Aloha Anon: Thank you for your comments. You've asked three good questions.
Q. Your analogy of natural flows and walking with the river is interesting. Could you expand a bit on this and how using a mathematics that flows with nature could alter science as we know it?
A. It is my contention that the very foundation of modern mathematics is built upon axioms and postulates that have little to no relationship to the natural world and are, at best approximations and at worse, misleading. Mathematics is based on discrete numerals; there is nothing fuzzy about a 4 or 9; because integers are defined to be constructed from monads which are defined to be equivalent to one another and hence discrete. There is nothing fuzzy about a meter - all meters are defined to be equal to one another. However, nature doesn't define anything to be equal to one another; everything changes with time. You are not the same person today you were yesterday, and you won't be the same person tomorrow. We don't skip, jump or hop from one scene to the next like a movie frame; we morph or flow, a continual, analog process. This is not unique to living organisms, the physical world does the same, but at a slower pace; the ebb and flow of tides, climate, even rocks disappear grain by grain until a pebble is left, and then that too is gone. At what point does a rock become a pebble, the pebble a grain of sand, and the grain a molecule? The lines we draw around things in order to call them the same are artificial boundaries that have meaning only in the human world, not in the natural one.
A river was first used as a metaphor by Heraclitus, and later by Plato. As a flow on earth it's a nice example, all sort of things can be carried along, some stopping for a spell, but eventually all ending up at some far off objective. As far as stepping in the same river twice, well as far as most are concerned one can do just that. We see the river, we give it a name, Mississippi River - sometimes it's turbulent, wild, other times placid and calm - but it's still the Mississippi River. We ignore the fact that as we stand in the shallows of the Mississippi River the water, and all that its carrying, swirling about our feet, is constantly changing. Hopefully, the concept of flows will make us more aware of the things that are continuously changing rather than concentrating on the river, which changes little from day to day and hardly at all in memory.
Q. How would this be different than the results of today's science which has it's own so called flow, a flow of continuously asking the same or similar question to demonstrate repeatability and achieve consensus?
A. It often appears that science does the same thing when replicating a previous experiment so as to verify or refute a previous one; and therein lies the rub. If an experiment cannot be replicated then how can one verify its veracity? Experiments utilizing inanimate objects can, usually, be replicated to a high degree and statistics applied. First, because inanimate objects typically change slowly over time, thus their similarities do likewise. So in a laboratory, where the many variables that thrive outdoors can be, more-or-less, controlled, one can flip a coin many, many times before anything different than a head or tail appear. However, take the experiment outdoors, over a mud puddle or sand box and, assuming a sea gull or dog doesn't grab the coin before it hits the ground, a third choice becomes apparent; the coin will occasionally land on its edge and remain so. Even physical experiments are not devoid of location.
Life might be considered as the physical world on steroids. Many of the same elements are involved but in unique ways. But life, unlike inanimate objects, has all sorts of behaviors that a coin can only aspire to. So obtaining the same level of repeatability with systems involving living organisms as with inanimate objects is much more difficult if not impossible. Without getting into the numerous ways statistics can be and are misused, suffice to say that the sample size and uniformity are quite important as to its validity; as mentioned in my essay the use of a sub-sub population class (undergraduates) to define human behavior. Most studies of natural attributes, humans in particular, end up with bulk of the sample grouped around a norm, with lesser numbers trailing off to either side; a distribution in the shape of a bell curve. We concentrate on the norm and those closely surrounding it, and all but ignore the outliers. Humans are unique, but some are more unique than others; for example, about one in sixty thousand of us, have the heart and other asymmetric organs on the opposite side. What medication, or procedure, might work for the majority might be fatal or un-performing for the outliers, or vice versa. If the sample is too similar then the results are only going to apply to those who are similar to the sample, and maybe not even then. Because there are near endless ways to group a sample, studies continue that appear to be addressing the same thing but are, in effect, looking at how it affects a different group. Soils are notoriously variable, back in the late 1940's and early '50's fertilizer studies were quite common; apparently little has been settled as they're still being conducted.
Q. Would the results remain similar, but our perception, understanding, and use of the results be what is profoundly different?
A. That would depend upon the system under discussion. Laboratory studies, where many variables can be controlled, would likely remain the same. Field studies would be different. Good, knowledgeable managers can generally move a complex, dynamical system towards, but not necessarily reach, a well thought-out and reasonable objective through continuous monitoring and timely reaction to inevitable changes - something that present mathematics cannot do. What the manager cannot foretell are all the incidental details that will be occurring as the system moves through time. I suspect that utilizing an analog-mathematics will increase the chances of getting closer to the objectives and will likely fill in more of the details. Our present economic system is based on a linear mathematics, which when applied to the natural world, is essentially that 'take and run' philosophy that helped us get to the agricultural age; it also got us to the present situations so eloquently discussed in the daily media.
