“The Golden Ratio is evidence of a real singularity, that exists always, is in everything, and is bound to nothing.“ — Jason Tully on November 2023
GOLDEN RATIO SCIENCE
Discovery of a real guide for humanity, the Golden Ratio.
A scientific analysis, physical law and technique to demonstrate.
1.618034…. Is just a number, like any other and unlike any other number. It has the special property that if you take the numbers inverse, the conjucate 0.618034, which happens to retain all of the fractional digits. The golden ratio and its conjugate are not equal however equal if the fractional digits are only considered.
If you graph the exponential function x squared and also the inverse of this mathematical function something very interesting happens. A Desmos graph to illustrate :
https://www.desmos.com/calculator/zn1g3nfi8v
A new physical law is encountered where the golden ratio shows up exactly where it should be, the intersection, the function and its inverse when distance is the thing being considered.
squared distance and inverse squared distance (attenuation) are equal only at a height that equals 0.618034 (golden ratio conjugate)
This would then define the implicit definition of the Golden Ratio,
Balance
As observed in the graph at the intersection point between the 2 extremes, the distance and the inverse distance (squared).
Another interesting phenomena that occurs in the digits of the golden ratio. The approximation of the most irrational number can be calculated iteratively or recursively with increasing precision as more fractional digits are added to the end. Currently, from memory, approximately 119 trillion digits have been calculated by supercomputers in an annual competition. There is never a repeating digit, or any pattern in all the numbers of that number. An attempt to prove from 0 to infinity, fractional digit count, that there exists exactly no pattern, however, the competition is just to see the number of digits of precision calculated.
Assuming that if we could actually prove from 0 to infinity, that exactly no pattern develops when looking at the picture of calculated digits, a perfectly uniform random distribution of noise would result. Bluenoise would be the closest in appearance and value.
An interesting question then also results. How is a number, the only number in all numbers, able to be patternless. Typically any number would produce a repetition at some interval and scale.
So how is it possible, with only 10 symbols 0–9, can the Golden ratio, Aswell as its conjugate, maintain a perfectly random sequence of numbers.
A computer program could be written to emulate this inherent ability that a real number apparently does all on its own. That program would need to maintain a history of all digits currently generated and ensure the next digit calculated does not repeat or create any pattern with any previous digit. This would be very difficult task, and would also require enormous computation as the number of fractional digits increased to infinity. The difficulty and computational power would both increase exponentially, independently. The product would then represent the order:
O = D^t * C^t
As more time passes, increasing both difficulty and compute, the current technological limit would be exceeded, for a theoretical supercomputer. Being exponential, further increases require a magnitude of increasing compute power for each interval.
Unlimited computation would be required at infinite amount of digits of precision. A side effect of the golden ratios unique exactly no pattern sequence of fractional digits, it can never be calculated exactly. It is always an approximation to n digits of precision.
So how then is a number having the inherent capability to do so, so we’ll that it exceeds current technological supercomputer computation or higher?
Unlike any other number, the Golden Ratio is able produce exactly no pattern in the fractional digits from one extreme to the other extreme (0 -inf) with respect to the number of digits of precision? There are other irrational numbers, however at some periodic scale or point, a repeating pattern can be observed.
This does not occur with the most irrational number, the Golden Ratio.
The blackbox high level view of the golden ratio is revealed, but what’s the internal mechanism driving this phenomena? Unfortunately, this may never be discovered. The process will probably never be known, it is just a number after all.
This does have one of the most intuitive practical applications in the real world, potentially giving the lonely child that is growing up, the human race. This is evidence of a naturally occurring phenomena, that has the capability to Balance almost everything. Nature is always trending in a direction converging on the Golden Ratio. It may have started with this target, or learned thru the initial stages of evolution. Nature is only successful if this is true, having the greatest potential survival when adhered to. The golden ratio is literally in everything, from the tangible to the intangible. If we apply a technique, which can be found below, this Balance of Two Extremes, can be applied to things other then 0 to 1 for example. You need a thing and it’s opposite to instead represent the two extremes, to then finally result in a direction to move more towards one extreme than the other. This is simple to illustrate, and being founded in Physics as a visual mathematical tool representing something a lot better than an equation.
