505: A Bunch of Rocks
|A Bunch of Rocks|
Title text: I call Rule 34 on Wolfram's Rule 34.
Cueball awakens to find himself trapped for eternity in an endless expanse of sand and rocks. At first, he uses this time to derive all of mathematics and physics, plus more, including quantum mechanics and general relativity. Next Cueball creates a computer that can process any possible function, out of rocks and rules for the interaction between rocks. He then simulates a particle followed by the interactions between particles, followed by the entire universe. The amount of time it takes to simulate the change in the universe merely from one instant to the next takes an extremely long time, as the time it takes to update just one row of rocks would be eons, assuming a realistic time to place each rock.
Cueball is using the rocks to build a cellular automaton, a computational model based on simple rules to advance from one state to the next. Certain cellular automata are Turing-complete, which means that they can be used to represent any conceivable algorithm if expanded infinitely, including simulating the physics of the universe. He specifically seems to be running Wolfram's Rule 110, which is capable of universal computation. When using Rule 110 for universal computation, one builds a background pattern, which can be seen in the comic as the pattern of smaller triangles, and then performs computation by sending out "rockets" to collide and interact with each other. Cueball can simulate the functioning of an entire universe because he has unlimited time and space (and rocks).
Cueball then apologizes for any flaws we see in the simulation. This implies that the audience is living in Cueball's simulation, making Cueball essentially God, and that he might make mistakes along the way.
The final frame cuts to a classroom where a bored student stares at his hands waiting for class to end. Cueball admonishes the student for thinking that class is lasting forever, the joke being that the boredom felt in a classroom is nothing compared to the boredom that inspires Cueball to spend his endless time toiling to keep the universe moving. Indeed, the minutes of lecture actually took many "billions and billions of millennia" for Cueball to simulate. Another possible explanation is that the entirety of this comic is a fantasy in Cueball’s mind as he zones out during a math lecture.
The title text suggests that Rule 34 should be called on Wolfram's Rule 34. Rule 34 (see 305: Rule 34) is a humorous rule of the Internet which states "If you can imagine it, there is porn of it. No exceptions." Wolfram's Rule 34 is a cellular automaton. Therefore, the title text says that either someone has made pornography featuring the cellular automaton in question, or someone has used the cellular automaton to produce pornography.
The three diagrams in the "Physics, too. I worked out the kinks..." panel are, from left to right:
- The Normal distribution of the Gaussian curve marking the points that represent a standard deviation of σ and 2σ. This is one of the fundamental building blocks of statistics. In quantum mechanics particles are viewed as inherently random, therefore the time at which a particle will decay, the position of a particle and its velocity are all calculated using similar curves. A deviation of at least σ occurs 32% of the time where a deviation of 2σ or more occurs about 5% of the time.
- The Epitaph of Stevinus, an explanation of the mechanical advantage of using an inclined plane. The inclined plane is one of the six classical simple machines, one of the fundamental building blocks of mechanical and civil engineering.
- The last graph is unknown. It may represent coupled pendulums, length contraction, or a hypothetical solution to something we haven't derived yet.
The graph that represents particle interaction is a Feynman Diagram. This shows the interaction of subatomic particles that collide and exchange some momentum via a photon. The slope of the middle line represents the distance moved and the time lost/gained during the interaction.
- [Cueball is standing in a desert with lots of rocks lying around. He is narrating his own situation. The first panel spans the entire width of the comic. The first line of text is written to the left of him, the second line to the right.]
- So I'm stuck in this desert for eternity.
- I don't know why. I just woke up here one day.
- [The next four panels take up the second line of the comic.]
- [Cueball stand in the desert.]
- I never feel hungry or thirsty.
- [Cueball walks in the desert.]
- I just walk.
- [Zooming out while Cueball continues to walk in the desert.]
- Sand and rocks
- [Zooming far out as Cueball again just stands in the desert. First line of text, above him, is a continuation of the text in the previous panel. The second line is below him.]
- stretch to infinity.
- As best as I can tell.
- [The next three panels take up the third line of the comic. The last takes up half the width.]
- [Cueball is sitting in the desert, in a contemplative position. First line of text above him the second below.]
- There's plenty of time for thinking out here.
- An eternity really.
- [Cueball is sketching stuff in the sand. First line of text above him the second below.]
- I've rederived modern math in the sand
- and then some.
- [Three different graph types are depicted. First line of text above them the second below.]
- Physics too. I worked out the kinks in quantum mechanics and relativity.
- Took a lot of thinking, but this place has fewer distractions than a Swiss patent office.
- [The next eight panels take up the fourth and fifth line of the comic. All pictures are the same size.]
- [Cueball is walking along the desert, laying out rocks on a line. Four has been deployed, he is laying down the fifth and has a sixth in his other hand.]
- One day I started laying down rows of rocks.
- [Cueball with a rock in his hand, continues to deploy rocks 16, in a more intricate pattern. There are grid-lines in the sand (5 rows, 6 columns), with each intersection either empty of filled with a rock. No rocks lay anywhere but at an intersection on the grid.]
