the gist

The improbable yet elementary case: describes several mutually-consistent mathematical accounts of the way in which (arbitrarily any) universal phenomena relate to one another (across arbitrary scopes/ domains of concern) – and builds to simple, inescapable, albeit counter-intuitive, #conclusions.

The following is an attempt to describe the case in prose, and is taken from a mastodon thread with @[email protected].

map territory

—have you ever considered the difference between: 1. a ’theory of everything’, and 2. a ’theory of theories’?

Perhaps the former emphasises territory, and the latter map? 1.

Map and territory are distinct, though inherently related.

—how might differences or similarities between 1. & 2. appear?

One difference might be some unavoidable delta, between map and territory – a limit to the precision of our understanding of the universe.

Perhaps 1. Is, in-practice, unattainable to us.

—is the theory-of-everything ’the mathematics itself’ – or ‘our interpretation of the mathematics’?

If the former, is there necessarily more than one expression? And the latter?

all map –all cognition, is necessarily abstract. all concepts relative, and contextual

Contextual concepts are isolated, aspectually 2, by contextual frame – as if observing any single physical object before us, from plural, materially distinct, momentarily and experientially isolated perspectives.

—in what way might we possibly hope to understand the universe, when all we can ever understand arrives slice by slice, in fractions of a whole?

What is cognition to the solution of this eternal puzzle?

complexity

—what of complexity, and composition? 3

Consider Lissi’s ’e8’, or similar. Super complex, right?

I think that this kind of thinking, that ‘a one-stop theory-of-everything must surely be super complex’ distracts us from a simpler entry-point to sense-making across universal phenomena.

Elsewhere, we seem to have fallen into a trap whereby, because some scientific measurements are now high-precision, that only equivalently high-precision is valid – even when charting otherwise anomalous phenomena.

Conclusions drawn from our interpretations of highly precise sources of information, somehow inherit the quality of precision, unjustifiably. As if, depending upon the stars to navigate, despite GPS existing 4, somehow invalidated otherwise informative observation and measurement, on some ‘would-be expedition to the unknown’

just get out – do it, make a sketch, and then iterate detail over time

Lissi’s e8 is a complex composition.

Which is fine, and useful, circumstantially. Though we don’t always need that level of detail. In-fact, we need simpler details to make sense of complex details – like a rosetta stone, to relate, or translate.

I suggest that our entry-point to that-kind-of-thing, is not the final composition, but the primitives which allow us :

  1. To more rapidly sketch phenomenal-spaces, in a universally applicable, verifiable, and composable manner
  2. Build up complexity and precision, as necessary

so, not ’this explains everything’ but ’this composes anything (formally, and verifiably)’

such that we might understand and explain, anything and everything, generally, then specifically, as necessary

Step: 1. Sketch general alignment first, then; 2. Relate special detail.

kuhn – fit, delta, anomaly

The improbable yet elementary case reinterprets Kuhn’s revolutionary paradigms, as transforming ‘open problem-space’ to ‘closed puzzle-space’

closed puzzle-space is finite, and far simpler than open problem-space

The problem, is one of map territory fit (how close did we get), and map territory delta (anomaly)

Intuitions include a 5 Class of tiling problem, which relates tile shape to boundary, and is concerned with ‘coverage’ – the tile visually represents a paradigmatic principal; boundary is defined by phenomenal scope (including all anomaly)

Where we contrive principals, we force anomaly upon ourselves.

—how might we avoid this?

—how (TF) do we compose maps of continuous territory, without contriving principals?

Kuhn’s revolutions are rare, because defining (contriving) new principal-boundary relations is hard

And intuitively: the more complex the principal; the more complex the boundary; the more complex a task to isolate a heuristic to transform open problem-space to closed puzzle-space.

consequently, look at the problems we have reconciling scientific disciplines

The last thing anyone thinks of doing is combining principles, and respective phenomenal scopes.

All that would do, is significantly complicate matters. Right?

🙈

Dramatic pause

puzzles

Let’s sit with :

  • The tiling problem
  • ‘Principle-boundary relation’
  • Composition
  • Paradigms of principals of measures
  • Etc

These are all ways of transforming open problem-space to closed puzzle-space (of resolving territory to valid maps)

Puzzles simplify, by limiting the number of possible steps for any solution, by constraining the space-of-all-possible arrangements.

Think of a (appropriate) jigsaw puzzle. A ten piece has fewer possible steps than a 100 piece. The space-of-possible arrangements (good or bad) is smaller.

