← Back to article

Equation 42 · The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

What does this equation mean?

ht+1=ht+ℓt−dt,h_{t+1}=h_t+\ell_t-d_t,

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsh_t+ell_t-d_t
Result or conditionh_t+1
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

ht+1h_{t+1}

Symbol h_t+1

developer capability evolve.

Understand this part →

hth_t

Symbol h_t

hth_t is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

tt

Symbol t

t is part of the quantity the equation computes from the expression on the right.

Understand this part →

dtd_t

Symbol d_t

depreciation of skills no longer exercised.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
addition

addition

Add the term after the plus sign to the term or group before it.

Understand this part →

subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Let developer capability evolve as ht+1=ht+ℓt−dth_{t+1}=h_t+\ell_t-d_t. where ℓt\ell_t is learning from agent-assisted work and dtd_t is depreciation of skills no longer exercised. Both depend on workflow. Requiring developers to predict behavior, inspect evidence, and explain accepted changes can raise ℓt\ell_t . Delegating opaque work and reviewing only summaries can raise dtd_t .

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

See this formula across 1 published context →

Browse the mathematical compendium →