[undersuit]

You want to know how the Tetromino does memory allocation and garbage collection?

I don't think the infinite board is that big of a deal. Turing Machines and Lambda Calculus have no limits on their memory space and we implement analogues of them in our limited memory space.

[woodrowbarlow]

i'm talking about the theoretical model, not the implementation details. i'm focusing on the definition of "infinity" here:

> On an infinite playfield, tetrominoes spawn at “row infinity” and column zero. When a newly spawned piece falls, it never gets closer to the floor due to the nature of infinity. This means, in finite—though potentially vast—time, the agent can shift the piece into any finite column. And once in position, the agent can hard drop the piece.

gate construction relies on "nudging" a block at a specific row as it is falling. but if blocks start at row infinity, the only way to get them down should be to hard-drop them -- which precludes nudging.

they've defined a new "semi-hard-drop" operation, and introduced it as a "generalization" of legal moves, but it isn't.

[undersuit]

Why isn't it? It just hides time passage. Oh no the computer gets a higher score... but it's not playing Tetris, the high score doesn't matter.

For instance: "For instance, if the agent emulates a semihard drop with a finite number of soft drops, then it will let a gravity drop serve as the final soft drop. "

[woodrowbarlow]

it's math: no amount of soft-drops (or gravity drops) can bring a block from row infinity to row x. subtracting one from infinity is fruitless.

[undersuit]

And you can't have an infinite tape, but no one is out there saying the Turing Machine is fake.

Consider this. Our physical implementations of turing machines work even though we don't have an infinite memory. We do encounter some limitations because of such.

The Tetrino also works. You can create it and run it on a finite board. It would be limited just at our physical machines are limited without access to infinite memory.

[woodrowbarlow]

i'm not saying it's impossible to model an infinite board using software (that's quite possible). i'm saying that if it's possible to soft-drop a block to an arbitrary row, then the model of infinity is faulty and inconsistent. and, unfortunately, both the infinite board and the soft-drop are required fundamental underpinnings of the proposed mechanism for computation.

[undersuit]

And I'm saying you don't need a board to be infinite to do work, you just need a board to be infinite to compute all work. Just like you need infinite tape for a Turing Machine to be able to compute all work.