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Re: 1155: "Kolmogorov Directions"

Posted: Thu Jan 03, 2013 11:48 pm UTC
by shpoffo
phlip wrote:To answer the inevitable question: this is from Kolmogorov complexity, which is the idea that a message that can be produced by a very short algorithm is simpler (and contains less information) than a message that requires a much longer algorithm to generate (ie a message that cannot be compressed well). Our protagonist in the comic has found a route for the other character to take which can be compressed very well, so it has low Kolmogorov complexity - as the description he gives is much shorter than a full list of directions. Of course, there's a difference between being well-compressed and being useful...


Thanks, when I first read the title (and was more-amused than normal) I thought of the Kolmogorov scale in fluid dynamics, where turbulence is characterized by the dissipation of viscose kinetic energy as heat. Super-super-small turbulence that is awash in background 'noise' (condensed matter regime)

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 3:01 am UTC
by Rotherian
danix wrote:MX always conjures Mexico for me. Which made me crosseyed when Macromedia started selling some weird MX versions of their stuff. I always wondered why Flash was getting a "Mexican" edition ... Flash MX. :lol:


So.....

The Mexican Missile?

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 3:31 am UTC
by da Doctah
bmonk wrote:She lives in a small, semi-rural subdivision, with a "Scorpion Drive" as well as "Scorpion Circle". They meet at one point, and Scorpion Drive, but not the Circle, meets itself.

When I was in college, the nearby town of Tyrone, New Mexico belonged to the Phelps Dodge copper-mining company and only employees of PD could own homes there. Some genius decided to commemorate the company's bread-and-butter by naming all the streets of Tyrone after copper-bearing minerals.

So if you had to visit your friend whose father worked in the mine, you might get directions like:

From Copper, turn left on Chrysocolla, past Chalcocite to make a right on Cuprite. Then bear left at Chalcopyrite, and it's right on the corner where Malachite turns into Tenorite.

Anyone who wasn't a geologist gave up after the first turn.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 9:39 am UTC
by orthogon
Hairy wrote:So what would people think if they heard the initials S.F. or A.L.? Asssuming that you know that it's a geographical location?

A.L. doesn't ring any bells as a location. However somebody I know has a mug plugging some presumably long-forgotten corporate initiative known as the "Occupational Risks Advice Line", which they have abbreviated to "AL" and used the strapline "Ask AL". Why they didn't use the full acronym is beyond me.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 2:50 pm UTC
by brenok
Hairy wrote:So what would people think if they heard the initials S.F. or A.L.? Asssuming that you know that it's a geographical location?


As a brazilian I'd think S.F. was referring to the city of San Francisco and AL the brazilian state of Alagoas. If I saw A.L. in a strict english language context, I admit I would have no idea of what it stands for.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 3:09 pm UTC
by PolakoVoador
brenok wrote:
Hairy wrote:So what would people think if they heard the initials S.F. or A.L.? Asssuming that you know that it's a geographical location?


As a brazilian I'd think S.F. was referring to the city of San Francisco and AL the brazilian state of Alagoas. If I saw A.L. in a strict english language context, I admit I would have no idea of what it stands for.


And I thought I would be the first brazilian to bring up Alagoas for AL. :P

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 3:26 pm UTC
by endolith
danix wrote:That's SOP over here (Mexico). In fact, the cashier him/herself will actually ask for the higher amount:


Happens in the USA all the time, too. Not sure why anyone would find this odd.

My approach is to get rid of any change in my pockets as quickly as possible, dumping it into a bucket that I take to my bank's coin-counting machine every few years.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 5:43 pm UTC
by omgryebread
Pfhorrest wrote:But in all honesty my post was mostly motivated by an ongoing peeve about people who live near large cities assuming the whole world revolves around their city, referring to it as "THE" City, and anyone who doesn't live in such a city as being "in the country" (as though smaller cities don't count as cities at all); or as seemed to be the case here, assuming local landmarks within their big city are the more likely referents for a name simpliciter (without further geographical identifiers) than a whole other, much larger referent somewhere further away.
In most cases, this makes sense. Most people's conversations tend to be mostly among people from the same area. I would never say, "I'm visiting a friend in the Brooklyn neighborhood of Baltimore", ever. Another Baltimorean is not going to assume I'm talking about Brooklyn, NY, even though that's more famous. Likewise, except for the immediate suburbs of Maryland's few other cities, there's rarely reason to assume "the city" isn't Baltimore or D.C. It can get amusing: Frederick is a mediumish city, but usually not thought of as urban Maryland, since it's slightly outside of the D.C./Baltimore metropolitan area. Or the somewhat hilarious "Upstate New York", a region consisting of the vast majority of the state.

