams you will _not_ have references with you. You
will thoughtfully and carefully plan your answers in advance, but
you will not have those references with you. What do you
need to take away for the things that you will need to know?
For your topics you will need to know who, what, where, and when
(usually quite vaguely, at this point maybe to the nearest 500
years will do). I will present lots and lots of mathematical
explanations and justifications. I will _never_ ask you to
repeat them. You will need to present your own mathematical
explanations and justifications in your research paper, but not of
the material that I do. You are responsible for the topics
you choose, not for everything. For now, relax, learn, enjoy
the freedom of learning, do your reactions, and keep a good
timeline.
*Content
Accolades: I feel I didn't do a very good job at lecture - I
_will_ do better, probably today because the standard is
low. Bah, ignore that, but … despite that, as a class you
inspired a nice collection of quick answers here. Good job!
Math is different from science because of proof.
The Rosetta Stone was writing about an event that they believed
was so important that it deserved to be written in all three
scripts ("a decree that says priest of a temple in Memphis support
the reign of 13-year old Ptolemy V, on the first anniversary of
his coronation"). There is no mathematics (aside from
numbers) in the Rosetta Stone.
We have a difficult time knowing motivation for such ancient
work. Surely some of it was practical and some of it was
exploratory speculation.
Ownership and claims of creation definitely were not considered
for a very long time. Would different cultures compete for
claims to discovery? At this point, different cultures don't
really interact much, but probably not. They'd be happy to
take from each other when they did.
I love when you teach me things ""I looked up the others
mentioned, and the Moscow Papyrus was also around 18 feet, and the
Reisner was about 11 feet." I thought the Ah-mose papyrus
was unusually long. Apparently I was wrong.
Cool. Being wrong is fun.
A trapezoidal prism is a particular kind of frustum, the kind
that the Egyptians worked with. A truncated cone is also
called a frustum.
It will be about 3000 years after the Egyptian circle before people start explicitly thinking about the constant that we now call π. The circle area formula is what the Egyptians discovered to work best. And, it's quite impressive.
16 1/2 1/8 = 16 + 1/2 + 1/8 and it wasn't simplified because of
the fixation on unit fractions.
False position is intentionally a two step process, it is not
successive approximation. It is intentionally using an easy
number and then fixing the result once. We will see it again
today.
We'll talk about the time when people start operating with
zero. It's a while to come … (millennia).
The sharing bread problem is perhaps the oldest example of an
artificial word problem. We see in the most ancient of
cultures mathematics done because if it interesting not
necessarily because it is useful. If you’re going to ask for
everything we study “why is this useful?” this will be a long
semester. The flip side is that Jeff talks about
a lot of history. Asking for each of them “what does this
have to do with mathematics?” will also get tedious. Learn
for the sake of learning, please. Put down your barriers of
resistance. Jeff and I appreciate context. We like
stories, we like knowing other things that are going on that is
interesting. We have broad and wide ranging interests.
We would hope that you do also, this is the joy of liberal arts
education. So, keep your mind and eyes open and you might
learn something surprising.
Oh, this is important in two directions. Cultural contact
happens when they interact. Mostly this is rare at this
point in history. When it happens it is noteworthy, but
generally it isn’t happening. It takes long time and
geographic proximity. Greco-Romans get some from Egypt and
Babylon in the time that passes between, Indian and Chinese are
both pretty isolated. The first with significant
incorporation of many cultures are the Islamic Empire, and that
will be a big deal when we get there.
Reading Reactions
Child monarchs do not end in antiquity, here's
a 3 year old who became king in 1995, and for that matter
Queen Elizabeth was only 25 when she ascended to the throne.
Nice that someone guessed this - yes, 60 minutes and seconds come from Bablyonian. I'll say more about this in lecture (so that you can react to it there - this is me being generous).
The ; and , used in the book (and our translations) are modern
and were not evident on the ancient tablets.
1/18 = 0; 3, 20 because 0 + 3/60 + 20/3600 = 1/18 (check it). I’ll try to keep this up when I talk about Babylonian numbers. Yes, this is the first human instance of place value, and that’s a big step.
Numbers - then and no - are more universal than language.
They are used cross cultures. They clearly were not as
universal then as now.
Hooray, solar eclipse! Think about this (and other
historical examples you can find) on 8 April.
Old reaction about the Bablyonian circle: What Jeff says is
C^2/12. How do we feel about this? = (2πr)^2/12, if
this were the same as πr^2, then π = 3, which is honestly what I
would expect from the ancients. The Egyptians were
impressive.
It’s a valuable and interesting question to ask what cultural
differences led to the differences in mathematics for Egyptians
and Babylonian. Egyptians pushed many demands for geometry
in their constructions. Babylonians had a heavily quantified
commerce and penal code. This led to more numeric and hence
algebraic work.