Though Newton is best known for his quantification of the force of gravity, it is his development of Calculus that really impresses me. He developed an entire system of mathematics in order to more accurately model the universe.
That’s all that mathematics is, of course. It is a way to model the universe in order to make both records and predictions. The predictive analysis part is fascinating, but it is really the recording part that led (and leads) to all the rest.
The purpose of predictive analysis, of course, is to answer the question, "How do we get there from here?" But first we have to answer the question, "Where are we right now?" And, of course, in order to answer that, we have to investigate from where we came.
This doesn’t mean we have to know the absolute beginning in order to begin. For instance, the Big Bang Theory gives us the ability to understand our place in the Universe even if it doesn’t answer the penultimate question. But we do have to pay attention to the way things are right now until we can discover a pattern.
Even the identity matrix doesn't work normally
It is this pattern which allows us to make predictions of varying degrees of accuracy about the future. The accuracy depends on the strength and continuity of the pattern we have discerned. We model a particular system through mathematics, thought experiments, or other, and then we can develop theories. If we can use our theory to accurately predict the future, then we have a reasonable assurance that we have accurately modelled that particular system within those particular constraints.
That is why we must pay close attention to the world around us. That is why we must pay attention to history. That is why, for instance, the argument that the cause of global warming is not important is foolish beyond belief. We have to understand how we got here in order to figure out how to get out. Without understanding cause and effect, we run the risk of using a cure that is worse than the illness. Mathematics is a useful tool we can use to help us define a pattern. Though it is not the only tool it is the one with the clearest rules.
A differential equation, to be solvable, has to be (among other things) continuous on the interval in which we are interested. As with most mortals , I am primarily concerned with the interval between my birth and death. My life has not been lived with mathematical precision. I have not been continuous.
Gandhi said that happiness is when what we think, what we feel, and what we do are in harmony. When I live parts of my life like that, then I consider myself continuous on that interval. Most of my life I have been in conflict with myself. I am not alone in this. The only examples of people who have been continuous their whole life I can find are in fiction: John Galt and Howard Rourke (from The Fountainhead).
When I am not in harmony I am not continuous. It makes me unpredictable. I am being pulled in multiple directions instead of driving myself towards my goal. My course corrections, as I vacillate between the conflicting parts of my personality, are great wastes of time and energy. It is much more efficient to spend a little time to bring myself into harmony before acting.
I cannot go backwards in time and change my behavior, but I try to change the present in order to create the future I desire. Ironically, I have a tendency to dwell on the past which interferes with my ability to create the future. Of all the bad habits I have left, that is the one I most desire to conquer. When I find myself off track, I try to get back on track as quickly as possible.
Today is the last day of the first of my life.
Don’t let yesterday take up too much of today –Cherokee Proverb
Well, I’m here to tell you now each and ev’ry mothers son. You better learn it fast; you better learn it young, ‘Cause, someday never comes.