In most cases, this makes sense. If someone asked for directions from Lexington, I'd probably start giving them directions from Lexington Ave or Lexington Market in Baltimore, unless I had reason otherwise. If I did ask this question of all my friends, I'd likely be very annoying and they'd stop hanging out with me. (Alleviating me of the need to give directions, I suppose.)

This heuristic fails online, of course, but it's not an unreasonable mistake.

Anyway, I assumed Lexington, MA, because I tend to forget there are states not bordering an ocean.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 5:55 pm UTC
by freezeblade
omgryebread wrote:...I tend to forget there are states not bordering an ocean.


I make this mistake all the time.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 6:13 pm UTC
by Davidy
thenonsequitur wrote:
TeddyB wrote:Has anyone actually tried to work out where these directions end you up (assuming it's in NYC)?


My first thought when I saw this question was "well, it depends on where on Lexington they are". But then it occurred to me that it doesn't matter, because there are only three possibilities.

Lexington Avenue in Manhattan runs south from 131st street down to 21st. Most east-bound intersections with Lexington (i.e. left turns off Lexington) are just numbered streets that go east to 3rd. So from most places on Lexington these directions will just have you take next east-bound numbered street over to 3rd avenue (some of these street numbers are prime, but none of them are highways). From 3rd avenue (prime, but not a highway), going back north, you will take the first available left turn onto another numbered street (as far as I know, none of these have a second name that is a president's name, but even in that case you'd just take the numbered street after that), and finally another left back on to Lexington. Rinse, lather, repeat. So from most places these directions will just have you circling a nearby block infinitely.

But there are a couple exceptions. If you start somewhere between 21st (the bottom of Lexington) and 22nd street, the only way to go when you hit 21st is right because it's a one-way street. From there you'll take the first left onto Broadway, then a left onto 20th, then a left onto Park, then back onto 21st. Alas, once again you'll just be infinitely circling a nearby block.

The other exception is if you start somewhere between 131st (the top of Lexington) and 128th street. This is much more interesting. From this stretch, you'll be taking the first left onto 128th at which point there are no left turns available, forcing you to turn right at the end of 128th, going down 2nd avenue. From here you'll take the first left onto 127th street, which will lead you around a turn and merge you into the end of 125th (aka Martin Luther King, Jr. Boulevard, which, many would perhaps would say unfortunately, is not the name of a president), heading east. This street ends up immediately merging into Harlem River Drive, which shortly thereafter merges into FDR drive (interestingly but irrelevantly, this is a highway named after a president), heading south. All the exits off FDR are to the right, however, so you'll take FDR all the way down to the bottom of Manhattan before it finally merges onto South Street Viaduct heading west. The turns into the Battery Park Underpass turning you left beneath battery park and merging with West Street, so you wind up heading up north on the west side of Manhattan. From there you'll take the first left onto Albany street and from there a left onto the outer edge of a tangled web of streets which are all named Esplanade (really). You'll follow this street down for a while and finally end up navigating a series of lefts in the tangled web of Esplanade streets until you wind up in a repeating loop. So in the end you find yourself on the southwest tip of Manhattan, circling Robert F Wagner Jr Park forever.

EDIT: Pfhorrest posted his response while I was composing this one. I had no idea where Randall lives, so I just went with the question as asked, doing it for NYC. As for Lexington, MA, for *that* you'll obviously need more information, as that is an entire town and not just a relatively short stretch of avenue.

The numbered streets in your example are hardly "highways" as described in the directions. This would seem to eliminate NYC as the location. In my own experience, I never hear of a roadway being mentioned without its type (road, avenue, street, etc) being affixed, unless it is already part of the conversation. Thus, "How do I get to Logan Road?" "Where on Logan do you live?" The original question asking for directions about "Lexington" does not imply prior discussion of a Lexington Road (Avenue, Boulevard, etc) and therefore the logical assumption is that Lexington is a geographical location.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 6:35 pm UTC
by exoren22
MakingProgress wrote:
LtPowers wrote:Only if the maze is two-dimensional and the entrance and exit are both along the outer wall.