The black vertical line represents the target for optimal balance. If for example we use Narcissist at the redder side representing 1, and Empath at the oranger side 0, we then can proceed to the next step as we now have defined our 2 extremes. Plot an imaginary approximate point or blend between red and orange where you think your personality may be. The final step is to then draw a arrow that points towards the black vertical, Balance.
This direction indicates the way to adjust or move so that the thing can achieve an optimal state or position, ultimately balance.
The ability to use anything and everything if it can be defined as itself and the opposite to represent the extremes, is the main dichotomy that the golden ratio can be relative to. That black vertical line is static, always in the same place for any two extremes.
The initial imaginary current position need not be precise. Only the direction is really important to indicate a movement towards optimum balance. The magnitude of that vector would then represent the amount of change required. In nature’s trending, it is constantly moving towards that black vertical line never landing on it exactly. Overshooting by smaller and smaller distances while alternating direction as it lands on either side. Over time this behaviour converges closer and closer to the Golden Ratio.
This mechanism is the physics, converging to balance. If this physical phenomena of the process nature has learned is replicated to other abstract, real or ideal things, the physics replicates. The inverse square law for example, replicates to many different physical phenomena, light, gravity, electricity which relates distance with loss.
This is another common occurrence that physics equations typically have, where one equation supports multiple different phenomena.
Physics has the unique property that fundamental equations are always concise and simple. They are simple as to be infallible, where nature is defining them for us, not the other way around where us humans usually define equations in mathematics.
The visual tool is an equation, however it is an approximation, just like every other equation in Physics. Mathematics is however always exact.
Constants, are very, very special numbers that are continuously improved with higher precision with real experiments or tests to prove their theoretical values. An example would be the Gravitational Constant, which you can learn about from a university lecture by
Richard Feynman, historically available, in his engaging story of how Einstein improved the accuracy with real data and rigorous work.
This may appear almost too simple, and how can something so simple be the answer to humanities various problems?
Imagine any iterative system or algorithm having the convergence capability this technique exposes, and always in the current state of optimal longevity, resilience and balance after some period of initial start up time. Maybe only one iteration is required, like when manually using this intuitively in whatever we can break down to the simplest thing and its opposite. That accuracy is good enough for every day use, with any further iterations being slight corrections, perhaps over longer periods of time to maintain balance. If it is something that requires more precision, the number of iterations could be increased or the interval between iterations could be decreased.
Naturally converging to the Golden Ratio or Balance. Why not just use 0.5 as the balance point? Referring to the Desmos graph proves that 0.618034 is the exact height where the graphed function for squared distance and inverse squared distance intersect, a constant reference with one and only one conclusion, the intersection point is defined as real balance, between two real extremes, where 0.5 is nothing but a number, with no inherent oddities or relation to the extremes, its nonspecific. Distance is also a real thing that can be measured, indicating physical origin.
Try the Three Simple Steps with a dichotomy that is simpler to deduce for your very first usage of the technique. An intuition should develop, and with more and more usage of technique, the strength of intuition increases with familiarity. This intuition also provides a reassurance of just how natural of a process this really is. Not everything used as extremes will apply with intuition, some can be too difficult to identify or be applied accurately. As complexity of the thing increases, the directional result becomes less and less accurate. Try to break it down into the simplest fundamental form first, then proceed with plotting the imaginary approximation point of where you currently are between the two extremes and finally the deduced direction result. Use the direction to change the original thing to a more balanced state. The magnitude is only to be considered if the amount of change can be accurately varied as to be effective, and potentially achieve balance faster. Remember that over time, some periodic interval, another iteration of this process should be performed to maintain optimal balance. Accuracy can be increased with more iterations, or shorter periods between iterations.
Now the final question becomes, How does the Golden Ratio, and the technique described, actually help humanity. If you imagine if this proof was discovered 4000 years ago, was taught and practiced by every human in common every day life for any problem or question, what would civilization look like today?
Typically civilizations in the past have a parabolic level of progress over a period of time. The falling side being the initial slow decline and then rapid collapse to zero. This has been repeated multiple times, resulting in a slower evolution of the species as a whole. If instead that was challenged at a point not to low that rapid descent is too steep to recover from in the short time interval remaining before zero, a bounce is produced on the falling side of the parabola. Nature has bounced many, many times, achieving the peak of the current parabola and then achieving a newer, higher parabola than before. If today, during the initial slow decline on the falling side, every person practices and builds intuition using the Golden Ratio technique for everyday problems or questions with regard to a thing that is successfully broken down into the two extremes, perhaps itself and its opposite, we can then integrate over the entire human species producing what I like to call the Big Picture. This would be an accurate gradient just the same as the gradient for each human. The more that everyone’s gradient is representative of balance, that black vertical line, the more balanced humanity will become.
