Posted by tromp 3 hours ago
Edit: I've misread the above comment and my number is is 64 bytes (significantly more than 64 bits. The largest 64 bit number through my approach would be `9↑↑↑↑↑↑9`, which is significantly smaller.
So basically you have a very low density of representable numbers (2^64 / w218), I wonder how quickly it grows as you use more and more 1-bits, and is there even a correlation between the bit pattern and the corresponding number value?
Everything else is word play.
Ultimately you seem to pick a random definition of computing and size and then work with that?
It seems far more natural to say that you're representing programs rather than numbers. And you're asking, what is the largest finite output you can get from a program in today's programming languages that is 8 bytes or less. Which is also fun and interesting!
That's what the post ends up saying, after first discussing conventional representations, and then explicitly widening the representations to programs in (non-cheating) languages.
There is unfortunately no mathematically rigorous way to define what is cheating, so it seems unreasonable to ask me for that.
B0 39 mov al,'9' //load character '9' to AL
CD 29 int 29h //print to screen
EB FA jmp short -6 //go againThe (implicit) rules of the game require the number to be finite. The reason for this is not that infinity is not obviously "the largest" but that the game of "write infinity in the smallest number of {resource}" is trivial and uninteresting. (At least for any even remotely sensible encoding scheme. Malbolge[1] experts may chime up as to how easy it is to write infinity in that language.) So if you like, pretend we played that game already and we've moved on to this one. "Write infinity" is at best a warmup for this game.
(I'm not going to put up another reply for this, but the several people posting "ah, I will cleverly just declare 'the biggest number someone else encodes + 1'" are just posting infinity too. The argument is somewhat longer, but not that difficult.)
If you are playing this game and can't produce a number that doesn't fit in this universe you are probably better suited playing something else. That's just table stakes. If it even qualifies as that. "Inscribe every subatomic particle in the universe with a 9 every planck instant of the universe until the heat death of the universe" doesn't even get off the starting line in games like this.
Another general comment: It feels like a lot of people are really flailing around here, and need to understand this is a game. It has rules. If you change the rules, you are playing a different game. There is nothing wrong with playing a different game. It is just a different game. The game is not immutably written in the structure of the universe, or a mathematical truth, it is a human choice. And there isn't necessarily a "why" to the rules any more than there's a "why" to why the bishop moves as it does in chess. You can, in fact, change that rule. There are thousands of such variants. It's just that you're playing a different game than chess at that point. If you don't want to play the author's game, then that's fine, but it doesn't change the game itself. And proposing different solutions is equivalent to saying that you can win a chess game by just flipping over the board and yelling "I win". You can do that. Perhaps you've even won some game. But whatever game you just won, it isn't chess.