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 …
*Content
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. Much like Babylonian tablets,
etching in stone endures.
Duplation is simpler, not more complicated. Be careful to
not say that simply because it is unfamiliar. Duplation only
involves doubling, or adding to itself.
We'll see false position again today. Here's a short
recap. We started with the number 7, wanted to get 19, but
got 8 instead. So, to fix our answer we take 7 and multiply
by 19 (what we want) and divide by 8 (what we got). It is
_NOT_ guess and check. It is intentionally choosing an easy
number to work with, getting an intentional wrong answer, and then
fixing it. It is _NOT_ recursive. It is specifically a
two step process.
I'm pretty sure that the Egyptian circle area formula was devised
because it produced good results, not from a theoretical basis,
although it is _possible_ they divided a circle into smaller
pieces.
The Moscow papyrus was also 18 feet long and had diverse
problems, not only geometry. Not quite as many as Ah-mose,
but still plenty. Papyri were scrolls.
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
There are many examples throughout history of children ascending
to sovereign. There are even plenty of examples where they
ascended upon their birth. 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.
"I'm grateful to be in a time of base 10 and not base 60" I
find the use of the word "time" here most interesting.
There's two questions … why is base 60 useful, and that is simple,
but there's a more interesting why did they start using it.
We'll talk about it today. Egyptians used nothing with base
60.
It seems natural to me that _gardens_ from 4000 years ago would
not survive. It is also natural that geometry was more
important in Egypt than in Babylon. 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.
What Jeff says for the Babylonian circle 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.
The closing quote about Thales and eclipse is a teaser for
Chapter 2.