I remember reading this out of curiosity about 3rd grade, in the US about 8-9 years old. I read the sequel right after, enjoying that too: https://en.wikipedia.org/wiki/Sphereland It triggered a life long interest in geometry and classical philosophical documents.
Game author Marcus Rowland created a "Flatland RPG" as part of his Forgotten Futures project (a series of games about Scientific Romances: the genre that later became SciFi): http://www.forgottenfutures.co.uk/flatland_lite.pdf
Although not the same article, there was a previous discussion on HN about Flatland a few years back. There's some interesting comments and links, I'll post the link here just in case there's not much traction this time around:
A related book you may find interesting is "Spaceland" by Rudy Rucker - it's set in Silicon Valley during the dot-com boon - a tech executive get's a visit from the 4th dimension. It's a hilarious and modern update to Flatland.
For people who think this universe is a simulation, maybe the simulation is possible because the next universe up has more dimensions. (Maybe the 20+ dimensions some string theorists talk about.) Despite Flatland, you can't really do much in 2D; the connectivity is too limited. 3D is a minimum for life.
Computing would work better in a higher dimensional space. Propagation delay is less of a problem because you can have more things closer to each other. Cooling would be easier with an extra dimension or two into which heat could be radiated.
But if higher dimensional beings want to run a universe simulation, 3D would be enough for entertainment purposes.
When you go one level deeper, you realize that there's no difference between a simulation of a universe and a universe.
This is only tangential, but a few months ago I vaporized 50mg of DMT after spending a day studying linear algebra and differential equations. You only ever take back flashes, but I remember seeing this higher-dimensional hypercube where every "face" of the cube was a 3 dimensional space. I came away from that trip feeling that our universe was just one of infinitely many solutions to a higher-dimensional equation. I still haven't decided if that makes any sense or not.
That's basically the string theory multiverse hypothesis. Why these physical constants? Because there's at least one universe each for all of them, and you're just in one of them.
A digestive tract could be replaced by a vacuole. I think that the game of life, and it's many variants, are a fairly strong indication that it is not impossible for complex, long term, self replicating processes to occur in a real 2D universe.
You don't need neurons for Turing completeness. Very simple cellular automata can compute any computable function. In fact, even in a 1D universe of cells Turing complete computation is possible:
Theres a difference between "visible space" and memory space. A turing complete 1-d simulation can have a physical space that is 3 dimensional. If you wanted to see it, as the oracle, you would need to run a function on the space. Think interpretation..not 1 for 1
You're trying to convert the 3D world as we know it to 2D, but there's no such restriction. There are other constructs in 2D that can be used for the same purposes.
Take Game of life for example. It doesn't matter that you cannot make circuits without crossing wires in 2D, Game of Life is turing complete anyways. A computer based on GoL is totally unlike our 3D computers, but can have the same capabilities. There's no reason to think that it would be any different with biology.
Or you can try comparing our 3D world with a hypothetical higher dimension. Our intestines are hollow cilinders, stable in 3D but not suited for 4D — in 4D you can look inside a 3D cilinder just like we can look inside a 2D-sphere (a circle) from our 3D perspective. A 4D creature would probably have a very different, more efficient, structure for this use case (food containment and nutrient absorption), which they probably wouldn't be able to just translate to 3D.
I think what matters more is the combination of shortcuts, how we define time, and the scope of a simulation.
E.g. if I want to simulate humanity, while I need to create the appearance of a universe, the scope of observation of the universe is very, very limited, so I don't need to actually simulate anything other than Earth and maybe a few minor bits and pieces of the solar system. Outside of that, I can take a leaf from the book of Elite, and simply have a way to generate whichever bits and pieces that those annoying astronomers happens to try to observe, to sufficient fidelity to feed into the simulation.
On Earth too, I could simplify drastically. E.g. there was a school of philosophy called Empirio-Criticism that believed only that which is directly observed by the senses exist (they are perhaps best known today through an obscure book by Lenin called Materialism and Empirio-Criticism [1] largely motivated by the fact that one of Lenins opponents in the Bolchevik party was leading supporter of the empirio-criticists). Ernst Mach - a physicist - caused some consternation, for example, by expressing doubt that atoms existed... As such it occupies a middle ground between Berkeleys Idealism and Materialism.
