Its 10 o' clock and you're looking for the bus home. This old lady turns up. Really old: she can't walk properly, can't sit without your help. You sit with her, and she starts talking. She tells you she's going to San Mateo, which is at least 2 hours by public transit. Honestly, you wouldn't have been able to make it that far at this hour.
She goes on to tell you how her old age home doesn't provide lunch and has no swimming pool. She also tells you about her family, who *should* be in Florida at this point (she hasn't seen them in years). She draws out a cigarette exactly like she's been doing for the last 78 minus 15 years. Well, 8 days lesser than that. She estimates next Thursday to be her 78th birthday. Asks about yours, you say October. She promises to quit smoking in October.
Once she's done with herself (and this particular festival she's been trying to find and attend all day), she asks about you. Battling her smokescreen, you tell her you're from India and are going to a graduate school at Davis. Like a pro, you continue to tell her your major is Electrical Engineering. She grabs only the second half of the major, but is impressed anyway. She asks you to explain, and you say computers. She's satisfied. Thankfully.
You find out that Mary's never been good at Math. She asks you whether you know calculus, because that's something she knows is tough. You tell her you've studied and passed it, which impresses her, for the most yet.
And then she asks you the toughest question you've ever seen or heard of. It hits you harder than any JEE problem you ever tackled, including Chemistry ones. It cracks your skull wider than it did during lectures of Analog Electronics or Circuit Theory (or, for that matter, Philosophy). No points for guessing - she has just asked you to describe calculus to her. And effectively, blown you out.
Explaining Calculus to a 78 year old should be an open research problem. Really, we should have International Conferences on how to do it. Here we are, at the bleeding edge of technology - we can do calculus in our sleep. We can differentiate while watching movies. We can integrate while taking a piss. We can cook dinner and solve DEs at the same time. Heck, we even have an acronym for Differential Equations. And yet, to explain it to someone with no background whatsoever, we don't know where to start. I didn't. No one knows how this should be done. You couldn't start with something familiar to the lady. Because nothing of that nature exists. There is no correct way to deal with this. What follows is an example of a wrong way:-
I started by a one line summary. "Sometimes if you split up things into pieces that are way too small, you can't just add them up to get the whole." This right-on-track but grossly imperfect summary of the last 200 years of mathematics collided with a spectacularly lukewarm what-the-hell-are-you-talking-about expression. I proceeded to give an example. "Imagine a car accelerating from 50 miles an hour to 60, in 10 seconds. Let's take a moment during this period, when the car's running at 55. How fast is the car running at the very next moment? It must be more than 55 because we're accelerating, but it can't be any more than 55 because its just the next moment. We study all this in calculus." Brilliant analogy, I thought. But you guessed it again - I got nowhere. Couldn't as much as half kid her. She got it too, and after a bit of thinking gave up on what might have been her last stab at calculus.
After disappointing her at my teaching ability (which, mind you, is a requirement for a PhD) I went further by forgetting to help her get on the bus. She walked so slow we (most importantly, I) almost missed the bus, so I ran ahead. But I'm not a complete ass - by running ahead I stopped it for the both of us. Clearly, I still suck.
She goes on to tell you how her old age home doesn't provide lunch and has no swimming pool. She also tells you about her family, who *should* be in Florida at this point (she hasn't seen them in years). She draws out a cigarette exactly like she's been doing for the last 78 minus 15 years. Well, 8 days lesser than that. She estimates next Thursday to be her 78th birthday. Asks about yours, you say October. She promises to quit smoking in October.
Once she's done with herself (and this particular festival she's been trying to find and attend all day), she asks about you. Battling her smokescreen, you tell her you're from India and are going to a graduate school at Davis. Like a pro, you continue to tell her your major is Electrical Engineering. She grabs only the second half of the major, but is impressed anyway. She asks you to explain, and you say computers. She's satisfied. Thankfully.
You find out that Mary's never been good at Math. She asks you whether you know calculus, because that's something she knows is tough. You tell her you've studied and passed it, which impresses her, for the most yet.
And then she asks you the toughest question you've ever seen or heard of. It hits you harder than any JEE problem you ever tackled, including Chemistry ones. It cracks your skull wider than it did during lectures of Analog Electronics or Circuit Theory (or, for that matter, Philosophy). No points for guessing - she has just asked you to describe calculus to her. And effectively, blown you out.
Explaining Calculus to a 78 year old should be an open research problem. Really, we should have International Conferences on how to do it. Here we are, at the bleeding edge of technology - we can do calculus in our sleep. We can differentiate while watching movies. We can integrate while taking a piss. We can cook dinner and solve DEs at the same time. Heck, we even have an acronym for Differential Equations. And yet, to explain it to someone with no background whatsoever, we don't know where to start. I didn't. No one knows how this should be done. You couldn't start with something familiar to the lady. Because nothing of that nature exists. There is no correct way to deal with this. What follows is an example of a wrong way:-
I started by a one line summary. "Sometimes if you split up things into pieces that are way too small, you can't just add them up to get the whole." This right-on-track but grossly imperfect summary of the last 200 years of mathematics collided with a spectacularly lukewarm what-the-hell-are-you-talking-about expression. I proceeded to give an example. "Imagine a car accelerating from 50 miles an hour to 60, in 10 seconds. Let's take a moment during this period, when the car's running at 55. How fast is the car running at the very next moment? It must be more than 55 because we're accelerating, but it can't be any more than 55 because its just the next moment. We study all this in calculus." Brilliant analogy, I thought. But you guessed it again - I got nowhere. Couldn't as much as half kid her. She got it too, and after a bit of thinking gave up on what might have been her last stab at calculus.
After disappointing her at my teaching ability (which, mind you, is a requirement for a PhD) I went further by forgetting to help her get on the bus. She walked so slow we (most importantly, I) almost missed the bus, so I ran ahead. But I'm not a complete ass - by running ahead I stopped it for the both of us. Clearly, I still suck.
1 comment:
Feynman Lectures on Physics, volume 1 :-)
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