PYTHON · NUMPY

What was left out

Detect an incomplete boundary in an energy claim by testing whether the omitted term can change the conclusion.

01Challenge

A robotics team publishes a locomotion energy figure and calls it the machine's efficiency. Decide whether the omission of compute is a rounding error or a reversal, using published figures.

02Model

Every energy claim draws a boundary, and the boundary is usually invisible. A locomotion figure that omits the computer was defensible for a decade because the legs dominated by an order of magnitude, and an omission that cannot change a conclusion is a reasonable simplification rather than a defect. What makes an omission serious is that it can flip the answer, and that condition is testable rather than a matter of judgement. Cost of transport for humanoids has fallen from the 1.6 range to about 0.42 in published work, while a current embodied compute module draws 40 to 130 watts regardless. The term that was safely ignorable is not ignorable at those efficiencies, which means the same omission changed status without anybody editing the document.

03Guided practice

Compute the omitted term as a share of the total at each of the published cost-of-transport values, and find the value at which the omission crosses a threshold you would refuse to ignore.

04Feedback

PASS WHEN You turned a judgement call into a test. An omission is acceptable while it cannot change the conclusion, and you found the exact point where this one can.

If your run fails, check:

share_omitted needs locomotion power from CoT times mass, gravity and speed, then compute over the sum.
Use the top of the compute envelope for the crossover search: the question is whether the omission CAN be decisive, not whether it always is.
If the crossover comes out above 1.0, check the direction of the while loop.

05Retrieve & space

An omission is acceptable only while it cannot change the conclusion, which is testable.
A boundary that was reasonable can become indefensible without the document changing, because the terms moved.
Ask of any claim what is outside its boundary and whether that term is growing.

06Mastery & project

State the general rule for when an omitted term must be disclosed, in terms a reader could apply to a claim in any field.

Find an efficiency claim that draws a boundary and identify the largest term outside it. Determine whether that term could change the conclusion, and say what you would need to know to decide.

GO FURTHER · THE LIVE PLAYGROUND

Where this crossover comes from ↗ · The same arithmetic with the gait under your hand, and the reference points marked.

← Choose the conditions, choose the answer What a signature buys →

PYTHON · NUMPY

What was left out

One omission, three eras of leg. Find where it stops being a rounding error.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you