But imagine if they were right in the context of a simulation: The simulation, like games like Elite or Minecraft, only instantiates what you can observe directly, and when you can no longer observe it, it is either discarded, or stored (e.g. Elite re-generates each solar system on entry; Minecraft after a while de-spawns any entities that are not contained, so e.g. you can maintain an animal farm, but only as long as the animals are in a small enough enclosure). Since you could introspect the mind of the simulation subject, you could determine (or change!) which details the subject remembers, and allow everything else to be re-generated as needed.
Furthermore, depending on the simulation goals, it'd not necessarily need every person in the simulation to be "real" - it could imbue persons you run into with a personality and generated mind just for the time you interact with them, and step their complexity up/down as needed.
It doesn't need to be correct, just to be believable by someone who has no memory that contradicts it.
Lastly, unless there are reasons we don't know that requires a simulation of a mind to run at a specific speed, a lot can be solved simply by slowing a simulation down.
In other words: If you first go down the rabbit hole of a simulated reality, things get hairy quite quickly.
If you can find it, "The Dot and the Line" is another brilliant tale along these (ahem) lines [0]
I've had a look around and cannot find it online, though the excellent animated adaptation is easy to find [1] - well worth picking up the hardcopy as a beautifully designed picture book.
I'd also recommend Norton Juster's other work "The Phantom Tollboth" as being another great math & science inspired kids fairy-tale type book [2]
Something that surprised me when reading Flatland for the first time was the seemingly high levels of both sexism and classism.
While the classism mostly consisted of the typical oft-repeated jabs that don't really mean anything, the sexism felt much stronger. So much so that I assumed that it was meant to be satire. But is it reflective of the views that were prevalent at the time it was written?
The sexism, while satire, is actually one of the reasons why I found it extremely difficult to read through. If I recall correctly, I stopped halfway through out of irritation!
Your inability to understand how periods, birth, and lack of muscle make the female portion of our species more fragile is an inability to confront uncomfortable truths. Equal rights does not mean equally capable bodies.
The idea that equal rights should mean equally capable bodies, or that the rights and titles afforded to someone should be determined by anything other than their humanity or proven ability, is both arrogant and extremely repulsive.
I shall not respond to any further comments from you, and the idea that you can persuade me out of this idea with points that are spurious at best, while simultaneously ignoring the entirety of human history, where women have fought and proven time and time again that they are equivalent in ability to men, is at best silly and at worst dangerously ignorant.
Equality is a mathematical term. Men and women are equal under the eyes of the law. But as for our bodies and minds, men and women are different. The book is written from a time where women still didn't have equal rights. Its just a relection of the time, not sexist and well.. not something to stick your fingers in your ears for..
I have the second one. It's... well, I don't know whether to recommend it or not.
Part of the conceit of the film is that it's continuously interrupted by snarky title cards. The action continues, you can hear the audio, but all you see is the title card. For me, this single thing completely ruined the otherwise excellent film --- they weren't required to understand the story, they didn't add anything to the theme, they just got in the way, every single time. They're painfully, painfully long, too.
If there was a version of the film which was otherwise identical but without the title cards, I'd definitely suggest checking it out. As it is, YMMV.
37 comments
[ 3.0 ms ] story [ 83.4 ms ] threadhttps://news.ycombinator.com/item?id=2086425
Computing would work better in a higher dimensional space. Propagation delay is less of a problem because you can have more things closer to each other. Cooling would be easier with an extra dimension or two into which heat could be radiated.
But if higher dimensional beings want to run a universe simulation, 3D would be enough for entertainment purposes.
This is only tangential, but a few months ago I vaporized 50mg of DMT after spending a day studying linear algebra and differential equations. You only ever take back flashes, but I remember seeing this higher-dimensional hypercube where every "face" of the cube was a 3 dimensional space. I came away from that trip feeling that our universe was just one of infinitely many solutions to a higher-dimensional equation. I still haven't decided if that makes any sense or not.
Cool. Did everything else appear "flat" in comparison?
Think electronics: no bridges -> no cables crossing
Think biology: any kind of digestive tract would split a purely 2D being in two.
Think neurons, and then think of the Four Color Theorem[0].
How are you going to feed the center cells all while trying to get a feedback loop?
https://en.wikipedia.org/wiki/Four_color_theorem
https://en.wikipedia.org/wiki/Rule_110
Still struggle with the idea of feeding said thing properly in 2d.
Take Game of life for example. It doesn't matter that you cannot make circuits without crossing wires in 2D, Game of Life is turing complete anyways. A computer based on GoL is totally unlike our 3D computers, but can have the same capabilities. There's no reason to think that it would be any different with biology.
