2891: Log Cabin

2024-02-08T17:06:01Z

162.158.166.6: /* Explanation */

{{comic
| number = 2891
| date = February 7, 2024
| title = Log Cabin
| image = log_cabin_2x.png
| imagesize = 353x265px
| noexpand = true
| titletext = I'm sure the building inspectors will approve my design once they finally manage to escape.
}}

==Explanation==
{{incomplete|Created by a TRAPPED BUILDING INSPECTOR APPROXIMATELY PI - HEY, COME BACK H! METERS TALL- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

[[File:log_cabin_golden_spiral.png|thumb|301px|Golden spiral (approximately) overlaid on the floor plan]]

This is a comic featuring a {{w|floor plan}}, presumably of a {{w|log cabin}}, and a pun on the word "log". The odd part about it is the right half, which appears to be infinitely recursive copies of the building, a self-similar {{w|fractal}}. The house as a whole represents a {{w|golden rectangle}} with a side ratio of the {{w|golden ratio}} (phi = 0.5 + (1.25 ^ 0.5) ≈ 1.6180339887...), with successively smaller living areas (further subdivided into rooms, to a common but shrunken and rotated plan) being square adjoined by a golden-rectangle of all smaller living areas in the manner of the areas defined by the classic {{w|Golden spiral}} diagram. The joke is that Randall is intentionally conflating the word "log" in the common phrase "log cabin," where "log" refers to the wood the cabin is made of, with a {{w|logarithmic spiral}}, as "log" is shorthand for "logarithm".

Every square subunit of the premises consists of a main combined kitchen/lounge area, with an adjoining shower-equipped bathroom, and a hallway leading to a closet and two bedrooms (a double-bed one with en-suite bath-equipped bathroom, and another with a single bed; both having suitable walk-in closet space). Between the kitchen and the dining table is the door that serves as the entry into the next inwards level of the floorplan.

A visitor can also walk in a spiral by using the doors in the building plan.

In the title text, Randall says that he is confident that building inspectors will approve the design of his log cabin, assuming they can escape. As one moves deeper into the infinite spiral of architecture, the entire log cabin ''seems'' to be a denser labyrinth of rooms and hallways.

It is unknown how the inspectors lost in the inner rooms would shrink in the same ratio, and would only have to head out through the last door they walked in through (or two, if they're currently in the en-suite) and then exit each 'main' area in turn until they exited the building itself. If they have any trouble at all (other than rescaling themselves), it would be that there is ''always'' a further inward area that they might consider needs exploring to fulfil their inspection routine. This construction could imply folded spacetime. To perform a correct inspection, the inspectors might need sufficient relation that inner rooms are identical to the outer rooms, and to solve algebraic equations for various parameters.

In any case, though, they would not need to physically enter the floorplan in order to approve the ''design'', so any risk of getting 'lost' would come solely from a psychological inability to break off from the infinite recursion. Approval of ''construction'' would be a different matter. Whether the floorplan could genuinely be infinitely recursive would depend on how Randall has presented it. Typically, these would be submitted as static images (as it is in the comic), in which case at some point there would be insufficient resolution to continue the recursion, effectively ending in a solid pillar. Randall, however, perhaps channeling his inner Black Hat, may have used a program that dynamically generates further levels as you zoom in to the image.

Alternatively, this may imply that the repetition continues outside of what is drawn here, continuing to grow larger as it moves further out. However, the apparent presence of external windows on the first four iterations, but no internal ones (and therefore no equivalent windows on the subsequent iterations) somewhat belies that possibility. In fact, the first iteration has windows on the 'southern' edge, for the single bedroom and seating area, for which there are no equivalents on any of the other iterations.

[https://www.generations-quilt-patterns.com/log-cabin-quilt-block.html Log Cabin] is also a classic quilting block, which starts with a tiny square and spirals outwards.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A drawing of the top view of a log cabin, which includes two beds, a kitchen, a bathroom and furniture. A smaller version of the log cabin is connected to the main building. An even smaller version is connected to the smaller version, and so on, forming a golden rectangle.]

