Mathematics – A Beautiful Thing, Really
As follows – mathematicians are
“misled
by an undue brevity. He (sic they) appears to think that, at this point, the
advocates of infinity are content with a vague “and so on” – a sort of etcetera which is intended to cover a
multitude of sins. But etceteras,
common as they are in ordinary mathematics, where they are represented by rows
of little dots, are not tolerated by the stricter symbolic logicians.”
Bertand Russell from his “Axiom of
Infinity” (pub. 1904)
I hope I don’t loose a bunch of readers with this. As, I have known a vast number of people in my
life. And, having been a true nomad for
all of my life, I have known quite a
lot of people. Also being kind of
gregarious and having one of those faces, I guess, where people just come up to
me and start talking. Sometimes it a bit
strange. On that – another day.
I was never particularly fond of Math as a young
student. At least until I started to
seriously study Art and then wound up getting into pottery, which led me to
glazes, which led me to chemistry. I
discovered that if you learned chemistry, as it applied to ceramics and glass
compounds, you could develop lots of
cool colors and other effects to apply to your pottery. I found it fascinating. This was my initial discovery of what I think
of as “Everything is pretty much a matter of systems and when you can fully get
around in any particular system,
you can somewhat control it. And,
thereby achieve things you never quite thought you could achieve.”
So, one thing, then another thing … and I got into computer
technology and computer coding and it epiphanized on my brain that the binary system was a fraud.
So, in reference to my own small curiosity, a tendency to
“question everything”, I spent some pondering this religious reliance our modern world has placed on the binary system, or Base 2. I am of the
generation where “computers” were in
vitro, in their gestation
stage. So, it occurred to significant
number of politicians that, in order to keep up with the balls-out science of the Russians during the Cold War, steps
needed to be taken. “Sputnik” was
spinning around the planet and, yes, you could just step outside on any clear
night and see it pass blinking overhead.
Whoah!!! Amerkans can’t let that happen. Can’t have our – oh, enough of that
nonsense. Anyway, us American High
Schoolers were tossed into a new hair-brained notion that we must learn “New Math”. Let us just say that after a couple of years
of totally disastrous results, where a major number of Baby Boomers learned to really, really
hate Math, things went back to
previous mediocre pursuits of American High School Math.
But, right from the beginning, I thought, “Wait! Hey – how can you have something you are
calling Base 2 when the only numbers you are using are “0” and “1”? I don’t see no “2” in Base 2?” Now, I was a teen-ager during a historical
period where American married couples
were shown on the primitive TV’s, we had at the time, as always sleeping in separate beds. (Huh? !!!) Now what just a minute! You got two
people and together they can produce another person and yet there is always a constant distance between them.
“Just how does that work?”
To me, it says right off that distance is something that exists
and is often just sort of thrown out of a lot of Math – and, obviously out of
the plots and scripts of all of the super-dumb sitcoms of that era. As Bertand Russell points out, it becomes a
kind magical element. Or, instead of working out the details, and hence the full logic, of a given calculation, you
simply throw in an “etcetera”; an,
and-so-on. Assuming thusly, “We got
this far, so quite plainly, we get to infinity in the same manner.” Once again, “Huh?”
I would take all of this and propose my own view; the only
element, and this not being composed of a single
entity, but more of an element
composed of a compound structure and represented
by an acceptable symbol, could that element
that conceived of the initial
proposition; i.e. infinity. Or, the only element which can possibly actually be infinite is that which attempts to
conceive of infinity. A circular
thought, or theory? OR, is it more of a fractal “the study of continuous but not differentiable functions”; initially proposed by Gottfried
Leibniz in the 17th century.
At any scale,
the math remains the same, whether drilling into is assumed to be details or out scaling toward an
overview. Take any part of a fractal,
drill it and drill it and drill and the complexity remains constant. So remove the restrictions of scale, remove the notion of vector
points and all that is left is of what is assumed to be a line is a construct
of fractions of fractions. It becomes no
longer possible to say, “What is the distance from point X to point Y?” The only question possible is, “What is the relationship of point X to point Y?”
It then becomes
impossible to measure distance. All that can be done is to plot relationships. In order to do this we come to a project I
have been working on for many years and here is the link to that new blog:
Since this study
is a matter of theory and conjecture based on Mathematics, and I
refer to Base 3 Calculus, I wouldn’t
expect a whole lot of people to give it a try.
But if you are in any manner open-minded and intellectually curious,
the Math used is truly only a tool to condense the theory proposed.
Thank you Dear Reader and Joy be unto you.
dalepeterson.us
Just published “Twelve
Roses for Kathy – A journey on a motorcycle out of the darkness of bipolar
disorder”
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