← All parts of this equation

Equation 5 · Part 7 · Why the Physical World Is Harder

subscript

tsense+tcompute+tactuate<1f.t_{\mathrm{sense}} + t_{\mathrm{compute}} + t_{\mathrm{actuate}} < \frac{1}{f}.
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Language models became substantially more capable by thinking for longer at inference time. That option is bounded on a robot, and the bound is not a matter of taste. A closed-loop controller running at frequency f must complete sensing, computation and actuation within one cycle: tsense+tcompute+tactuate<1ft_{\mathrm{sense}} + t_{\mathrm{compute}} + t_{\mathrm{actuate}} < \frac{1}{f}. The pi-zero model is documented as producing actions at up to 50 Hz for dexterous tasks [ 3 ] , which leaves a 20-millisecond budget for everything. No amount of chain-of-thought fits in 20 milliseconds. Worse, missing the deadline is not merely slow: a controller that arrives late in a contact-rich interaction is acting on a stale world model, and in a stiff contact the resulting force error…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.