The correct response to uncertainty is *not* half-speed

I think for me the problem is that I'm not being Bayesian. I can't make my brain assign 50% probability in a unified way. Instead, half my brain is convinced the hotel's definitely behind me, half is convinced it's ahead, they fail to cooperate on the epistemic prisoner's dilemma and instead play tug-of-war with the steering wheel. And however I decide to make up my mind, they don't stop playing tug-of-war with the steering wheel.

Reminds me of the motto "Strong Opinions, Weakly Held". There's no point having a blurry opinion, or not expressing what you believe to be the most likely candidate for a good way forward, even if it's more likely by only a small margin. By expressing (and/or acting on) a clearly expressed, falsifiable opinion, you expose it to criticism, refutation, improvement, etc. And if you hold it weakly, then you will be open to reconsidering. Refusing to make up your mind, and kindof oscilating between a few options, perhaps waiting to see where the wind blows, has its advantages, but especially when it comes to getitng things done, is most often a clear loser. Despite this, our brains seem to prefer it instinctively, maybe due to some ancestral environment echoes about being proven wrong in the eyes of the tribe?

Very good and timely observation. A study came out just a few a days ago in Nature Neuroscience showing that the brain tends to implement competing sensorimotor policies simultaneously (a sort of model averaging), at least at the beginning of a movement: Parallel specification of competing sensorimotor control policies for alternative action options. (With this link you should be able to go through the paywall.)

By the way, this form of policy averaging is not wrong per se; it is wrong with respect to a given goal (aka loss function). It's not ideal if you want to reach the hotel (0-1 loss); it could be locally optimal (probably still not globally optimal, depending on your posterior), if you wanted to minimize the average (squared) distance from the hotel. Which is not what we usually want to do for hotels (if we are uncertain between building A and building B we are not just happy to stand in the middle), but it might be the right loss function in other cases.

Wasn't sure if should have stayed at a job or applied for grad school, so I quarter-assedly worked on school applications while quarter-assedly pretending to work until I got fired.

I thought the heuristic was "if I think I passed the hotel, I was going too fast to notice. I better slow down so I see it when I come up on it, or so I might recognize a landmark/road that indicates I went too far." We slow down not because we are splitting the difference between turning around and continuing on. We slow down to make it easier to gather more information, a perfectly rational response.

Anyone have a better procedure for fixing this than the following?

1. Notice the feeling.
2. Treat it as a signal that your S1 wants you to search for cheaper ways to figure out which option is right than continuing to drive. Search for cheaper ways and execute them. Make it a thorough search and show your S1 the thoroughness of your search. Acknowledge the awfulness of "drive back and forth in an expensive search pattern" and only choose that as a last resort.
3. If you don't immediately become much more certain of which way the hotel is in, and the "go 30mph" feeling does not go away, treat it as a signal that your S1 thinks the thought process by which you chose (under evidence-starvation) is wrong, which does not necessarily mean that the conclusion is wrong.
4. List the ways your S1 thinks you're biased which are screwing up your evidenced-starved reasoning.
5. Perform sanity-inducing rituals to counter those biases. (Think about your actual goal of getting to the hotel as soon as possible, forgive yourself for maybe driving past it, imagine all 4 outcomes (60mph forward, 60mph backward) x (get to hotel on next try after this, don't get to hotel on next try after this) and how you would feel about them)
6. If the feeling is still there, this procedure has failed.

Imagine an undirected graph where each node has a left and right neighbor (so it's an infinitely long chain). You are on a node in this graph, and somewhere to the left or right of you is a hotel (50/50 chance to be in either direction). You don't know how far -- k steps for an arbitrarily large k that an adversary picks after learning how you will look for a hotel.

The solution that takes 1 step left, 2 steps right, 3 steps left, etc. will find the hotel in O(k^2) steps. Is it possible to do better?

I suspect half speed is actually a rational decision given some underlying model AnnaSalamon was not aware of explicitly.

For instance, she may intuitively feel that she just passed the hotel. If so, then being extra careful to look well for features and marks around you that could give you hints of whether this happened could work best at half speed. Are there fewer hotels around? Is it a residential area? Does the amount of economic activity seems to be increasing or decreasing as I move in this direction? Then, you can turn around and get there faster.

Formalizing the precise model that would make half-speed the rational choice may be a bit complicated. But that's what the Bayesian approach to cognitive sciences would try to do first.

The old joke about the guy searching for his spectacles under the stoplight even though he lost them elsewhere feels applicable.

In many cases people's real drive is to reduce the internal pressure to act, not to succeed at whatever prompted that pressure.  Going full speed and turning around both might provoke the shame function (I am ignoring my nagging doubts...), but doing something, anything, in response to it quiets the inner shouting, even if it is nonsensical.

This article only makes sense if there's no confusion about whether a building is your hotel or not. Half-speed makes a lot of sense if you're interested in paying close attention to what is going on around you. It's also very useful to slow down if you become drastically uncertain, because if you don't know where you're going it's better not to be going in random direction at full speed while you're thinking about it.

I read this and all I could think of was myself and a script I have just been running away from writing. I talk more about it than I do actually writing it because the first draft got some criticism. I should just write the 2nd draft, get to know what I did wrong, what I did better and keep writing. How else would I improve if the thought remains only in my head?

For the hotel example I think slowing down initially isn't a bad idea. It allows your mind room to think but you don't want to stay at that speed because you do want to get to the hotel eventually. You need to in that time make a decision, forward or backward and strategy to adopt so you don't speed up and still maybe miss seeing the hotel because you are driving fast in unfamiliar territory.

