explain xkcd - User contributions [en]

2956: Number Line Branch

2024-07-10T03:50:12Z

172.70.251.170: added other phi

{{comic
| number = 2956
| date = July 8, 2024
| title = Number Line Branch
| image = number_line_branch_2x.png
| imagesize = 469x235px
| noexpand = true
| titletext = Attention all passengers: This is an express sequence to infinity. If your stop is not a power of two, please disembark now.
}}

==Explanation==
{{incomplete|Created by a SECOND BOT TO REDUCE CONGESTION - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic likens the {{w|number line}} to a line of a railroad or subway system. These often have branches where different trains continue on to a different destination, with different stops along the way. In the number line, one branch (presumably the original) contains ordinary numbers, while the newly opened branch consists of some completely different numbers, denoted with various symbols as an analogue to those we use as digits. The branches seem to split at π. The new branch proceeds slightly more quickly than the traditional numerical branch.

The new numerals look a bit like characters from non-Latin alphabets:
* The first numeral looks like the Brahmi letter "𑀩" (ba).
* The 2nd numeral has no obvious analogue, but it looks a bit like the Tifinagh Letter "ⵎ" used in the Berber languages, a backwards version of the Phoenician letter "yod" (𐤉), or a sideways π.
* The 3rd numeral looks like the Phoenician letter "qoph" (𐤒) or the Greek Phi (φ, Φ).
* The 4th numeral looks like the Aramaic letter Ṭēth, written as "𐡈" in its ancient form.
* The 5th numeral looks like the uppercase Greek character "delta" (Δ).

Putting these 5 phonemes together gives a word that sounds a bit like "bisect," which is what mathemeticians have done to this number line, splitting it into two.

The sequence ending with a bold mark at Δ (whereas the original number line fades out) suggests that it is the end of this branching sequence. Mathematicians, apparently, could only afford to construct 5 additional numbers, or their research hasn't yet found other numbers.

The title text makes a parallel between a train stopping at a station and a numerical sequence "stopping" at a number – that is, taking it as a value. It's a spoof of announcements that are typically made on trains, so that riders can confirm that they're on a train that goes to their desired station; an "express train" typically makes fewer stops so it can serve the most popular stops and reach its final destination sooner. In this case, the express train only stops at powers of 2; presumably the "local" stops at every integer. Powers of 2 are 2, 4, 8, 16, 32, and so on, such that the interval between stops grows exponentially larger.
* Mathematically, an express train like this would get to its scheduled stops much faster, but it would not actually have any fewer stops overall. Mathematicians that study infinities generally regard all "countably" infinite sets as being the same "size." Infinity is not a fixed value, rather it's the concept of "does not end," so it's paradoxical to try to take a train to a destination that is, by definition, not a single destination. By way of analogue, it's akin to promising to stop hitting your little brother only after you've done so forever.

A fictional number was previously shown in [[899: Number Line]] ("gird"), and fictional ''numerals'' were shown in [[2206: Mavis Beacon]]. And similar treatment of mathematics as public infrastructure was seen in [[2735: Coordinate Plane Closure]].

In the Boston area, where Randall lives, the subway does not run express (unlike NYC), but some commuter trains do run express. For example, the Worcester-to-Boston line has an express train that departs Union Station in Worcester and arrives at South Station in downtown Boston, significantly reducing travel time by skipping several stops.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[The number line for natural numbers, going from 0 to 10 and trailing off, with a marker at 0 to indicate that it is the start of the sequence. At about pi, the line branches off into a second line, which contains five odd-looking symbols, and stops at the fifth one. The first, below 4, is a square, the second is a pi rotated 90° counterclockwise, the third resembles a closed phi, the fourth is a spiral, and the fifth is a triangle.]

:[Caption below the panel:]
:Good news!
:After thousands of years, mathematicians have finally opened a second branch on the number line to reduce congestion.

{{comic discussion}}

[[Category:Math]]

2956: Number Line Branch

2024-07-10T03:49:26Z

172.70.251.170: added phi

{{comic
| number = 2956
| date = July 8, 2024
| title = Number Line Branch
| image = number_line_branch_2x.png
| imagesize = 469x235px
| noexpand = true
| titletext = Attention all passengers: This is an express sequence to infinity. If your stop is not a power of two, please disembark now.
}}

==Explanation==
{{incomplete|Created by a SECOND BOT TO REDUCE CONGESTION - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic likens the {{w|number line}} to a line of a railroad or subway system. These often have branches where different trains continue on to a different destination, with different stops along the way. In the number line, one branch (presumably the original) contains ordinary numbers, while the newly opened branch consists of some completely different numbers, denoted with various symbols as an analogue to those we use as digits. The branches seem to split at π. The new branch proceeds slightly more quickly than the traditional numerical branch.

The new numerals look a bit like characters from non-Latin alphabets:
* The first numeral looks like the Brahmi letter "𑀩" (ba).
* The 2nd numeral has no obvious analogue, but it looks a bit like the Tifinagh Letter "ⵎ" used in the Berber languages, a backwards version of the Phoenician letter "yod" (𐤉), or a sideways π.
* The 3rd numeral looks like the Phoenician letter "qoph" (𐤒) or the capital Greek Phi (Φ).
* The 4th numeral looks like the Aramaic letter Ṭēth, written as "𐡈" in its ancient form.
* The 5th numeral looks like the uppercase Greek character "delta" (Δ).

Putting these 5 phonemes together gives a word that sounds a bit like "bisect," which is what mathemeticians have done to this number line, splitting it into two.

