# 2217: 53 Cards

53 Cards |

Title text: Well, there's one right here at the bottom, where it says "53." |

## Explanation

In this comic, Cueball claims that he has found a way to manipulate a 52-card deck into a 53-card deck by shuffling and rearranging the cards, presenting a complex-looking diagram to support his claim. Ponytail naturally disputes the claim immediately, which Cueball counters by challenging Ponytail to prove that his math is wrong.

The comic is a satire of the way that conversations tend to go between physicists and perpetual motion enthusiasts (or cranks in general). Perpetual motion is the idea that it could be possible for a mechanical system to work indefinitely without any external input of energy. The laws of thermodynamics absolutely prohibit this, so the only way that this could be possible is if the laws of thermodynamics are wrong. Unfortunately, the laws of thermodynamics are some of the most foundational and well-tested laws in science, so perpetual motion is considered to be a pseudoscience, pursued only by ignorant or quixotic cranks.

One of the things that you could do with a perpetual motion machine is to violate the law of conservation of energy - that is, you could create free energy out of nothing, simply by building a mechanical device. This is likely what Randall is satirizing with the idea of a process that can generate an extra card out of nowhere - it makes no physical sense, but nonetheless Cueball is convinced that he has found a way to do it.

A common defense employed by pseudoscientists, when challenged on their ideas, is to issue a counter-challenge and demand people prove them wrong, as Cueball does in this comic. This is a fallacious line of argument, since the fact that Ponytail cannot prove Cueball wrong does not mean that he is right. Nonetheless, this aggressive defense often works to discourage argument, since it takes far less effort to make a claim than to refute it.

Possibly, Cueball's plan involves usage of the Banach-Tarski paradox, a mathematical theorem which describes a method of "dismantling" a solid sphere, rearranging the component pieces, and reassembling them into two solid spheres identical to the original. This is only possible in a mathematical ideal case, because the "component pieces" are actually dense sets of points; every neighborhood, however small, contains points of multiple pieces. Such a procedure cannot be performed on playing cards, which are discrete (zooming far enough into a single card, you get a neighborhood containing only that card and no others). Cueball's operations of shuffling and rearranging are analogous to the operations used in the Banach-Tarski operation, which involves only moving and rotating the component pieces without changing their shape. The Banach-Tarski paradox was also referenced in 804: Pumpkin Carving.

In the title text, Ponytail responds to Cueball's challenge with snark, claiming that the most obvious error is the fact that the formula's result is "53". The implication is that his math results in the wrong *answer*, which is proof that the calculations must contain errors. This, of course, starts with the assumption that Cueball's claimed result is impossible, rather than attempting to find the flaws in his specific method. Because most people would conclude, by basic physical reasoning, that merely shuffling and rearranging a deck of cards cannot increase the number of cards in the deck, that feels like a safe assumption. By analogy, increasing the amount of energy in a system only by moving and transferring energy should be equally impossible, on its face.

## Transcript

- [Cueball and Ponytail are standing next to a flowchart, with Cueball gesturing to it.]:
- Cueball: I've found a way to turn a 52-card deck into 53 cards by shuffling and rearranging them.
- Ponytail: No, you haven't.
- Cueball: How do you know?! I challenge you to find an error in my math!

- [The flow chart consist of 15 boxes of different sizes, connected with arrows. In four of them (top, bottom and two in the middle) a deck of card is shown. Next to the top and bottom a number is written, near the other two, which are the only round boxes, numbers are shown in one of the nearby boxes instead. Beneath the top box there are two boxes with readable text. The other 7 boxes, without numbers or card decks have unreadable text. From top to bottom are the readable content:]
- 52
- Shuffle
- Cut
- 21
- 38
- 53

- [Caption below the panel]:
- Every conversation between a physicist and a perpetual motion enthusiast.