Anyone have an example of a two-dimensional maze with the entrance or exit not along the outer wall ?

Image
DAMN how do I resize images??

This would be interesting in real-life

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 6:39 pm UTC
by Klear
exoren22 wrote:
MakingProgress wrote:
LtPowers wrote:Only if the maze is two-dimensional and the entrance and exit are both along the outer wall.


Anyone have an example of a two-dimensional maze with the entrance or exit not along the outer wall ?

[BIG DAMN IMAGE]
DAMN how do I resize images??

This would be interesting in real-life


Ironically, the left/right hand approcha works for that one =)

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 6:40 pm UTC
by brenok
But you can solve this maze only using the "right hand" rule.

Edit: ok, ninja'd

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 6:42 pm UTC
by Pfhorrest
omgryebread wrote:This heuristic fails online, of course, but it's not an unreasonable mistake.

It's specifically that failure which I'm complaining about. In a preestablished geographic context of course everything makes perfect sense. My complaint is about people who either forget that the internet is not limited to their locale and they're chatting with people all around the world (annoying because stupid), or who assume that the rest of the world places the same prominence on things as they would in a context not centered around them and their location (annoying because arrogant). I'll gladly say "I'm going downtown, brb" to my friends around the world in a chat, and there it's clear that I mean the center of wherever urban area I happen to be nearest to. But I would hesitate to ask for directions even from my rather unique (in the English-speaking world) city name without also specifying the state (in the process making clear that I mean a city and not a street or something), just because for all I know there might be another one somewhere or someone may just have no idea where that is. If there was a much more prominent location which also shared the same name, I would be even more cautious. And unless someone already knew what city I lived in, I would never expect anyone to understand where "The City" was (and in any context I'm likely to use it, it would refer to the area within the formally incorporated city boundaries of whatever location previously established in context, differentiating only from the unincorporated areas surrounding it but likely sharing the same name).

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 7:14 pm UTC
by dudiobugtron
Klear wrote:
exoren22 wrote:
MakingProgress wrote:
LtPowers wrote:Only if the maze is two-dimensional and the entrance and exit are both along the outer wall.


Anyone have an example of a two-dimensional maze with the entrance or exit not along the outer wall ?

[BIG DAMN IMAGE]
DAMN how do I resize images??

This would be interesting in real-life


Ironically, the left/right hand approcha works for that one =)

Here's a not-very-hard maze which you can't use a hand-rule for.

maze.png
No left-hand-rule for this maze

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 7:25 pm UTC
by mathmannix
OK, I'm trying this. I'm just going to use Google Maps and an address I made up - 65 Munroe Road, Lexington, Mass.

Left on Munroe (not named after a President!). Left on Woodcliffe. Left on Spring. Left onto unnamed road (uh-oh...). Left onto unnamed road. Left onto unnamed road which dead-ends. U-turn (left) at end.
Left onto unnamed road. Left onto Hayden Ave. (whew!)
Left onto Waltham. Left onto Marrett. Left onto Grassland St. Left onto Payson street. Left onto Bridge, which dead ends. U-turn (left). Left to stay on Bridge. (Left onto dead-end Valleyfield, then back to Bridge.) Left onto Waltham again.
(Endless loop!)

OK, that didn't work. Hurt by lack of Presidents, apparently!

Hmmm... maybe I'm going about this the wrong way. Lexington, MA has streets named Washington, Adams, Lincoln, Grant, Hayes, Roosevelt, Taft, probably some others. And Franklin if we're doing first names too. Cambridge has a Wilson, Madison, ... OK that's not going to work either. Would you count Hancock? He was President of the Continental Congress, although that's more like Speaker of the House today.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 10:13 pm UTC
by prosfilaes
Pfhorrest wrote:Assuming Lexington Ave in NYC, or even Lexington, MA, seems parochial when there is the much more nationally prominent Lexington, KY to be the more obvious referent.


Much more nationally prominent? The 63rd largest city in the US, versus the city it's named after that had the first battle of the American Revolution and thus should be known to every American? I'd say it's at best a toss up.

Re: 1155: "Kolmogorov Directions"

Posted: Fri Jan 04, 2013 10:23 pm UTC
by Coyne
Pfhorrest wrote:(I'm curious, for the person who said Alberta, Canada; is that ever written with the periods like that? I would expect it to always be "AL").

