2049: "Unfulfilling Toys"

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speising
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Re: 2049: "Unfulfilling Toys"

Postby speising » Wed May 22, 2019 10:05 pm UTC

There's nothing arbitrary about the number 27. Think about the difference between an ordinary Rubik's cube and one constructed of independent cubes.

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Re: 2049: "Unfulfilling Toys"

Postby Archgeek » Wed May 22, 2019 11:54 pm UTC

speising wrote:
Grimer11 wrote:Long-time reader, new forum user. I've been forced to create an account in these forums in order to take issue with the alt text of this comic. There are not "27 independent blocks" in a Rubik's cube. That is all.

that is true, but nobody had claimed there were. in fact, the alt text explicitly says they didn't make it.

Wait, how many are there, then? 20, with the six face centers being paired off together about the central hub?
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Re: 2049: "Unfulfilling Toys"

Postby rmsgrey » Thu May 23, 2019 12:34 am UTC

Grimer11 wrote:
speising wrote:
Grimer11 wrote:Long-time reader, new forum user. I've been forced to create an account in these forums in order to take issue with the alt text of this comic. There are not "27 independent blocks" in a Rubik's cube. That is all.

that is true, but nobody had claimed there were. in fact, the alt text explicitly says they didn't make it.


I understand that but it's a (very common!) failure in logic to think there are 27 blocks on a Rubik's cube and the alt-text clearly infers this. Had the author intended an arbitrary number of blocks (as you claim) he wouldn't have used the oft-incorrectly guessed number of blocks on a Rubik's cube, he would have instead used a seemingly random number like 20 or 30.


Normally, I wouldn't nitpick this, but since you created your account solely to nitpick badly...

* It's not clear that the alt-text deduces that there are 27 blocks in a Rubik's cube (nor does it imply it).
* speising did not claim that the author intended an arbitrary number of blocks. He didn't even suggest it.

The alt text says that they were going to do a falling-apart [equivalent of a] Rubik's cube that was just [some number of] independent blocks stuck together with magnets. To make something that looks like a Rubik's cube, but which is actually made of independent blocks, the natural choice would be to make it out of 27 unit cubes, with 26 unit cubes as a secondary option. Making it out of 20 unit cubes and one cross-shaped center piece, while more true to an actual Rubik's cube, would be a less natural choice for a joke one.

Archgeek wrote:Wait, how many are there, then? 20, with the six face centers being paired off together about the central hub?

There are 21 pieces - 8 corners, 12 edges, and 1 piece consisting of the six central facelets with a connecting structure to hold them together.

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Flumble
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Re: 2049: "Unfulfilling Toys"

Postby Flumble » Thu May 23, 2019 1:02 pm UTC

Sidenote: the blocks of a normal rubik's cube are not only dependent because you have to rotate 9 of them at a time, but also because there are 12 separate permutation groups. For example, there's no way to twist a rubik's cube and end up with just one corner rotated wrongly. And that's not even considering putting on the stickers wrongly, e.g. having a white-yellow edge where white and yellow are opposite faces.

Speaking of, that could make for an interesting 27 independent blocks puzzle: just arrange the magnets and colours in such a way that there is only 1 (or a few) solution(s).
Wait, that's not what Randall meant with the title text, is it? I thought he meant just 27 identical magnetic blocks. But that's hardly "really cool", unless making non-cube-shaped things with the blocks qualifies.

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Re: 2049: "Unfulfilling Toys"

Postby Reka » Thu May 23, 2019 2:22 pm UTC

Grimer11 wrote:I understand that but it's a (very common!) failure in logic to think there are 27 blocks on a Rubik's cube and the alt-text clearly infers this.

I don't think the alt-text does any such thing. Yes, an actual Rubik's cube has 26 blocks, not 27, because the center one is replaced by the rotating mechanism. But a hypothetical magnetic cube could, hypothetically, have a block in the center, with magnets on its sides to hold the assembly together.

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Re: 2049: "Unfulfilling Toys"

Postby Pfhorrest » Thu May 23, 2019 3:30 pm UTC

The title of this comic keeps making me think of small dildos.
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Re: 2049: "Unfulfilling Toys"

Postby Grimer11 » Thu May 23, 2019 5:37 pm UTC

You all make very good points and I can appreciate you coming to the author's defense from all sorts of clever angles.

