Babylonian Algebra

After seeing how the Babylonians solved algebra I have become very thankful for modern methods. The Babylonian method was very convoluted and quite frankly hard to follow. When thinking about the question that was posed to us on the class blog "How could one state a general mathematical principle in a time before the development of algebra and algebraic notation?" and I was quite perplexed. I had a very hard time coming up with a solution. The Babylonian method reminds me a lot of the way I used to do math when I was younger, I was never a very attentive student but I somehow got by in math. The teacher would teach the class the "correct" way of doing things, but since I never paid attention I would just come up with my own method. Depending on the year and teacher, they would either care or not care about me using my own method. For example, in grade three we learned long division, but I just decided on my own method. The teacher was fine with it because I got the correct answer, but as time has gone on division questions I was given got harder and harder until my method didn't work anymore. I never learned the proper way to do these questions. I see the Babylonian methods like this, there was no way to answer these questions, so they made one up. Their method does work, but the modern method is the easier option and I view it as the correct one.

"Is mathematics all about generalization and abstraction?". Yes, I believe that it is. Generalization is important for a ground-level understanding of math, knowing these general rules is important. Examples of which are "BEDMAS", which stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. This is the rule for the order at which to follow for algebra. In real life however, not every situation is cookie cutter. The abstractions and intricacies of math are important for this. 

While thinking about different areas of mathematics it is difficult to think of ones that can be explained without algebra  (especially as a finance major, we use a lot of algebra!). Even geometry, at its most basic core of calculating the area and edges of a rectangle uses algebra to fill in the missing gaps. 

My conclusion is that the Babylonians did an extremely impressive job explaining mathematical concepts, given their limited resources. Also, I never thought I would be so thankful for algebra!

Babylon-Style Table

 

Column 1	Column 2
2.5	18
3	15
3.36	12.60
4	11.15
5	9

Base 60

 I must say, it has never occurred to me to use base 60 as opposed to base 10 or 100. When giving it some thought however, it does make a lot of sense. The most obvious use of base 60 is time, 60 seconds in a minute, 60 minutes in an hour, but then 24 hours in a day? Seems interesting to me. It appears that this time system was invented by the Babylons, who derived this system from the Sumerians, who used it as early as 3500 BC (according to the Guardian). When reading about this, I wondered to myself, why not 100 seconds in a minute or ten hours in the AM and PM? It turns out that using twelve hours for morning and twelve for the afternoon or night is much more useful. Twelve is divisible by two, three, four, (not five), six, and itself. Ten on the other hand only has three divisors. Sixty also has twelve divisors. Sixty and twelve both have more divisors than any number below them (many of these facts are also courtesy of the guardian). It turns out my first thought that base 10/100 was superior to base 12/60 isn't correct. In fact, I'm glad that civilizations after the Babylons adopted this system, it seems to work pretty well. 

The Crest of the Peacock

I've never really thought about how history was written, I have just always taken all history I have ever learned to be fact. This is why the first point that stuck out to me was that history is written by winners, which makes total sense when you think about it. This can relate to Math, war, science, or anything of the such. When one civilization conquers another it can easily force its history and way of living upon the other. 

I was also very interested to read about how theories such as the Pythagorean theory took years upon years to come up with. It is a very selfless act if you think about it, dedicating your life to something that will be used by many generations after you. I'm sure it is also a very rewarding task, knowing that although you may die that your theorem will live on. 

Lastly, I thought that the portion that focussed on the Mayans was very interesting. It is fascinating how the Mayans and Babylons from ancient Mesopotamia utilized a similar math system and figures. They were also the "inventors" of the number zero. I put inventors in quotations because of course zero was always there, but the Mayans were the first to quantify it and use it in math. This is yet another part of this reading I never thought about before, how had no one "invented" zero before then? Quite interesting.   

Hello World

 Hi my name is Brock, and I love the history of math!