Once we fix the tile-boundary relation :

  1. Open problem-space is transformed to closed puzzle-space
  2. We’re no longer free-styling coverage
  3. It’s all puzzle from there – compositionally complex sure, but always simpler that open problem-space

we oughtn’t fear compositional complexity (closed puzzle-space) as we do open problem-space complexity

Kuhn’s revolutions of isolated disciplines are rare, because each time, someone has to resolve open problem-space to closed puzzle-space, and solve the principal-boundary relation (the math and tiling problem describes this in detail)

From this origin, adding more complexity just makes everything more complex (reconciling isolated scientific disciplines, etc)

Unless…

Almost there ! 😜

Consider :

  • At almost every previous point in history the space-of-all-possible concerns was must much smaller (back to t=0)
    • No biological matter yet
    • And the chemistry was far simpler than today

—what of the tile-boundary relation then?

Whether now or then, when we switch focus to everything, we no longer need to contrive the tile-boundary relation, it is set—everything

By definition, somewhere ‘in there’, is the first tile/ principal, and whichever t value you pick, the boundary is always fixed, to everything

There never was open problem-space, only ever closed, finite, puzzle-space.

All we need to do – is consider everything, everywhere, all at once (😉)

common measures

If we consider everything as a single phenomenal scope, what are the common measures?

—are common measures now, different to t, at any time before now?

Remember, for isolated disciplines, commonality is arbitrary complex.

But also remember, that territory is continuous, which includes time; and our maps ought to represent continuation through time.

—what about earlier common measures?

Earlier common measures must be simple, as space-of-all phenomena was smaller.

—do primitive phenomena still exist? (yep)

So universal common measures which are common across simpler phenomena, must be simpler still…

Hold on…

When we consider the universal phenomenal scope through time, commonality across all, remains fixed to the earliest tile, regardless of subsequent boundary complexity.

Isolated disciplines are hard, because each time, we contrive the tile-boundary relation.

A unified paradigm, is fixed. We do not need to contrive a tile-boundary relation. And universal common measures are necessarily the simplest possible common measures across any possible intersection of any possible phenomena.

conclusions

The improbable yet elementary case :

  1. Is that the simplest of all scientific paradigmatic revolutions, is necessarily scientific unification
  2. And we needn’t wait for some hard open problem-space to be resolved to finite closed, puzzle-space – it always was
  3. When we consider everything in place (everything, everywhere ~ all at once), there is only puzzle-space, and unified endeavours, and composable maps, of composed territory

The unified paradigm is the simplest of all paradigms.

So simple, that we look right past, every time.

The improbable yet elementary case :

  1. Our universe is simpler than we commonly understand
    1. (In-fact, simpler than is possible to understand by the isolated scientific disciplines of an ununified scientific endeavour 6)
  2. Because
    1. Universal common measures are necessarily the simplest, they are also the most constrained (as constraints necessarily align with everything) – so, the universal paradigm, by applying to everything, formally, validates all, and in doing so, itself
    2. We contrive all complexity which does not compositionally derive from universal common measures
      1. Two kinds of complexity: innate, and; contrived
      2. Reducing contrived complexity simplifies, even if innate complexity increases: as the former is incoherent; and the latter, coherent complexity, or constraints, are clues 7 to puzzle space
  3. As follows

    1. The task of solving any problem is simplified as the space of all possible solutions is reduced to the space of all circumstantially sufficient solutions 8

    2. The simplest and most-assured way to resolve approximately all present-day scientific anomaly, is not to attempt to tackle each anomaly individually in isolation (whether in part or whole), but to consider all anomaly together, in-place, as part of a continuous whole

our universe is simpler than commonly understood, because ours is a coherent universe, and in a coherent universe, -anything- -cannot- happen

notes

test coverage

Consider test coverage.

In a coherent universe, with universally consistent compliance with the same fundamental constraints (which we presently observe) :

  1. Prefer theories which are consistent with the highest number of distinct phenomena
    • Prefer integration test area, over unit test precision
      • (Even if initially visibility is not recursive)
  2. When scope of concerns is arbitrarily defined :
    1. Every unit test is a relatively scoped integration test, and
    2. Inconsistent integration tests are invalid

  1. Map territory ↩︎

  2. Sometimes plurally ↩︎

  3. precision, circumstances, #tbc  ↩︎

  4. flaky coverage perhaps? #tbc develop ↩︎

  5. Novel? ↩︎

  6. On coherence and constraints ↩︎

  7. On coherence and constraints ↩︎

  8. The space of all possible solutions includes the range incoherent, through circumstantially sufficient, to coherent ↩︎