iSoul In the beginning is reality.

Convergent induction

History of Chemistry, Simplified

The simplest universe has only one kind of substance, which was the first scientific theory, that of Thales (ca 585 BC) who stated that the origin of all matter is water. Then there was Anaximenes, who held that everything in the world is composed of air. Xenophanes said, It’s all Earth. No, it’s all fire, said Heraclitus.

Empedocles combined them all in his theory that all matter is made up of four elemental substances – water, air, earth, and fire – in fixed quantities. The Pythagoreans taught that all things are composed of contraries. Aristotle combined the four elements of Empedocles and the contraries of the Pythagoreans and said that every substance is a combination of two sets of opposite qualities – hot and cold, wet and dry – in variable but balanced proportions.

Leucippus and Democritus disagreed with this approach and took the opposite position that all matter is made up of imperishable, indivisible entities called atoms. The atomic approach languished until many years later it was revived during the Renaissance. It was further developed by Dalton and others in the 19th century. Basic combinations of atoms, called elements, came to be seen as the building blocks of all substances. The list of elements was expanded into the Periodic Table which is key to the very successful science of chemistry today.

The so-called Ockham’s Razor, which may be stated “entities must not be multiplied beyond necessity”, is usually understood as a preference for simplicity. But it ignores trade-offs between, for example, a plurality of substances and a plurality of entities. Which is simpler, Thales’ single substance in many forms or Democritus’ single form but many entities?

Convergent Induction

There are three related lessons to be taken from this brief historical review: (1) science starts with simple, extreme positions; (2) for every simple, extreme position there is an opposite simple, extreme position; and (3) science develops complex, intermediary positions between simple extremes.

(1) It is well-known that science follows a principle of simplicity (parsimony) which leads it to start with overly simplified ideas, find their empirical weaknesses, and then gradually add complexity. As A.N. Whitehead said, “Seek simplicity and distrust it”.

(2) Simplicity comes in pairs. This is demonstrated in the case of chemistry between the extremes of one or a few substances and the opposite extreme of many atoms. There is the simplicity of a few unique entities vs. the simplicity of many uniform entities. There is also the simplicity of simple stasis vs. simple dynamics. These contrary simplicities have loomed large in the history of science, and many other subjects.

(3) While science begins with simple, extreme positions, it does not stay there. It progresses toward complexity. In an analogue to the mathematical theorem that any bounded increasing (or decreasing) sequence is convergent, simple extremes provide the bounds that ensure progressive induction converges.

Thus science proceeds via convergent induction, which is bounded by simple extremes and seeks empirical adequacy by progressively converging toward a complex mean. The process is progressive in that each step introduces a complexity not present before. Convergence is ensured by bounding the progression with simple extremes.

It is most usual to begin with one extreme and work in the direction of the other extreme rather than to oscillate between opposites in a convergent way. In general, there are two strategies for inductive logic: (1) assume the most about what is unknown and (2) assume the least about what is unknown. Natural science takes approach (1) and statistical science takes approach (2).

There are two directions for each of these approaches. Statistical science may be approached from the direction of maximal or minimal knowledge. For example, if there is knowledge of the physical source of variability such as by examining a pair of dice, then a frequentist direction may be best. If little is known except some empirical data that are gradually available over time, then a Bayesian direction may be best.

Natural science also has two directions. The most that can be assumed about what is unknown is that it is like what is known. But that may be either because it is a different form of the same thing or because it is a different combination of the same constituents. The former direction is top-down, macrocosmic, whereas the latter direction is bottom-up, microcosmic or atomic. The atomic direction has proved to be the most fruitful for natural science.

Since the convergent is a kind of mean between the initial extremes, that leads to the question of whether it would be possible to follow means instead of extremes. One could start with a simple mean between the extremes and then adjust it to another mean as need be. Perhaps this would be more efficient.

October 2010

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