| --- |
| title: "House Oversight: Estate Documents (Nov 12) (HOUSE_OVERSIGHT_012971)" |
| source: "House Oversight: Estate Documents (Nov 12)" |
| sourceUrl: "https://www.justice.gov/epstein" |
| date: "2026-01-01" |
| category: "House Oversight" |
| eftaNumber: "HOUSE_OVERSIGHT_012971" |
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| --- |
| |
| 3.6 Postscript: Formalizing Pattern |
| 55 |
| Using this definition of pattern, combined with the formal theory of intelligence given in |
| Chapter 7, one may formalize the various hypotheses made in the previous section, regarding |
| the emergence of different kinds of networks and structures as patterns in intelligent systems. |
| However, it appears quite difficult to prove the formal versions of these hypotheses given current |
| mathematical tools, which renders such formalizations of limited use. |
| Finally, consider the case where the metric space M has a partial ordering < on it; we may |
| Definition 3.1. R. € M is a subpattern in X € M to the degree |
| K- JDEM true(R< P)dig |
| JPEM diX |
| This degree is called the subpattern intensity of P in X. |
| Roughly speaking, the subpattern intensity measures the percentage of patterns in X that |
| contain R (where "containment" is judged by the partial ordering <). But the percentage is |
| measured using a weighted average, where each pattern is weighted by its intensity as a pattern |
| in X. A subpattern may or may not be a pattern on its own. A nonpattern that happens to |
| occur within many patterns may be an intense subpattern. |
| Whether the subpatterns in X are to be considered part of the "mind" of X is a somewhat |
| superfluous question of semantics. Here we choose to extend the definition of mind given in |
| Goe06a to include subpatterns as well as patterns, because this makes it simpler to describe |
| the relationship between hypersets and minds, as we will do in Appendix ??. |
| HOUSE_OVERSIGHT_012971 |
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