Not sure if the earlier message said AL, but the normal abbreviation for Alberta is "AB".

I suspect that somewhere deep down there is coordination between the US and Canada on this, to avoid conflicting abbreviations. We have "AK" for Alaska, so in principle, "AB" would be a workable abbreviation for Alabama, just as "AL" would be workable for Alberta. The fact that these do not collide suggests coordination.

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 3:43 am UTC
by Rotherian
mathmannix wrote:OK, I'm trying this. I'm just going to use Google Maps and an address I made up - 65 Munroe Road, Lexington, Mass.

Left on Munroe (not named after a President!). Left on Woodcliffe. Left on Spring. Left onto unnamed road (uh-oh...). Left onto unnamed road. Left onto unnamed road which dead-ends. U-turn (left) at end.
Left onto unnamed road. Left onto Hayden Ave. (whew!)
Left onto Waltham. Left onto Marrett. Left onto Grassland St. Left onto Payson street. Left onto Bridge, which dead ends. U-turn (left). Left to stay on Bridge. (Left onto dead-end Valleyfield, then back to Bridge.) Left onto Waltham again.
(Endless loop!)

OK, that didn't work. Hurt by lack of Presidents, apparently!

Hmmm... maybe I'm going about this the wrong way. Lexington, MA has streets named Washington, Adams, Lincoln, Grant, Hayes, Roosevelt, Taft, probably some others. And Franklin if we're doing first names too. Cambridge has a Wilson, Madison, ... OK that's not going to work either. Would you count Hancock? He was President of the Continental Congress, although that's more like Speaker of the House today.


Ahem.

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 6:14 am UTC
by Pfhorrest
Rotherian wrote:
mathmannix wrote:OK, I'm trying this. I'm just going to use Google Maps and an address I made up - 65 Munroe Road, Lexington, Mass.

Left on Munroe (not named after a President!).


Ahem.


Wrong vowel. Monroe is a president. Munroe is a cartoonist.

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 6:26 am UTC
by Davidy
dudiobugtron wrote:
Klear wrote:
exoren22 wrote:
MakingProgress wrote:
LtPowers wrote:Only if the maze is two-dimensional and the entrance and exit are both along the outer wall.


Anyone have an example of a two-dimensional maze with the entrance or exit not along the outer wall ?

[BIG DAMN IMAGE]
DAMN how do I resize images??

This would be interesting in real-life


Ironically, the left/right hand approcha works for that one =)

Here's a not-very-hard maze which you can't use a hand-rule for.

maze.png


I don't think this, in its entirety, is a maze. You have a structure within a square with two openings, within another square with one opening, within another square with one opening. The actual maze is three levels down, and it does meet the right hand solution.

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 11:19 am UTC
by orthogon
Davidy wrote:I don't think this, in its entirety, is a maze. You have a structure within a square with two openings, within another square with one opening, within another square with one opening. The actual maze is three levels down, and it does meet the right hand solution.

I had believed for decades that you could get out of any maze with a hand rule. Yet it's obvious now that it will only work if the walls are contiguous, which isn't the case for dudiobugtron's structure. But I can't stomach the suggestion that dudiobugtron's structure isn't a maze at all, at least in the everyday language sense. I suspect a circular argument whereby a maze is defined as something you can solve with a hand rule.

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 6:30 pm UTC
by RobIrr
On directions, I remember one memorable occasion where I was told the property I was looking for was "half way" along a road. Seemed OK until I reached that point, and realised I had no idea of how long the road I was on was going to be, and thus, no idea of where the half way point was ...

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 7:43 pm UTC
by dudiobugtron
orthogon wrote:
Davidy wrote:I don't think this, in its entirety, is a maze. You have a structure within a square with two openings, within another square with one opening, within another square with one opening. The actual maze is three levels down, and it does meet the right hand solution.

I had believed for decades that you could get out of any maze with a hand rule. Yet it's obvious now that it will only work if the walls are contiguous, which isn't the case for dudiobugtron's structure. But I can't stomach the suggestion that dudiobugtron's structure isn't a maze at all, at least in the everyday language sense.

In any maze where there is a start and finish on the outside wall, there is necessarily a path between the two which chops the walls of the maze into at least two disconnected parts. I don't thing 'contiguity of walls' should be a defining part of what it is to be a maze, otherwise the only mazes would be ones with a central finish point.

