The Foundational Circle
Ilexa Yardley 25 November 2009
I am planning to cross the street. I glance, first, to the other side. There is an invisible line between me and a point directly across the street from me. This line forms the diameter of an imaginary circle between me and the other side of the street, my destination.
This line and circle are stationary, or stable, as long as I do not move.
We can note that I can know this point exactly, but it is not necessary that the point be in an exact location. It can be inexact and exact at the same time (I can keep the circle stable, independent of the point, while I watch for traffic; there are a finite number of circles between me and my destination, as long as my destination does not move).
I look left to see a truck travelling in my direction. I am heading south to north. The truck is heading west to east, perpendicular to the line between me and my destination.
There is an imaginary circle around the truck, which tells me whether or not I have to worry about it (notice it). (I compare the imaginary circle around the truck to the imaginary circle around me). I look right and there are no vehicles approaching. So I do not have to worry about a truck (a circle) to the east.
There is an imaginary line between me and the truck. There is also an imaginary circle which is changing size as the truck reaches me (because the diameter between me and the truck is getting smaller as it moves closer to me).
I know I have to decide whether or not to walk in front of the truck, or whether to wait until the truck has passed. There is no traffic light where I am standing. The truck is moving, and I am still. I am not afraid to dart in front of the truck because I know how much time I have before he will hit me.
The truck sees me, or, some would say (insist), the truck driver sees me. He may not realize there is an invisible line and circle that is changing size between us (it is getting smaller as he is getting closer). He has no way of knowing whether or not I will dart in front of him.
I do not know the exact distance to cross the street. Likewise, I do not know the exact distance to the truck. Someone could measure it, but it is not necessary that I know the distance to make the calculation about whether, and-or when, to cross. I may not even realize I am using a circle to make this calculation; more correctly, the circle is using me to make this calculation.
Not only do I not need to know the distance, I also do not need to know the truck’s speed or whether or not he is accelerating, decelerating or maintaining a steady speed. I also do not need to know whether or not the truck is maintaining a perfectly straight line as it moves forward. (The circle takes care of all of this for me.)
I learned about these distances and speeds, how to calculate them formally, that is, but that was far too long ago, and, as I remember it, the ideas did not capture my attention. They somewhat bored me. I wondered, why would I need to know this? I am pretty quick on my feet, and, somewhere along the way, I mastered crossing streets in traffic without knowing a lick of physics!
(Later on, I found out, when I took an entry-level airline pilot’s test, I should have paid attention more in physics class. These calculation strategies would have come in handy for the test, while, silly me, I had thought, I’d never need them. Forgive me, though, I certainly digress.)
There is a relationship between the circle I have formed with the moving truck and the circle I have formed with my destination, directly across the street. One circle knows the other.
How do I know this?
As I was crossing it occurred to me. It made itself known to me. It talked to me, this hidden circle.
That is, and this is quite important, some other circle, far away, perhaps, but also maybe fairly close, it wouldn’t matter, would know whether it was present or not, the relationship between these two circles, one my destination, the other an interruption to this destination.
At any rate, for me, it was lucky this third circle was in the picture, no matter whence it was calculating.
That is, the third circle, between circle one (between me and my destination) and circle two (between me and the truck) could return quite a bit of useful information to me, if I cared to pay attention(and even if I didn’t the information transfer was still taking place). (Actually there were many more than two circles involved, as you will undoubtedly note fairly quickly.)
However, the third unknown circle, in a circle with both my circles, was (is) carrying the definite-stable-reliable-certain-linear relationship (proportion) between diameter and circumference, so that as one changed the other could be calculated, and the result neatly returned to me; all of this silent and in an instant too small to notice (not in any timeframe at all, actually).
Further, if half of the circumference were released from its connection to the (changing) diameter of the first circle, I would have a reducing or expanding triangle which would also be able to form a calculation and return an answer to me.
This triangle would actually be three diameters of circles, which, if they changed in relationship to each other, could return more triangles and circles with corresponding relationships to each other.
If the lines were perpendicular at any (every) point, I would have a Pythagorean triangle, which would also yield correctly proportional (exact) information. If the lines got out of whack (became not perpendicular), the third circle, could calculate, using itself, how far out of whack, and, again, return the answer to me.
All of these would tie (must tie) to some original circle somewhere (not necessarily present at all) which was (is) carrying the base relationship (circumference and diameter, where half circumference becomes, instantly, a second diameter, and then a third, ad infinitum), and which is in charge of the entire transaction (all of the transactions everywhere).
This is how the invisible line and circle (diameter and circumference) tied together by pi is used (can be observed) as a foundational calculator, as well as a foundational entity and process, and a foundational observer, to return any answer to any system.
Counting in circles is possible because the half-circumference and diameter are always in a mandatory arithmetic relationship which converts to geometric (it speeds up or combines with itself) if the user needs to know distance, speed and acceleration at the same time (these can never be separated, but, then again, they always can).
(You can see this varied, yet certain, proportional reality painting itself in mollusks quite easily, where speed and acceleration turn into lines and circles which are not supposedly perfect.)
Without time (space) we would have no movement (no two circles), instead just one (hidden, abstract) circle.
If we (you) can translate everything into (relative, absolute) distance and then from that (correspondingly) speed and acceleration (speed and size, time and space, process and entity), and tie them all together via pi, we (you) have figured out how (and why) everything operates.
I have left the detailed diagram(s) for you to draw (there are far too many, by design, and you can find some of them if you pass through a stack of physics or biology journals).
For now, just notice, the third invisible circle is doing all the work, not me, not the truck, not my destination, (not you) and certainly nothing any more (or less) complicated than what I have just explained.
Something quite simple, can combine quite quickly (readily) into a myriad of useful information. Not all of this information is numeric. But without the numeric reality, no other information would be possible.
Coincidentally, computers, using circles and lines (zeros and ones), are provided their intelligence by this same third circle.
Two circles from (into) one create (destroy) (an intelligent) third.
The person, truck, and destination in the above example are arbitrary words.
All entities (and processes) are ones, twos, and threes, following this exact same script.