Distance becomes a score

Move the input and watch distance from a target become a scalar score. Find the symmetry yourself.

Teaching model · computed in your browser

Distance from unity

Move the input, watch the distance from 1 change, and calculate the score yourself.

U(x)=\frac{1}{1+|x-1|}

x is a real input and |x − 1| is its absolute distance from 1. The displayed domain is −3 ≤ x ≤ 5; the mathematical function is defined for every real x.

Try this: compare x = 0 and x = 2. Why do they produce the same score?

Experiment controls

Input x 1-3 to 5 · step 0.05

The default worked example is shown below.

Distance |x − 1|0

Unity score1

Maximum1Reached only at x = 1

At x = 1, distance is 0 and the score is 1. The peak is at x = 1.

Substitute, then simplify: U(1) = 1 ÷ (1 + 0) = 1. Equal distances on either side of 1 give equal scores. A score of 1 is a property of this function; it is not evidence of consciousness.

Reference inputs
x	Distance from 1	U(x)
-1	2	0.3333
0	1	0.5
1	0	1
2	1	0.5
3	2	0.3333

Turn exploration into understanding

Learn the ideas behind this lab.

Follow a worked example, practice on your own, and return to the original project sources.

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