When you hear "logic," what comes to mind? Probably strict rules, truth tables, or the classic "if A, then B." It all seems clear—until you try to apply it to real life, where things rarely fit so neatly. But what if logic isn't just about formulas? What if, at its...
Abstract Handling large-scale sparse matrices is a fundamental task in many scientific and engineering domains, yet standard in-memory approaches often hit the limitations of available RAM. This paper introduces FlexChunk, an algorithm employing a chunking strategy and disk caching for efficient sparse matrix-vector multiplication (SpMV) specifically designed for matrices exceeding...
it's valid critique and highlights the speculation in BH computation (overhead from Hawking decoding, scrambling of input, GR latencies, unknowable interiors). But the model doesn't rely on it: The theorem proves external silence via density bounds alone (growth intersects finite limit, forcing compact non-emissive states), internals irrelevant, whether computable or not. If impractical, systems stagnate earlier (r≤1, silent anyway). Resolution holds: Thermo + geometry = quiet universe.
Updated article emphasizes this (thanks to feedback like yours)
Thanks for the insightful counterpoint is spot-on that optimizing for signal-to-noise by forgetting noise could stabilize info without collapse. In fact, thanks to feedback like yours, I've updated the article to more clearly integrate this in the "noise forgetting" note, showing it leads to r=1 (silent stagnation) or, if any growth remains, eventual finite-time silence via the theorem. It strengthens the model without changing the core resolution: Silence prevails either way
When you hear "logic," what comes to mind? Probably strict rules, truth tables, or the classic "if A, then B." It all seems clear—until you try to apply it to real life, where things rarely fit so neatly.
But what if logic isn't just about formulas? What if, at its core, it's about something even simpler: noticing the difference between one thing and another?
Textbooks start with symbols: P → Q, ∀x, ∃y. But maybe real logic begins earlier—at the moment we first draw a line between "this" and "not this."
This article offers a look at logic from an engineering angle. The goal isn't to throw out what you know, but to add a... (read 3107 more words →)
Abstract
Handling large-scale sparse matrices is a fundamental task in many scientific and engineering domains, yet standard in-memory approaches often hit the limitations of available RAM. This paper introduces FlexChunk, an algorithm employing a chunking strategy and disk caching for efficient sparse matrix-vector multiplication (SpMV) specifically designed for matrices exceeding available memory. Our experiments demonstrate that FlexChunk achieves near-linear O(N) time complexity and linear memory consumption scaling up to matrix sizes of 100M×100M, processing the largest case in 1 minute 47 seconds with a peak memory footprint of 1.7 GB. A comparison with the optimized SciPy library reveals a key trade-off: while SciPy offers significantly faster computation for in-memory matrices, FlexChunk excels in... (read 2054 more words →)
The poetry case really stuck with me. Claude’s clearly planning rhymes ahead, which already cracks the “just next-token” intuition about autoregressive models. But maybe it’s more than a neat trick. What if this spatial planning is a core capability—like the model’s not just unrolling a string, but navigating a conceptual space toward a target? One could test this by checking how often similar planning circuits pop up in multi-step reasoning tasks. If it’s building a rough "mental map" of where it wants to land, that might explain why bigger context windows boost reasoning so much. Not just more data—more room to plan. Has anyone tried prompting or tracing for this directly?
Thanks for the detailed feedback. It helps clarify things.
On progress and civ defs. Progress here means net info growth with r greater than 1. Civ means any entropy reducing info system or negentropic node. It is pure thermo and physical not cultural. Reject it and the paradox is trivial. No growth means no visibility.
BH as civ or engineered. Fair. Smearing bits on horizon does not sound like a livable setup and computation seems dubious. But the model does not need it. Theorem forces external silence via density. Compact dark states whether engineered or not.
Galaxy stagnation with noisy buildup. Possible but thermo makes it impossible to reach that scale. Spreading costs explode before... (read more)