Or you can try comparing our 3D world with a hypothetical higher dimension. Our intestines are hollow cilinders, stable in 3D but not suited for 4D — in 4D you can look inside a 3D cilinder just like we can look inside a 2D-sphere (a circle) from our 3D perspective. A 4D creature would probably have a very different, more efficient, structure for this use case (food containment and nutrient absorption), which they probably wouldn't be able to just translate to 3D.
https://en.wikipedia.org/wiki/The_Planiverse
http://www.csd.uwo.ca/faculty/akd/PERSONAL/books_and_article...
E.g. if I want to simulate humanity, while I need to create the appearance of a universe, the scope of observation of the universe is very, very limited, so I don't need to actually simulate anything other than Earth and maybe a few minor bits and pieces of the solar system. Outside of that, I can take a leaf from the book of Elite, and simply have a way to generate whichever bits and pieces that those annoying astronomers happens to try to observe, to sufficient fidelity to feed into the simulation.
On Earth too, I could simplify drastically. E.g. there was a school of philosophy called Empirio-Criticism that believed only that which is directly observed by the senses exist (they are perhaps best known today through an obscure book by Lenin called Materialism and Empirio-Criticism [1] largely motivated by the fact that one of Lenins opponents in the Bolchevik party was leading supporter of the empirio-criticists). Ernst Mach - a physicist - caused some consternation, for example, by expressing doubt that atoms existed... As such it occupies a middle ground between Berkeleys Idealism and Materialism.
But imagine if they were right in the context of a simulation: The simulation, like games like Elite or Minecraft, only instantiates what you can observe directly, and when you can no longer observe it, it is either discarded, or stored (e.g. Elite re-generates each solar system on entry; Minecraft after a while de-spawns any entities that are not contained, so e.g. you can maintain an animal farm, but only as long as the animals are in a small enough enclosure). Since you could introspect the mind of the simulation subject, you could determine (or change!) which details the subject remembers, and allow everything else to be re-generated as needed.
Furthermore, depending on the simulation goals, it'd not necessarily need every person in the simulation to be "real" - it could imbue persons you run into with a personality and generated mind just for the time you interact with them, and step their complexity up/down as needed.
It doesn't need to be correct, just to be believable by someone who has no memory that contradicts it.
Lastly, unless there are reasons we don't know that requires a simulation of a mind to run at a specific speed, a lot can be solved simply by slowing a simulation down.
In other words: If you first go down the rabbit hole of a simulated reality, things get hairy quite quickly.
[1] https://en.wikipedia.org/wiki/Materialism_and_Empirio-critic...
I've had a look around and cannot find it online, though the excellent animated adaptation is easy to find [1] - well worth picking up the hardcopy as a beautifully designed picture book.
I'd also recommend Norton Juster's other work "The Phantom Tollboth" as being another great math & science inspired kids fairy-tale type book [2]
[0] https://en.wikipedia.org/wiki/The_Dot_and_the_Line
[1] https://www.youtube.com/watch?v=OmSbdvzbOzY
[2] https://en.wikipedia.org/wiki/The_Phantom_Tollbooth
While the classism mostly consisted of the typical oft-repeated jabs that don't really mean anything, the sexism felt much stronger. So much so that I assumed that it was meant to be satire. But is it reflective of the views that were prevalent at the time it was written?
I think your argument is nothing more than a quip, and not a very good one at that.
I shall not respond to any further comments from you, and the idea that you can persuade me out of this idea with points that are spurious at best, while simultaneously ignoring the entirety of human history, where women have fought and proven time and time again that they are equivalent in ability to men, is at best silly and at worst dangerously ignorant.
We detached this subthread from https://news.ycombinator.com/item?id=11892858 and marked it off-topic.
https://en.wikipedia.org/wiki/Flatland_%282007_film%29
Part of the conceit of the film is that it's continuously interrupted by snarky title cards. The action continues, you can hear the audio, but all you see is the title card. For me, this single thing completely ruined the otherwise excellent film --- they weren't required to understand the story, they didn't add anything to the theme, they just got in the way, every single time. They're painfully, painfully long, too.
If there was a version of the film which was otherwise identical but without the title cards, I'd definitely suggest checking it out. As it is, YMMV.
Hey, it's on Youtube. https://www.youtube.com/watch?v=Mfglluny8Z0