However, I'm stubborn, and I refuse to believe that it wasn't a failure of logic. I simply came on here to try to educate the author that there are actually only 26 faces on a Rubik's cube because clearly he did a quick back-of-a-napkin maths, as most people do, thinking 9 faces times 3 is 27 instead of thinking a little deeper and coming to the actual amount of faces.

Regardless, we're arguing about what someone else was thinking which is pointless because you can't ever really know. We're going to need a ruling from the man himself! I'd wager a small fortune if he came on to weigh in and he were being truthful he would admit that he just off-hand assumed there was 27 without giving it more than 2 seconds thought. That is all I'm trying to say.

Edit to say: Reka -
I don't think the alt-text does any such thing. Yes, an actual Rubik's cube has 26 blocks, not 27, because the center one is replaced by the rotating mechanism. But a hypothetical magnetic cube could, hypothetically, have a block in the center, with magnets on its sides to hold the assembly together.


If author said that was their intention and where the 1 extra piece came in I would accept that.

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Flumble
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Re: 2049: "Unfulfilling Toys"

Postby Flumble » Thu May 23, 2019 8:15 pm UTC

Grimer11 wrote:I simply came on here to try to educate the author that there are actually only 26 faces on a Rubik's cube because clearly he did a quick back-of-a-napkin maths, as most people do, thinking 9 faces times 3 is 27 instead of thinking a little deeper and coming to the actual amount of faces.

Actually there are 6*9=54 faces on a rubik's cube*. And I refuse to believe you simply used the wrong word (like you did with "amount[sic] of faces"). :mrgreen:


*Not counting all the partial faces that are hidden when the cube is in cube shape ...or all the tiny faces I drew on those faces. Really, how can you call those blocks "cubies" and not give them all derpy faces?

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orthogon
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Re: 2049: "Unfulfilling Toys"

Postby orthogon » Fri May 24, 2019 11:55 am UTC

Grimer11 wrote:
speising wrote:
Grimer11 wrote:Long-time reader, new forum user. I've been forced to create an account in these forums in order to take issue with the alt text of this comic. There are not "27 independent blocks" in a Rubik's cube. That is all.

that is true, but nobody had claimed there were. in fact, the alt text explicitly says they didn't make it.


I understand that but it's a (very common!) failure in logic to think there are 27 blocks on a Rubik's cube and the alt-text clearly infers this. Had the author intended an arbitrary number of blocks (as you claim) he wouldn't have used the oft-incorrectly guessed number of blocks on a Rubik's cube, he would have instead used a seemingly random number like 20 or 30.


But the object that the alt-text describes would (or at least could) have 27 blocks. (Sorry, wasn't up to date when I hit "Reply").

What I'm not clear about is whether there's an arrangement of north- and south-poles and soft iron that works.
xtifr wrote:... and orthogon merely sounds undecided.

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Flumble
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Re: 2049: "Unfulfilling Toys"

Postby Flumble » Fri May 24, 2019 1:00 pm UTC

orthogon wrote:What I'm not clear about is whether there's an arrangement of north- and south-poles and soft iron that works.

If you're okay with losing the freedom of placing any block anywhere, all you need is 13 blocks (edges and the center) with souths pointing outwards and 14 blocks (corners and face centers) with norths pointing outwards (or vice versa). Otherwise you'll need an octagon of north and south poles on each face to support 4 orientations for any two faces. (If you imagine one magnet lying on the middle of a face, an opposing face (i.e. a copy rotated 180° in 3d space) has its mirror image, so it has a north pole where the original had its south pole and vice versa. And so will any symmetrical arrangement of magnets and notably any rotational symmetry. So 4 magnets in a circle will give you clingy faces at 4 orientations.)

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Re: 2049: "Unfulfilling Toys"

Postby rmsgrey » Fri May 24, 2019 2:00 pm UTC

Grimer11 wrote:You all make very good points and I can appreciate you coming to the author's defense from all sorts of clever angles.

However, I'm stubborn, and I refuse to believe that it wasn't a failure of logic. I simply came on here to try to educate the author that there are actually only 26 faces on a Rubik's cube because clearly he did a quick back-of-a-napkin maths, as most people do, thinking 9 faces times 3 is 27 instead of thinking a little deeper and coming to the actual amount of faces.

