Chapter 23. Learning from Experience

1 Poincaré1 describes the process of creation of a mathematical formulation thus:

If a new result is to have any value, it must unite elements long since known, but till then scattered and seemingly foreign to each other, and suddenly introduce order where the appearance of disorder reigned. Then it enables us to see at a glance each of these elements in the place it occupies in the whole. Not only is the new fact valuable on its own account, but it alone gives a value to the old facts it unites. Our mind is frail as our senses are; it would lose itself in the complexity of the world if that complexity were not harmonious; like the short-sighted, it would only see the details, and would be obliged to forget each of these details before examining the next, because it would be incapable of taking in the whole. The only facts worthy of our attention are those which introduce order into this complexity and so make it accessible to us.

2 This description closely resembles the psychoanalytic theory of paranoid-schizoid and depressive positions adumbrated by Klein. I have used the term “selected fact” to describe that which the psychoanalyst must experience in the process of synthesis. The name of one element is used to particularize the selected fact, that is to say the name of that element in the realization that appears to link together elements not hitherto seen to be connected. The representations of the selected facts may then be seen to have a similar coherence if the appropriate representation for a number of selected facts can be found. The selected facts, together with the selected fact that

appears to give coherence to a number of selected facts, emerge from a psychoanalytic object or series of such objects, but cannot be formulated in accordance with the principles governing a scientific deductive system. Before such a system can be created the selected facts have to be worked upon by conscious ratio