The sequence ending with a bold mark at Δ (whereas the original number line fades out) suggests that it is the end of this branching sequence. Mathematicians, apparently, could only afford to construct 5 additional numbers, or their research hasn't yet found other numbers.

The title text makes a parallel between a train stopping at a station and a numerical sequence "stopping" at a number – that is, taking it as a value. It's a spoof of announcements that are typically made on trains, so that riders can confirm that they're on a train that goes to their desired station; an "express train" typically makes fewer stops so it can serve the most popular stops and reach its final destination sooner. In this case, the express train only stops at powers of 2; presumably the "local" stops at every integer. Powers of 2 are 2, 4, 8, 16, 32, and so on, such that the interval between stops grows exponentially larger.
* Mathematically, an express train like this would get to its scheduled stops much faster, but it would not actually have any fewer stops overall. Mathematicians that study infinities generally regard all "countably" infinite sets as being the same "size." Infinity is not a fixed value, rather it's the concept of "does not end," so it's paradoxical to try to take a train to a destination that is, by definition, not a single destination. By way of analogue, it's akin to promising to stop hitting your little brother only after you've done so forever.

A fictional number was previously shown in [[899: Number Line]] ("gird"), and fictional ''numerals'' were shown in [[2206: Mavis Beacon]]. And similar treatment of mathematics as public infrastructure was seen in [[2735: Coordinate Plane Closure]].

In the Boston area, where Randall lives, the subway does not run express (unlike NYC), but some commuter trains do run express. For example, the Worcester-to-Boston line has an express train that departs Union Station in Worcester and arrives at South Station in downtown Boston, significantly reducing travel time by skipping several stops.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[The number line for natural numbers, going from 0 to 10 and trailing off, with a marker at 0 to indicate that it is the start of the sequence. At about pi, the line branches off into a second line, which contains five odd-looking symbols, and stops at the fifth one. The first, below 4, is a square, the second is a pi rotated 90° counterclockwise, the third resembles a closed phi, the fourth is a spiral, and the fifth is a triangle.]

:[Caption below the panel:]
:Good news!
:After thousands of years, mathematicians have finally opened a second branch on the number line to reduce congestion.

{{comic discussion}}

[[Category:Math]]

Talk:2810: How to Coil a Cable

2023-08-03T10:08:03Z

172.70.251.170:

I don't actually know what name of 'coiling' it has, but the way I was taught to coil an AV cable (by an AV technician), and these days mostly use with long (garden-mower) power extensions, was ''maybe'' the 'quarter-turn' - though it's not a quarter, so maybe not - in finger-rotating the latest "end of loop" around the axis of the cable to leave it effectively twistless in its looped form (whilst introducing a 'one twist per loop-so-far' longitudinal twist in the still trailing unlooped cable that easily 'rolls-out' as you progress towards the free end/drag the length towards you). Done right, it's like smoothly 'drum-winding' the cable. But you ''can'' over-/under-twist the cable (especially if it has an internal/inherent twisting, like those christmas lights probably have with probably two entwined single-cores) so you may need to keep an eye on the multiloop you're forming and backtrack a bit if it looks like it's starting to figure-of-eight from the combined helical forces. But tricky to get perfect, may have a bit of a loop-twist (that only stays untangled due to it being ultimately hung on a hook). Maybe I've just not been taught the right methods by a powercord expert. [[Special:Contributions/172.70.90.20|172.70.90.20]] 19:39, 2 August 2023 (UTC)

: That first method is pretty much how I was taught by a guy with rather expensive microphone cables. It really does help the cable to last longer, since it's not stored with a twist. As a bonus, coiling a rope or extension cord this way also lets you throw it without it tangling in midair. Just make sure to hold onto/step on the non-thrown end... [[Special:Contributions/108.162.237.142|108.162.237.142]] 20:12, 2 August 2023 (UTC)

Another profession that deals with hose/cable managment is nursing (e.g. in operating room). Don't know if they have any techniques distinct from those in the mentioned professions. [[Special:Contributions/172.69.135.82|172.69.135.82]] 21:50, 2 August 2023 (UTC)

Still wondering how topology factors into this... as of this comment, there's no explanation. - [[Special:Contributions/172.70.130.234|172.70.130.234]] 22:38, 2 August 2023 (UTC)

:Probably referencing [https://en.wikipedia.org/wiki/Knot_theory Knot Theory]. [[Special:Contributions/141.101.76.97|141.101.76.97]] 23:17, 2 August 2023 (UTC)

As a sailor once explained to me, the AV method (over/under) can potentially form a clove hitch around one's ankle while on deck, hence their use of figure-8. Meanwhile, there's another technique espoused by the likes of 'Essential Craftsman' where you basically use a chain stitch to hold it all together. [[User:Nayhem|Nayhem]] ([[User talk:Nayhem|talk]]) 00:35, 3 August 2023 (UTC)

This sentence makes absolutely no sense to me:

: ''... alternating each obvious helix loop with a backhand loop (backwards helix turn) where the loop curls the same way as the other loops, but its 'helix height' is backwards ...''

I think I need an "Explain Explain xkcd"... 😕 [[User:IMSoP|IMSoP]] ([[User talk:IMSoP|talk]]) 10:03, 3 August 2023 (UTC)

See also https://people.maths.bris.ac.uk/~majge/hjce.06.pdf "Knotting probability of a shaken ball-chain" [[Special:Contributions/172.70.251.170|172.70.251.170]] 10:08, 3 August 2023 (UTC)