How to start this week’s reflection? That is the question I have been asking myself for the past twenty-two minutes, blankly staring at my computer screen. This week was not particularly exciting. We learned about Boolean Algebra, which is basically another way of expressing logic notation and set notation, except with different symbols. I didn’t really enjoy this week’s proofs because I kept confusing the and + in Boolean Algebra with “multiply” and “add” in regular algebra.
The “1″ in Boolean algebra represents the Universal set or the tautology. When multiplying (and/intersect/dot) by 1 in Boolean algebra, the same thing happens as in regular algebra: the quantity (or sets) remains the same because of the identity property. However, adding (or/union/plus) is different. In Boolean algebra, since 1+1=1, adding 1 to any side of an equation (or is it sequence?) does not alter or affect the other side at all, while in normal algebra, adding 1 to the other side is required to maintain the equality.
I believe that set equivalences are the easiest to use because they do not involve anything similar to normal algebra, so I am saved the confusion that Boolean algebra gives me. Also, since the and are clearly distinguishable from the upper case variables unlike the and in logical notation, set notation is also easier to read.
Logical notation, set notation, and Boolean algebra are actually the same thing, but I prefer set notation because of its visual simplicity. However, Boolean algebra is more convenient when creating logic gates and logic circuits.
I didn’t really understand how Boolean Algebra could be used in real life, though. Since it is just a representation of logic, I don’t see how it could actually be used in computer things, but that’s probably because I’ve never been interested in computers. What disappointed me a lot was that, while the logic, binary, and venn diagrams we learned at the beginning of the year could be used sometimes in real life to help win arguments or look smart, Boolean Algebra seemed flatter and narrower, with less applications.
Logic circuits are a more physical way to write/draw/describe Boolean Algebra. They use lines to connect these sail-shaped things. When I first saw the logic circuits on Thursday, I thought, “Yay visual stuff!” Five minutes later, I was thinking, “Oh my cloud when does this line drawing end?” This supports one of my essay theses that I wrote last year, “Every advance in technology and knowledge has neither good nor bad impact; everything has their beneficial and harmful sides.” Though logic circuits are much easier to comprehend than straight Boolean Algebra notation, they are annoying to draw. Metaphorical connection to personal life: Check!
Since Boolean algebra does not apply to clouds or singing, I will close with something else. George Boole once wrote “No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.” When I did the proof for DeMorgan’s Law, I accidentally put + instead of in one place, and I had to redo the whole thing. It looked amazingly beautiful for a few seconds after I finished. Then I sighed and moved on to the next problem.
Photo credit: “The Ideal Address,” tugwilson via Flickr, (CC) BY-NC-SA 2.0.
On a totally math-unrelated note, tragedies are everywhere in my life. Xiaolu, yes, I like to read tragedies and I love to write tragedies in which someone dies because it creates intense emotion. I love putting intense emotion in my stories. I would like to read tragedies in class instead of The Odyssey, which ends happily.
And Irene, my prophecy has come true, just like Halithersês Mastoridês’ prophecy of Zeus’ eagles came true as the suitors of Penelope came to ruin. I am first post this week.
Cecilia, who would like to refrain from talking about her failing and intensely embarrassing Allstate audition on Saturday which she most likely did not pass and now views her life as a tragedy because of it (Yes, I am aware that was run-on.)