1155: Kolmogorov Directions

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Kolmogorov Directions
People get really grumpy when they realize you're giving them directions for how to go to the store and buy a GPS.
Title text: People get really grumpy when they realize you're giving them directions for how to go to the store and buy a GPS.


Andrey Kolmogorov was a mathematician who worked, among other things, on defining computational complexity. Roughly speaking, the Kolmogorov complexity of a string (of bits, words, symbols, etc.) is the shortest description that allows an accurate reconstruction — or, in some variants, the length of the smallest program which will output the original string.

Cueball's method of giving directions is very reminiscent of Kolmogorov's method of determining complexity. However, it is unlikely they know all the presidents, nor can calculate prime numbers in their heads, and so will have trouble with certain parts. These directions may have minimal Kolmogorov complexity, but they are non-intuitive and are likely not the shortest or quickest way to get there, considering that they consist mostly of left turns.

This is not the first time Cueball has had difficulties with directions, and here we see he hates giving directions as much as he hates receiving them.

The joke in the title text is that Cueball just sent his friend to a store to buy a GPS device to give him the correct directions. (By the time this comic was published, GPS-enabled smartphones had already largely displaced dedicated GPS devices,[1] but Cueball could be talking to a person who does not wish to own a smartphone.)

The superfluousness of giving directions as opposed to using a GPS is the subject of 783: I Don't Want Directions.


[Cueball on the phone.]
Phone: How do I get to your place from Lexington?
Cueball: Hmm...
Cueball: Ok, starting from your driveway, take every left turn that doesn't put you on a prime-numbered highway or street named for a president.
[Caption below the panel:]
When people ask for step-by-step directions, I worry that there will be too many steps to remember, so I try to put them in minimal form.

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How does Cueball know that? Davidy22[talk] 05:17, 2 January 2013 (UTC)

I really like the title text on this one. 07:19, 2 January 2013 (UTC)

It's reminiscent of "What time is it?" "It's time to buy a watch." --Prooffreader (talk) 12:24, 2 January 2013 (UTC)

Although, the GPS doesn't know everything. Mine has led me astray, now and then. Took me to an Ikea which had never been at the address it indicated; took me to a shopping centre and left me to my own devices finding one restaurant in 40 acres of other stuff; took me to someone rural whose street address turned out to be a postal superbox, a couple of miles from my friend's actual home. Of course, usually Cueball is right and the directions-giver is wrong... still, ask. 20:03, 2 January 2013 (UTC)

Randall is way too sadistic and double-entendre prone to take this comix at face value, as if only about a math theorum. What if it carries implicit context of Manhattan, and the need to check math logic against practical reality?

Lexington is one way, southbound. Except midtown where one would hit York Ave/Sutton Place (possibly going backwards on a one way street after the first left, depending on starting point), or in a section of East Harlem with Pleasant Ave, every avenue one passes is a prime numbered one, until hitting FDR Drive, or unless the street cuts off at 3rd Ave. IOW, one would make one turn and dead end at the East River (or 3rd), unless one were in a block where a 2nd left on York or Pleasant led to an infinite loop the other end of which would be back on Lexington passing the starting point. For half the potential starting addresses, one would primarily drive backwards on one way streets.

Let's hope the directions recipient is walking the 1 to 4 blocks East if that means a Westbound car traffic only street. If in a section with an infinite loop, who's the ideal character to be a victim of Cueball's perverse joke? I have seen a real GPS route away from the destination, where driving across a creek would be required to follow bad GPS routing. 06:34, 3 January 2013 (UTC)

This is the most bizarrely incomprehensible passage I've ever read. Hats off to you sir. 22:30, 10 November 2015 (UTC)

I would have thought that Randall meant the town of Lexington, Massachusetts, since he is lives in this area, and there's a Munroe Cemetery. The problem is the lack of highways mentioned, and the definition of number in the sense of highway designation. For instance, if I see a highway designated 2A, I can no longer assume that the highway number is decimal, but does that mean hexadecimal? does that mean I must interpret all highway numbers as hexidecimal, and determine their prime-ness from there? The other problem is the 'named after a president' - Assuming this is restricted to the USA, does this apply only to popular designations, or any name, however long forgotten about? because, looking at the map of Lexington, you will see that there are NO highways named after presidents. Oh, the worries. 18:34, 4 January 2013 (UTC)

  • It says "street named for a president", not "highway named for a president". And Lexington, Massachusetts, does have an Adams Street and a Grant Street, as well as a Taft Avenue, a Coolidge Avenue, and possibly others. However, Cueball's directions imply that the street has to be named for the president to qualify, as opposed to being named for someone else with the same last name. (There must be some cities with "Clinton Street"s that were named for Vice President George Clinton, Governor DeWitt Clinton, or someone else other than Bill Clinton.) -- 07:09, 5 January 2013 (UTC)

Or maybe those *are* directions to a store to buy a GPS... 20:58, 4 January 2013 (UTC)

I am sincerely amazed that multiple fans of xkcd, having found this page and wished to participate in the discussion, demonstrated such serious comprehension issues with the simple directions in the comic. (Or maybe their sarcasm sailed over my head? This is the internet, after all...) One (presumably) mis-read the prime-number prohibition as applying to numbered streets instead of highways; the other misinterpreted the exclusion of streets named for presidents as referring to highways. In both cases they spent time considering how the directions given would apply in the real world, and composing their comments here -- where the actual comic and the text transcript are right here on the page! -- without, it seems, realizing their mistakes. This suggests that even the apparently-simple directions in the comic were not sufficiently simple after all... or, perhaps, that humans are worse at directions than we thought. — 14:54, 3 April 2013 (UTC)

Arguably, the directions are ambiguous in text form. As you suggest, they could be validly parsed as "take every left that doesn't put you on a (prime-numbered highway) or (street named for a president)", or they could be understood as "take every left that doesn't put you on a prime-numbered (highway or street) named for a president. In the first parsing, the listener should avoid (prime-numbered highways) and (streets named for a president). In the latter, the listener should avoid (highways and streets) which are both prime-numbered and named for a president. The lack of an indefinite article between "or" and "street" leaves both options open. If the directions had been "take every left that doesn't put you on a prime-numbered highway or **a** street named for a president", the second parsing would not be correct. Fortunately, when spoken aloud, the intended parsing is clear by whether there is a short pause between "highway" and "or". 19:31, 22 January 2016 (UTC)

I came here to discover what's wrong/significant about prime numbered highways and streets named after presidents, LOL! Like if prime numbered highways tend to lead out of town or something else I never noticed. But seeing a complete lack thereof in either the explanation or the comments, I guess that means these are just peculiarities which make these directions work, that taking every left would guide you onto such a highway and such a street which would take you the wrong way. While I fully agree with the previous commenter about the potential ambiguity introduced by how you parse the sentence, not only does it seem like it's meant to be parsed as two separate exceptions, but also that combining BOTH prime numbered AND presidents' names seems to be getting ridiculously specific, LOL! After all, highways will TEND to only have numbers, and streets will TEND to only have names. I also note that it's unlikely Cueball is meant to be messing with this person, leading them the wrong way, as if that were the case this would probably be Black Hat instead. - NiceGuy1 05:18, 27 January 2016 (UTC) I finally signed up! This comment is mine. NiceGuy1 (talk) 06:08, 9 June 2017 (UTC) All but one prime number is odd. Odd interstates go north/south. Therefore, all but one prime interstate highways go north/south. I hope this answered your question.

He missed the perfect opportunity to use Black Hat calling a person who lives on Roosevelt Street. 09:26, 15 August 2017 (UTC)