A TIME CAPSULE

Temporary Shelter 1 — Geometry 101
December 19, 2011

It began with a Geometry 101 lesson: the Platonic solids—especially the tetrahedron and octahedron.1

Following their geometry inward, by repeatedly dividing by 2, led to an unexpected question:

  • How far does this structure go?

We followed it toward the Planck scale, then asked how far the same structure extended outward.

  • The result suggested a remarkably compact way to map an enormous range of physical scales in the shortest number of steps.

We said, “We can explore the universe in just over 202 steps.”

[Explore the STEM project →]

Temporary Shelter 2 — What had others done?
2012-2013

For roughly two years, we looked for precedents.

We found Kees Boeke’s Cosmic View: The Universe in 40 Jumps, a remarkable high-school-originated base-10 map of scale. We also examined later work, including  Gerard ‘t Hooft’s 2014 Cosmic View update [1, 2].

Our question became more specific:

  • What happens if the scale of the universe is indexed from the Planck thresholds by repeated doublings rather than by decimal jumps?

In 2012, we also sought advice from physicists including Frank Wilczek and Freeman Dyson. Their correspondence is preserved as part of the record.

  • The correspondence documents within which we sought their advice is not presented as endorsement of the 81018 model.

[Read the correspondence →]

Before an idea becomes a theory, it is often just an observation lying around waiting to be noticed.

The original record remains available in full.

[Open the 81018 Method →]

REFERENCES

  1. Our textbook: Geometry, Pearson/Prentice Hall (2004), p. 515: the Platonic solids; our chart

GEOMETRY 101

The tetrahedron and octahedron were our working objects.

We did not begin with a cosmological theory. We got started in this special corner of our project by following the geometry—dividing by two and asking a very simple question:

  • How far does this structure go?

The answer led unexpectedly toward the Planck scale, and then outward again.

  • What began as a classroom exercise became a proposed STEM tool:Explore the universe in just over 202 steps.
  • This is where the 81018 investigation began.

We went looking for what others had already done.

After finding Kees Boeke’s Cosmic View: The Universe in 40 Jumps (1957) we discovered a black-and-white film done by American designers Charles and Ray Eames who did A Rough Sketch for a Proposed Film Dealing with the Powers of Ten and the Relative Size of Things in the Universe (1968). In 1977 it was re-mastered with IBM, touting a visualization of logarithmic thinking. Then came Phil and Phylis Morrison’s coffee-table edition of Powers of Ten (1985 edition) and the visualizations done for the early web by high-school students, Cary Huang and Michael Huang (twin brothers).

Then, we found a more recent work extending Boeke’s idea by Gerard ‘t Hooft and Stefan Vandoren titled, Time in Powers of Ten (2014).

Our question was different: What would happen if cosmic scale were indexed from the Planck thresholds by repeated doublings rather than by decimal jumps?

During this period we also sought guidance from working physicists. The correspondence with Frank Wilczek and Freeman Dyson is preserved here as part of the record.

The correspondence documents that we sought their advice. It does not constitute endorsement of the 81018 model.

That distinction matters.

1957 — Boeke: 40 jumps
2011 — Geometry 101: Follow the geometry, chart of 202 notations
2012 — 81018: What happens with binary doublings from Planck scale?
2012 — Wilczek/Dyson: Ask people who know more
2026 — Synthetic peer review: Ask many systems to reconstruct, challenge, and test the argument (on-going)

The 81018 Method

A framework for examining an unconventional model without assuming its conclusion

Observation → Mathematics → Model → Hypothesis → Test → Evaluation

81018 is an open investigation. It proposes that some of the apparent complexity of the universe might emerge from a small number of relationships involving scale, geometry, constraint, symmetry, and continuity.

  • That possibility is not the conclusion of this page.
  • The purpose here is more basic: How should we examine an idea like this?
  • The method begins by separating what is observed from what is constructed, what is mathematically derived from what is assumed, and what is hypothesized from what has actually been tested.
  • The objective is not to prove the 81018 model.
  • The objective is to make it clear enough to challenge.