- Each new row followed from the last in a simple pattern.
- [Zooming out showing even more laid out rocks. Cueball is seen directly from above, and we see his shadow falling on the grid of rocks (7 rows, 14 columns).]
- With the right set of rules and enough space,
- [Continues to zoom further out showing clear triangular patterns (with no rocks) in the laid out grid of rocks. Cueball is not seen. (8 rows, 42 columns). First line of text above the grid, the second line below.]
- I was able to build a computer.
- Each new row of stones is the next iteration of the computation.
- [Zooming far out (no Cueball) with rows intersected by five clear V lines on top of them. The V's are drawn inside each other, with the smallest V at the top right, and the other V's starting just to the right of the previous one, and then continuing the same distance past the previous V, as the total length of the first V. The "*" in the first line of text above this grid, references to the footnote below written in a smaller font.]
- Sure it's rocks instead of electricity, but it's the same* thing. Just slower.
- [Cueball stands in contemplative pose (on a clean white background - i.e. no dessert).]
- After a while, I programmed it to be a physics simulator.
- [A black panel with white drawings and text. A small white dot (a particle) is labeled by two arrows coming of two binary strings.]
- Every piece of information about a particle was encoded as a string of bits written in the stones.
- [A Feynman diagram showing two particles interacting. Two arrows going in and out with a snaking line between them.]
- With enough time and space, I could fully simulate two particles interacting.
- [The next two panels take up the sixth line of the comic. The second panel takes up three quarter of the width.]
- [Cueball standing before the vastness of the desert, with his programmed lines of rock stretching to infinity.]
- But I have infinite time and space.
- [A black panel with white drawings and text. Depiction of two large galaxies, one with four jets coming out of its center, the other a flat disc. Several smaller galaxies and/or stars are shown around them.]
- So I decided to simulate a universe.
- [The next four panels take up the seventh line of the comic. They are of similar widths.]
- [Cueball is walking by his grid of rocks, lines indicate he has just thrown another rock down in its place. It falls so hard it sinks into the sand that splashes out around it. The 14 rocks above him lies on the grid, four other below this grid, have not been used yet.]
- The eons blur past as I walk down a single row.
- [Zoom far far out to show multiple rows of rocks. It is not very clear that there are several triangular patterns (with no rocks) in different sizes in the laid out grid of rocks. There are about 50 rows and 90 columns. There are six large triangles on top of each other at the left edge. To the right there are three even larger triangles from top to bottom, the one in the middle further to the left than the one above, but further right than the bottom one.]
- The rows blur past to compute a single step.
- [Shows the placement of two particles in the simulation.]
- And in the simulation...
- [The two particles have moved just long enough as to not overlap with their the previous position which are shown as an after-image with faint gray lines. The text continues directly the one from the previous panel.]
- another instant ticks by.
- [The next two panels take up the eight line of the comic. They each take up half the width.]
- [A Cueball like person (you) observes a mote of dust vanish.]
- So if you see a mote of dust vanish from your vision in a little flash or something
- [Cueball is standing between two rocks on the ground, while holding two rocks, one lifted up to his head. The first line of text is above him. It is a direct continuation of the text in the previous panel. The second line stands below to the right of him.]
- I'm sorry. I must have misplaced a rock
- sometime in the last few billions and billions of millennia.
- [Cueball stands in the "clean" part of his infinite desert, in front of the vastness of his infinity of infinite lines or rocks.]
- Oh and...
- [A Cueball like student sitting in a classroom with his head in his hands, Megan sits behind him and a teacher points to the blackboard; A clock shows the time at five minutes to ten.]
- If you think the minutes in your morning lecture are taking a long time to pass for you...
- This comic is available as a signed print in the xkcd store.
- The Swiss patent office line refers to Albert Einstein, who was employed as a Swiss patent clerk while coming up with his theory of special relativity. This joke is also referenced in 1067: Pressures. Also, there is a standing joke that very few important inventions have come from Switzerland, since the country hadn't been involved in the world wars, and thus has not been part of the weapons race, nor was it a driving force in the preceding Industrial Revolution.
- In the center of the comic, the binary numbers pointing to the particle are both 42. This is a reference to the comedic answer to the Ultimate Question of Life, the Universe, and Everything from the The Hitchhiker's Guide to the Galaxy series.
- Cueball mentions that if we see an artifact flutter in and out of reality he must have made a mistake in the last "billions and billions of millennia." This implies that the small period of time the artifact is present in his time is much longer than our universe has existed. That is a very long time. However, because it was a really long time, the difference could be more than just a small mote of dust disappearing.
- The line "I've rederived modern math in the sand and then some," is possibly referring to "Surreal Numbers: How two ex-students turned on to pure mathematics and found total happiness" by Donald Knuth. The Surreal numbers are a system of numbers that includes the familiar real numbers, but are infinitely more dense. Knuth wrote a novelette about a young couple who find themselves stranded on a deserted island (much like Cueball), and spend much of their time deriving the properties of this number system from a few base axioms.
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