
Maths in Science – an interview with Don Knuth (2015) - mjs
http://authenticinquirymaths.blogspot.com/2015/11/maths-in-science-interview-with-don.html
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davidivadavid
That makes sense in terms of bit flipping, but does it make sense in terms of
distance?

Assuming your mouth is a unit square, where you have to hit the four
"corners", with no distance between inside and outside, with Knuth's pattern,
I have to travel 5 units.

Meanwhile, doing inside/outside clockwise only requires 4 units.

Am I missing a joke or something? Why, for instance, would you go across your
mouth twice just to clean your upper teeth?

~~~
abecedarius
I don't understand your alternative or how you get 5 and 4. Knuth's algorithm
travels 12 sides of your 'square' (3 sides times inside+outside times
upper+lower) plus the distance between upper and lower (once).

(TIL I brush my teeth just the way Knuth does. Except sometimes mirror-
flipped.)

~~~
davidivadavid
Let me see. I may not have been very clearheaded and have miscounted.

Left upper outside to right upper outside is 1 side of the square (distance
between left and right).

Right upper outside to right upper inside is 0 (I was assuming no distance
between inside/outside, maybe that's not a good assumption).

Right upper inside to left upper inside is 1 (distance between left and right
again).

Left upper inside to left lower inside is 1. (between upper and lower).

Left lower inside to right lower inside is 1. (left/right).

Right lower inside to right lower outside is 0.

Right lower outside to left lower outside is 1. (right/left).

Overall, that's 5.

Meanwhile, if I do:

Left upper outside (0)

Left upper inside (0)

Right upper inside (1)

Right upper outside (1)

Right lower outside (2)

Right lower inside (2)

Left lower inside (3)

Left lower outside (3)

I get 3 (not 4, don't have to close the square).

Now, making it 1/0 is maybe not a fair assumption, but the width/height of
your jaw seems higher to me than the width of your teeth, so minimizing the
number of times you go left/right/up/down seems sensible, doesn't it?

TIL Don Knuth only brushes the sides of his teeth.

~~~
abecedarius
OK. I took your rough square as: left side, front, right side all have teeth
along them; the rear of the square opens into your throat with no teeth. Since
we're taking it to be a unit square, each side is of length 1. Knuth's
toothbrush travels a total distance of 12 in those units, plus the upper-to-
lower distance, which'd be some moderate fraction of 1.

I don't understand by what units you're counting, that they uniformly measure
a distance. Maybe you're tallying moves that are not brushing? That'd be 1 for
Knuth, the upper-to-lower transition. But it's OK! We don't need to argue
about a joke.

~~~
davidivadavid
The square is the cartesian product upper/lower X left/right (upper left,
upper right, lower left, lower right). I was only counting moves from left to
right or top to bottom (along the sides of the square), so I suppose those are
moves that aren't brushing (because I assume the actual brushing varies
little). How would that be 1 for Knuth?

~~~
abecedarius
Because Knuth's path never interrupts brushing except the one time it moves
from upper to lower teeth.

~~~
davidivadavid
That seems a little arbitrary to me. You have to switch how you hold the brush
to go left/right (unless your brush is double-sided). For example, I can't
imagine his first move, from upper left outside, to upper right outside, to be
continuous.

And you might as well argue that you're not interrupting either when going
from top to bottom. I mean you're just continuing the same movement after all.

Damn, who knew brushing teeth could be so complex.

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latenightcoding
I know it was a honest mistake, but I would hate myself if I ignored an email
from Don Knuth

~~~
OJFord
The author seems to feel similarly.

We've all done that though, I'm sure. Maybe not one from Professor Knuth (!) -
but overlooking an important email's something we've all done... I hope?

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dang
Url changed from [https://beebo.org/haycorn/2016-02-24_how-knuth-brushes-
his-t...](https://beebo.org/haycorn/2016-02-24_how-knuth-brushes-his-
teeth.html), which points to this.

Submitters: HN prefers original sources. If you want to highlight some detail,
such as a tooth-brushing algorithm, you can always do so via a comment in the
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