Really Useful Engines

Continued from Part 1:

What is Entropy? – Part 1

1. The Grammar of Entropy
2. Algorithmic Information Theories of Life
   1. Life as a Demon: The Cost of Information
   2. The Algorithm of Survival
   3. Coding for Diversity
   4. Life-Forms Must Be Efficient
3. The Mathematics of Efficiency
4. Universal Really Useful Engines
5. Compossibility: The Thermodynamic Case for Diversity
   1. The Ethics of Aliens
   2. Does Time Stop for A Sufficiently Knowing Being?
   3. The Final Cycle
6. Footnotes

The Grammar of Entropy

“**But entropy, heat, past and future are qualities that belong not to the fundamental grammar of the world but to our superficial observation of it. ‘If I observe the microscopic state of things,’ writes Rovelli, ‘then the difference between past and future vanishes … in the elementary grammar of things, there is no distinction between “cause” and “effect””**1

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“you cannot step into the same river, for fresh waters are ever flowing"1

Entropy is a fundamental concept representing change and flow in the universe. It reflects the transformation of usable energy and the complexity of information uncertainty navigated by life-forms.

In a recent article on inequality I incorporated the concept of entropy, so it seemed worthwhile explaining this much misunderstood concept:

In this article I want to break down some key concepts about wealth and income distribution utilising concepts from thermodynamics and entropy to show how gamed current economies and societies are and, more importantly, how we can undertake long term policy changes to fix it.

The G20 recently released the Global Inequality Report,1commissioned by the G20 South Africa Presidency in November 2025 and led by Joseph E. Stiglitz. It characterises global inequality as an “emergency” and a “policy choice,” asserting that the negative trends can be reversed. The report finds that 83% of countries globally exhibit high income inequality encompassing 90% of the world’s population. This crisis is primarily driven by wealth concentration, which is far higher than income inequality.

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Continuing the previous article:

The Limits Of Language & Logic

1. Gödelian Incompleteness and Turing’s Halting Problem
2. The Limits of Logic & the Influence of Entropy
3. Non-Duality
4. The Limits of Language
5. Footnotes

Gödelian Incompleteness and Turing’s Halting Problem

Hui Yang, “Nursery of New Stars”, University of Illinois, Wikipedia, NASA, 1995.

A kingfisher in a shaking flight over the river Berkel in Vreden / Germany / NRW, Joefrei

“…As kingfishers catch fire, dragonflies draw flame;

As tumbled over rim in roundy wells

Stones ring; like each tucked string tells, each hung bell ’s

Bow swung finds tongue to fling out broad its name;

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