ArticlesRambling Discussion
Wednesday night’s discussion over milkshakes started from a definition of a billabong before proceeding to the dubious relationship between π and river lengths, before stumping us as we tried to work out, in our heads, the length of one cycle of a sine curve.
Integrals Not Integral to My Life
By my count, this was the fourth time I had ever (ever!) wanted to find an integral outside of a maths class, since I first learnt to integrate twenty years ago.
I completely failed to even begin to work out how to do it.
The third time I had the opportunity was in 1994, and it was while helping a friend with her uni assignment. So, it was still uni-related. I had the complete worked out answer there in front of me in the text book, and I still had trouble following it!
In my day, computing was taught as part of a Maths degree, and the Maths department wasn’t going to graduate anyone who couldn’t prove advanced theorems about calculus – no matter how little they cared. The number of hours – nay, the number of weeks or months of my time that I spent learning how to find integrals (at school and at uni) was a complete and utter waste of my precious and oh-so-short life.
I am not being anti-mathematics here. For example, I found Discrete Maths interesting and even enjoyable. I am just protesting that I had to study topics that did not interest me, and I knew at the time I was studying them would never be of use to me.
It was during one of these interminable maths lectures that I realised the solution; the idea that is going to make me my second million. (Once my first million dollar idea finally takes off, so I have time to develop this.) In hindsight, it seems quite obvious.
Maths Insurance
Every year you pay a premium to the maths insurance company. The amount is based on your job and claim history. If you come across a maths problem you need solved, you simply ring up the company’s call center. It is full of otherwise-unemployable maths postgraduates, waiting for your call. They will solve your maths problem for you!
With no risk of ever being stumped on the number of inter-quartile ranges between a near and far outlier, you can drop out of maths class, and use the time saved to do something more financially rewarding.
I only wish this idea was around back when I was doing my uni exams.
Comment by Alastair on August 27, 2007
Good idea, but like all insurance companies they would soon work out ways of screening out the high-risk from the low-risk applicants. For instance, if you were actually doing a maths course there is a greater-than-usual chance that you would actually need to perform maths problems in later life. This would naturally raise the premium, or perhaps even make you uninsurable.
Which may even be some kind of consolation, depending on your point of view.
Comment by Julian on August 27, 2007
Alastair, I agree, but the basis behind this idea is that, because I had maths insurance, I wouldn’t need to undertake a maths course in the first place.
Comment by Alastair on August 28, 2007
Umm, if you were doing exams at the time (as per the final paragraph in the post) wouldn’t you already be enrolled in the course?
On integrals. Like you I have forgotten most of the details about them. At the time I seem to remember quite enjoying them, but then again I studied applied maths so I Would Say That, Wouldn’t I?
However I certainly value the concepts behind them and have found them helpful on many occasions. For example, integrals are (IMHO) key to understanding Mark Dominus’ solution to the envelope paradox, despite it being an ostensibly discrete maths problem. In fact, I’m not sure how you would understand a probability curve withough having some idea about integrals. That’s worth the price of admission surely?
Comment by Alastair on August 28, 2007
Can I strike that bit? Dunno what I was thinking there.
Comment by John Y. on August 28, 2007
Hey, did anyone else notice that Mark Dominus’s archive widget is almost exactly like Julian’s? Well, almost exactly like earlier, more space-efficient but less user-friendly versions of Julian’s? 😉
Comment by Julian on August 28, 2007
Alastair,
Yeah, you got me, but on a technicality. Let me correct my position to “I only wish this idea was around back when I was about to enrol in maths courses.” or perhaps “I only wish this idea was around back when the committees were determining the minimum requirements for my degree; perhaps they would accept a pledge to pay maths insurance for the rest of my life.”
As for the envelope paradox, let me start by saying it is one of my favouritest paradox puzzles! I couldn’t solve it for myself when I first heard it, and had to search rec.puzzles for the solution. 🙁
Do you really need training in integrals to understand it though? I have explained the envelope paradox to intelligent people who never went to uni… I think they understood it.
I’d make some flippant comment about never learning how to find the area under the curve of f(x)=rand(x), but you’d pin me down on a technicality again! 🙂
Comment by Julian on August 28, 2007
John,
Shh! Don’t mention the archives plugin. I still haven’t fixed it for Firefox (in the default font size), and I am feeling guilty!
Well-spotted though – he seems to have taken a very similar approach to me.