PRB-29

Uniform entropy

Discrete uniform entropy.

Reading speed

GoverningUniform entropy

Governing equation

H=\\log_2 n

$n \in \left[2, 64\right]$

where

n: n (—)
H: Uniform entropy (bit)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

H=\\log_2 n

$n \in \left[2, 64\right]$

$n = 2$ $H = 1$

Along the curve

②

Domain of the variable — blue

n_{\min} = 2,\quad n_{\max} = 64

$n \in \left[2, 64\right]$

$n = 2$ $n = 2$

Along the curve

③

Response curve — green

H=\\log_2 n

$n \in \left[2, 64\right]$

$n = 2$ $H = 1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}H}{\mathrm{d}n}

$n \in \left[2, 64\right]$

$n = 2.39$ $H^{\prime} = 0.609$

Along the curve

Lecture brief

Historical brief

Bernoulli trials, Poisson, Gauss, Bayes and Shannon entropy turned chance into a calculus of belief and noise. The lab computes likelihood, interval and information in SI-free counts. This sheet (PRB-29 — Uniform entropy) is the form associated with Uniform entropy. Working symbols: $n$ $\rightarrow$ $H$ . Discrete uniform entropy. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

H

from

n

in Probability & statistics via

H=\\log_2 n

Discrete uniform entropy. Use it when a real probability & statistics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

n = 8.000\,\mathrm{—}

, the governing relation

H=\\log_2 n

yields

H = 3.000\,\mathrm{bit}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

n n8 —

Outputs

Uniform entropy H3.000 bit

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Discrete uniform entropy. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube