The reproducible reality
Math is the key to understand and describe the universe. The question is: can we consider the opposite situation always true? I mean, is it possible to reproduce in the real world all the ideal abstractions that are possible in the math world?
Think for instance to the irrational numbers. These are numbers that cannot be expressed with fractions. A ratio between two numbers always produces a rational number that has a finite number of digits after the point. Neper’s number is irrational. All square roots of non perfect square numbers are irrational and so Pi is an irrational number.
Pi is the ratio between the circumference and the diameter of a circle and can be calculated in many different ways.
One example is Gregory Leibniz’s series:
Another is Nilakantha’s series:
These series should go to the infinite, but, when we cut them at a certain point, we are rationalizing Pi, making it explicable and reproducible as a single fraction.
Why an irrational number is not reproducible in the true life? Because all technologies, even the most precise, have a finite precision and cannot replicate a number with infinite digits after the unit. Here you have an image of the precision that can be reached with standard tool machines.
When we polish a surface, we can attain a precision of 0.01 micrometer. This means that when we want to produce a piece of steel Pi millimeters long we will be able to produce a length of 3,14159mm but then anything more.
So we have to rationalize a number when we want to reproduce it as a real object. Rationalizing means cutting it into a finite fraction.
Making rational the irrational to describe the Earth
The film Pi, Faith in Chaos by Darren Aronofsky, about which two articles where published on this blog (part1 and part2), ends with number PI expressed as a simple fraction. In the last scene when Jenna, the young Chinese girl, approaches Max in a park, asking maths problems, she proposes a question that will stay unanswered: How much is 748:238? The answer should be a good approximation of PI, but Max smiles and simply sits on the park bench observing the blowing of the trees. This comes out after a long and difficult search for the long number that should have had the power to give a final description of the universe. After this “cutting” Max Cohen seems to reach the peace that was missing before. The idea is that the universe could, maybe, be described with a precision that, step by step runs to infinite, but there is a main body, a base, the 95% of the total (3/3,1415=0,95), that you have to find first, just to seize the comprehension. In the description of the universe you should be satisfied when learning that a good deal of results have already been obtained when you reach a basic grasp of the main subject. More precise data have to be considered fractals, a repetition of the main body on a smaller scale. That will be studied in a second moment with the consciousness that nobody will arrive to understand with an absolute precision the whole creation : “Only God is perfect” is a noteworthy statement in Aronofsky’s film… And even the Bible in Ecclesiastes 3:11 states: “He has made everything beautiful in its time. He has even put eternity in their heart; yet mankind will never find out the work that the true God has made from start to finish” . There will always be a smaller fractal to study , but till that point you have to rationalize (to cut) in order to find the bigger fractal. The risk , on the opposite, could be not to be able even to find the correct description for the more visible and bigger parts of the reality we live inside.
Reality is irrational and can be described with fractals.
In Mechanics, for instance, it is usual to linearise near the working point what is non linear by using the Taylor series that can be cut when necessary. The non linear function becomes a sort of main linear function plus a negligible part that is an order of magnitude smaller that the main part. The little error made is considered negligible but also necessary to allow the comprehension of the function in a simpler way.
So how can we rationalize Pi? On the following table there are some fractions that can be used to express PI.
All these fractions are approximations of the real value of Pi. Each of these fractions is reproducible with growing difficulty as the error we make decreases.
We can think again to the molten sea in Solomon’s temple. I will quote from a previous post: “ We should notice that the Bible alludes to Pi in 2 Chronicles when describing the molten sea of copper. Some scholars interpret this to mean that the value of Pi is simply 3, as you can deduce from the passage where Solomon gives instructions about the forging of a large copper basin that was to be filled with water. It was a large ornamented molten sea that stood upon twelve fashioned bulls. It could have had the function of a natural observatory. Here is the story as narrated in the second book of Chronicles: “And he proceeded to make the molten sea, ten cubits from its one brim to its other brim, circular all around, and its height was five cubits, and it took a line of thirty cubits to circle all around it.” (2Chron. 4:2-5) When you calculate the proportions between the diameter and the circumference of the basin you will notice that the result is 3. We should probably consider the fact that the basin could be taken as a model of the sky above the earth and dynamic is involved. Time should be considered.”
Time has to be considered because any scientific inquiery has necessity to start from the first major fractal before to pass to the minor one and so on.
So, as for a first approximation, to define the major fractals describing the sun, the moon, the stars and all the firmament orbiting over the earth, you should keep in mind this rule: PI=3.
Quite interesting is the fact that using PI=3 you can keep on describing the universe by applying Demlo numbers to all its components, as a sort of divine proportion. We have already spoken about all these numbers in a previous article on our blog. The link here.
Now, let’s try some calculation about the sun, for instance.
All these data have already been given:
|Radius [Km]||Height [Km]|
The circumference or orbit of the sun can be calculated with this formula:
C=2*π *r where r is the radius and π is 3.
|Cancer tropic orbit||39960||=360×111|
|Capricorn tropic orbit||79920||=360×222|
The same calculation could be done for moon, stars and planets.
In conclusion, we can say that reality is irrational; in fact irrational numbers can be used to describe all natural phenomena. But our mind is rational, and can grasp and produce only rational numbers, with a precision, that, with time, gets better. Anyway, there is a time pressure that forces intelligence to study first the major fractals and later on only the minor ones.
By now, dear friends, we are just starting to imagine the dawn of the major fractals.