On any given night, if you don’t brush your teeth before bedtime, nothing bad will happen to you. In fact, you’ll get a few extra minutes to read in bed.
Yet if you never brush your teeth, all your teeth will fall out.
At any moment, it is rational not to brush your teeth — brushing isn’t much fun, and unless you crave fresh breath at night there’s no upside. But it is rational to brush your teeth in general, because you probably don’t want rotten teeth.
Similarly, any given day you’re better off staying in bed reading comics and drinking tea and never leaving the apartment. But if you stay in bed every day, you’ll end up with bed sores, (probably fired from your job and evicted), and you’ll look back, from your dying moments in the gutter, at a life devoid of experiences or memories.
Every decision we make is made in the moment. And at the moment we make the decision, the rational decision is one that, with a longer view, we would regret.
You probably think that the solution is to look ahead and decide now that at all future nights you will choose to brush your teeth. But of course you know there may come a night — when you’re locked out of the house, or when you wake up, confused and with no shoes, in a bathroom stall in another state — when you’ll have to cheat. And on any given night it is rational to cheat. Cheat tonight and there will be no repercussions. Every night this is true. Until it isn’t.
Like most people, I am not thwarted by this problem. I still brush my teeth! But it is never clear to me, as I do it, why I am working against my present best interests for literally no reason.
I don’t have a solution to this problem, other then behaving irrationally. I have yet to find anyone who does. That’s why they call this the toothbrush problem.
Refutation & Overthrow... 
Might be solved if we factor into our rational calculus that human beings are (as far as I can tell) largely habit driven creatures and effort-aversive creatures. Habits seem to minimize effort, making task that would be difficult at any given time easy if done regularly. Also, habits keep us from forgetting to do things.
So, if present-self identifies in any way with future-self, it might mean something like “having gone through great effort to establish this habit that lets me experience minimal discomfort brushing my teeth at night–I opt to reap those benefits here and now rather than squander this effort for short term minimal gain at the expense of either a) losing my teeth in the future from having lost this habit or b) having to exert effort to re-establish the habit in the future.”
This doesn’t entirely eliminate the problem–there’s probably some number of times a month you can skip out on a habituated activity and still retain the benefits of habit. Then we have to decide why I’m not choosing right now redeem all of my free ‘habit squandering freebees.’ But, doing that would a) sacrifice insurance for those needed cheat days and b) we’d need to exert effort to figure out how many habit cheat days we get. That’s a moderately high cost for, what, at best a quarter hour of reading over a month?
pedantically and joke ruiningly yours,
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Joke?
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So I think this isn’t a problem (or rather the problem is with how you state the issue, stated properly, it isn’t a problem) but I do think this is very similar to something I consider a problem.
First, why it isn’t a problem. If we say that for every x hours that you don’t brush your teeth, the risk of getting a cavity goes up y%, then it is pretty easy to come up with a cost benefit analysis depending on how much you dislike brushing your teeth and how much you dislike cavities.
Let’s say there were a negative lottery: you take a ticket and get a dollar, if your ticket gets drawn, then you lose a million dollars (or the town murders you so that the corn harvest is good, but lose $1 million makes the cost benefit analysis easier). Your statement of the problem is saying that every time you play is a free dollar until suddenly it isn’t, but that’s not good risk assessment. To actually calculate if it is worth playing, you need to look at the odds of being drawn to figure out the expected value of the ticket ( $1 – $1000000*(odds of being drawn)).
Now, the thing I do think is the problem: We’ll call it the local maxima problem. Let’s say you are in a unsatisfying relationship. Things aren’t bad, but perhaps they could be better. However any change you make is going to definitely result in things getting worse in the short term. If you break up with your partner, you’ll be alone, there will be life adjustments to not having them in your life anymore, you will need to start dating again which you haven’t done in forever and is full of uncertainty. Now, this change could result in you meeting someone who is a better match for you and things will definitely never get better if you never change, but it isn’t guaranteed things will get better. Maybe you will die alone or never meet anyone as good as your current partner. You don’t know what the long term consequences will be. You only know that the short term consequences will be negative. You do not know if you are at a local maximum and much higher points are available or if you are at the global maximum and should stay put. Should you definitely make your short term future worse in order to change your long term future (possibly also negatively)?
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Speaking as someone with a great job and a relatively inexpensive apartment a couple of blocks from a revival movie theater, the local maxima problem is near and dear to my heart.
Now, your lottery example I understand, because I understand rolling dice and the principles are the same. I was about to say in toothbrushing, there’re no dice to roll — skip one day and you’re not probably not getting a cavity; you’re not getting a cavity! But I guess that by day three or eight or whatever you are rolling dice. So that’s fair.
But what about getting out of bed? You’re always better off staying in bed day by day.
Actually, maybe this isn’t a problem and you should just stay in bed.
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