I suspect a circular argument whereby a maze is defined as something you can solve with a hand rule.

Looks that way!

Re: 1155: "Kolmogorov Directions"

Posted: Sat Jan 05, 2013 10:20 pm UTC
by orthogon
This is a Davidyan maze, i.e. the walls are contiguous, but is non-Dudiobugtronian.
IMAG0900.jpg

Solution:
Spoiler:
IMAG0902.jpg
Left-hand-rule solution. If you insist that you have to come out of the exit, you have to go in and wriggle all around the "output" side of the maze until you get back to the exit.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 2:10 am UTC
by Elmach
Generally when one speaks of solving a maze, one assumes to stay inside the maze.

Unless this is an example of why one of the arguments above is wrong.

EDIT: I think I get it? If a maze has contiguous walls and has the entrance and exit on the outer walls, then the only solution is to go around the maze? (which of course works with left-hand/right-hand technique because we know that the entrance and exit are in the same region and that the walls are contiguous, therefore the left/right-hand technique ends up in a loop.)

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 2:59 am UTC
by Rotherian
Pfhorrest wrote:
Rotherian wrote:
mathmannix wrote:OK, I'm trying this. I'm just going to use Google Maps and an address I made up - 65 Munroe Road, Lexington, Mass.

Left on Munroe (not named after a President!).


Ahem.


Wrong vowel. Monroe is a president. Munroe is a cartoonist.


Good catch. In my defense, I was posting under the influence of a combination of cyclobenzaprine, zolpidem, furosemide, tramadol, and divalproex (all prescribed for around bedtime), so my thinking was a bit fuzzy.

tl;dr - mea culpa.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 3:30 am UTC
by da Doctah
Rotherian wrote:I was posting under the influence of a combination of cyclobenzaprine, zolpidem, furosemide, tramadol, and divalproex (all prescribed for around bedtime), so my thinking was a bit fuzzy.


Dude, I am so never playing Scrabble with you!

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 4:27 am UTC
by Rotherian
da Doctah wrote:
Rotherian wrote:I was posting under the influence of a combination of cyclobenzaprine, zolpidem, furosemide, tramadol, and divalproex (all prescribed for around bedtime), so my thinking was a bit fuzzy.


Dude, I am so never playing Scrabble with you!


1. Proper nouns are generally discouraged in Scrabble, so I wouldn't be able to use them.

2. Even if they were allowed, the only ones I could see being able to be used are zolpidem (either having a single letter in common crosswise to an existing letter, or on either side of pi or id), furosemide (on either side of rose or semi, tramadol (either single crosswise with an existing letter, or on either side of ram, mad, or ado), or divalproex (appended to the end of diva or on either side of pro) - which, come to think of it is most of them.

3. I hardly ever score more than 400 points in Scrabble, which is probably on the low end of those that frequent xkcd.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 5:13 pm UTC
by da Doctah
Rotherian wrote:
da Doctah wrote:
Rotherian wrote:I was posting under the influence of a combination of cyclobenzaprine, zolpidem, furosemide, tramadol, and divalproex (all prescribed for around bedtime), so my thinking was a bit fuzzy.


Dude, I am so never playing Scrabble with you!


1. Proper nouns are generally discouraged in Scrabble, so I wouldn't be able to use them.

2. Even if they were allowed, the only ones I could see being able to be used are zolpidem (either having a single letter in common crosswise to an existing letter, or on either side of pi or id), furosemide (on either side of rose or semi, tramadol (either single crosswise with an existing letter, or on either side of ram, mad, or ado), or divalproex (appended to the end of diva or on either side of pro) - which, come to think of it is most of them.

3. I hardly ever score more than 400 points in Scrabble, which is probably on the low end of those that frequent xkcd.


And you could do cyclobenzaprine wrapped around an existing lobe, zap, and an isolated e, suitably placed, on top of which you'd get the bonus for clearing your rack; I know people who pull rabbits like that all the time.

Did you ever google oxyphenbutazone? Yes, there are hits for its use in pharmaceutical contexts, but the "I'm feeling lucky" response talks about how it's believed to be the highest-possible scoring play in Scrabble using the standard dictionaries.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 7:15 pm UTC
by exoren22
OK, so no one has come up with the easy, short solution, assuming a path through the maze from start to finish exists?

