Toolstransformers from scratch · B of 4

Weight Times Sand

The second half of attention: the output. The cabinet is the one from figure A. Each drawer gives weight × its sand to one cup, and the cup adds the three parts. The total in the cup is the output.

~/tools/transformers/pour-cup

move across to turn the queryfig B

output 2.47 = .80×2 + .14×5 + .06×3

What is what

Drawers: Open by their weights, as in figure A. Drawer 1 is blue, drawer 2 orange, drawer 3 green.
Sand: The value of each token: 2, 5 and 3 units, in the color of its drawer.
Cup window: One layer for each drawer, weight × sand, drawer 1 at the bottom. The scale beside it reads the total.
Readout: The same sum as numbers, for example output 3.73 = .38×2 + .57×5 + .04×3.

How to play

Moving the pointer left and right across the drawing turns the query, as in figure A.
The arrow keys turn it 10° at a time. The 0 key points it straight up.
With no input, the dial turns by itself.
A drawer with a large weight gives a thick layer; a drawer that is almost shut gives almost nothing.
The output always stays between 2 and 5, the smallest and the largest amount of sand.
With the query straight up, the orange drawer has the largest weight, so the output leans toward 5.

Each drawer gives weight × value, and the cup adds the parts. Because the weights add up to 1, the output is a weighted average of the values. The directions of the arrows and the amounts of sand are examples.