h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

that there's a hiatus in the malestrom that is currently chaotic crunch times I am suddenly quite wary and unsure what's happening to find that instead of rushing late to work now that labs tend to run overtime (especially in chemistry) I've arrived 2 hours before the bio lecture tonight by Dr. Blobel. So I actually have one lovely hour to reflect just how gloriously I failed my first math 171 test. This momentous moment in a liliocentric world will be marked by a blog. Aw, shucks...

Maths is okay, usually. Today we were actually delving/burrowing our way into infinity, to which he asks "what's infinity?" and told us to think of the largest number and then add one to it. The highest number I could think of was a google, 10 raised to the 100th power or 10^(10^2)... which actually came from somebody writing a maths textbook and asks his infant to come up with a word that would stand for the most unimaginably large value hence "google") now the owners of google also own a googleplex, the name of the garage they first were working in but a googleplex apparently is 10 raised to the 1000th power or 10^(10^3) or in other words numbers so large that they don't make sense to finite beings like us. I could talk about how in bio lab tody a girl tells me that one of her instructors told her "if you wrap parafilm around a bottle, you can pass it through a metal detector easier" as he used to smuggle chemical samples into the country. Despite that fascinating fact or that one of the 8 boys in my chinese class has dressed up as a lady in purple for a skit that got videotaped, ponytails and flowers and all, cross-dressing doesn't beat out maths, which is all I can think about still. Bear with me.

Grrr, the professor has a sense of humour. He tells us how the numbers originate from the middle east it was before 2000 bc or something but he couldn't recall. Anyway he seems to get distracted by his own thinking a lot which is always good, I reckon, just not while teaching some vital technique (hahaha those exist?). So it seems the somarians would get their fish to market have somebody else sell it and if you don't count the fish you give the other then there's an argument so what they would do to keep tally of the fish given vs the fish sold was to make clay little fish and put them into another clay ball and when the time comes just break open the clay ball to see how many clay fish are in there. However you won't always want to break these so after a while they have clay fish drawn on the outside, marking that there are three inside the ball, and later the writing was known as more stylized fish (weird marks made by sticking the stylus in that run vertically) and somehow still later they moved the symbols 90 degrees and there's your maths in the middle east.

What was the point of the blast from the past other than to watch the man grin rather endearing to see such enthusiasm in one so weathered?

"Are there more integers than even integers?" If my first set is 1, 2, 3, 4, 5... and the second set is: 2, 4, 6, 8, 10... and they both go up to inifinity.

Yes. Back to infinity. And no, there isn't more integers than even integers.

Why? Perhaps it would help to look at the sets like this.

1, 2, 3, 4, 5...

2, 4, 6, 8, 10...

as long as there is a one to one correspondance it won't matter the values

Oh cool! we would mutter as we students "get it"

But do we really understand? He quickly skims over that there are more than just integers i.e. fractions etc thanks to a german mathematician but we won't go into it now as my 5 mins are almost up...

He says I have a hotel with an infinite number of rooms. # rooms = infinite

now each one of these rooms are filled w/ one person and is considered to be full

one dark stormy night a traveller walks up in the lobbey and asks for a room...

"sorry we're full"

"but you have to give me a place to stay"

"sure, no problem" and the hotel folks found the room for one more...

How since all the rooms are full?

I thought about the dorms, ours actually since I have two roommates. can't he just share but nope, the prof says no sharing allowed.

How?

A minute passes... I can see him grinning.

"Easily. You just get on the intercom and say 'sorry everybody get your belongings and move to the room next to yours"

so in room 1 goes to 2, 2 goes to 3, 3 goes to 4, 4 goes to 5...

and so on. the stranger takes the first room, room #1.

Okaaaaay. We get that, sorta. Just keep 1, 2, 3, 4, 5... in mind. So we think. Another minute passes.

Different scenario: Hotel A inifinite # of rooms, full. There's another hotel, Hotel B, same setup and full except they had bad spinach or something that makes Hotel B inhabitable and somehow they have to move all their folks to Hotel A... How would we make room for an infinite host of patrons?

"can we ask them to move a floor up?" a guy asks. "no, you must have a specific number in mind"

Hotel A: "Easy. You get on the intercom and ask "sorry everybody gather your belongings and move to the room w/ twice your room number."

1 would move to 2, 2 to 4, 3 to 6, 4 to 8, 5 to 10...

Remember the integers and even integers correspondance? Infinity, indeed!

1, 2, 3, 4, 5... pairs w/ 2, 4, 6, 8, 10...

Hotel B: "Everybody please move to the room with twice your room number plus 1"

So whoever in room 1 would be moving to room 3 which was just emptied out, room 2 to room 5, etc etc. You figure it out. So simple, but nonsensical piffling!

Well that took more than 5 mins explaining but hey I enjoyed it... what's it? maths!!

Give the teacher what he likes? I think he just likes folks to try harder, which I shall do, with practice, zeal, prudence and hopefully more brain cells left by the time final exams roll around! As we'd say in history "if at once you don't succeed try to fail again."

I'm going back to work. Thanks for reading,

Lil

Maths eh.. MAths is alright, I like History and Classics more

Yup and some wizen little chinese man could calculate the total time it took to carry out those manouvers, if the person could not move to the new room till he had passed the key to the window lock to the new occupent, even if the females to twice as long as the males but only a third of the them where females.

math 171 test. is 171 slightly harder than 170?

Maths is good. Is it art or science or neither? One feature of math I like is that once a proof is made it becomes the body of math, that we build on - meaning grows. In Physics we have model 'a' that replaces model 'b'. Sometimes model c breaks both model 'a and b'. It does not necessarily progress linearly up towards a 'fuller' meaning. (I have a Physics and Cybernetics background - I have a Cybernetics example below as well!).

Here is a site on infinity you may enjoy: http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001o-esm-intro-tirosh.pdf#search=%22cardinal%20infinity%22

Be sure to look at the definition of cardinal infinity (my bet for the next pope).

Here is a joke about Maths and Cybernetics (two male) students. They both go to a party and there is a lovely girl they are attracted to. The Cybernetics student gives a joint test for who should approach her. He says let's both walk half the way, then divide the remaining distance by a half and walk that distane and repeat till the goal is achieved. The math student, in digust walks off muttering ('zeno'), the Cybernetics student being a pragmatist fufills his test by walking straight up to the girl and stops (he has achieved his intended goal) a polite talking distance away. Infinities are a mental construct. Construction is a physical definite.

http://en.wikipedia.org/wiki/Zeno's_paradoxes

hahaha

thanks folks

math 171 (integral) is the next step up from math 161 which is basic calculus

I am starting to understand improper integrals. I reckon

Improper is a good expression for the debate between the 'inventors of calculus/fluxions' Leibniz and Newton, check out their 'debate'; http://en.wikipedia.org/wiki/History_of_calculus

Some say it slowed down its development, but I suspect it spured it on. There is nothing more useful to the reasoned and logical development of a subject, that its proponents being emotionaly involved with their ego's simultaenous development in competition!

ooooh thanks for that one I cannot imagine having missed seeing this for so long. anyway I --> maths final on the 14th, fun fun fun