Kids are taught that when crossing the street, they should check for oncoming cars by looking left, then right, then left again. Why left again? Isn’t that redundant? You already looked left.
You could imagine that the advice makes sense because during the time he was looking right, cars appeared coming from the left that he did not see when he first looked left. But then wasn’t the first left-look a waste? Maybe not because at the first step if he saw cars coming from the left then he knows that he doesn’t have to look right yet. But then shouldn’t he insert a look-right at the beginning in hopes that he can pre-empt an unnecessary look-left?
I thought for a while and in the end I could not come up with a coherent explanation for the L-R-L again sequence. When you can’t find an example, you prove the counter-theorem. Here it is.
Take any stochastic process for arrival of cars. Consider the L-R-L again strategy. Consider the first instance when the strategy reveals that it is safe to cross. Let t be the moment of that instance that the L-R-L again strategy looks to the left for the second time.
Now, consider the alternative strategy R-L. This strategy begins by looking right, then when there is no car coming from the right it looks left and if there is no car coming from the left he crosses. If he is using R-L there are two possibilites.
- The traffic from the right is not clear until time t. In this case, by definition of t, he will next look left and see no traffic and cross.
- The traffic from the right clears before t. Here, he looks left and either sees clear traffic and crosses or sees traffic. In the latter case he is now in exactly the same situation as if he was following L-R-L from the beginning. He waits until the traffic from the left clears and then re-initializes R-L.
In all cases, he crosses safely no later than he would with L-R-L again, and in one case strictly sooner. That is, the strategy R-L dominates the strategy L-R-L. Three further observations.
- This does not mean that R-L is the optimal strategy. I would guess that the optimal strategy depends on the specific stochastic process for traffic. But this does say definitively that L-R-L is not optimal and is bad advice.
- He might get run over by a car if after looking left for the last time he crosses without noticing that a car has just appeared coming from the right. But this would also happen in all the same states when using L-R-L. Crossing the street is dangerous business.
- I believe that the rationale for the L-R-L advice is based on the presumption that the child will not be able to resist looking left at the beginning. Starting by looking right is very counterintuitive. Under this theory, the longhand for the advice is “Go ahead and look left at the beginning, but when you see that the traffic is clear, make sure you look right as well before crossing. And if you see traffic and have to wait for it to clear, don’t forget to look left again before starting out because a car may have appeared in the time you were looking right.”
19 comments
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July 20, 2009 at 11:19 pm
K
My thoughts:
I would imagine that the LRL strategy is taught because children sometimes make mistakes (they are small).
If one looks RL, but makes a mistake when looking left and does not see a car that should have been noticed, that person is dead. With LRL, it gives two chances to catch any “mistake” a person might make. A person can also after stepping out into the street look R again as a second check for the first R look.
July 21, 2009 at 2:14 am
Thijs
An important element of the strategy should be the fact that cars coming from the left pose a much greater danger than those coming from the right. Cars from the left are on your side of the road; if you decide to step into traffic they are the ones with the least reaction time. With perfect observation this should not matter (it’s either safe or not) but with kids there is good reason for making them double-check.
November 17, 2016 at 1:15 pm
summershoe
This was my thinking as well. Critical systems have built-in redundancy because there may be no recovering from a fault. The extra time spent looking left is well worth it. If you watch people crossing there’s a 2nd R as you reach the middle of the road, for the same reason. Also, in practice you’re carrying speed as you approach the road so an initial L is required to confirm you can hold speed as you look right.
July 21, 2009 at 2:54 am
Kurt
Is the strategy L-R-L (again) or L-R-L (again)-R (again)?
That is you use the L-R-L strategy to get into the street, but then get another R as you pass the point of relevant L-watching and are beginning to fear whats happening on the R.
I view this as an overview of each side, then a detailed analysis of each side as you proceed.
The R-L strategy may not work for those who walk somewhat slowly. By the time they get to the part where the R information is relevant, the information is too old to matter.
