Monday, April 30, 2007

Beans equalises!

The famous quote by JF Kennedy springs to mind, well it's been changed slightly:

And so, my fellow readers, ask not what this blog can do for beans; ask what beans can do for this blog.

OK that was lame, but here's 'the original' (pfft) if you're interested. (No reason why you should be, I mean mine's pretty cool right?) Well if you're still shaking your head at that 'quote', then please don't look at the time of this post. One could ask what the heck I'm doing awake at this time, and equally why the heck am I posting!

However don't worry, I have a good reason for both, so enough of that head shaking. (Note: since it is way before my normal waking up time, I can be forgiven for being more disjoint than normal I hope!) I hadn't originally seen myself sitting here and posting. I mean I didn't just have a 'dream' about posting right now and so didn't wake up to 'fulfill' my dream, in case you're still scratching your head. (It'd have been coolish if so, then maybe I can claim to have at least accomplished one of my dreams. :D ) So I awoke. Surprisingly awake, if I may say so myself. I mean it's been a while since I've woken up and properly been awake straight away. I'm not a caffeine junky (coffee=not nice) but I've been sluggish this past week, which I'll put down to 'stress'. (We all need something to blame).

So I'm awake as one can be and my desk seems to be glowing in an unearthly like light. It's my mechanics homework calling out to me! Wow- it actually did feel like one of them freaky dreams, which you can never tell if it's real! (the light was the lamp BTW! I'm not seeing things just yet.) I sit on the chair- roll my sleeves up and get a fresh paper. Then I look over the first bit of question one and once again deduce the same equation of motion (thankfully).

The gears in my head are slowly changing. I switch over to the lane in the right to overtake part i. But alas, it's the next part which causes me to once again check my speed and stop accelerating. I look at my 'beautiful' diagram, and complain to it that why can something as beautiful as a laptop/bean falling down a building cause me such great pain. Now if this was actually my dream- which I'm not so sure about anymore- the picture would have replied: 'Look beyond the 'beauty' beans and stop being a dumbo! This is what you're meant to do....'. Any wild guesses as to what happens next?

I'm telling you this is darn spooky- kids don't read on! I mean it must have spoken to me, there is not other logical explanation as to why I then managed to 'see' what to do! (Any ideas?)

The equation of motion which I had was:
What I'd stupidly done was called the distance at the top of my window as x and the time at that distance as zero. Hence the distance after 1m was x+1 and t=0.05. This I realise is wrong, because the equation of motion would then be different (since I deduced it when t=0 and x=0 - the initial conditions which I'd just contradicted). I knew that I had to consider two things, but what they were was the issue.

So in this moment of madness (as some may call it) when my paper spoke to me, I quickly altered my diagram to what it should say. At time t, the distance was x and at that time t+0.05 the distance was x+1! Now I was in business. Why is it that when you feel that you're doing the right thing, you suddenly start accelerating again? I mean I did slow myself down again just in case I came to a grinding crash again, but the adrenaline rush had kicked in (i.e. slowing down was difficult). Believe it or not this is all on an empty stomach, which is now complaining!

Thanks to this moment of 'madness' I now had two equations:

Eliminating the x's gave me a time. The time then gave me the distance, which then gave me the right answer :D (Well after once again drawing for the 'fun of it', the ten floors below me!) If you checked the question sheet out you would have probably noticed that there were answers on the last page. I don't deliberately look at them until after I've done the problem (lesson learnt from semester one, weeks 1-6!). You see in the exam it's not like I'm going to be given the answers right? (Although I wouldn't mind!)

So onto question 2 it was. I think I've managed to complete this question, but only just! Dare I say that beans equalises and scores another? Nah that's pushing it since I used my notes a lot for the second question, whereas the first one was actually a goal scoring moment! It was such a brilliant moment, that I had to post the highlights here -straight away! That should make you guys feel special as well! I mean you must have been following the proceedings of this game- it was much better than the cricket world cup for that matter. OK, I'll shut up now and go celebrate by having some good old breakfast. Hopefully my mechanics lecturer won't mind me being dopey today, since after all I do have a good excuse! I'll soon be finding out whether the mumbo jumbo about kernels was correct as well. Shame I can't nod of again- drat that adrenaline! ;)


tdstephens3 said...

ole, ole ole ole, ole, ole

tdstephens3 said...

check out Alexandre Borovik's recent post about Abstraction - I think this is a good discussion topic - for us undergrads to chime in on, it is our education, right?!!!

I am comming up with some reaction to this - abstraction is one strategy we have to "create" the mathematics we are learning as undergrads. (acurately referred to by: "Mathematics, especially as taught at the undergraduate level, has nothing to do with helping students get to the essence of something. Undergraduate mathematics is primarily taught as instruction in a foreign language.")
So, where do we pick up this abstraction? and how do the interplay between our courses i.e. Linear Algebra and Diff Eq, Calculus, Elem. Algebra... constitute some form of abstraction - or undguided opportunity for abstraction - also, what are some useful tips for the interested undergrad to develop some of this fabled mathemtical capability? Terrance Tao in What's new makes some remark about 'the time when I was able to derive the necessary equations" or something to that effect --

well, all of this will be sorted out, for now - I will read the links provided in that post and try to formulate something interesting to say.

beans said...

I was coming to the conclusion that the people reading this blog are not football fans! :D

I mean, the build up to that goal wasn't particularly impressive but the goal was sweet! (in my opinion anyway.) I guess if it had been in the last minute, then maybe it would be more impressive.

About that abstraction thing- yeah, I read it a while ago and have yet to form concrete thoughts on it.

My take is that the more your practise and expose yourself to the material, the more better you will aiding yourself to answer 'weird' questions or things in general.

I think the best us undergraduates can do is take a keen interest in the subject and work hard. I don't think mathematical ability can be taught. I mean its the way I said about the artists- we imitate drawings first, and so we imitate indirectly what our lecturers teach us. I also look to them to hopefully pick up tricks and other useful stuff. (I guess books like 'solve it' by Polya are handy as well.)

(I think I'll probably comment in maths under the microscope after doing some more reading as well!)