The mathematics of Zen-ness

Most internal mental models that provide this "Zen thing" are acquired as a result of experience. In the world of e-business, where constant change and uncertainty compromise the value of experience, we have to rely, like the professional poker player, on mathematical constructs.

However, the mathematics we need for Zen-ness is not the type of mathematics that mathematicians use. We need only a rough understanding of the underlying concepts. We won't want to get into any complicated formulae or rigid proofs. For Zen-ness, we can generalise the mathematical concepts and pervert their use for our own purposes. Mathematicians might go into fits of apoplexy when they see the way we distort and misuse their concepts, but, how many brilliant mathematicians make it to become successful businessmen?

An email to an Internet discussion forum typified the hostile attitude of many mathematicians to the misuse of their precise formulations. It offered the proposition: "The square root of minus one has the odour of garlic" as an example of a distortion of mathematical principles. This, claimed the poster, was using mathematical constructs outside of their strict mathematical meaning. The poster described this as "modal misrepresentation". He condemned all statements of this type as being completely meaningless because they can never arrive at a point where the truth or falsity of a proposition can enter into the discussion.

The poster continued by listing a few examples of this "modal misrepresentation": examples where he thought popularization was not accurately portraying the correct mathematical principles. His examples were "Networks, Cellular Automata, Chaos, Fractals, Heuristics and above all, Emergence". As these are the very concepts that we are dealing with in this book, it is worth a moment to see why he thinks it is wrong to apply these terms to situations outside of their strict mathematical context.

To the poster, the items in this list came into the same category as the proposition about the square root of minus one and the smell of garlic; his reasoning told him that if you cannot arrive at a point where truth or falsity come into the picture, the proposition has no value.

What this poster had missed was that the current use of these mathematical terms is not about propositions at all: their current popularity is due to the fact that they provide practical conceptual models to give a rough understanding of some of the underlying features of complex dynamic systems. True, they cannot lead to anything mathematically exact or conclusive, but, they can provide a first order approximation of what is happening. This is a whole lot better than nothing and can give a distinct competitive advantage over a competitor who has no model at all.

Certainly, this woolly use of mathematical concepts will never arrive at any point where the truth or falsity of a proposition can enter the discussion, but, it will provide that enigmatic quality of, what we are calling here "The Zen thing": a rough guide to what is going on in a seemingly confusing world. This is why there is now a flood of popular interest in Networks, Cellular Automata, Chaos, Fractals, Heuristics and Emergence.

People are looking for this Zen-ness because is will allow them to compete successfully in the perplexing and complex environment of the Internet and E-Business. Meanwhile, the more precise mathematically minded might be left behind, indignant, bewildered and probably floundering in their own attempts to understand the complexity of the Internet.

One of the reader's of the original draft, Robert Moorhead from Austin, Texas, made the following comment:

As I read, something bothered me that I couldn't put my finger on. After some reflection I came to the conclusion that the Zen analogy strikes me as fuzzy, in the sense of ill-defined. I suppose because of the unfamiliarity of the subtler aspects of Eastern thought to Western minds. I understand the point Peter is making, but I think the argument could be better served by appealing to more, I don't know..., concrete or rational, I suppose.

Tor Norretranders, in his book "The User Illusion" makes the point that human consciousness is only capable of processing a couple of tens of bits of information a second, while our senses (or unconscious) are constantly processing millions of bits per second. The difference in input is not just discarded, but in Norretrander's view, is processed at a less conscious level to appear as intuition or gut feelings. This is a VERY simplified version of the Zen concept, but it seems to me to get at Peter's (and Mrs. Brisby's) point in a more direct way.

Robert Moorhead

Robert Moorhead is quite right, this use of Zen to explain a non logical approach is fuzzy, but, this is the whole point of describing it as Zen ­it is because the conclusions are fuzzy. But, this fuzziness is a lot better than being blind.

What type of playing field is the Internet?

Judging from Industrial Age corporate attitudes and dogmas, it would seem that at some point in time, probably around the middle of the twentieth century, the conventional way of doing business became relatively stable. This stabilisation allowed much of business activity to become standardised, with procedures being established and universal protocols agreed. This stabilisation enabled business practice to become not only more effective and efficient, but, teachable. This had many advantages, not the least of which was to allow corporations to expand and take over vast tracts of trade and commerce.

The Internet and the advances of computers and digital communications have thrown a big spanner in the works of these established Industrial Age business practices. Suddenly, there has arisen the potential for using new techniques, new strategies and on such large scales that it is almost certain to disrupt the established order of the Industrial Age. The changes are already starting to happen and more and more people are becoming aware that something new is afoot.

Despite this general awareness, very few Industrial Age managers and executives are taking seriously the evidence that these changes are escalating into chaotic turbulence. Few appreciate that the advances in computer technology and digital communications are liable to throw the whole system of trade and commerce into a radically new state. The new state is likely to involve completely new ways of doing business, requiring different attitudes, methods, procedures and protocols from those that evolved during the Industrial Age. This would make many traditional business practices redundant. Much of current training and educational material will be rendered useless; previous experience might count for little.

The industrial revolution brought people in from the countryside to work in factories and offices. Business activities became centralised at specific geographical locations. Towns and cities grew up, with populations becoming more and more concentrated at focal points. With the possibilities now available for computer enhanced, digital communication, it is now no longer necessary to concentrate populations in quite the same way. This could dramatically reverse the trend for populations to concentrate at population centers, leading on to who knows what other changes in living and life-styles.

Already, we have deskless offices and virtual businesses where employees live hundreds, even thousands of miles away from each other. There is no need to travel into work each day if the work can be done just as easily at home or in a place of exotic scenery. If the changing patterns of business allow a better life-style, a better way to live, isn't it likely that this is the way things will go?

Such changes do seem possible, even probable and when talked about will get heads nodding in agreement. But, of more practical concern is not 'if' these changes will take place but 'when' and 'how'. This exposes a vast conceptual divide between Industrial Age and Information Age thinking: the conceptualisation as to how and when these changes might take place are totally different.

Industrial Age thinking will be familiar with order and organisation and see changes taking place gradually and linearly with ample warnings and signs of impending change. Information Age thinking will be familiar with the chaotic characteristics of complex dynamic systems and will be expecting changes to take place unexpectedly, suddenly and dramatically with no warnings or signs that changes are afoot.