It's Saturday! (cue theme music)
La la la la, la la la la, Virgil's world! La la la la, la la la la, Virgil's world! Virgil loves Panera, but not math too! That's Virgil's worlddddd!!!!!!
(end theme music)
Today, I was supposed to meet Momo and xiy for a little studying-for-math-finals party at our local Panera. The party (okay, it wasn't a party) was supposed to start at 2. I didn't see them until after 3. This is what happened:
2:00 - arrive at Panera. Look around and realize that I'm the first one there. This does not please me. I order a cafe mocha and sit in a booth, then I finish the weekend math homework that I started in class on Friday.
2:05 - the mocha is very tasty.
2:10 - Momo calls and says she'll be there in about seven minutes.
2:15 - well, I suppose I'll do my Latin homework, too...
2:25 - maybe I should do this science homework as well....
2:30 - sike. I don't understand this science homework.
2:45 - where is everybody?
2:50 - maybe we were actually meeting at three....
2:55 - *calls xiy's house* May I please talk to xiy? Oh, she's at Panera? I'm here, too, but....
3:05 - Momo and xiy were on the other side of Panera the whole time, and they just didn't see me because I was in a booth and I'm so short that I was hidden.
*headdesk*
After that, it was quite enjoyable. We studied for math (meaning: complained about our math teacher and probably solved a total of two and a half proofs) and then watched the police show up outside and talk to this guy in a hood, who we're pretty sure was a spy.
While we were complaining about the horrors of geometry, xiy brought up a very valid point, which I would like to share:
A point is really nonexistent, because it's zero-dimensional and doesn't actually take up space, technically.
A line, however, is made up of an infinite amount of points... but how is it that a line can be one-dimensional?
According to what we've been taught, anything times zero ought to equal zero. However, this point-line case study proves the zero times infinity is, in fact, infinity.
Therefore, by the zero property of multiplication....
GEOMETRY IS A LIE...
...CREATED BY THE ADMINISTRATION FOR THE SOLE PURPOSE OF TORTURING US.
I rest my case.
GET WELL SOON, HOUSE!!
Epsilon greater-than,
Virgil
Another reason geometry is a lie:
ReplyDeleteOkay, so a line segment is part of a line, right? And a line segment has distinct endpoints and length, right?
And a line has infinite length, right?
Right. So I remember learning somewhere that whatever you do to infinity, it remains infinity. Adding/subtracting/multiplying/dividing infinity still gets you infinity.
So. A line segment--a part of a line--would therefore have the length of 'part of infinity.' And part of infinity IS STILL INFINITY.
THEREFORE, a line segment would technically have the SAME LENGTH as a line. How is that still 'part of' a line? How does that 'end'?
Ugh. >.<
[House's dad, if you see this comment, please tell me if I reasoned this incorrectly.]
lol you /are/ really short.
ReplyDeleteYou do know that some infinities are bigger than other infinities don't you?
ReplyDeleteYou need to be very careful with infinities. Infinity (the little infinity) + 1 is still infinity as you say. There are infinitely many positive integers and infinitely many negative integers --- put them together to get all integers and you get the same number of total integers as there are just positive integers. Sounds absurd - but the reason is you can count them.
You can also count all rational numbers so even if you throw all of those fractions in with the integers you still have the same size (countably infinite) number of numbers.
Stunning.
But throw in the irrational numbers to get all of the real numbers and suddenly you have a bigger infinity. It's an infinity you can't count. There are more irrational numbers than rational. It's a fairly consistent fact in math that we spend most of our time studying well behaved things even though there are many more badly behaved things in our world.
A line segment doesn't have the same length as a line -any two line segments do have the same number of points even if they are of different lengths.
Math just gets prettier and prettier.
Now stop saying Geometry is just a lie. That's like saying the game of monopoly is just a lie. The game of monopoly is not the game of chutes and ladders. Both, however, have rules and you can understand how to play each according to their rules.
Take that further, Crazy Eights is not the same as Spit - they both have different rules even though they are even played with the same exact basic components (the cards).
Geometry starts with a set of rules - necessary assumptions and definitions. Some sound stupid like "a point is that which has no dimension" or "given a line and a point not on the line there is exactly one line through the given point that doesn't intersect the given line". But how is that any dumber than "each player begins with 2 $500 bills, 2 $100 bills ..." or "collect $200 when you pass go" or "go to Jail if you roll doubles three times in a row on one turn"
We accept the rules in board and card games and just enjoy seeing where they take us. Geometry can be the same.
Well the same if Monopoly had a 3 hour final exam coming up in two weeks.
Yours,
House's dad
*reads House's dad's comment*
ReplyDelete*attempts to comprehend*
*processing... 11.4% complete*
*system failure*
*mind = blown*
I think my brain just broke, but in a good way. :D
ReplyDeleteNow, see, if only the math teacher could explain it like that. . .
Also, returning to the zero times infinity thing, it's actually what's known as an "indeterminate form". It usually arises in algebra when you're trying to make a substitution that would normally be illegal (like one that forces you to divide by zero) but at which the expression looks like it should be nice and well-behaved. Through a process called "taking the limit" (which basically consists of plugging in numbers very close to the illegal number to see if the expression is approaching a specific value) you actually can evaluate these "illegal" substitutions. So, in a sense, zero times infinity can equal any real number you want (depending on the specific indeterminate form you pick).
ReplyDelete---Not House's Dad.
Just thought you should know that I may start signing things off with "epsilon greater than" :)
ReplyDelete