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# Discussion

"This page was last edited [tomorrow]." Okay, good to know. Tomorrow starts three hours from now, my time. This comic reminded me of this article: https://arstechnica.com/science/2019/10/corkscrewing-bouncy-ion-drive-would-provide-thrust-in-different-universe/ 172.68.38.88 00:44, 19 October 2019 (UTC)

I can do this, but my flowchart would be different and involve secretly inserting a joker, using the shuffling as cover for the move. Collect a deck of 52 cards and have a spectator count the cards. - Secretly hide a joker from the deck in your off-hand (the one without the deck). - Shuffle the cards, letting the hidden card drop on top of the deck. - Keep shuffling, so the inserted joker is well mixed into the deck. - Have a spectator count the cards, looking only at the backs. - 53. Nutster (talk) 04:56, 19 October 2019 (UTC)

Actually this is also what encryption scientists have to face talking to not so few encryption enthusiasts who just invented their own encryption method162.158.234.112 07:01, 19 October 2019 (UTC)

- Ohg V unir na haornnoyr pvcure! 162.158.158.253 13:52, 19 October 2019 (UTC)
- The difference is that those "own excryption methods" usually work ... not well, but at least little. Now, the algorithms which claim to compress ANY input to smaller size, those tend to be suspicious ... -- Hkmaly (talk) 22:15, 19 October 2019 (UTC)

Wait, isn't perpetual motion (w.r.t. a inertial reference frame) possible, at least according to Newtonian mechanics? Just launch something into space at high enough speed and "watch" it wander away forever. Extracting (an unbounded amount of) energy from that object is a totally different story... --162.158.234.94 10:11, 19 October 2019 (UTC)

- Not really, as even in vacuums particles randomly come into existence. Eventually enough would be in the path to slow it to a stop. 162.158.62.151 17:37, 19 October 2019 (UTC)
- Not in Newtonian mechanics. Those random particles are result of quantum physics - and in quantum physics, EVERYTHING is possible, just unlikely (there is extremely small but nonzero probability that all particles in macroscopic object would exhibit tunneling effect moving them in same direction, for example). -- Hkmaly (talk) 22:15, 19 October 2019 (UTC)
- Even in Newtonian mechanics, the energy would be sapped from the object eventually. Space isn't completely empty. The object will occasionally hit particles that will alter its kinetic energy. Also, as it encounters gravitational fields, there will be stresses and strains in the material of the object and the objects creating the gravitational fields. As an example, think of the Earth rotating in space. It's actually slowing down because of the tidal effect caused by the Moon. Some of the rotational energy is being imparted to the Moon, but some of it is let as heat through friction from the movement of tides. Jeremyp (talk) 13:39, 22 October 2019 (UTC)

- Not in Newtonian mechanics. Those random particles are result of quantum physics - and in quantum physics, EVERYTHING is possible, just unlikely (there is extremely small but nonzero probability that all particles in macroscopic object would exhibit tunneling effect moving them in same direction, for example). -- Hkmaly (talk) 22:15, 19 October 2019 (UTC)
- Vacuum fluctuation (particles), i.e. quantum weirdness, cannot cause trouble. This is because all working QFT, where these vacuum fluctuations appear, take as assumption the strict local conservation of energy-momentum 4-vector, which is the generalisation of what our OP is asking about. This is a fundamental backbone of all modern physics, not just Newtonian mechanics, and the only known violation is in cosmology. Needless to say, when we talk about perpetual motion machines, we have to start by omitting this trivial class. That is, we do not call systems that achieve perpetual motion by exploiting the conservation of linear or angular momentum alone, as perpetual motion machines. Some machines of that form that convert the energy and momentum from one part to the other could be a perpetual motion machine, because in those cases it is possible for the efficiency of conversion to be imperfect, in which case it will always practically be imperfect, leading to the eventual failure. Luckily, on Earth and in practice, there is no need to be careful, because even the linear or angular momentum special case, would be interacting with air---the best vacuum we can get, are still not perfect; it is not perfect even in actual space outside Earth. It just doesn't exist anywhere. 162.158.165.118 20:49, 21 October 2019 (UTC)
- Uhhh, and what about
*Ptolemaic*Mechanics? SOMETHING is keeping the spheres rotating. Seems Randall hasn't really thought this comic through. Someone should challenge him to prove that his comic is true in all idealistic conceptions of the real world. (Please sign off, and make edits separate from others'.)- This was a reply to earlier comments. Randall's comic stands funny as-is. 162.158.166.125 19:25, 26 October 2019 (UTC)

