0 & then Sum ...

Gradient

When looking at this "wonderful" pix taken by yours truly, the relationship of infinity to zero applies as said entities are complimentary to each other as one requires the other in order to become complete, something beautifully illustrated by the Yang/Yin symbol showing the two forever transitioning from zero to infinity while, at the same time, possessing some of the characteristics of the other depicted by dots of opposing color residing in the center of each. 

Yin and yang (/jɪn/ and /jæŋ/), yinyang,[1][2] or yin-yang[3][2] is a Chinese philosophical concept

that describes opposite but interconnected forces. 

With this in mind, it seems 0's are hardwired into the brain because zero, like infinity, journeys to forever, a concept really hard to let go of without question. :)

Around 2,500 years ago, Babylonian traders in Mesopotamia impressed two slanted wedges into clay tablets. The shapes represented a placeholder digit, squeezed between others, to distinguish numbers such as 50, 505 and 5,005. An elementary version of the concept of zero was born.

Hundreds of years later, in seventh-century India, zero took on a new identity. No longer a placeholder, the digit acquired a value and found its place on the number line, before 1. It's invention went on to spark historic advances in science and technology. From zero sprang the laws of the universe, number theory and modern mathematics.

“Zero is, by many mathematicians, definitely considered one of the greatest — or maybe the greatest — achievement of mankind,” said the neuroscientist Andreas Nieder, who studies animal and human intelligence at the University of Tübingen in Germany. “It took an eternity until mathematicians finally invented zero as a number.”

Mark Belan/Quanta Magazine

Perhaps that’s no surprise given that the concept can be difficult for the brain to grasp. It takes children longer to understand and use zero than other numbers, and it takes adults longer to read it than other small numbers. That’s because to understand zero, our mind must create something out of nothing. It must recognize absence as a mathematical object.

“It’s like an extra level of abstraction away from the world around you,” said Benjy Barnett(opens a new tab), who is completing graduate work on consciousness at University College London. Nonzero numbers map onto countable objects in the environment: three chairs, each with four legs, at one table. With zero, he said, “we have to go one step further and say, ‘OK, there wasn’t anything there. Therefore, there must be zero of them.’”

Factoid, The ancient Greeks hated the notion of zero. This is why Zeno's Paradox works. :)

Achilles and the tortoise

Everything's connected. 

Hunter's Moon

Existence doesn't care ...

The ghosts of long dead galaxies shine away as depicted in this amazing image, proof positive existence doesn't care if we're alive or dead. At the same time we bask in this beautiful yet eerie light of a largely empty reality, the void buzzes with fearsome energy, driven by the quantum fluctuations of virtual particles forever winking in and out of existence as needs warrant.

In 1654 a German scientist and politician named Otto von Guericke was supposed to be busy being the mayor of Magdeburg. But instead he was putting on a demonstration for lords of the Holy Roman Empire. With his newfangled invention, a vacuum pump, he sucked the air out of a copper sphere constructed of two hemispheres. He then had two teams of horses, 15 in each, attempt to pull the hemispheres apart. To the astonishment of the royal onlookers, the horses couldn’t separate the hemispheres because of the overwhelming pressure of the atmosphere around them.

Von Guericke became obsessed by the idea of a vacuum after learning about the recent and radical idea of a heliocentric universe: a cosmos with the sun at the center and the planets whipping around it. But for this idea to work, the space between the planets had to be filled with nothing. Otherwise friction would slow the planets down.

He was right.

Engraving of the Magdeburg hemispheres experiment by Caspar Schott

Perhaps von Guericke was right all along. “Nothing contains all things,” he wrote. “It is more precious than gold, without beginning and end, more joyous than the perception of bountiful light, more noble than the blood of kings, comparable to the heavens, higher than the stars, more powerful than a stroke of lightening, perfect and blessed in every way.” 

As stated in BRT, Zero & Infinity extend to forever.

Endgame

We live in a quantum universe; a universe where you can never be quite sure about anything. At the tiniest of scales, subatomic particles fizz and pop into existence, briefly experiencing the world of the living before returning back from where they came, disappearing from reality before they have a chance to meaningfully interact with anything else.

This phenomenon has various names: the quantum foam, the spacetime foam, vacuum fluctuations. This foam represents a fundamental energy to the vacuum of spacetime itself, a bare ground level on which all other physical interactions take place. In the language of quantum field theory, the offspring of the marriage of quantum mechanics and special relativity, quantum fields representing every kind of particle soak the vacuum of spacetime like crusty bread dipped in oil and vinegar. Those fields can’t help but vibrate at a fundamental, quantum level. In this view, the vacuum is singing to us, a harmony underlying reality itself.

Crescent

Infinity/Nothing ...

