Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name or formally describe).
The four rules of the cartesian methods are:
The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.
In order to justify my claim that the cartesian method is an analysis (or compression) technique, I shall comment these rules one by one.
1. this rule is made by several parts:
- “never to accept anything for true which I did not clearly know to be such”
- “to comprise nothing more in my judgement than what was presented to my mind”
- “so clearly and distinctly as to exclude all ground of doubt”
The first part looks like a thinking hygiene: be sure about your hypotheses.
The second part has to do with the limitations of our brains capacity to process a complex topic. As such, these limitation have nothing to do with the topic under study. Of course we can’t advance our understanding of a subject if we can’t wholly grasp it in our minds. However, is important to remember that when we splice it in smaller, more understandable parts, we introduce an element which has nothing to do with the subject of study, but with our capacity of understanding (and our prejudices, indeed, as witnessed by the fact that the same research subject is spliced differently in different epochs or places, according to cultural prejudices and not biological “computing power” reasons).
The third part has entirely to do with our limitations. In order to understand the topic, we have to use techniques which “exclude all ground of doubt”. The great importance of doubt as a tool for understanding is one of the most viral parts of the cartesian method. It is one of the main ingredients of the scientific method.
2. two parts here as well:
- “to divide each of the difficulties under examination into as many parts as possible”
- “and as might be necessary for its adequate solution”
While the first part is clearly an analysis technique, the second part tell that the purpose of understanding is to find a solution for a sequence of problems. Each small part, each difficulty has to be solved. To make a comparison, say that we have a huge cake to eat, so we chip at it with our small mouths, claiming that our goal is to well chew each bite.
This is a compression technique: we divide the cake into bites, then, as we chew each bite, we forget about the others. The bad part is that the cake is not just the sum of the bites.
3. This is the most problematic rule, because here is given total priority to the understanding over the subject of understanding. The analysis and compression technique from the rule 2 is taken to extreme: first is suggested something like an eager evaluation
- “to conduct my thoughts in such order that”
- “by commencing with objects the simplest and easiest to know, I might ascend […] to the knowledge of the more complex”
- “little and little, and, as it were, step by step”
… then, in order to be sure that the eager evaluation works,
- “assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence”
otherwise, who cares about the subject of understanding as long as I can produce an working algorithm? Then, we study the algorithm and we forget what was all this about. This looks like the most harmful part of the cartesian method and the main source of the cartesian disease…
4. … until we read the last rule:
- “in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted”
But if we already renounced at the subject of study and we already (recursively) replaced it with an artificial division, enumeration and analysis technique, this rule is only a proclamation of the superiority of understanding of reality over the reality itself: if the understanding of reality is internally coherent, then it is as good as the reality itself.
Conclusion. The cartesian method is designed as a technique for understanding performed by one mind in isolation, severely handicapped by the bad capacity of communication with other isolated minds. It was a very efficient technique, which is now challenged by two effects of its material outcomes:
- better communication channels provided by the www,
- mechanical, or should I say digital, applications of the method which largely surpass the capacity of understanding of one human mind, as witnessed for example by the first computer aided mathematical proofs, or for another example by the fact that we can numerically model physical phenomena, without understanding rigorously why the method works.
UPDATE: if you read this, then you might be interested to read “Descartes, updated” at The “Putnam Program” blog.