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我反复思考着两个看似矛盾的事实，直到你眯起眼睛仔细审视它们。1 - 图灵说：任何离散过程都可以在一个按需增长的纸带上模拟。不可逆性——因此信息丢失——是内嵌的。2 - 大卫·多伊奇：物理世界从根本上是可逆的；任何历史的比特都不会真正被删除。现在，我要补充一些我最近才完全理解的东西：对于任何有界区域可以容纳的信息量，存在一个普遍的上限——一个贝肯斯坦式的上限。超过这个上限，额外的比特不会被存储；它们会被抹入几何结构、能量和曲率。换句话说，宇宙对计算施加了拓扑限制：你可以永远计算下去，但你必须不断地将状态折叠回同一个有限的结构中。所以，我认为正确的思维模型不是“更大的纸带，更大的 RAM”。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）会导致信息泄漏到上限之外。我有一个 O(1) VM 的玩具实现——无论我运行多少步，活动单元集都不会超过一个固定的、小的常数。往返测试通过，并且纸带保持稀疏。它很慢而且很脆弱，所以我不会在完善它之前发布它，但几何结构感觉是正确的，我可以将相当一部分算法从 O(N) 重写为 O(1)，用内存换取一点计算量。为什么要分享这个？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？”，而是问“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，图灵给了我们基础，多伊奇给了我们上限，我想我开始凝视中心。好奇是否有人认为这不仅仅是哲学练习。还有其他人熟悉类似的东西吗？

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I keep circling back to two facts that seem incompatible until you squint just right.1- Turing says: any discrete procedure can be emulated on a tape that grows as needed. Irreversibility—and therefore information loss—is baked in.2- David Deutsch: the physical world is fundamentally reversible; no bit of history is ever truly deleted.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.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.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 computeWhy 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 centerCurious if anyone else thinks this is more than philosophical exercise. Anyone else familiar with anything like this?

提问 HN：如果宇宙本身只用 O(1) 的内存运行会怎样？