The Infinity in Nature:  A Religious Conclusion of Science

Copyright 2015, John Manimas Medeiros



Quantification, number, precision, infinity, belief, in religion and science:

The purpose of this work is to propose an explanation for the concept of "infinity" in science and religion, and to make a concise and clear statement about a religious limit on science.  In other words, by "religious limit" I mean a physical reality that human science will never enable us to capture or control.  And therefore, state a final and conclusive religious concept that can be observed but not studied or isolated or explained or imitated or duplicated by technology or scientific inquiry.


Conformity is the most powerful force in the human mind and character.  Is that statement true?  Can it logically be partially true?  Logically, no.  Either it is true or not true, and there is a social-psychological force more powerful than conformity.  So, what would it mean if this immediate statement were true?


If"Conformity is the most powerful force in the human mind and character" were true, then that would mean that our impulse to believe and act in accordance with social expectations would be the moving force behind our public thoughts, speech, plans and behavior.  Everything we think, say and do would be consistent with what people expect us to think, say and do, or that is socially approved by our community and culture.  By identifying the reverse or inverse of conformity, we will clarify this controversial observation, thusly:  if much of what one thought, said and did was contrary to or opposed to common social "norms," that is, the beliefs, speech and behavior that is "normal" in one's community and culture, then one would be labelled as "deviant" or abnormal, or disturbed or insane, or "nuts."  Clearly, we all get the message from society, from birth until death, that some things are "normal" and others are not normal.  We get messages that tell us what is expected, accepted, normal, conforming behavior.  All that we can think, say and do that will not get us into trouble.  And while we live our lives through this forest of normal messages, we learn and use concepts of quantity, number, precision, infinity, belief, in religion and science.  And all of these are very important.  We make use of quantities and numbers constantly, buying something, measuring something, keeping records, talking to another person about when and where something is planned, when we tune into a radio or television signal, and so on.  We communicate about what we believe, our opinions, daily.  We are all exposed to the concept of "infinity," something that has no limit or end point.  All this is maintained by habit, but still there are deep questions about what each of these concepts means.  Let's begin with quantity, number and precision.


Soon after we are able to speak, we are introduced to the concepts of "small" and "large," "more" and less."  That is followed by what is really a lifetime of acquiring and using words that express a form of "quantification," the most common being the cardinal numbers 1, 2, 3, etc.  The ordinal numbers are first, second, third, etc.  Each number can be spelled out as a word, of course, and they are used for various measurements of quantity:  length, width, height, weight, volume, and later on numbers may be used to designate sound, tone, intensity of light, and so on.  Other words are used also.  For example, "light" green is used to distinguish from "dark" green, which could be described as a quantification of "greenness."  We can use other symbols for order, such as the English alphabet:  A, B, C, D, etc.  As we continue our educational experience and divide our fund of knowledge into fields or categories, we learn to use special forms of quantification for some of those fields, such as grams, micrograms and milligrams in the field of pharmacology.  To this day, maps of towns in America may use chains and rods as measures of length for plots (or plats) of land. 


If one takes measurement seriously, such as a mathematician or a physicist or a chemist, one learns that the concept of "precision" is extremely important in all of the physical sciences.  And, all forms of quantification are "approximations" because until we have divided a measurement down to the smallest possible particle, the units or subdivisions of our measurements can always be more precise.  Only nature, or Nature, possesses perfect precision in the natural world.  Every measurement we make is made by means of a comparison and by means of a device or a machine.  All such devices or machines are "artifacts" which means they are manufactured, made by human hands.  They do not possess the perfect precision of nature.  We are habit forming creatures, and our patterns of using numbers and numerical calculations become more and more automatic as we make use of them.  Our numbers become real to us, as concrete as a stone or a tree.  And we are led to a conclusion that mathematics is real and is the source of all that we measure.  And, since we measure everything, we are likely to conclude that mathematics is the source of the natural world, or a basic cause of its existence.  However, if we apply a concentration of logic to this question of "What is mathematics?" we can also be led to a conclusion, by logic and careful observation, that mathematics is a product of the human mind.  In either case, our concern with number and quantity includes the fascinating and challenging concept of infinity.  It will be a surprise to some that a mathematician named "Cantor" argued that there is more than one kind of infinity.  I suspect that this idea is ridiculous, but many mathematicians agree that there is more than one infinity.  For me, that which is infinitely large is not very large and not extremely large and not even larger than anything else.  Anything that is infinitely large is outside of meaningful comparison with anything else.  If there is an infinity of the universe, or a "Big Setting," then it is the Setting that encloses all other settings and there is nothing outside of that Big Setting.  If there is something that is infinitely small, then it equals nothing.  But then again, can we be certain.  Could it be that infinitely small might still be something that is not nothing.  These kinds of questions are not just semantics, because they challenge us when we pretend that we understand reality.  For example, when we ask how large the universe is, we can see by observation of history, that we begin with a relatively small vision of the universe and then as our instruments of detection improve we make our vision or image of the universe bigger and bigger as our technology proceeds.  The most logical conclusion therefore, based on the information we have, is that the universe is as large as our instrumental detectors are able to detect.  This logical viewpoint is virtually the same as saying that the universe is as big as we can see, or, we cannot argue convincingly that the universe is larger than what we detect.  This same logic can be applied to the concept of the smallest possible particle.  As our microscopic technology proceeds, we "discover" particles that are smaller than the small particles we previously thought were the lowest boundary of smallness.  Consider, for example, that we have been certain for some time of the existence of neutrinos, but we were also certain that a neutrino had no detectable mass.  To say that a particle has no mass is really, in the world of honest linguistics, the same thing as saying it does not exist.  But, recently at the beginning years of the twenty-first century, somehow someone discovered that a neutrino does actually possess mass, an extremely small mass, but apparently not an infinitely small mass, because it is so difficult for us to distinguish between infinitely small mass and zero mass.  We cannot, obviously, because we do not have an instrument to make that measurement for us.  But we still have the concept of infinity.  Infinity in the world of numbers means "no end," or no last number or no last decimal digit.  The infinite truth is, that if we are performing a calculation, and we say -- as mathematicians sometimes do say -- that the result of the calculation is an endless series of non-repeating decimal digits, that means we do not now and never will have the finished number, because the number, by definition, does not have a finish. 


Let me say a few things about science and scientists:

A)  A true scientist closes no doors.

B)  Incomplete knowledge equals an incorrect belief.

C)  If we contemplate a future, we are compelled to anticipate a revision.

D)  Nature measures with infinite precision; we do not.


Therefore, in our efforts to grasp the meaning of infinity, we have to consider our habits of conformity, and our realities in regards to measurements and precision.  Nature's precision must be infinite, and we need keep in mind that our artifacts for measuring things do not possess infinite precision.  Every device and machine that we make, every instrument of detection and measurement, does not have infinite precision.  The human artifacts of measurement have limited precision.  This means that we may rely upon a measurement that is not as precise as the REAL measurement.  The REAL measurement that is exact and not an approximation occurs within the boundary of Nature but outside the limit of human capacity.  Nature measures with infinite precision; we do not.  And I believe I understand the full implications of this reality, and I call it "Infinity in Nature" and it leads me to a conclusion that the universe IS NOT MATHEMATICAL.


The Pythagorean statement that "Proportion is everything" means that the universe is proportional and our mathematics is our detection of proportion.  We have discussed the real physical universe for centuries as though it is the result of complex combinations of diverse forces, such as gravity, electromagnetism and light, and possibly also mass and "the weak force" and "the strong force" and possibly forces that behave according to laws that are different for the "very small" from the laws for the "very large."  I propose a Theory of Evolutionary Proportion wherein "proportion" is actually the most fundamental force of Nature that governs all physical matter, the evolution of matter that we designate as "non-living" and matter that we designate as "living."  Our mathematics is a sensory product, like what we see with our eyes and what we hear with our ears.  With our brains, we detect proportion, and the product of that detection is proportion converted to language and symbol:  all that we call "mathematics."  I propose that the sufficient evidence in support of evolutionary proportion, in addition to all of the proportions that we observe in both geometry and in the decimal notation of numbers, is the fact that we can construct the line length value of 1 and then construct, in proportion to that 1, the value of pi exactly as a straight line.


Hiram Key and Unification Construction: matter first measures itself and then proceeds to assemble itself into the non-living and living real, physical universe:


This amazingly simple construction (the Hiram Key or Self-Reciprocal Construction) is proposed to reveal both the natural value of one in proportion and a proposed theory that this proportional reality enables matter to measure itself before it assembles itself.


Using only the compass and straightedge, construct a circle and the external tangent square, which means the sides of the square are tangent to the circumference of the circle.  Use a convenient size.  Observe that we can construct numerous angles (G) greater than 45 degrees extending from the lower right horizontal side of the square passing through the center of the circle, and then extend such a line, being the hypotenuse of a right triangle, upward further to a point intersecting with the square at the upper left horizontal side of the square.  That line X now is a diameter of the circle plus the smaller, additional length that extends outside of the circumference of the circle to the vertex of the angle of interest (G) that is greater than 45 degrees.  It is important to observe that by nature (or Pythagorean formulas) the shorter hypotenuse that extends outside of the circumference has a line length value that is exactly equal to the reciprocal value of X, the same as being equal to the inverse of X.


Observe the cosine of the angle, and the inverse, the secant.  Then we contemplate, but do not measure or designate, that the value of the base of the right triangle has a line length value of 1.  In our right triangle with sides A (altitude), H (hypotenuse) and B (base), we now have H = secant of angle G, B = 1, and A = sqrt(H^2 -1).  These are familiar facts.  However, consistent with accepted geometric theorems and corollaries, there is another set of fixed proportional relationships.  Let (1/X) = R. 


A =  X^2 -1     and      H =  X^2 + 1               X = A + A + R

          2X                                2X


AND, most important of all, no matter by what factor we multiply the three sides of the right triangle, the proportion of Side B to all other lines in the construction is 1, one and only one by nature, and not by arbitrary operator designation.  Drawing below:


And, if and when we can begin with the right triangle where H = sqrt(5), and the value for line length X = sqrt(5) + 2, and then proceed to construct a straight line length equal to pi exactly, we can then construct circles and squares exactly equal in area, and therein we are enabled to discover and understand how the real, physical universe measures and assembles itself.  It is reasonable to think of these geometric facts as the secret of life in the universe, the acronym being SOLITU.  This is what the Pythagoreans were pointing to when they told us to construct a pentagon and that "proportion is everything."  Construction of pi exactly as a straight line is described in the Unification Construction, included on the jmanimas website as "SOLITU- G" 



The Unification Calculation (Construction) - abbreviation of "SOLITU - G":

Here is the calculation that I have discovered and have asked that be run on high precision (math co-processor) computer calculators.  I believe the outcome of this calculation is of the highest importance for our understanding of what mathematics is and the origins of the real, physical universe.  I thank anyone who performs this calculation on a high precision computer for the public good.  The true scientist closes no doors.


A check on the validity of the Unification Calculation can be completed in a few minutes using a hand held scientific calculator or a desktop computer calculator in scientific view.  I have used my calculator that allows saving six values in memory (A, B, C, D, E, F)

First:  There are six values to be calculated (NOT COPIED) and saved:

1)  D = 3.1416407864998738178455042012388       (save this value)

2)  F  = 3.1446055110296931442782343433718      (save this value)

3)  E  = 3.1418181818181818181818181818181      (save this value)

4)  V  = 3.1426968052735445528926416093549      (save this value)

5)  Q =  3.1399111679090046934014154186896      (save this value)

6)  HG  = (1 / 0.1118) =  8.9445438282647584973166368515206

            or for convenience we use (1 / 1.118)  = same digits divided by 10

            let HG = 0.89445438282647584973166368515206 (save this value)


These calculated values take me less than three minutes: [using degrees]

1)  D = 1.8, square root, + sqrt(1.8), then save

            = 3.1416407864998738178455042012388   


2)  F = sine 18, times 2, sqrt, * 4, then save

            = 3.1446055110296931442782343433718


3)  E = 0.55, press (1/X) key [inverse], times 1.44, times 1.2, then save

            = 3.1418181818181818181818181818181


4)  V = (40/9) = 4.444 …, that * sqrt(0.5), then save



5)  Q = [ (E * V)  / F ], then save

            = 3.1399111679090046934014154186896


6)  (1/0.1118)  There are several ways to construct this number, but the following

            procedure seems most convenient:  let HG = (1/1.118)