Nature is already doing this all the time, surving ultimately as to propose that currently the universe still exists, no critical fall back to absolute zero.
Humans need to not isolate and consider themselves separate from nature. Animals needs to be forgotten and referred to as species for proper scientific accuracy, with humans — an intelligent species being in that exact same list. Human, you very much are a part of nature, as any other.
If we follow Nature’s exact same target for Balanced progress, evolution of our species will be continuous, achieving large magnitudes of higher Scale over time. It may also be possible to modify the periodic interval of the parabola representing the rise and fall of civilization that has repetition extending n parabola to infinity. Changing the frequency, I warn however, could introduce new real physical consequences, of which could change the parabola shape altogether and be unpredictable. I would advise against any adjustment, if found at some point in time to be possible. The risks outweigh the benefit provided by potential frequency adjustment.
Civilization, forever forward can then also have a lifetime that is not defined, open, survival at its best, aligned with nature. Most bad things in the universe have only local effects, the whole of Nature is only marginally affected, as Nature has evolved to a state in which survival is generally guaranteed and growing even stronger as more time passes on.
It’s time to understand one of our greatest problems:
SELF IMPORTANCE
This would be contradictory to the humanistic model proposed. Having every individual achieving a different target with perhaps no commonality, is not how nature works. Instead it has a guide, a real number, that through a yet undefined mechanism, achieves convergence on the best way to survive.
Balance actual begins to make a lot of sense now, a gradient of perhaps rational to irrational where the desired or optimal gradation is the reference to achieve. It is also in the same spot, in every gradient that can be deduced into 2 extremes. This solid guide finally gives the children of earth a parent.
The Golden Ratio was first discovered 4000 -5000 years ago, first in use by the Egyptians. Did they discover it, or were they possibly informed of it? What does history tell?
The Egyptian civilization did after all still fail, didn’t it? Was this ancient knowledge forgotten after the initial discovery? Or was it a local effect from a bad thing?
So one than further deduce, that the Golden Ratio is only a guide, with no guarantees of survival and balance being always achieved. Is the local area relevant? Very much so with relation to its NEIGHBOURS. Local Balance is then also affected by non local, relative things out of our control, generally. The probability or occurance appears to be that there are then, truly, more good balanced things in the entire universe than bad unbalanced, at either extreme things. As mentioned before, Nature’s resilient survival is only affected marginally by local effects, good or bad, however clearly way more area is already occupied good from the evolution of nature, the universe, to today. The logical, illogical, physical, non-physical effects of the golden ratio are not local, it is simply global as you can implicitly deduce from the physics of a phenomena so incredible, it may be able to fix all of humanities hardest problems with more research and application of these fundamental, mathematical, physical laws that apparently make the whole thing tick, and continue to tick rather than fail. Reality has embedded this number into everything imaginable, hidden by two extremes which may never be deduced, to give a way for reality to be survival focused, indicating longevity is the desired effect to prioritize for all of creation. This universe has a little helping hand, so that the potential lifetime can be as long as possible. It’s literally anagolous to a regulator, never allowing that either extreme is the current state of things. How does a simple number produce effects so profound, that the way it actually works will always be unknown, a blackbox, a real mystery of mysteries.
Perhaps you see a fuzzy type of physics or science being presented here. There is evidence, the math actually doesn’t have much to do with it, as we really are just looking at a number here, right?
There are patterns that match other physical equations like the inverse square law repetition in multiple physical phenomena. The physics is better visually as a gradient, visual physics if you will, that communicates the math intuitively, and with practice builds real intuition. It is simple, infallible, concise, concrete, solid, unwavering, real.
There you go kid, now go find your parents.
https://www.shadertoy.com/view/mdfyDj
Reference Golden Spiral
https://www.shadertoy.com/view/dssyDS
Golden Mirror in Space
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Golden Ratio Technique, Gradient © 2023 by Jason Tully is licensed under Creative Commons Attribution-ShareAlike 4.0 International
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