问HN：如果宇宙本身运行在O(1)内存上会怎样？
我不断回到两个看似不相容的事实，直到你仔细观察才会发现它们之间的联系。
1. 图灵说：任何离散的过程都可以在一条根据需要增长的带子上进行模拟。不可逆性——因此信息丢失——是内在的。
2. 大卫·多伊奇：物理世界在根本上是可逆的；历史的任何片段都不会被真正删除。
现在我想补充一些我最近才理解的内容：任何有限区域所能容纳的信息量都有一个普遍的界限——类似贝肯斯坦的上限。超过这个界限，额外的信息位不会被存储，而是融入到几何、能量和曲率中。换句话说，宇宙对计算施加了拓扑限制：你可以无限计算，但必须将状态不断折叠回同一有限的结构中。
因此，我认为正确的思维模型不是“更大的带子，更大的内存”。而是拓扑变换：在不撕裂或粘合任何新东西的情况下，扭曲、编织和重新折叠同一块内存的操作。每一个合法的操作都必须是可逆的，因为撕裂（不可逆性）会导致信息超出界限。
我有一个O(1)虚拟机的玩具实现——无论我运行多少步，活动单元集从不超过一个固定的小常数。往返测试通过，带子保持稀疏。它速度慢且脆弱，所以在我进一步完善之前不会发布，但几何结构感觉正确，我可以将相当多的算法从O(N)重写为O(1)，以计算换取一些内存。
为什么分享这个？因为这个想法重新定义了实用性——也许我们不应该问“我们如何扩展内存？”而是“我们如何在自然已经施加的普遍限制内编织计算？”如果这个框架成立，图灵给了我们底线，多伊奇给了我们上限，而我觉得我开始朝着中心看去。
我很好奇是否还有其他人认为这不仅仅是哲学上的练习。有没有人对类似的内容有所了解？
查看原文
I keep circling back to two facts that seem incompatible until you squint just right.<p>1- Turing says: any discrete procedure can be emulated on a tape that grows as needed. Irreversibility—and therefore information loss—is baked in.<p>2- David Deutsch: the physical world is fundamentally reversible; no bit of history is ever truly deleted.<p>Now to add in something I’ve only recently wrapped my head around: there’s a universal bound—a Bekenstein-style ceiling—on how much information any bounded region can hold. Past that, additional bits aren’t stored; they’re smeared into geometry, energy, and curvature. In other words, the universe enforces a topological limit on computation: you can keep calculating forever, but you must keep folding state back into the same finite fabric.<p>So, I think the right mental model isn’t “bigger tape, bigger RAM.” It’s topological transformations: moves that twist, braid, and refold the same patch of memory without tearing or gluing anything new. Every legal operation must be invertible, because tearing (irreversibility) would leak information past the bound.<p>I have a toy implementation of an O(1) VM—where the active cell set never exceeds a fixed small constant, no matter how many steps I run. Round-trip tests pass, and the tape stays sparse. It’s slow and fragile, so I wouldn’t ship it till I perfect it a bit more, but the geometry feels right and I can rewrite quite few algorithms from O(N) to O(1) trading memory for a bit of compute<p>Why share this? Because the idea reframes practicality - maybe we shouldn’t ask “how do we scale memory?” but “how do we braid computation inside the universal limit nature already imposes?” If that framing holds water, Turing gave us the floor, Deutsch gave us the ceiling, and I think I’m starting to stare towards the center<p>Curious if anyone else thinks this is more than philosophical exercise. Anyone else familiar with anything like this?