Regardless, we're arguing about what someone else was thinking which is pointless because you can't ever really know. We're going to need a ruling from the man himself! I'd wager a small fortune if he came on to weigh in and he were being truthful he would admit that he just off-hand assumed there was 27 without giving it more than 2 seconds thought. That is all I'm trying to say.

Edit to say: Reka -
I don't think the alt-text does any such thing. Yes, an actual Rubik's cube has 26 blocks, not 27, because the center one is replaced by the rotating mechanism. But a hypothetical magnetic cube could, hypothetically, have a block in the center, with magnets on its sides to hold the assembly together.


If author said that was their intention and where the 1 extra piece came in I would accept that.

If you made a 3*3*3 cube out of unit cubes, you'd use 27 cubes.

You could make a visually identical hollow cube out of 26 cubes by omitting the (entirely hidden) center cube.

An actual Rubik's cube has 54 coloured facelets distributed between 21 pieces, 20 of which very loosely resemble cubes, but the title text implies that the fake cube doesn't have a piece equivalent to the central spindle piece.

If Randall simply said "A Rubik's cube is a 3*3*3 cube, that would be 27 individual cubes" then that's still not a failure of logic. Including or omitting the invisible central cube is a choice, not a question of logic.

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Re: 2049: "Unfulfilling Toys"

Postby Grimer11 » Fri May 24, 2019 9:12 pm UTC

Flumble wrote:
Grimer11 wrote:I simply came on here to try to educate the author that there are actually only 26 faces on a Rubik's cube because clearly he did a quick back-of-a-napkin maths, as most people do, thinking 9 faces times 3 is 27 instead of thinking a little deeper and coming to the actual amount of faces.

Actually there are 6*9=54 faces on a rubik's cube*. And I refuse to believe you simply used the wrong word (like you did with "amount[sic] of faces"). :mrgreen:


*Not counting all the partial faces that are hidden when the cube is in cube shape ...or all the tiny faces I drew on those faces. Really, how can you call those blocks "cubies" and not give them all derpy faces?


Bahaha sigh.. not faces. ! +1 for you. I assume you drew the same face on the same color (6 different face variations) or did you manage to draw 54 different variations of faces, one for each block face? That would be impressive.

rmsgrey wrote:If you made a 3*3*3 cube out of unit cubes, you'd use 27 cubes.

You could make a visually identical hollow cube out of 26 cubes by omitting the (entirely hidden) center cube.

An actual Rubik's cube has 54 coloured facelets distributed between 21 pieces, 20 of which very loosely resemble cubes, but the title text implies that the fake cube doesn't have a piece equivalent to the central spindle piece.

If Randall simply said "A Rubik's cube is a 3*3*3 cube, that would be 27 individual cubes" then that's still not a failure of logic. Including or omitting the invisible central cube is a choice, not a question of logic.


Maybe "Failure of Logic" is too harsh a term. I chose that phrase because asking someone how many blocks (not faces! haha) are on a standard Rubik's cube is akin to questions that you might find on an IQ test that aim to deduce to what degree you can logically think through a problem. If you chose B) 27 instead of D) 26 then that was your logical reasoning failing.

Is 'Randall' the author of xkcd? I need to find out how we can ask him what he was thinking directly. :D

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Re: 2049: "Unfulfilling Toys"

Postby rmsgrey » Fri May 24, 2019 9:44 pm UTC

Grimer11 wrote:Maybe "Failure of Logic" is too harsh a term. I chose that phrase because asking someone how many blocks (not faces! haha) are on a standard Rubik's cube is akin to questions that you might find on an IQ test that aim to deduce to what degree you can logically think through a problem. If you chose B) 27 instead of D) 26 then that was your logical reasoning failing.

Is 'Randall' the author of xkcd? I need to find out how we can ask him what he was thinking directly. :D


But 26 is also wrong. A Rubik's cube is 21 pieces. Or, if you count the rotating center facelets on each face as separate pieces, then a Rubik's cube would be 27 rigid pieces (20 cubies and the central spindle made up of a central piece and 6 rotating facelets - plus some springs which are non-rigid)


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