Research - (2021) Volume 10, Issue 6
Received: 07-May-2021
Published:
30-Jun-2021
, DOI: 10.37421/2169-0316.2021.10.299
Citation: Seun Ayoade. "Ramanujan’s Summation Makes Perfect
Sense-Philosophical Musings on the Number Minus 0.08333 Vis a Vis Cellular
Dust [The Microzymas]." Ind Eng Manage 10 (2021): 299.
Copyright: © 2021 Seun Ayoade. This is an open-access article distributed
under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the
original author and source are credited.
“……the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + ⋯ = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum…….”
Srinivasa Ramanujan, 27 February 1913.
The last few lines of a 19th century poem go-
Take, O boatman, thrice thy fee
Take, I give it willingly
For, invisible to thee
Spirits twain have crossed with me
The PassageBy Johann Ludwig Uhland (1787-1862).
When the mathematician Charles Lutwidge Dodgson (Lewis Carroll) quoted the above in Sylvie andBruno, he could very have been preemptively contemplatingsomething akin to Ramanujan’s summation. To many people Ramanujan’s summation seems as weird as the characters in Alice In Wonderland. When you look at Ramanujan’s summation in a very broad mathematical and philosophical sense and not in the limited arithmetical sense, things become much clearer however.
All the disputations about the veracity of Ramanujan’s summation have arisen because the disputers don’t have a basic understanding of what numbers (natural or otherwise) are. Once these people raising commotion on the internet and elsewhere realize that numbers, by nature, are abstract and make absolutely no sense unless attached to an entity of time, space or matter all arguments will change focus to asking how, why and when Ramanujan’s summation makes sense. So the sum of all numbers is minus one twelfth AND is unity (1) and is infinity. The way 100 cents is one dollar and 60 seconds is 1 minute and is 60/3600 hour and is 0.01666 hour. Ramanujan’s summation is presently being used to understand String Theory, showing it is true and very real. I hereby call on scientists to utilize Ramanujan’s summation to decipher the behavior (association and dissociation) of the microzymas (cellular dust) [1].
Proofs of the perfect feasibility of Ramanujan’s summation stand before us in the workings of nature. The proof is probably ingrained in the subconscious of all mankind. We ourselves in our very cells prove Ramanujan to be true. We start out as a spermatozoa and an ovum, then a zygote and then cell builds upon cell till we reach our peak and then reach senescence and perish. Our cells die and the entire summation of our existence has been reduced to zilch! Or has it?[2-4].
The concept of plenty being reduced to little; and nothing apparently becoming something and vice versa is evident in the carbon cycle, hydrological cycle, Kreb’s cycle, phosphorus cycle, sulphur cycle, nitrogen cycle, conservation of energy and momentum etcetera. Even statements in religious texts bear this out. We see before us things being added together and giving results that are asymmetrical and “unexpected”. Hence adding two oxygen atoms gives an oxygen molecule. Three oxygen atoms gives ozone. Oxygen is transparent and odorless while ozone is pungent and bluish in colour.
Today there are laymen and even well-educated holders of physics and mathematics degrees who vociferously insist that The Ramanujan Summation is wrong. They remind me of the primitive man who argued with the explorer who discovered him that there had to be some poor fellow trapped in the music box and gramophone who was singing therein. “How can the sum of all numbers be minus 0.0833?” is not the question to ask. “Under what conditions do the sum of all numbers become minus 0.0833?” is the better question. For example if I reported in a journal that I added one to one and got one [1+1=1] I would raise eyebrows, but if I explained that I added one spermatozoa to one ovum and got one zygote all would become clear. WITHOUT DEFINED PARAMETERS THE “BEHAVIOUR” OF NUMBERS CAN AND DOES DEFY LOGIC.
Other examples include:
8 eggs + 30grams of butter + 12 spoons of sugar = 1 cake [8+30+12=1]
20 boys + 20 girls = 1 class of pupils [20+20=1]
One million men + two million women + six hundred thousand children =one city
[1,000,000 + 2,000,000 + 600,000 = 1]
These are very oversimplified examples that seasoned mathematicians could object to as not being representative of the Ramanujan summation, but the principle is sound.
Is there a simplified example of how the sum of all numbers could be infinity, unity and minus 1/12? Oh yes, the sum of all numbers can be infinity, 1 and -1/12; only not at the same time. Confused? Let me explain. A mathematical formula, any and every mathematical formula, is a shortcut and a means of travel. Supposing we encountered a rectangular football field and wanted to know its area. We could do it the easy way or the hard way. We could cumbersomely measure the field, patch by patch or we could apply the formula: area = length X breadth. Using this formula we would only need to measure the length and breadth to know the area of the field. Assuming MrRamanujan hated formulae and calculators and decided to add all numbers by hand with paper and pencil. He would have died still doing the arithmetic! Even if he had lived 200 years and had full access to all the paper on earth he would never complete the task because time would not stand still for him, genius as he was. When numbers are tied to time they behave “funny”. Supposing I had a spaceship and flew to planet ‘X’ and dropped 12 newborn baby boys and 12 newborn baby girls there. If I returned to the same planet two years later I would find zero babies there, but I would find
Hence 12+12=0=24 Twelve plus twelve babies has become zero babies but twenty four toddlers.
If I returned to the same planet fourteen years laterI would find zero babies, zero toddlers but twenty four teenagers, and if I returned thirty years later I would find zero babies, zero toddlers, zero teenagers and twenty four adults. When I explain it this way the numbers make sense to you. However if I told you that I calculated 12 plus 12 and got zeroes and 24. [That is, 12+12 = 0 =0 =0 =24] you would say to me “the first three answers are wrong, only the fourth answer makes sense”. If I returned to this planet 200 years later and found no babies, no toddlers, no teenagers, no adults but 24 skeletons with 206 bones a piece I can represent my findings thus:
12 + 12 = 24 = (206 X 24)
12 + 12 = 24 = 4,944
12 + 12 = 4,944
Could minus 0.0833 be a nexus that could be used to “gauge” a time machine? [5]
Numbers, without context, are abstract and weird. Ramanujan’s summation makes perfect sense when you realize that!
Take, O boatman, thrice thy fee
Take, I give it willingly
For, invisible to thee
Spirits twain have crossed with me.
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