- Uhhh, and what about

Getting a 53 card deck from a 52 card deck is easy. First, cut the deck twice. Then, shuffle all parts together; be sure to suffer thoroughly. Finally, take off the top 5 cards, sneak in the Joker on the bottom while nobody's looking, and put the five cards at the "middle". Because of skewed philosophy, you will have gotten a 53 card deck!162.158.122.186

“The amount of energy necessary to refute bullshit is an order of magnitude bigger than to produce it.” -Alberto Brandolini Menoshe (talk) 22:03, 19 October 2019 (UTC)

Note that while it shouldn't be possible to obtain energy from nowhere, there ARE methods which makes hard to find where the energy comes from, and some may be useful (say, perhaps as a new kind of battery?). Also, anything involving not-completely-understood phenomena, like black hole for example, might actually generate energy from source we don't know about yet (parallel universe or something like that). Meanwhile, lot of theoretical designs of perpetual motion machines without working prototype only contain steps which can't possibly get energy anywhere and are completely useless ... -- Hkmaly (talk) 22:15, 19 October 2019 (UTC)

- Black hole physics are one of the best understood. No part of understanding them requires parallel universes. The thing that is really a headache in General Theory of Relativity is that we still do not have a good, localised, way to express the energy stored in the gravitational field. Landau-Lifshitz pseudo-tensor is proved to be unique given the assumptions, but starts with a subtraction of the matter stress-energy tensor, and violates precisely this comic---it says that some gravitational wave situations don't carry away energy, when in fact we know those have to carry away energy. Better defined notions, like ADM energy, are global energy, not localised energy, so that we do not know what they mean, practically. However, even though we are still not fully understanding what mathematical quantity would correctly map to gravitational field energy in the theory, we still do know that it has to be gravitational field energy, and that it has nothing to do with parallel universes. Just to hammer down the singular mistake in your nice comment. 162.158.165.118 21:01, 21 October 2019 (UTC)

In the picture it seems that he cuts the cards into a pile of 21 cards and 38 cards (thus making 59 cards) I'm sure that helps his argument (or he can't count.

- Yeah, I noticed that mismatch too!

Actually, I interpreted the "cut" as referring to that one old trick where rectangular objects (usually banknotes) would be cut in half and then rearranged with small pieces missing, making one more object than there used to be. This of course would not be a case of "rearranging and shuffling".

(If you're wondering why this doesn't work for*actual*banknotes, that's because the existence of serial numbers makes this trick far harder, and the*repeated*serial numbers on most modern notes make it effectively impossible. But back in the 19th century this actually used to be a problem.) --172.69.54.33 19:26, 21 October 2019 (UTC)

Perpetual motion is so easy that we've already done it. The universe isn't going to stop expanding anytime soon, afterall. Also, Voyager (and some other space probes). Everything is perpetual motion in space at solar escape velocity until/unless it hits something. 162.158.214.88 18:35, 20 October 2019 (UTC)

- This case is by definition excluded from the discussion of perpetual motion. See above for my longer version on it. 162.158.165.118 21:03, 21 October 2019 (UTC)

You can always rearrange the matter making up the 52 cards, into 53 smaller cards. 108.162.212.17 19:21, 20 October 2019 (UTC)

It's easy to prove, using the Banach-Tarski theorem Cellocgw (talk) 12:39, 21 October 2019 (UTC)

- If you show me how to dissolve the cards into subatomar theoretical dots by shuffling, I agree. --Lupo (talk) 13:36, 21 October 2019 (UTC)

Sigh... I really don't like having to keep challenging Kynde, who I believe is a well-intentioned contributor... but as soon as I saw the rewritten explanation with confusing phrasing and broken English, I knew that it was him who did it, and honestly... it just makes the article worse. It's harder to read and comprehend, contains irrelevancies, and swings between explanatory points incoherently. It was, honestly, okay as it was (specifically this version). I don't really know what to do about it. I'm of the "be bold in making edits" school of wiki-ing, but I don't want to just flush away other people's well-meant contributions. Hawthorn (talk) 15:01, 21 October 2019 (UTC)