July 21, 2009 at 3:29 am
Armoured
There are two good reasons why a L-R-L strategy would dominate (in part mentioned above):
1) Judging speed: this is critical – you are not just checking for the presence of cars on the left, you are checking for their speed. This can only be judged over some period of time, even if the period of time can be quite short. But the danger of making an error for any vehicles coming on the side closest to you (in drive-on-the-right jurisdictions) means that it is much wiser to extend this period of judgment. If you can judge speed in, say, 1/10th of a second while glancing, a half-second to glance and look to the right and back, you have extended your time to judge speed by five or six times – with a significant increase in accuracy.
2) As noted above, errors in judging speed/arrival/presence of cars on the right can partially be corrected while crossing. In practice, most people _while crossing_ will have another chance to look to the right (so their strategy is really L-R-L,R).
June 29, 2016 at 1:19 pm
Anonymous
So what is the best theory while driving is it left right left or is it right left right I understand everybody knows when walking you go left right left but when you’re in the vehicle I would think right left right because for safety there is 2 second rule before you proceed through an intersection.with that said I wonder what’s best when Crossing in a car.
July 21, 2009 at 9:28 am
Beezer
Actually it’s L-R-L-R-R-R-R! Particularly in Boston or New York.
July 21, 2009 at 11:21 am
Lance
This post caused me to watch my 11-year old daughter just do R-L when she crossed the street this morning. When I asked her why not L-R-L, she said it was “wasted effort”. A little economist in training.
July 29, 2009 at 2:21 am
jeff
lovely.
July 21, 2009 at 11:25 am
Sean Crockett
Great topic. I think the principle advantage of L-R-L is that once L is sufficiently clear you can “cheat” into the road a littler further as you look to the right. If right is sufficiently clear, you continue your momentum forward and look back to the left to make certain you judged the ETA of oncoming traffic well enough (or in NJ, to see how much oncoming traffic has speeded up to prevent you from getting across the street…). There’s no cheating into the road if you look to the right first.
However, I don’t think you want children to “cheat” into the road, I think they should be confident both directions are completely clear before they begin to cross. I suspect L-R-L (with cheating) is what adults do naturally, so they have assumed this is the best advice to pass on to children without realizing that what makes it optimal for adults is something you don’t want children to do. I want my kid to look both ways twice before starting into the street to be absolutely confident nothing is anywhere close to her crossing point (in case something was missed on the first look). But I’ve taught her L-R-L-R so that as she gets older she’ll discover the cheat and not think I was dumb for teaching her R-L-R-L.
July 21, 2009 at 11:59 am
David Pinto
My daughter was in car accident because she did a R-L. When she looked right, she saw a car down the street, but mistook it for the car that was usually parked in that spot. She made a pattern recognition error. Luckily, no one was hurt.
July 21, 2009 at 2:06 pm
rbhui
I’d go with the ‘mistakes’ reason too. And surely I’m not the only person who does a kind of L-R-L-R-L-L-R-R-R like a crazy bobblehead…
July 22, 2009 at 4:09 pm
Lawrence M
I agree with Sean Crockett. I think we teach kids to cheat b/c of our driving habits. When I drive, I look left so I can judge how far into the intersection I can cheat without impeding traffic. Then I look right. If it’s free on the right, then I look left again to make sure no one has come and then as I’m making my way to the middle of the intersection, I actually look right again.
September 4, 2009 at 10:27 pm
Anonymous
I think it’s because when your crossing the street most traffic comes from the left, so first you’d look left once that’s clear you’d look right to make sure your clear to the right as well and one last time to the left and make sure there is no oncomming traffic that has appeared while looking right. On your way across the street there is time to glance again to the right. That’s my opinion on why they are taught L,R,L
September 25, 2009 at 2:26 pm
Steffen
Here is an observation that supports Tijs’ view (that cars coming from the left are more dangerous). I googled and it seems like in England they teach “Right, left then right again”. No scientific proof here but would this be likely if it is a non-optimal strategy.
Especially when you can’t see very far to the left a second look could be very beneficial before you walk….
May 17, 2017 at 3:15 pm
Anonymous
What the fuck
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July 2, 2018 at 8:26 pm
Jard
Dude, I was just confused on why I got a practice drivers question wrong, but this is an amazing analysis. You made my day with this article.