The Six-Stage Workflow

1. Observation

What do we actually observe?

  • Begin with measurements, established data, documented mathematical results, or other identifiable evidence.
  • An observation should not acquire a theoretical interpretation merely because that interpretation fits the model.

2. Mathematics: What follows mathematically?

  • Definitions, equations, geometric constructions, numerical relationships, scaling rules, recurrence relations, and other mathematical statements should be examined on their own terms.
  • A mathematical relationship may be interesting or exact without yet having a physical interpretation.

3. Model: What structure are we proposing?

  • A model organizes mathematical relationships into a representation of some aspect of reality.
  • For 81018, this includes the proposed base-2 scale architecture, geometric constructions, Planck-scale starting assumptions, notations, and relationships among the structures under investigation.
  • A model is not automatically a description of nature simply because its mathematics is internally coherent.

4. Hypothesis: What physical interpretation are we adding?

  • Here the investigation crosses an important boundary.
  • A mathematical structure may suggest a physical interpretation, but the interpretation is an additional claim.
  • That claim should be identified explicitly.
  • This is where assumptions become hypotheses.

5. Test: What could nature tell us?

A serious hypothesis should lead, where possible, to a discriminating test.

A useful test should specify what observations or calculations would:

  • support the hypothesis,
  • weaken it,
  • distinguish it from competing explanations, or
  • falsify the proposed version.

If no meaningful test is presently available, that limitation should be stated rather than concealed.

6. Evaluation: What happened, and what should change?

  • Evidence does not exist merely to accumulate support.
  • A result that conflicts with a prediction is information.
  • A calculation that exposes an inconsistency is information.
  • A competing interpretation that explains the same observation more successfully is information.
  • Evaluation therefore includes a willingness to revise, narrow, replace, or abandon a claim.

The model must remain subordinate to the evidence.

Seven Operations for AI-Assisted Examination

Artificial intelligence does not provide scientific validation.

It can, however, be used as an instrument for examining an argument from multiple directions.

The seven operations below are intended to make that examination more systematic.

1. Reconstruct the Argument

What exactly is being claimed?

  • Reduce an argument to its essential sequence.
  • What is observed?
  • What is defined?
  • What is calculated?
  • What is assumed?
  • What interpretation is proposed?
  • What prediction follows?

If an argument cannot be reconstructed clearly, it is not yet ready for serious evaluation.

2. Identify Assumptions

  • What must be accepted before the argument can proceed?
  • Every investigation contains assumptions.
  • Some may be mathematical definitions.
  • Some may be empirical premises.
  • Some may be modeling choices.
  • Some may be physical conjectures.
  • Some may be philosophical commitments.
  • They should not be allowed to hide inside one another.

An assumption should remain identifiable as an assumption unless independent evidence elevates its status.

3. Check Symbolic Consistency

Do the mathematics actually agree with itself?

Check:

  • definitions,
  • units,
  • dimensions,
  • indices,
  • equations,
  • recurrence relations,
  • numerical values,
  • geometric relationships,
  • transformations,
  • boundary conditions.

A compelling narrative cannot repair an inconsistent equation.

Conversely, finding an error in one calculation does not automatically invalidate an entire model.

The task is to determine exactly what the error affects.

4. Generate Objections

  • What is the strongest case against this argument?
  • Do not ask only whether an idea is plausible.
  • Ask what a knowledgeable critic would attack first.
  • Generate alternative explanations.
  • Identify hidden premises.
  • Look for circular reasoning.
  • Ask whether the same evidence could support a competing model.
  • The strongest criticism should be made visible rather than treated as an obstacle to be overcome privately.

5. Compare Interpretations

Does the mathematics have only one possible meaning?

  • A mathematical structure can sometimes support more than one physical interpretation.
  • Therefore: mathematical consistency does not automatically establish physical meaning.
  • When multiple interpretations are possible, they should be compared rather than silently choosing the one most favorable to 81018.