Unfortunately, plenty of physicists make the same mistake, losing sight of the fact that math is only a model that must conform to reality, a-la Zeno's Paradox. That's how you end up with silly claims of "if you can [go faster than light] [travel through a wormhole between two distant points in an expanding universe] you'll go backward in time". Or how about the pseudoscience of explaining failed models by assuming that there must be "dark" matter or energy, instead of acknowledging that the model, itself, must be fundamentally wrong the way an actual scientist would. — Kazvorpal (talk) 16:53, 21 October 2019 (UTC)

- What are the chances that the global scientific community, who are setup to attack each other to win funding, would require outsiders to tell them that dark matter and dark energy are indications that their models are "fundamentally wrong"? It just goes to show how rarely you talk to scientists. Cosmologists are always apologising for not knowing what dark energy is, treating them only as the cosmological constant (other alternatives are always explored, but none offer significant improvements upon cosmological constant simplicity). But the dark matter situation already merit a few observational wins, and are starting to look more and more like postulating neutrinos, which is a winning precedent. For two examples, firstly, we have observed localised dark matter causing gravitational lensing. Secondly, we see some galaxy collisions that have dark matter in the wrong place due to the collisions. These evidences are enough to convince most astrophysicists that the basic picture seems correct. Other than this, you should also work on understanding more about how theory and experiment interact in physics, before commenting more upon the matter. 162.158.165.118 21:17, 21 October 2019 (UTC)
- You fail to understand: Even if something eventually turned up that they could claim is the equivalent of dark energy or matter, it would be an accident, and change nothing about how anti-scientific they had been. The methodology they use is not only wrong, but essentially identical to that used by advocates of the geocentric model when prosecuting Galileo. Dark matter and energy are epicycles and deferents, ridiculous tweaks to models that fail to naturally match observation. Any model that can't hold up to the simplest, barely-scientific benchmark of simply matching observation naturally is a failure. Any adjustments made are a departure from its fundamental premises. At that point it might as well be astrologers tweaking star sign analyses. — Kazvorpal (talk) 01:26, 22 October 2019 (UTC)
- Well, do
*you*have a model that matches reality better than what we have? Please enlighten us. Even the geocentric model matched observations and was regarded as ok for a few centuries until we got a better model. Since we don't have a better model, we should try to find evidence or otherwise for the model/s we currently have. 162.158.158.213 (talk)*(please sign your comments with ~~~~)*

- Well, do

- You fail to understand: Even if something eventually turned up that they could claim is the equivalent of dark energy or matter, it would be an accident, and change nothing about how anti-scientific they had been. The methodology they use is not only wrong, but essentially identical to that used by advocates of the geocentric model when prosecuting Galileo. Dark matter and energy are epicycles and deferents, ridiculous tweaks to models that fail to naturally match observation. Any model that can't hold up to the simplest, barely-scientific benchmark of simply matching observation naturally is a failure. Any adjustments made are a departure from its fundamental premises. At that point it might as well be astrologers tweaking star sign analyses. — Kazvorpal (talk) 01:26, 22 October 2019 (UTC)

- What part of "Cosmologists are always apologising for not knowing what dark energy is" do you not understand? That you have a fundamental lack of understanding what the scientific method says upon such conundrums does not mean that you are correct, or that the scientific community should abandon ship and all go ape nuts. You also show your ignorance by trying to link the dark duo to Galilean trials, for they are different in fundamental ways. Not least that scientists today are openly asking for outside ideas to give a better description of dark energy and entertaining all promising leads, as opposed to the closed-minded "Earth isn't moving" of Galilean trials.

- The actual Galilean trials were an unholy trinity of a) paradigm shift b) leading questions style biasing via unnatural restriction of focus c) doctrinal dangers. A paradigm shift is already exceedingly difficult to bridge the conversational gap, but importantly, at the time, people believed that celestial mechanics behaved differently from earthly mechanics, whereas Galileo's strongest arguments come from pointing out that Aristotelian mechanics and Ptolemy's cosmology had to be abandoned and unified into one complete mechanics. Their narrowing of scope only to celestial mechanics is thus already biasing them into a failure mode that they were ill-equipped to understand.