            0.9 * 0.8 = 0.72,          + 4 = 4.72  

            / 5 = 0.944,      + 8 = 8.944

            / 8 = 1.118,      inverse = (1/1.118) = 0.894454382826475, then save



Next Step:  we will calculate a new value "A" and a new value "B"

and then subtract value B from value A.  Let A-B = C:


A =  [ (V)^2 / E],  / sqrt(cos 36)          [degrees]        


            = 3.49498323774898999309129431119694  (A), then save A


            note that  / by sqrt(cos 36) is the same as times sqrt(sec 36)]


B =  [ (V)^2 / D) ] =  3.14375317901321112588817420275095, then save B


THEN:  A minus B = C = 0.351230058735778867203120108445054 


Our 3.49498323774898999309129431119694 

minus our 3.14375317901321112588817420275095


= 0.351230058735778867203120108445054  = C    ***



Next StepC is now our value of interest, because:


C times 5 = 1.75615029367889433601560054222527


times HG (1/1.118) =  1.57079632708308974598890925064872


[same as C * 5 * 0.89445438282647584973166368515206  ], and that value


being 1.57079632708308974598890925064872


times 2 = pi exactly, 3.141592654 … 16617949197781850129744 


to the 9th decimal place -- the known level of precision for the desktop calculator.


OR, 0.351230058735778867203120108445054 times 10, / pi


=  1.118000000 20511883699932630279168  precise to the 9th decimal place.



IS EQUAL, IN THEORY, TO 0.1118 TIMES pi exactly. And there is a meaningful connection to the geometry of the sqrt(5) and the golden section (1.618033988…) and the construction of the pentagon: 

sqrt(1.25) = 1.118 …  0339887498948482045868343656

which = golden section - 0.5  and as one employs electronic calculators of greater and greater decimal precision, the outcome will add the matching decimal zeros, but will not necessarily be followed by all zeros, because electronic calculators are machines, dependent upon the limitations of their parts, but Nature has no limit on precision.  The precision level of Nature alone is perfect, but we do not have a machine, not even an electronic machine, that can match the perfect precision of Nature.  BUT, we can infer from the extension of the zeros with the increase in precision that C does = 0.1118 * pi exactly.  And that evidence is sufficient to propose my Theory of Evolutionary Proportion.


The Theory of Evolutionary Proportion offered to be ruled out before dismissed:

Proportion is everything means that the real, physical universe is governed by a fundamental natural force, or the fundamental natural force of evolutionary proportion.  And our organic brains are the intellectual center of a technological animal, a calculating, learning, observer.  Number and all that we enclose in the field of mathematics is in reality our sensory detection of proportion.  The force of proportion generates the shapes of all physical things, the non-living and the living, and both the non-living and the living originate and evolve virtually simultaneously.  My proposition is not that I have submitted convincing proof, but that there is enough evidence that this theory must be taken seriously and must be ruled out by rigorous scientific experimentation before it is dismissed as certainly incorrect.  And the primary reason why it needs to be taken seriously before being dismissed is because of the limitations of our calculator artifacts.   


Electronic calculators are also machines, human artifacts with limitations:

Remember, only Nature calculates and constructs with perfect or exact precision.  We assume, by way of a habit of trust in our technology and instruments that an electronic device is perfectly precise because its essential "parts" are electricity and electronic components.  The "parts" in the microscopic circuits are so small, so close, bordering on the size of molecules and atoms, it must achieve perfect precision, but it does not.  A calculator is a manufactured machine like a swiss watch or an internal combustion engine.  It has physical limitations.  And for an electronic calculator the physical limitations include imperfect precision, or a limit on precision.  That is why those who manufacture electronic calculators and mathematical co-processors accept the responsibility to assign a designated level of precision to a designated digital decimal place.  Therefore, if performing the unification calculation on calculators of progressively greater decimal precision still results in positive decimal digits extended after a series of zeros, that is not proof that the result of the unification calculation is really not 0.1118  times pi exactly.  It could be the result of the imperfect precision of the electronic calculator.  It could be that this particular calculation is so central to the reality of Nature that it crashes into the extremely small boundary between the great precision of the calculator and the perfect precision of Nature.  It could be that this particular difficulty in matching the perfect precision of Nature in this particular calculation is the KEY that was called the "Hiram Key" in ancient times.


What about that infinity?  Is the universe infinite?