:[Caption below the panel]:
: Log cabin

{{comic discussion}}

[[Category:Engineering]]
[[Category:Math]]
[[Category:Puns]]

Talk:2891: Log Cabin

2024-02-08T16:58:14Z

162.158.166.6:

:: "''The odd part about it is the bottom right corner, which appears to be infinitely recursive copies..''"
The whole right side is the left side, shrunk and recursed. Each iteration rotated 90 degrees. The 'shrink' is about 1.616 by my squint, a lot like a "[https://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]" LOGarithmic spiral, as NickM says. [[User:PRR|PRR]] ([[User talk:PRR|talk]]) 19:49, 7 February 2024 (UTC)

::This is a LOGarithmic spiral [[Special:Contributions/172.70.210.103|172.70.210.103]] 19:52, 7 February 2024 (UTC)NickM

:: It is precisely the golden ratio, assuming the left side is a square [[User:Terdragontra|Terdragontra]] ([[User talk:Terdragontra|talk]]) 22:09, 7 February 2024 (UTC)

Assuming a standard 36" wide front door, then the next "front" door would be 22.27 inches, then 13.78 inches, then 8.53 inches, at which point I doubt the inspector could squeeze through it, though I guess they could still take a peek inside the next recursion. [[Special:Contributions/172.68.34.58|172.68.34.58]] 20:57, 7 February 2024 (UTC)

Infinite bedrooms, infinite baths, close to schools and shopping. [[Special:Contributions/172.69.247.48|172.69.247.48]] 21:00, 7 February 2024 (UTC)
::Government: Your property tax comes up to infinite dollars. --[[Special:Contributions/172.71.26.160|172.71.26.160]] 21:45, 7 February 2024 (UTC)

Interesting comparison with the archetypal "labyrinth". It's actually a fractal version that only avoids being unicursal-with-no-dead-ends due to the off-living-room private spaces being quite trivial offshoots. Which arguably makes it ''fairly'' classical in nature. [[Special:Contributions/172.70.90.114|172.70.90.114]] 21:18, 7 February 2024 (UTC)

Should there be a mention that due to the limitations of the image format, it only actually achieves eight iterations? Which makes sense given that construction materials also have limits, and is still enough that the inspectors might be a bit confused if they don't pay close enough attention. [[Special:Contributions/172.69.60.216|172.69.60.216]] 23:21, 7 February 2024 (UTC)

Write it [https://www.explainxkcd.com/wiki/index.php?title=2891:_Log_Cabin&diff=prev&oldid=334498 how you want], I just wanted to avoid calling a room with no bath (but a shower) as a "bathroom", especially when I was mentioning a 'bathroom' with an actual bath in it so soon after. Not that there's a completely unambiguous term for the room with the toilet/lavatory/whatever in it. (For reference, for me it's "the toilet", despite that also being the porceline item itself, and even that is derived from a hairdressing cloth, through a string of euphemisms. But knew that wouldn't be accepted by the wider readership.) [[Special:Contributions/172.70.85.26|172.70.85.26]] 01:49, 8 February 2024 (UTC)
:In the USA, any room with a toilet and sink is typically called a "bathroom" whether or not there is a literal bath within. [[Special:Contributions/172.70.131.3|172.70.131.3]] 09:33, 8 February 2024 (UTC)
::Don't think it's particularly a US/UK thing - it's pretty commonly called a 'bathroom' in the UK too. I think the point of the editor above was the potential for confusion between the ''two'' 'bathrooms', and how to avoid it.[[Special:Contributions/172.69.43.243|172.69.43.243]] 09:44, 8 February 2024 (UTC)
:Using a language that allows to say "Sh*thouse" in a nice way (praised be the diminutive!) helps in such cases...[[User:Tier666|Tier666]] ([[User talk:Tier666|talk]]) 10:15, 8 February 2024 (UTC)
::There is a {{wiktionary|Thesaurus:bathroom|truly astounding range of terms}}, in English alone, (and I can think of several not included there, even discounting the rather localised overly-vulgar ''or'' overly-polite ones). [[Special:Contributions/172.70.90.221|172.70.90.221]] 11:38, 8 February 2024 (UTC)
Are there any non-Euclidean geometries in which you could fit this house without having to shrink the rooms or the people? [[Special:Contributions/172.68.3.44|172.68.3.44]] 16:42, 8 February 2024 (UTC)

One way to build this would be with robotics that alter the structure as the visitor moves, like a holodeck. This could give the perception of the visitor shrinking forever, and the robotics wouldn’t let them leave until they rewalked their entry path. Another way would be to just make the rooms get too tiny to enter and hide the missing ones around a corner. [[Special:Contributions/162.158.166.6|162.158.166.6]] 16:58, 8 February 2024 (UTC)

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2891: Log Cabin

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