Psychologist Gerd Gigerenzer once compared the three approaches to the three Freudian selves in unconscious conflict.

A Bayesian analysis of the data from a simple experimental design is straightforward. Recall that the theorem implies that the posterior is the likelihood weighted by the prior…

What, then, are the parameters of the normal distribution? An idealized, normal distribution is fully determined given two quantities: its midpoint and its width.

Why are normal distributions so normal? The answer is partly because of selective reporting. In physical systems, an indefinite number of random factors combine to affect an outcome. 

The shape of a probability distribution reflects – albeit very indirectly and cryptically – logical properties about the generating mechanism underneath.

We saw with the brain-as-a-Bayesian-statisticians that the number of hypotheses we can entertain is limited…

The insight that science will progress faster if it focuses on differentiating evidence, is extremely profound, and the most important concept in the philosophy of science.

If we let the unconscious cognitive processes constitute a filter, we find not only the filtration of how the brain collects data, but also biases in what hypotheses it focuses evidence acquisition on.

In philosophy of science, the fact that the hypothesis space is never exhaustively specified is known as “under-determination of theory by data”.

Selection effects also figure heavily in discussions regarding the eerie nature of mathematics, and as physicist Eugene Wigner said, its “unreasonable effectiveness” in physical predictions.

If you ever find yourself forced to summarise the ideas of western philosophy in a single metaphor, then the concept of a “self-modifying filter” may be your safest bet.

Information theory introduced the image of system boundaries as implicitly projecting “input categories” upon reality, parsing it into “variables” with an associated space of possible outcomes. 

So far reality has been depicted as a disorderly mist, fractured with a scatter of low-entropy pockets – “systems” – that feed on each other in a swirling, co-adaptive dance towards ever-increasing complexity.

“Order” and “disorder”, we have seen, are observer-dependent categories of a dynamical system’s state space. What characterizes disordered states, relative to any observer, is that different disordered states do not differ in any meaningful way.

Shannon’s measure of information is actually known as “entropy”, a word better known from thermodynamics, whose famous second law states that, in a closed system, it always increases to a maximum

Most psychologists studying perception and cognition today argue that Gibson’s radio-metaphor is flawed because a brain, unlike a radio, identifies a “signal” not directly, but in a memory-dependent way.

The language used so far may have seemed too removed from the number-crunching chores of experimental science to be anything else than a whimsical indulgence. 

The idea that any system can be said to have its own ontology – its own distinctive way of carving up reality – means that its structure distinguishes between “inputs” and couples these to certain “outputs”.

Ontology rests on the idea that reality is not perfectly uniform – that it has discontinuities. To develop a sense of these “contours”, hierarchy theory provides a crude and attractive account that makes for a good beginning.

“Ontology” is sometimes described as “carving nature at its joints”, reflecting the idea that we are substructures of some evolving fabric – colorless, soundless, and flavorless – that has contours.

The aim of the preceding sections was to introduce for the general reader the concept of hierarchical thinking – to raise awareness of how both the observer and the observed contribute in perception, not unlike how the fishing net and the water contents interact to determine what kind of fish is captured. 

The unreasonable ubiquity of hierarchies should be suspect. Is the fact that you need a B to get from A to C – the fact that any accomplishment stands on the shoulders of giants – so trivial and arbitrary so as to be practically worthless?

Lest we forget, you too are a system pervaded by hierarchies. Like all other systems, the human observer has a surface that defines discontinuities in information flow.

We concluded last section by linking Simon’s watchmaker parable to Holland’s multiplier effect to show that reproduction’s inevitable incorporation of error creates an innate bias to increase complexity.

The mechanisms that afford the hierarchy its position as the central architectural principle in complexity can be understood at greater depth with reference to the signal/boundary framework by John H Holland.

“Why is reality structured at all?” was what Herbert Simon, an extraordinary polymath regarded as one of last century’s most influential thinkers, asked himself in his watchmaker parable from the article “The Architecture of Complexity” (1962).

Quite possibly you too have walked across an abandoned university campus, numb from a last-minute revision-session in the library, with a quivering kind of wonder at the contrast between the physical reality surrounding you, and the cerebral strives in abstract-land that left your mind in such a somber state.

Towards the close of childhood, there typically comes a moment of realization that our time is finite while the knowledge out there isn’t.

This collection is about the scientific endeavor to find concise descriptions for how patterns in Nature are generated, and this is an endeavor that has taken twisted and unexpected turns