When it comes to post-Newtonian physics, let’s take General Relativity, it is easy for most of us to ignore it in our daily lives and in our thinking. The fundamentals of General Relativity are relatively easy to understand. We experience these things firsthand and the examples can be related in simple scenarios involving elevators in freefall, accelerating rockets, balls bouncing on a moving train flat car or station platform.
As far as we are concerned, it has little impact on our social relations or what we believe we are doing most of the time. Even physicists do not go around expressing themselves in those terms, if for no other reason than they are not a common frame of reference for the rest of us.
With biology and psychology, however, the subjects touch us more closely. As these studies deal directly with our bodies and our behavior, opinions tend to slip in more readily. Also, unlike General Relativity, these studies hit us where we live and can be described with observable examples that seem to have more immediate relevance.
This has advantages and disadvantages. We naturally have different points of view when we look at things we can observe. Findings in these studies and their implications for what we actually do, how we do it, personally and in our social relationships, are matters of interest. Our interest is no longer strictly scientific.
You may have picked up on something else here, depending on how carefully you happen to read.
More frequently than not when we believe we are thinking rationally something else is going on because of the words and the concepts we use to shape our thoughts and their metaphoric nature. Outside of mathematical expressions, our ideas are not strictly limited to quantity or precise expression at all.
It is not only that we have tendencies to shift in our thoughts among different modes of expression and to allow feelings in. The words themselves just don’t work the way most of us believe they do, and unless one is just thinking and talking alone, what is being said becomes open to others’ interpretation. And it needs to be. That is part of what communication is for.
Math is not entirely free from these complications. It is easy to make errors when what is being described approaches reality. The more rudimentary stuff most of us learn in school and then run away from the rest of our lives is based on false assumptions that things are fixed instead changing all the time, which was necessary, in order to prove the opposite. Go figure, literally.
But let’s consider numbers figuratively. Because numbers can be connected immediately with things, such as our fingers and toes, we become very familiar with them early in our lives. It is a good place to start.
In mathematics, here’s how we define integers:
in·te·ger /ˈin(t)əjər/ noun
- a number that is not a fraction; a whole number. “M represents a positive integer greater than one”
- a thing complete in itself.
In a certain sense all integers are equal in that they are of a class of things, even when we also know they have different values. We know that 1010 (“ten to the tenth power”) is a big quantity, numerically. Also, when we say it or see it on the page, it takes up more space than 1 (“one”). But they are both the same in terms of being whole numbers.
Then there’s 0, “zero,” which represents nothing, while spatially its character is bigger than one and has two syllables when we say it. If zero is a thing complete in itself, a whole number, but also represents nothing, how can that be? Nothing in math is a concept, as it is also a word. If we consider, Wallace Stevens’ poem “The Snow Man,” the word and concept of “nothing” can express different things if we make it so with our intentions.
The intention here is not sophistic but to bring attention to the way our minds get confused by certain concepts, patterns of expression, and in time. Evolution is something generally accepted as a theory based on ever-increasing solid empirical findings. It is also a word with other meanings, including the concept of progress.
Because of that connection it is easy to misunderstand the theory. Single-celled creatures, like numbers as a category of things, are no better or worse, of no less value than humans in strict evolutionary terms. But that is not how we consider ourselves compared to cockroaches or to other contemporary animals.
We can dispense with some attitudes, such as biblical notions of humans’ having dominion over everything else. However, practically, in our lives and in our thinking, we do not strip away all vestiges of ideas of comparison and value. For example, because we descended from a common ancestor and speciated from mice, the common misconception is that we represent an advancement over rodents.
Species do not progress from one to the next in the sense of being superior. If we want to think about it as a competition, which is hardly scientific, it is not at all certain that we are winning in our struggles against rodents.
Anyone who has had to deal with gophers in the garden knows sometimes the rodents win the battle. Also, rodents as a group are still with us and may be around long after we go extinct. They have distinct advantages in critical areas of adaptability and procreation.
Thinking and even empirical observations are rarely strictly scientific. The closer the findings are to how we live and who we believe we are, the more interested we become. Where interests are involved, politics are present.
In a very real sense, the harder we try to limit the effects of metaphors and irrational features and focus our thoughts to be more scientific or mathematical, the greater the chance that we are engaging in circular reasoning, resorting to proof-like arguments and definitions. This is anything but scientific in most matters we are considering. Sure, if someone simply repeats what we said, in a sense that’s a repeat of our performance, but it is not an experiment or even a proof in the mathematical sense.
A great deal depends on where we start, the assumptions that often go unstated or are taken for granted, to be commonly understood. This is in part why throughout history up to now, intelligent educated persons have often made incredible errors at worst and, at best, simply fail to entertain alternatives, by asking more and better questions. We fail to probe our thinking band y raising exceptions and objections.
Getting back to numbers, even the coldest and most rational of us under the influence of some form of mild sedation, or with the science cap firmly on, have feelings about them. People have favorite numbers. Negative numbers seem to be less than positive numbers, not just because they are, mathematically, numerically speaking, but also because the echoes in the language make them seem so.
Who really gets into alternatives to base ten number systems? I suppose binary might really do it for some people, but does anyone get excited about hexadecimal? Hex? That sounds like something to do with spells and witchcraft.
Here we are again stuck with words. But who has time for this? What makes us think we don’t? Why is it that we don’t have time for so many things, things we would like to think about and do?
I Dwell In Possibility 