I used to like to think that PI was the rational ratio of 22/7. Then I recently found a proof that PI is irrational.
The basic irrational numbers are less than 1, have no end and cannot be represented as the ratio of two real numbers. They can attach themselves to real numbers causing the result to be irrational. They are numbers that do not have repeated sequences, like .3333… which is 1/3. Changing the base system does not make them rational. They are in a class all by themselves and include complex imaginary numbers expressed as a multiple of the square root of -1. They might be thought of as the trash bin of math.
What is even more disturbing is to realize that most of today’s physical equations include PI. Whether or not Newton solved the problem with differential calculus remains a question to me. But for now it would seem any equation containing PI or any equation containing a term derived from PI is flawed. Hopefully there are smart people today who have isolated the problem.
Speaking of Newton, Newton’s differential of time, dt lim>0, is an attempt to define an EXTREMELY SMALL increment of time, called “instantaneous”. In a similar fashion, Einstein was concerned with the “simultaneity” of two entities which must have considered the smallest increments of time.
Imagine the second hand of a clock traveling a full revolution around from one minute to the next.
Question: How far has the end tip of that second hand traveled after 1 minute? Math tells us 2R x PI, where R is the length of the second hand. But if PI is irrational, that distance traveled ,ie, the length of the circumference of the circle traversed by the tip of the second hand, is also irrational, because a real number times an irrational number is irrational. The same applies to any discrete point on the clock’s second hand.
So what is the explanation?
Premise 1: In 1, 2 or 3 dimensions you cannot travel an irrational distance.
Premise 2: That the smallest length is the planck length, could it not be that this is the point at which 3 dimensions transition into an irrational time dimension, or zone, where no units of measure can exist? In other words, smaller units of distance break down to time itself, making it possible to express velocity as a multiple of time, albeit time can be any tiny irrational number.
As it was moving through the two dimensions of the clock face, the clock’s second hand was also moving through time. The impression that a connected circle has been enscribed by the clock’s second hand must be an illusion due to an overlap of the end point and start point, the irrationality occurring as a result of a small unmeasurable time gap between the two, thereby actually following a corkscrew traversal through the 2 dimensions of the clock face and time. Thus, time must give rise to the irrational zone where linearity breaks down and curvature begins.
Now consider the matter of splitting the clock circle into equal parts. Yet this is no longer possible, because PI is irrational. This leads us to conclude that repeatability becomes a matter of randomness in the irrational zone.
3. On Time And Space:
The mathematical representation of spacial structures requires the use of a 3 dimensional reference system wherein discrete points are defined. This reference system is shown graphically as 3 intersecting lines orthogonal to each other and expressed mathematically as 3 coordinate points (x,y,z). But to continue defining this reference system, Einstein added time as a fourth dimension, represented as a fourth coordinate point, t, and expressed mathematically as (x, y, z, t). The only way of graphically showing this system is via the motion of 2 or 3 dimension images.
We must always remember that this reference system is man made and never construe it to be reality itself. We must always be cognizant of the fact that VIRTUAL REALITY is not REALITY.
Einstein’s Relativity Theory views space and time as a single entity. In the past, I have found it a little difficult to consider space and time as one entity, preferring to analyze the two separately. However, what I have presented here indicates the two are parts of the same entity, ie “distance”, one part being rational and linear with the other part being irrational. So the reality may be that we are in a one dimensional universe. I see no conflict with Einstein’s Theory.
Is time a manifestation of spacial structure?
Are spacial structures a manifestation of time?
Is there any relationship at all between time and structures?
The explosion of structured living things during the earth’s Cambrian Period would appear to hold some answers. But exactly what is unclear
What is the relationship between time and gravity?
This sounds like a redundant question, given Einstein addressed it in his General Theory Of Relativity. But I still have questions.
That gravity affects time pieces is a curiousity, coupled with the fact that gravity induces constant changes in veloclty of 3 dimensional objects toward each other based upon their respective masses. Einstein explaned this in terms of the fabric of space-time itself changing.