Most important to hold in your mind, although not, obviously, to think about, is that lying in front of you is a practical infinity of ways to occupy your thoughts with non-taxing but highly amusing activity. Ginning up or practicing card tricks, if you can find cards, or playing Gin or Go Fish, or working on your timing with a handy straight man, say. Naturally you should also find things that you can do without any aid from tools or a random man or woman (possibly also tools), for such things can fail you, and anyway you shouldn't put your trust in just any fool who's on your train car (if, that is, your particular long duration is that of a train trip--but this point is good for all trips and waitings of any kind during which you might run into an unsavory sort).
To say again what I just said, if clarity was lacking:
the imitation of an atom is your path to avoiding thought and maintaining numbth. Twiddling your thumbs is not too low an action for you, if you wish to gain your goal. A crowd can, I admit, assist you, but you must not plan on that!
So what can you do without such aid? Singing a song (softly, so as not to disturb) is a possibility, or, staying in an artistic ambit, you could do what Johann did in Italy, and tap out with your nails a lyric's sixfold dactylic rhythm.
If, contrarily, your mind works happily with math, you can turn to counting tricks to pass many hours. This can start you off:
Say I own two rabbit coops (if rabbits stay in coops, that is), which I'll call "A" and "B". I also own two undying androgynous rabbits, and I put a rabbit in A and a rabbit in B, and I wait many days. A day runs as follows: at noon copulation by B rabbits occurs with all A rabbits, and all rabbits stay in A. At midnight rabbit-kids, born of original A-rabbits, go into coop B, and attain physical maturity rapidly--in fact by six A.M.. On Sundays too this occurs, for rabbit lust can't put off its satisfaction.
How many undying androgynous rabbits will I find in coop B in a fortnight? A month?
Such topics in counting can occupy your mind for an arbitrarily long duration, if you try to find a solution that would hold valid not just for "a fortnight or a month", but for any amount of days.
Such ways of avoiding thought might, though, smack to you just of that thing which you sought to avoid! I admit, it is an idiosyncratic mind that finds its fun in what many of us would gladly abandon to a math class. Not involving such rigors--or, you might think, any rigor at all--you could bring along a simplistic book or monthly journal, or that sort of thing; nothing you'll think about too hard, just words on which you can train your sight, and an occasional satisfying flap of turning papyrus.
No doubt you can find ways that I said nothing about of accomplishing this goal. This squib's only aim was to start you on a road to procrastination and days full of thoughts full of nothing. I wish you all much luck in whiling away any long duration that might stand in your path!