So, I have argued here that no human made calculator can match the infinite precision of Nature.  I wish to present one more argument and a prediction that defines the meaning of infinity in the universe.  I have believed for many years that the real, physical universe is infinite in one direction, the outward direction.  In other words, the size of the universe is infinite.  There is no outward boundary where the universe ends and either nothing or something else exists outside of the infinite universe.  And I have believed that the universe IS NOT infinite inwardly, on the grounds that there is a smallest possible particle.  That would mean, if correct, that there is no particle of matter that is infinitely small.  For example, even the lowly neutrino possesses extremely small mass.  But let me reconsider.  Let me think about what the universe would be like if it were infinite in both directions, both inwardly and outwardly.  That would mean there is no smallest possible particle, but instead there is a particle or particles that are infinitely small.  Strange and contradictory this seems.  But let us continue this line of thinking.  We do have evidence that in the real, physical universe all large things --  the macro-world -- are the outcome of very small particles and very small forces.  Therefore, it can be said that the very small is the origin and source of the very large, even the source of the infinitely large universe.  What would that mean?  That would mean that we cannot see, cannot detect that which is the final and ultimate source of reality.  There is something infinitely small that results in the infinitely large.  Since we cannot detect it, it is like a "ghost," a spirit, a breath, outside of our capacity to capture, study, measure, examine.  If there is a thing or a force that is infinitely small, then I propose that it is now and forever beyond our capacity to subject to scientific inquiry.  It is the Holy Spirit and the Great Spirit, something that cannot be known, no matter how many millions of years our organic brains shall evolve.  I propose that although we may develop and manufacture artificial intelligence, we shall crash against the limitations of all manufactured artifacts, and just as Mary Shelley wrote the story of the creature assembled by the scientist Dr. Frankenstein, a creature that was human in every respect except that it had no soul, we shall never be able to create a robot that has a soul, because we are the evolutionary product of the evolution of nature, and any artificial intelligence that we create will not possess the qualities and character that can be bestowed only by the natural evolutionary process over time.  All that is "natural" is what it is as the result of a genetic process over extreme intervals of time.  Artificial genetic assembly, over short intervals of time, cannot be equal.  If this thought experiment is correct, then we shall never conquer the infinitely small, and the spark of life that we detect with our imagination shall forever be out of our reach, thank God.  We may come to imitate almost all things, but we shall never construct an imitation soul, and therefore no robot shall ever be equal to a naturally evolved human being.


Are extraterrestrials biological robots (biobots)?