Spoiler:
Place a hand (I'm a leftie) on a wall, and follow it. If you come back to a previous spot, put your other hand on the opposite wall, and follow that. Repeat process as necessary.


Edit: Of course, I said the solution is short, executing it, however, may take a while.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 7:35 pm UTC
by orthogon
Elmach wrote:Generally when one speaks of solving a maze, one assumes to stay inside the maze.

Unless this is an example of why one of the arguments above is wrong.

EDIT: I think I get it? If a maze has contiguous walls and has the entrance and exit on the outer walls, then the only solution is to go around the maze? (which of course works with left-hand/right-hand technique because we know that the entrance and exit are in the same region and that the walls are contiguous, therefore the left/right-hand technique ends up in a loop.)

Yes, I think so. To be honest, I'm not quite sure what point I was making. Possibly that dudiobugtron's excellent observation:
dudiobugtron wrote:In any maze where there is a start and finish on the outside wall, there is necessarily a path between the two which chops the walls of the maze into at least two disconnected parts.

... is strictly only true if the maze is solveable, which I'm sure dudiobugtron was taking as axiomatic. My maze (if a maze it is) had a start and finish on the outside wall but there wasn't a path between the two, hence the walls could be contiguous (but didn't have to be). And I was quite tickled by the idea of going around the outside, on the basis that nobody said you couldn't, especially since the left-hand rule takes you that way.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 9:56 pm UTC
by Davidy
orthogon wrote:
Davidy wrote:I don't think this, in its entirety, is a maze. You have a structure within a square with two openings, within another square with one opening, within another square with one opening. The actual maze is three levels down, and it does meet the right hand solution.

I had believed for decades that you could get out of any maze with a hand rule. Yet it's obvious now that it will only work if the walls are contiguous, which isn't the case for dudiobugtron's structure. But I can't stomach the suggestion that dudiobugtron's structure isn't a maze at all, at least in the everyday language sense. I suspect a circular argument whereby a maze is defined as something you can solve with a hand rule.


If you had a maze set up in your living room, would your front door and the four walls of the room, plus any other doors, count as part of the maze? If you find a cornfield maze, is the gate in the fence surrounding the maze also part of the maze? As René Descartes said immediately before he disappeared, I think not. Dudiobugtron's structure is a maze contained within three fences/rooms. Drawing lines and calling it a maze doesn't make it a maze. It would seem that you would consider a square or circle with a hole cut into the wall to be a maze.

Re: 1155: "Kolmogorov Directions"

Posted: Sun Jan 06, 2013 11:19 pm UTC
by dudiobugtron
Davidy wrote:If you had a maze set up in your living room, would your front door and the four walls of the room, plus any other doors, count as part of the maze? If you find a cornfield maze, is the gate in the fence surrounding the maze also part of the maze? As René Descartes said immediately before he disappeared, I think not. Dudiobugtron's structure is a maze contained within three fences/rooms. Drawing lines and calling it a maze doesn't make it a maze. It would seem that you would consider a square or circle with a hole cut into the wall to be a maze.


If drawing lines and calling it a maze doesn't make it a maze, what does make it a maze?

Are any of these three things a maze? (Use the inline scroll bar to see all three)

maze2.png
Mazes
maze2.png (8.16 KiB) Viewed 4046 times


If not, why not? If some of them are, and others aren't, why? What's the difference?

Rotherian wrote:3. I hardly ever score more than 400 points in Scrabble, which is probably on the low end of those that frequent xkcd.

400 points is pretty high for me!!! I don't think I've ever gotten that high.

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 4:43 am UTC
by Davidy
dudiobugtron wrote:
Davidy wrote:If you had a maze set up in your living room, would your front door and the four walls of the room, plus any other doors, count as part of the maze? If you find a cornfield maze, is the gate in the fence surrounding the maze also part of the maze? As René Descartes said immediately before he disappeared, I think not. Dudiobugtron's structure is a maze contained within three fences/rooms. Drawing lines and calling it a maze doesn't make it a maze. It would seem that you would consider a square or circle with a hole cut into the wall to be a maze.


If drawing lines and calling it a maze doesn't make it a maze, what does make it a maze?

Are any of these three things a maze? (Use the inline scroll bar to see all three)

maze2.png


If not, why not? If some of them are, and others aren't, why? What's the difference?



