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adrianN

You can run the Game of Life, and that's Turing-complete. So I see no reason why 2D intelligence can't exist.

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Strict 2D?

Think electronics: no bridges -> no cables crossing

Think biology: any kind of digestive tract would split a purely 2D being in two.

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.

Not convinced.

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

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:

https://en.wikipedia.org/wiki/Rule_110

Ok, you get points for that, TIL :-)

Still struggle with the idea of feeding said thing properly in 2d.

Like he said, vacuoles.

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.

There is a book from the 80's called "The Planiverse" which described the biology of some 2d creatures and it agreed with you.

Yes, that would be "The Planiverse" by noted computer scientist and author (and sometimes conspiracy theorist) A. K. Dewdney.

https://en.wikipedia.org/wiki/The_Planiverse

http://www.csd.uwo.ca/faculty/akd/PERSONAL/books_and_article...

Wow, this is the best read I've found in a long time. Thank you both very much for pointing it out :D

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