Connections in Math: the two kinds of random
The article distinguishes two forms of lossless compression: statistical compression based on symbol frequencies and algorithmic compression based on short generating programs. It uses the example of a million random digits versus the first million digits of π, which are statistically indistinguishable yet differ in compressibility. The piece explains entropy as a measure of surprise and argues that statistical redundancy is not the sole source of compressibility.
- ▪A file of random digits and a file containing the first million digits of π have identical statistical distributions but differ in compressibility because π can be generated by a short program.
- ▪Statistical compression exploits uneven symbol frequencies, as captured by entropy, to reduce average message length.
- ▪Algorithmic compression relies on a concise description of the generating process, allowing compression even when symbol frequencies are uniform.
- ▪Entropy quantifies the average surprise of a source and sets the lower bound for lossless statistical compression.
- ▪The article concludes that compressibility can arise from both statistical redundancy and underlying algorithmic structure, not just the former.
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Record
| Original publisher | Stillthinking |
| Canonical URL | https://stillthinking.net/posts/connections-in-math-two-kinds-of-random/ |
| Publication time | Sun, 05 Jul 2026 23:31:30 +0000 |
| Retrieval time | 2026-07-06T00:08:10.539Z |
| Last seen | 2026-07-06T00:08:10.539Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | B9ujGViQFsdX |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
Rights status (four layers)
WeSearch handling by dimension
| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
July 2, 2026 math Connections in Math: the two kinds of random Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made. Picking up a puzzle I left lying around Last post, right at the end, I dropped a puzzle and walked away from it. Here it is again, because this whole post is basically me refusing to let it go. Imagine two files, and each one holds a million digits. The first one is pure noise — imagine I rolled a ten-sided die a million times and wrote down the results. The second one is the first million digits of π\piπ. Now look at them the way a statistician would: count how often each digit from 000 to 999 shows up.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Stillthinking.
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