# Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments

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## Abstract

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## 1. Why Biology Looks so Different from Physics

People think of biology as a very accidental science. One where what we have today is a result of a whole series of accidents …But they think of mathematics, for example, as the exact opposite. As a very non-accidental, completely sort of determined-by-higher-principles kind of science …I actually think it’s the opposite way round.

#### 1.1. Individuation and the Value of Information

## 2. Stochastic Environments and Biological Thermodynamics

#### 2.1. The Information Content of Life

#### 2.2. Requisite Variety

#### 2.3. Markov Chains

**Figure 1.**An example of a simple 5-state Markov chain with simple transition probabilities represented as a stochastic finite-state automaton diagram.

## 3. Computation and Life

Brenner said much the same thing in his recent essay in Nature [20]:DNA is essentially a programming language that computes the organism and its functioning; hence the relevance of the theory of computation for biology.

He continues:The most interesting connection with biology, in my view, is in Turing’s most important paper: ‘On computable numbers with an application to the Entscheidungsproblem’.

Arguably the best examples of Turing’s and von Neumann’s machines are to be found in biology. Nowhere else are there such complicated systems, in which every organism contains an internal description of itself.

#### 3.1. Complexity and Algorithmic Structure

#### 3.2. The Information Content of Organisms and the Extraction of Energy from Strings

## 4. Life, Predictability and Structure

In calling the structure of the chromosomes a code-script, we mean that the all-penetrating mind, once conceived by Laplace …could tell from their structure how the egg would develop …

#### 4.1. Simulation of Increasingly Predictable Environments

#### 4.2. Energy Groups

**Figure 2.**Energy groups: Possible extraction values from the different energy groups among all the ${2}^{n}$ strings of increasing length $n=4,\dots ,7$. Each figure can be read as follows: Taking the first plot (top left), there is 1 string that has an energy return of 0 units of energy (0000); 4 strings that return 1 unit of energy (e.g., 0100); 6 strings that return 2 units of energy (e.g., 1100); 4 other strings that return 3 units of energy (e.g., 0111) and finally 1 string that can return the maximum energy (1111).

**Figure 3.**Shift of the distributions of energy groups for strings of increasing length $n=4,\dots ,7$, modeling a very simple potential predictable environment represented by a 1-order HMM (compared with a 0-order HMM in Figure 2) in a scenario for $p\ne 0.5$, where given a state, an organism can potentially make an optimal choice based on the transition value of the next state according to p. The bulk of the values, measured by a negative skewness, clearly lie to the right of the mean, indicating the predictability of the environment (mirrored by the learning capabilities of living organisms) and therefore a possible positive energy extraction.

#### 4.3. Organisms Survive (only) in Predictable Environments

#### 4.4. DNA, Memory in Simple Organisms and Reactive Systems

## 5. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Zenil, H.; Gershenson, C.; Marshall, J.A.R.; Rosenblueth, D.A. Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments. *Entropy* **2012**, *14*, 2173-2191.
https://doi.org/10.3390/e14112173

**AMA Style**

Zenil H, Gershenson C, Marshall JAR, Rosenblueth DA. Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments. *Entropy*. 2012; 14(11):2173-2191.
https://doi.org/10.3390/e14112173

**Chicago/Turabian Style**

Zenil, Hector, Carlos Gershenson, James A. R. Marshall, and David A. Rosenblueth. 2012. "Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments" *Entropy* 14, no. 11: 2173-2191.
https://doi.org/10.3390/e14112173