[DSRP Evidence](https://dsrpevidence.org/)

# When the Map Is Better Than the Territory

## Details

**Authors** Hoel, Erik P.

**Year** 2017

**Publisher** Entropy

**Kind of work** article

**Discipline** Information Science

**Secondary disciplines** Neuroscience, Complexity Science

**Applied** false

[Read it at the publisher](https://doi.org/10.3390/e19050188) 
10.3390/e19050188

## In authors' words

### What they set out to do (purpose)

To show that a coarse-grained macroscale description of a system can be more informative about its causal structure than a fully detailed microscale one, and to ground this in Shannon's channel capacity.

### Who or what was studied (sample)

Formal toy systems: three 4-state Markov chains, an 8-state Markov chain with a coarse-grained macroscale, and a light switch versus a light dial.

### How they did it (methods)

Effective information (mutual information between interventions and their effects) is decomposed into effectiveness and the entropy of the intervention distribution, and compared across scales.

### What they found (results)

For the 8-state chain, effective information is about 0.55 bits at the microscale and 1 bit at the coarse-grained macroscale, a gain of 0.45 bits. The three 4-state chains have 2, 1 and 0 bits. A switch gives 1 bit and a dial 8 bits. Macroscale descriptions can therefore carry more causal information than microscale ones.

## Commentary

### In short

Using small information-theoretic models, the paper shows that a coarse-grained description of a system can capture its cause-and-effect structure better than the full detailed one.

### Response

The result concerns wholes described at a higher level having causal properties not found at the level of their parts (system), measured as how strongly interventions determine effects (relationship). Caveats: only the abstract and the first part of the text were read, the examples are toy models, and the paper frames scale in terms of causal models rather than observer vantage, so the fit to perspectives is not claimed.

**Patterns it shows** S, R

Formal proof or model

**Added** 2026-10-26

**How to cite this** Hoel, Erik P. (2017). When the Map Is Better Than the Territory. Entropy.