Having a strategy with which is speed N can be a good approach and also stopping to ask questions. Either way, i think the tug of war going on in the mind is a necessary tool that slows us down, gives the mind time to think before preceding

Although not as clearly as the other links, Lawful Uncertainty seems quite relevant to this article.

Huh. I think I've been doing this at my current (crappy, unlikely to lead anywhere, part-time remote contract programming) job. Timely!

Nah... in the hotel example, you slow down as to not maximize your mistake if you've made one. If you have doubts, they are probably justified enough to do something to examine the evidence while minimizing the fallout.

Before you set out on the trip, you'd likely have checked some map and had an idea of how far to travel along the road the hotel is located on. You'd say, "Oh. It's 17.8 miles after I turn onto highway 99. Got it."

Then, you turn onto highway 99, but you'd be thinking about something other than "17.8 miles to go". You'd be thinking about the big meeting you had the next day, or the cramp in your leg, or your ex-girlfriend, etc. So x miles would pass, and you'd lose track of what the value of x was.

At this point, you're right that driving full speed either forward or back would optimize your arrival time IF you guess right. But during the time you are trying to make a decision, it makes rational sense to slow your speed a bit and think. (30 mph seems excessive in a 60mph zone)

You probably didn't pass the hotel yet. I'd say it's north of 50% probability. While you were daydreaming about the big meeting and your ex, you weren't completely distracted from the task of finding your hotel—you were just daydreaming, not actually dreaming. Add this to the fact you'd have some reasonable idea of how many miles you'd traveled since turning onto hwy 99, and it's a 50.1%+ chance you didn't miss your hotel yet.

Slowing down for a minute is certainly preferable to just turning around the moment you have a doubt. It's also better than just proceeding through your doubts at the same speed and making the problem worse.

Slowing down gives you a chance to look around and check for clues that you may have missed, or not yet arrived at the hotel. It allows you to think and reason through the evidence. Did you already pass a commercial district and now you are in the rural boonies? Or have you not yet seen an area where a hotel might be?

The other examples don't seem to fit the first analogy that well. If the point is "it's rational to commit to one thing since half-assing two things tends not to work" then I agree, but it's not terribly novel stuff. (65 upvotes? Really?)

I've been making this mistake for the past few years of my life

#feelsbadman

If you believe that you will have evidence in the future that enables you to decide between in front of you and in back of you, driving slowly may be the optimal decision. For instance, assume you think that the hotel can be in one of two locations, either a specific spot ahead of you or a specific spot behind you, and you are not equidistant from those two locations, you will receive evidence a fixed time in the future, and if you travel at half speed you will receive the evidence when you are equidistant between the two possible locations. Then travelling at any speed (that doesn't pass the hotels) will not change the average distance to the hotel at the moment you find the evidence, but travelling at a speed designed to put you in the middle when you get the evidence will reduce the worst case scenario without affecting the average. Therefore you should travel at half speed. Furthermore, it may reduce the average as well if the chance of receiving evidence varies on how much total distance you have travelled (seeing a landmark that you know is past or before the hotel would be evidence, for instance).

Of course I've defined this scenario in a bunch of arbitrary ways, but they aren't really necessary to make the optimal result travelling at half speed, they just make the optimality easier to demonstrate.

When there's no clear winner, the winner can't take all.

https://en.wikipedia.org/wiki/Winner-take-all_in_action_selection

Good post.

Though as is often the case, there is already a well-known saying that encapsulates this idea: "do it properly or not at all".

There's an important category of choices: the ones where any good choice is "acting as if" something is true.

That is, there are two possible worlds. And there's one choice best if you knew you were in world 1, and another choice best if you knew you were in world 2. And, in addition, under any probabilistic mixture of the two worlds, one of those two choices is still optimal.

The hotel example falls into this category. So, one of the important reasons to recognize this category is to avoid a half-speed response to uncertainty.

Many choices don't fall into this category. You can tell because in many decision-making problems, gathering more information is a good decision. But, this is never acting as if you knew one of the possibilities for certain.

Arguably in your example, information-seeking actually was the best solution: pull over and take out a map or use a GPS.

It seems like another important category of choices is those where the best option is trying the world 1 choice for a specified amount of time and then trying the world 2 choice. Perhaps these are the choices where the best source of information is observing whether something works? Reminds me of two-armed bandit problems, where acting-as-if and investigating manifest in the same kind of choice (pulling a lever).

As a general response to uncertainty, half-speed can have advantages. Specifically:

• This signals your uncertainty to others - someone more familiar with the area may offer to help.
• When (and if) help is offered, you are less likely to have gone too far the wrong way.

Now, neither of these were applicable in your specific hotel case - had there been anyone to ask, you could have stopped and asked, and going slowly in a car doesn't really help you. So it makes a lot of sense to ignore the default strategy in that case - and, in fact, in several other cases as well (it's a common heuristic, but it really doesn't apply in a lot of situations)

Either way, fullspeed was best. My mind had been naively averaging two courses of action -- the thought was something like: "maybe I should go forward, and maybe I should go backward. So, since I'm uncertain, I should go forward at half-speed!" But averages don't actually work that way.

Averages don't work that way because you did the math wrong: you should have stopped! I understand the point that you're trying to make with this post, but there are many cases in which uncertainty really does mean you should stop and think, or hedge your bets, rather than go full speed ahead. It's true there are situations in which this isn't the case, but I think they're rare enough that it's worth acknowledging the value of hesitation in many cases and trying to be clear about distinguishing valid from invalid hesitation.

I suppose this is a good example of such roads. My general impression is that people are nitpicky because it would be rather difficult to miss a hotel, especially on a long, visual-infinity, featureless roads like that.