A reminder

As the next generation has learned: If your kid wakes you up in the morning saying "I don't feel good," you have about 30 seconds to get them to the sink before the trouble starts.

Advice

Einstein said "Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand." He also said something often simplified:

Found in Montana Libraries: Volumes 8-14 (1954), p. cxxx. The story is given as follows: "In the current New Mexico Library Bulletin, Elizabeth Margulis tells a story of a woman who was a personal friend of the late dean of scientists, Dr. Albert Einstein. Motivated partly by her admiration for him, she held hopes that her son might become a scientist. One day she asked Dr. Einstein's advice about the kind of reading that would best prepare the child for this career. To her surprise, the scientist recommended 'Fairy tales and more fairy tales.' The mother protested that she was really serious about this and she wanted a serious answer; but Dr. Einstein persisted, adding that creative imagination is the essential element in the intellectual equipment of the true scientist, and that fairy tales are the childhood stimulus to this quality." However, it is unclear from this description whether Margulis heard this story personally from the woman who had supposedly had this discussion with Einstein, and the relevant issue of the New Mexico Library Bulletin does not appear to be online.

Variant: "First, give him fairy tales; second, give him fairy tales, and third, give him fairy tales!" Found in The Wilson Library Bulletin, Vol. 37 from 1962, which says on p. 678 that this quote was reported by "Doris Gates, writer and children's librarian".

Be careful about taking such advice. When the grateful bird tells you how to get to the magician's castle, she may be making some automatic assumptions about how you travel. Little inconveniences like the crevasse may have escaped her notice.

Einstein was, contrary to the story about his elementary school grades, very good at math. For some of us mastery comes easily. It may not have played as great a role in his internal history as the difficulties with understanding light.

Just to get a feel for the matter, consider the papers from his Annus Mirabilis. In all of these, creativity/genius played a big role. What else would you need? How much math?

The photoelectric effect is simple and profound: light exists in chunks, with each different frequency having a different energy. In a phototube, light hits a surface with a coating of cesium or some such easily ionized atom, and knocks loose electrons that an electric field pulls away for measurement. "Einstein noted that the photoelectric effect depended on the wavelength, and hence the frequency of the light. At too low a frequency, even intense light produced no electrons. However, once a certain frequency was reached, even low intensity light produced electrons."

This is pretty easy to understand without much beyond elementary algebra. Creativity played a big role here. Score one for Einstein's Quotes.

Brownian motion isn't something you've noticed unless you spend some time looking through microscopes. Tiny particles jiggle around randomly. Einstein devised a model in which the molecules of the fluid the particles sat in bounced randomly off the sides of the speck; sometimes more on one side and sometimes more on the other. And by "devised a model" I include doing the calculations to show that this was potentially the cause of Brownian motion. That required more than just algebra--statistics and understanding limits was needed too. Score one for Oops: Solid Math Background.

On the Electrodynamics of Moving Bodies might give a little clue about the math required to study the matter. Maxwell's Equations use calculus and differential equations, and although the Special Theory of Relativity is easily explained using elementary algebra, getting there needed some ways of thinking about vectors that aren't entirely elementary. Score one for Oops: Solid Math Background.

E=mc^2 was explained in a separate paper working out consequences of the previous one. The math isn't terribly hairy, but it requires understanding the previous paper, so I don't think I can score this one so easily.

So: Creativity 1, Oops 2. Of course creativity alone wouldn't have gotten Einstein anywhere with the photoelectric effect unless he had some background knowledge (energy, momentum, how the experiments worked) to draw it out on. And my experience teaching freshman physics lab suggests that not everybody acquires that framework.

Feynman wrote "If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in."

Happiness

I heard a quote today from a book I've never read Eat Pray Love: "Happiness is the consequence of personal effort. You fight for it, strive for it, insist upon it, and sometimes even travel around the world looking for it. You have to participate relentlessly in the manifestations of your own blessings. And once you have achieved a state of happiness, you must never become lax about maintaining it. You must make a mighty effort to keep swimming upward into that happiness forever, to stay afloat on top of it."

I googled the author and book. She had the resources to travel the world looking for herself. In context her advice (not just the quote above) seemed to me ... well, C.S. Lewis described it:

‘I beg your pardon, sir,’ said Vertue. ‘I had not seen it in that light. I will certainly act as your servant for a day or so if you wish it. I had not understood that it would be such a burden to you to cook for yourself. I don’t remember that you said anything about servants when you were outlining the good life last night.’

‘Why, sir, said Mr Sensible. ‘When I outline the principles of the steam engine I do not explicitly state that I expect fire to burn or the laws of gravity to operate. There are certain things that one always takes for granted. When I speak of the art of life I presuppose the ordinary conditions of life which that art utilises.’

‘Such as wealth,’ said Vertue.

‘A competence, a competence,’ said Mr Sensible.

‘And health, too?’ said Vertue.

‘Moderate health,’ said Mr Sensible.

‘Your art, then,’ said Vertue, ‘seems to teach men that the best way of being happy is to enjoy unbroken good fortune in every respect. They would not all find the advice helpful.’

A few exercises...

Tall and tan and young and lovely,
The girl who looks so Swedish goes jogging,
And as she passes each one she passes goes "Ow"
Oh, but her knees knock so badly.
How can I tell her of biomechanics?
Yes, I would give advice glady.
But I thought it would be impertinent. And when she finally stopped to walk, and her walking stride also had the same feature, I was glad I hadn't made any suggestions...