RECOGNITION
PHYSICS INSTITUTE
Our Science / Meaning & language

Our Science / Meaning & language

What does a record preserve?

A record can preserve how things relate and what happened between them. It can also lose a distinction that matters. Recognition Science studies meaning through this physical question: what survives an interaction, a comparison or a change of description?

An example you can follow

The same counts can hide a different history.

Start at the marked corner of a cube. Travel around one face, A, and then around a second face, B. Now reverse their order: B, then A.

Both journeys return to the same corner. Both cross the same directed edges the same number of times. A table of crossing counts therefore gives the same answer for both. An ordered record can still tell them apart.

Journey 1: A, then B

Around the first face, then the second.

Journey A then B: 8 of 8 crossings. Current corner 0.x₁x₂x₃x₄x₅Start
Retained loop recordx₅⁻¹ x₂⁻¹

Journey 2: B, then A

Around the second face, then the first.

Journey B then A: 8 of 8 crossings. Current corner 0.x₁x₂x₃x₄x₅Start
Retained loop recordx₁ x₅⁻¹ x₂⁻¹ x₁⁻¹

Crossing countsIdentical for the two journeys.

Retained loop recordsDifferent, with the starting corner fixed.

Reference treeMarked edgeTravelled edge
The starting corner stays fixed throughout the comparison. The loop record retains distinctions that crossing counts discard. “Start again” lets you watch both records form, one crossing at a time.
How to read the symbols

Seven edges form a reference tree: they connect every corner without making a loop. The remaining five edges are marked x₁ through x₅. Crossing a marked edge in its arrow’s direction records its symbol; crossing against the arrow records its inverse, shown by ⁻¹.

Keep the symbols in order. Whenever adjacent symbols are inverses of each other, cancel that pair. A crossing followed by its undoing contributes no retained loop. The two journeys above leave different reduced records.

The choice of reference tree gives us a way to write the record. Once that choice and the starting corner are fixed, the distinction can be checked exactly. The full illustrated guide explains the construction.

This is a small, exact example of a larger requirement. A description must preserve the distinctions needed for the comparisons it is meant to support. Totals alone cannot recover order once it has been discarded.

In our formal language work, composing records, undoing operations and retaining their order are explicit operations. Meaning has a structure that can be compared and transformed.

A physical carrier

Light carries relations.

An electromagnetic wave has amplitude and phase. Relative phases determine how waves interfere. These relations have measurable effects, and they can survive transmission from one place to another.

The RS construction studies a comparison window with eight complex samples. Each sample records an amplitude and a phase. To describe the window’s internal pattern, remove its common component, separate out its overall strength, and identify states that differ only by one common phase rotation.

  1. 01 / SAMPLE
    8
    Eight complex amplitudes

    Read one complete eight-step window. Each sample has size and phase.

  2. 02 / REMOVE THE MEAN
    7
    A neutral pattern

    Subtract the shared component. Seven independent complex coordinates remain.

  3. 03 / SEPARATE STRENGTH
    ‖z‖ = 1
    A normalized pattern

    For a nonzero pattern, keep its shape apart from its overall magnitude.

  4. 04 / IDENTIFY COMMON PHASE
    ℂP⁶
    A geometric state

    A common phase rotation represents the same point. Relative phases remain.

The resulting space is complex projective six-space, ℂP⁶. The superscript counts six complex dimensions, equivalent to twelve real dimensions. The eight-sample window and these identifications are the conditions of this construction.

Calling this a geometry of meaning gives a precise task: determine which relations distinguish one state from another and which changes leave those relations intact. Comparing a pattern with every possible normalized neutral probe determines its projective state. The comparison uses the squared magnitude of their complex inner product. A label can change while the represented state remains the same.

There is also a physical construction behind the samples. In a periodic, finite Maxwell system with eight time positions and eight spatial positions, superposed travelling waves can realize every neutral sample pattern. This establishes a carrier within that specified system. Applying the construction to a particular optical apparatus also requires its sampling and control conditions.

The geometric state and the ordered loop record preserve different information. A description of meaning must retain whichever distinctions its physical operations can reveal; one representation does not automatically replace the other.

From a carrier to a language

A language must preserve what it says.

Suppose two encodings use different symbols for the same physical operations. A faithful translation must preserve the distinctions between those operations and the way they compose. Changing the symbols must not change what the represented operation does.

This is the sense in which we study a universal language: a common structure for representing distinctions, relations and transformations across their different physical expressions. The formal work develops ordered records, relational statements and encodings whose equivalence can be proved under stated rules.

The exact results have defined domains. The relational language includes atoms, conjunction and existential quantification. The encoding results specify the operations and equivalences a translation must preserve. Extending those results to the full range of human language requires further connections.

Meaning is physical because the represented distinctions and transformations belong to physical reality. Language gives us a way to retain, combine and communicate them.

Why this matters elsewhere

What happened can matter after the totals agree.

Ethics and economics also need descriptions that preserve relevant history. A transfer, a promise and a repayment may leave identical current balances while involving different obligations. Their account must retain the distinctions needed to determine what people can do and what they owe one another.

The cube example establishes a precise loss of order. The ethical and economic work develops the physical relations and histories needed for its own questions.

Continue to Ethics & Economics

Read further

Follow the construction.