So now lets take an extreme case that there is 1 mile of regular walking before the moving walkway which is also 1 mile long. Suppose I walk at 2 mph with laces undone and 4 mph when they are done up and that the walkway moves at 4 mph. And lace tying takes 30 seconds.

If I do my laces up at the beginning then my journey takes
30 secs (lace tying) + 15 mins (1 mile at 4mph) + 7.5 mins (1 mile at 8 mph) = 23 mins

If I wait until the walkway to do up my laces then my journey takes
30 mins (1 mile at 2 mph) + 30 secs (lace tying on walkway) + (1 mile – 30 secs at 4mph)/8 mph
= 30 mins + 30 secs + (1 – 1/120 * 4)/8 hours
= 30 mins + 30 secs + 29/30/8*60 mins
= 30 mins + 30 sec + 58/8 mins
= 30 mins + 0.5 min + 7.25 mins
= 37.75 mins

So with this set of assumptions it is faster to tie your laces at the beginning rather than wait until you you get to the walkway.

I suppose I included the Proust sentence because one could use it as a springboard for a more general discussion of parsing sentences, which though it would normally be labelled as linguistics rather than mathematics is nevertheless a highly mathematical process and moreover one that is important in mathematics. So it could help with the general aim of encouraging people to think mathematically, and also of demonstrating that mathematics is about more than just the topics taught at A level.

That’s not very relevant to maths education, perhaps, but then I’m a bit puzzled as to why you tackled the Proust in that context.

With all due respect to anyone who embarks on such an undertaking as translating Proust’s magnum opus, Moncrieff’s English version is needlessly awkward. For example, why translate “au contraire” as “on the contrary” when we are not seeing opposites? “By contrast” or “on the other hand” would have been much closer to Proust’s meaning. Likewise, Moncrieff preserves the plural for “les mêmes défauts” (the same defects) but not for its antecedents “des dehors de froideur, etc.”, changing them to singular (a shell of coldness, etc.). This makes parsing an already difficult text still harder.

Moncrieff worked in the 1920s and died in 1930 (which is why his translation can be hosted on Project Gutenberg for free). However, subsequent translators have produced far superior work.

Yes, the price of a hardbound copy of a recent, award-winning translation will set you back a good chunk. But if you are planning to make this your bedtime reading for a couple of years, it’s just a few pennies a day… much less than some other vices.

Other than that nitpick, I enjoyed very much reading your account of teaching math to secondary school students and the ensuing discussion.

Professor Gowers’s account of his discussion with the students of prophetic dreams reminds me of a poignant passage in Richard Feynman’s autobiographical “Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character wherein he describes a clock that stopped in the hospital room the minute his wife died and discusses the temptation (of some) to offer a supernatural explanation.

My point is: parsing Proust (or Joyce, or Musil, or…) in a class certainly doesn’t aim to reduce Proust’s intended meaning, it still is the unavoidable necessary first step. What Gowers did, of course, had other than literary intentions, namely mathematical, and since I presume this was clear to the students, then reconstructing the parsed text in a more linear fashion is at least a mathematically legitimate little exercise. “At least”, but not quite just that: I know that as a reader of literature I’m urged to do this “exercise” very, very often, and not at all because I’m also a mathematician.

Because, actually, there is this other way to look at it: Proust might want us to spend that time parsing and reconstructing, linearizing and going back again, just to make sure that the information on the predicate that comes later imprints itself as much as necessary…

For any Australians reading this there is the Mathematicians in Schools program run by the CSIRO, http://www.mathematiciansinschools.edu.au/, which aims at getting opportunities like this set up.

If with no shoe lace tying one can travel the distance in time

t = x / d1 + (x+y)/d2

Then if one ties his lace before the moving walkway and shoe lace time takes t_shoes.

t = t_shoes + x / d1 + (x+y)/d2

Note, this time is added because we are not covering any distance while tying shoes.

and if on the walkway

let d3 = distance traveled on moving walkway while tying the shoe
d3 = y * t_shoes

t = x/d1 + t_shoes + (x+y)/(d2-d3)

So while they both have the same drop in velocity, in case one the person covers 0 distance during the velocity drop and in case 2 they cover y*t_shoes distance, leaving less distance for the rest of the journey over which they move the same speed.

The problem is — while I can see that you’re right, I can’t see why I’m wrong, in my first comment above.

This is a fascinating problem: so simple to express, yet so hard to think about.