6. Propose Possible Tests

What could distinguish this proposal from its alternatives?

  • A useful prediction should be sufficiently specific that someone else can investigate it.
  • Where possible, identify:
  • Prediction → Data → Method → Expected result → Alternative result
  • The purpose is not to accumulate confirming examples.
  • The purpose is to expose the proposal to evidence capable of distinguishing among explanations.

7. Expose Overstatement

Does the language claim more than the evidence supports?

This is a particularly important part of the 81018 method.

Words such as:

proves
derives
explains
confirms
demonstrates
establishes
solves

should be examined carefully.

Sometimes a more accurate statement is:

suggests
is consistent with
permits
motivates
raises the possibility of
provides a candidate explanation

This is not merely a matter of style.

Scientific credibility depends partly on calibrating the strength of a statement to the strength of its evidence.

What AI Can—and Cannot—Do

  • AI systems can be useful participants in this process.
  • They can reconstruct arguments, identify assumptions, check symbolic relationships, generate objections, compare interpretations, search for contradictions, suggest possible tests, and identify language that appears stronger than its supporting evidence.
  • They can also make mistakes.
  • They can reproduce assumptions.
  • They can confuse a plausible interpretation with an established result.
  • They can manufacture confidence where the evidence is weak.
  • And different AI systems can agree with one another for reasons that have nothing to do with whether a physical claim is true.

Therefore:

AI agreement is not evidence of physical truth.

AI-assisted analysis is a methodological tool.

The resulting claims remain subject to mathematical scrutiny, empirical testing, expert criticism, and revision.

What Counts as Evidence?

The 81018 investigation attempts to distinguish among several levels of statement:

Observed

  • A result supported by identifiable observation or measurement.

Mathematically established

  • A result that follows from stated definitions and mathematics.

Model-dependent

  • A result that follows only after adopting the assumptions of the model.

Hypothesized

  • A proposed physical interpretation that remains to be tested.

Philosophical

  • An interpretation concerning meaning, value, ontology, or other questions that may extend beyond empirical physics.

These categories can interact.

They should not be confused.

What Would Change Our Minds?

This may be the most important question in the entire investigation.

For each significant hypothesis, we should ask:

  • What result would make us revise it?

A hypothesis that can accommodate every possible outcome is difficult to test.

A model that can never be wrong has ceased to function as an empirical hypothesis.

Therefore, whenever possible, 81018 should identify:

  • What would support the proposal?
  • What would weaken it?
  • What would falsify it?

And when a prediction fails, the record should remain visible.

A Living Record of Corrections

The 81018 project is a continuing investigation.

  • Earlier formulations may be incomplete.
  • Calculations may contain errors.
  • Terminology may become too strong.
  • An interpretation may turn out to be unsupported.
  • A proposed connection may fail.
  • Those events should not be hidden.
  • They are part of the investigation.
  • A correction is not an embarrassment to the method.

The ability to identify and correct an error is evidence that the method is functioning.

The goal is therefore not to preserve every earlier claim.

The goal is to preserve the reasoning well enough that another person can see:

what was proposed → what was questioned → what was tested → what changed.

The Standard for the 81018 Investigation

The standard is simple:

  • Make the claim clear.
  • Make the assumptions visible.
  • Make the mathematics checkable.
  • Make the objections welcome.
  • Make the tests possible.
  • Make the failures visible.
  • Revise when necessary.

81018 does not ask the reader to accept a conclusion before examining the argument.

It asks the reader to walk the argument with us.

  • Check the maps.
  • Check the instruments.
  • Question the assumptions.
  • Open the next shelter.
  • And if the evidence tells us that we have taken the wrong path—
  • change the map.

Please note: Part of a larger discussion about (1) Planck Length and Planck Time, (2) the inverse of Planck Time, the Planck Frequency, (3) our model assumptions, (4) a look at discrete geometries, and (5) a look at what our model is attempting to add to that discussion.
Return to to the September 2026 Continuity-Symmetry-Harmony homepage. (244529)