- This cannot be compared with the issue today, because opponents of dark matter are free to work on modifications to Newtonian/Einsteinian gravity (MoND), or others. There is neither a paradigm shift, nor indoctrination at play, nor ad hoc separation of concerns. Now, physical theories are allowed to have some free parameters, as long as not so many as to eliminate the possibility of predictions. It is thus telling that dark matter is wildly successful compared to MoND in its predictive powers---we even know that the dark matter cannot be hot type, i.e. not neutrinos, for example, and must be cold dark matter. They also move normally according to Einsteinian gravity, so no shenanigans. These show that the dark matter scheme is scientific and totally could be used to kill off dead ends. Like your ridiculous ignorance, that obviously failed to see how your own argument about "Even if something eventually turned up" already failed the neutrino test, which was why I brought it up the last time around. Leave science to the professionals and stop repeating stupidities---we know everything you are talking about, and have analysed them to be of negative value. 172.69.134.93 20:00, 26 October 2019 (UTC)

Well, since it's a non-closed system that is receiving energy... and matter is just solidified energy... :) I'm going to say that Cueball is right so long as his flowchart also contains a StarTrek replicator somewhere. 172.68.90.64 20:08, 21 October 2019 (UTC)SiliconWolf

Where's the Banach–Tarski reference! There should totally be an earth-shattering Banach–Tarski reference. 162.158.58.219 21:36, 21 October 2019 (UTC)

- I agree. Reading this comic led me to google for Banach-Tarski, even if it wasn't mentioned by name. Saibot84 03:25, 23 October 2019 (UTC) -- Saibot84 (talk)
*(please sign your comments with ~~~~)*

Agreed: There should totally be some sort of Axiom of Choice joke here as well. 172.68.70.34 (talk) *(please sign your comments with ~~~~)*

See also Sam Loyd's "Get Off The Earth" puzzle (and similar illusions where shifting pieces of a larger picture changes the number of objects by redistributing pieces of each one). -- SteveMB (talk) *(please sign your comments with ~~~~)*

Something, something, infinite chocolate 162.158.166.109 (talk) *(please sign your comments with ~~~~)*

Fairly sure if I put enough pressure when forcing cards together I can create additional cards by cutting one down the center (splitting the face and the back) 172.68.174.22 20:56, 7 November 2019 (UTC)

I feel like the present explanation misses the mark a bit.

The thing about magnets and electricity and water and levers and marbles and so on is that we understand these things and we understand how they shuffle energy around - these things can be accurately and precisely described by the laws of physics we have and are deeply familiar with and have thoroughly tested. If you know how shuffling, cutting, and rearranging playing cards works, then you can prove, mathematically, that shuffles and rearrangements cannot create or destroy cards ... and if you know how Newtonian mechanics, quantum mechanics, general relativity, and so on work, then you can prove, mathematically, that no machine described by these laws can create or destroy energy.

Historically, however, essentially all proposed perpetual motion machines - all over-unity free-energy machines - propose to function using magnets, electricity, water, levers, marbles, and so on. In fact, these machines are often described *by their proponents* using the very equations of Newtonian physics and the like; their proofs attempt to use, like Cueball does with playing cards in the comic, understood operations from theories where energy is conserved to create new energy. We know how shuffling a deck of cards work and we know how moving a magnet through a coil of wires work, and neither of these operations can do what they are claimed to do in the way they are claimed to do it.

And yes, when challenged, the proponents will demand their critic find the error in their proof. But the fact that the theory says 52 cards at the top and 53 cards at the bottom when *everything between* is shuffles and cuts and rearrangements is proof enough that something is wrong, because you can't make new cards or new energy by shuffling the stuff you already have around. Packbat (talk) 12:42, 4 June 2021 (UTC)

Convert one of the cards into a unit sphere, invoke the axiom of choice and apply Barach Tarski Paradox to transform it into two spheres, then reverse the first step to get two cards. Arachrah (talk) 19:54, 8 April 2022 (UTC)