I have consumed a great deal of literature, much of which is respectably scientific, about the evidence that superior beings, usually labelled as "extraterrestrials" have visited Earth for thousands of years, intervened in our development, and abducted human beings for study and possibly also for experimentation.  I know that for many people it is "abnormal" and weird and not scientific to take this material seriously.  But I said the true scientist closes no doors and I meant it.  The UFO literature is complex, extensive, and confusing.  Taking into consideration all anecdotes and the testimony of professionals, the reports of police officers, pilots, military officers, and scientists as well as vast numbers of the general public, it is still difficult to come to a conclusion as to what such beings are doing, if the material is credible.  Why do they always escape us?  Why do they appear to be extremely interested in us but also extremely reluctant to communicate with us?  If they are studying us, why are they studying us?  Are we experimental animals in a laboratory?  How do they see us?  Are we the same as insects or rodents to them?  Do they want us to succeed?  What would be their conception of our success?  Do that want to use us for genetic material?  Do they want to eradicate us?  Control us?  Use us as a source of labor?  Are we related to them?  Are we descended from them?  Are we hybrids?  On and on the questions are generated and rarely lead to convincing answers.  We just cannot be certain who or what they are.  But I have a proposal that would be consistent logically and would be a reasonable explanation for all of their wide varieties of reported behaviors:  they are not living humanoid beings; they are biobots.  Here is my argument.  We have produced "drones" or "unmanned aerial vehicles"  (UAV).  They can perform military tactical missions and gather intelligence, among other things.  Just for fun, one could probably use a drone to deliver a pizza.  We also have developed aircraft that exceed the physical limits tolerable for a living human body.  Pilots of modern tactical aircraft must wear a "flight suit" that is as sophisticated as a space suit that enables them to withstand the gravitational accelerations and other atmospheric conditions that apply to high-altitude, high velocity, and quick maneuverability flight.  Military pilots even have to be prepared to "black out" or "red out" and be unconscious for a few seconds while the aircraft continues on its flight.  We are also working on artificial intelligence and robots to perform labor.  At the time of this writing it is possible to purchase a robot that looks like a living human maid and "she" will serve tea and cookies to you and your guests.  But can her boyfriend fly a jet fighter?  Well, I think you get the picture.  It is logical that our three technologies of surveillance UAV, robot, and extreme tactical aircraft, will be brought together in the near future.  We will go back to that extreme jet fighter and see if we can manufacture a robot, possibly a robot with biological parts, to fly it for us, and then would not be subject to the physical limitation of a human pilot.  A robot pilot might be able to fly a jet plane that goes 5,000 miles per hour and turns on a dime.  So, this line of thinking, though it seems crazy at first, suggests that all of the extraterrestrials that people have observed, in vehicles or face to "face" have actually encountered biobots and not humanoid animals like us.  This would explain ALL of the reported behaviors.  They approach but do not make mutual contact.  They appear to have devices and force fields designed to repel us and keep us away from them, except when they want to capture us and study us.  They definitely appear to be studying us, but we never get invited to lunch.  Their maneuvers and strange modes of contact indicate "intelligence" but not any emotional interest.  They appear to be studying us by rote, but not by an impulse of curiosity.  The UFO material would all be consistent if they are a kind of extremely advanced robot that looks human because the equipment of the human form is the most practical:  a head, eyes, arms, hands, etc.  Their "ears" are invisible and their "mouths" are so small because they do not need to eat anything.  They seem to "speak" by means of telepathy, not by producing audible sound.  They appear to do things that living humans could not do.  All of this is consistent with an extremely advanced kind of robot.  How convenient.  Just like us, the extraterrestrials prefer to get dangerous work done without risking the life of a living humanoid flesh and blood person, when they can.  And there is one more thing.  Our current experience with space exploration suggests that human beings, as we are now, could not really travel through deep space.  We get all kinds of challenging results, exposure to radiation, bone loss, blood pressure and heart issues, the possibility of mental problems arising from confinement and the extreme isolation and dependence on complex machines.  All this suggests that we might actually have to evolve into different animals in order to be able to travel on long voyages through space.  OR, we could manufacture biobots to perform that work for us.  After all, photos of Mars, from Mars, are really far more practical than standing in the middle of no atmosphere at minus 70 degrees F and snapping a selfie.  Just because we can say "infinity" does not mean we can visit it and have a taco.    


Advanced robots do a good, though perfunctory job:

If all of the "extraterrestrials" visiting us (or abducting, examining, engineering) are in fact biobots, the "UFO" reports include evidence and testimony that supports such a conclusion.  The reported UFOs generate measurable radiation, magnetic forces, static electricity, and either gravity or anti-gravity.  They also are alleged to possess technology that suspends the human brain's capacity to create new memories, hence the missing time but still with an imprint of emotional trauma as a result of the abduction experience.  Again, all of this is consistent with a highly advanced robot that is designed to perform a restricted set of operations:  paralyze, anesthetize, examine, complete a medical exam or procedure, return the subject to the scene of the abduction or nearby; end of session.   But no UFO abductee story -- check it out yourself -- has every included a description of behavior that looks like the human variety of spontaneity or free will.  Never, ever, has a tall grey, or a short blue, or a snakey-faced reptilian ever said, "Heh, would you like a cup of coffee?"  To the extent that abductee reports are accurate, the UFO visitors are bureaucrats from the heavens, as sensitive and perfunctory as a drive-through car wash.  None of these kidnappers has ever said, at the end of a date:  "Sorry for the inconvenience.  Have a nice day." or, what would be of cosmic significance, a statement similar to "I like you."  I argue this:  there is no human touch because there is no human.  They are not biological entities in the same way that we are, not the outcome of a deep time evolution of an animal life form.  Even though they may have organic components, gelatinous lumps of primitive protoplasm, they are still machines.  They send reports across the cosmos to willful beings very far away.  Those distant beings, interested in who and what we are, keep records.  If you always wanted to feel that someone really understood you, rest assured.  Their understanding of what we are is not based on poetry and song.  It is based on all that happens here, including much that you do not know because it is a matter of national security.         

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