Both Wikipedia and Websters define mazes as a complex, elaborate and confusing series of branching passages through which the solver must find a route. Your first two examples are labyrinths with a single through route and no branches. Your third example is a maze with two dead end branches. A labyrinth is topologicaly equivalent to a tube; a maze is topologicaly equivalent to a tube with branches.

I answered your questions; you did not answer mine. Want to give it a try?

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 4:51 am UTC
by phlip
So, how complex, elaborate and confusing does it have to be to count as a maze? Should we set the threshold at, say, 25 milliPrimers, or is that too high?

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 6:06 am UTC
by Steve the Pocket
danix wrote:That's SOP over here (Mexico). In fact, the cashier him/herself will actually ask for the higher amount:

Bill is $64.
*Danix shows a $100 bill*
Cashier: Do you have the $4?
Danix: Sure!
*Danix pays $104*
*Cashier gives $40 in two $20 bills*

Ta-da!

Which is why the Dilbert strip ends up being hilarious. The higher amount method is common in places where cash registers aren't always available, because it's easier to calculate/get change. With a cash register, you just put in the higher amount and it'll do the math for you anyway! :lol:
bmonk wrote:You mean normal people don't do this? I do it to reduce the spare change I have in my pocket to a reasonable minimum.

This wasn't something obvious like $10.03 for a $7.53 order or something; it was the sort of pair of figures where at first glance you'd have no clue what the connection was supposed to be and think he was trolling or something. I think the difference turned out to be some dollars and a quarter, since all three digits were different and there was some carrying involved. Like $5.83 and $11.08 for example.

danix wrote:MX always conjures Mexico for me. Which made me crosseyed when Macromedia started selling some weird MX versions of their stuff. I always wondered why Flash was getting a "Mexican" edition ... Flash MX. :lol:

Way off topic, but I was severely disappointed that I never saw any software released in 2010 with the extremely-cool designation "MMX".

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 7:04 am UTC
by dudiobugtron
Davidy wrote:
dudiobugtron wrote:
Davidy wrote:If you had a maze set up in your living room, would your front door and the four walls of the room, plus any other doors, count as part of the maze? If you find a cornfield maze, is the gate in the fence surrounding the maze also part of the maze? As René Descartes said immediately before he disappeared, I think not. Dudiobugtron's structure is a maze contained within three fences/rooms. Drawing lines and calling it a maze doesn't make it a maze. It would seem that you would consider a square or circle with a hole cut into the wall to be a maze.


If drawing lines and calling it a maze doesn't make it a maze, what does make it a maze?

Are any of these three things a maze? (Use the inline scroll bar to see all three)

maze2.png


If not, why not? If some of them are, and others aren't, why? What's the difference?



Both Wikipedia and Websters define mazes as a complex, elaborate and confusing series of branching passages through which the solver must find a route. Your first two examples are labyrinths with a single through route and no branches. Your third example is a maze with two dead end branches. A labyrinth is topologicaly equivalent to a tube; a maze is topologicaly equivalent to a tube with branches.

I answered your questions; you did not answer mine. Want to give it a try?

Sure, although the question wasn't aimed at me. My maze was complex and branching, it just had some parts to it which weren't complex. But so does every maze. It seemed like you just didn't like the bits that were obviously unconnected. Is it the obviousness of it which you have an issue with? or the disconnectedness?

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 10:37 am UTC
by -is
Hehe. The way from my aunt's place to my Grandfather's place was like that, only simpler:
Turn right on even-numbered turns, left on odd.

Re: 1155: "Kolmogorov Directions"

Posted: Mon Jan 07, 2013 10:42 am UTC
by -is
Arariel wrote:
Davidy wrote:An example of extreme simplicity in directions for solving a very complicated problem is in finding ones way through a maze - simply continue walking, keeping your right hand on a wall and you will eventually reach the exit.

A maze with walls that form a square somewhere within it (or other close-ended shape). You put your right hand on it, you'll walk around in a circle.


To be exact: the right (or left) hand rule only works for mazes that are (graph-theory) trees (that is, interconnected and loop-free). It's not guaranteed to work for forests that are not trees (loop-free but not interconnected), neither for graphs that aren't loop-free. (But if you start at the exit to begin with, you can't get to the part of the wall that's not connected to the exit).

All without re-reading, so check with a textbook before you enter the pyramid.