6:00 AM

While taking a walk, yours truly finally understood the connect of infinity to nothing as each is endless. Both entities extend to forever, something in concert with Tao and the Yang/Yin symbol showing how one aspect of reality endlessly slides into the other while both possess some of the characteristics of the other until the end of time. Simply astounding says it all. 

Zero also works. :)

Chasing infinity

A Trip to Infinity, a stellar documentary from Netflix, describes infinity as a concept connected to zero as both describe something beyond the notion of number in trying to describe reality in a way indirectly related to Tao or Zen as both attempt to describe existence without the need to parse numbers. Yours truly has talked about infinities within a finite space as seen by the Mandelbrot set, the Menger Sponge and Cantor Dust as all three endlessly subdivide space in ways most enchanting to viewers like myself. Another take on infinity centers on chaos as the law of initial conditions and the inability to exact repeatability is, as quoted below, is but a dream as seen by the Lorenz Attractor, endlessly moving through 3 space, coming close to repeating a given track but never quite getting there.  

To whit ... As seen by the beautiful Lorenz attractor, used in monitoring temperature variations in weather patterns, the notion of exact repeatability in open systems (in this case, temperature) is but a dream, something duplicated, among other things, in the variance of planet orbits, the growth of ferns or the dripping of a water faucet. Additionally, what is also seen from this research is the emergence of complex behavior coming out of seemingly simple systems, something that has forever changed how we view reality. "and so it goes." KV/Slaughterhouse Five" BRT Sunday, 2007.

Why are we so intrigued by the infinite? Maybe it’s because of the tension between our finite lives and the seemingly unbounded range of our imagination, between the limits that we experience and the possibly infinite universe that we inhabit. Young people can think that life will last forever; older people, realizing that it will not, might look for a semblance of immortality in their legacies. Buzz Lightyear, in “Toy Story,” teaches kids that life is full of infinite possibilities; Hamlet, as he laments the finitude of life, remembers Yorick as a man of infinite jest. Perhaps to make sense of infinity, even just a little, is a way to feel some control and comfort in the face of life’s big questions.

Out of context - 2020

The Life of Pi - Infinities Writ Large

It's nice to see a post in the NY Times regarding infinities, something BRT talked about in an article titled Infinities Within Infinities whereby the notion of an infinite number of infinities residing in the multiverse is equally possible in finite space as subdividing 2, 2 1/2 and 3 space to ever finer dimensions can be accomplished in elegant fashion using the genius of Cantor, Mandelbrot  and Menger, among significant others, to make it happen.

In reality, Pi really is the most accessible way to view infinity as no real math is required save that knowing Pi = the ratio of a circle's circumference C to its diameter D, and is approximately equal to 3.14159 etc., etc., etc. until the end of time. :)

Yes, infinities, plural. The popular notion of infinity may be of a monolithic totality, the ultimate, unbounded big tent that goes on forever and subsumes everything in its path — time, the cosmos, your complete collection of old Playbills. Yet in the ever-evolving view of scientists, philosophers and other scholars, there really is no single, implacable entity called infinity.

Instead, there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes and charms. Some are tailored for mathematics, some for cosmology, others for theology; some are of such recent vintage their fontanels still feel soft. There are flat infinities, hunchback infinities, bubbling infinities, hyperboloid infinities. There are infinitely large sets of one kind of number, and even bigger, infinitely large sets of another kind of number.

There are the infinities of the everyday, as exemplified by the figure of pi, with its endless post-decimal tail of nonrepeating digits, and how about if we just round it off to 3.14159 and then serve pie on March 14 at 1:59 p.m.? Another stalwart of infinity shows up in the mathematics that gave us modernity: calculus.

In closing, Wikipedia says it best...More than just irrational, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.

Needless to say, we won't talk about Zero, a most dangerous notion the ancient Geeks avoided at all costs. Just ask Zeno to see why. :)

The Taxpayer's Gift

"The Ouroboros often represents self-reflexivity or cyclicality, especially in the sense of something constantly re-creating itself, the eternal return, and other things perceived as cycles that begin anew as soon as they end (See Phoenix). It can also represent the idea of primordial unity related to something existing in or persisting from the beginning with such force or qualities it cannot be extinguished."

The Ouroborus and zero have always fascinated me as both tie together seemingly opposite concepts in elegant fashion. With Zero, nothing and infinity reside side by side while with the Ourborous, renewal and futility rule.

In science, Fredrich Kekule dreamt about the snake and linked it to atomic structure.

"At Kekule's time, scientists believed that the structure of atoms was 'unknowable' as they believed that anything which acted with atoms created a reaction thereby keeping the atomic structure in constant flux. Kekule, however, doubted this hypothesis and spent years studying chemical structure. The exact nature of the structure eluded him until one evening when he let his conscious mind go and allowed his unconscious to take over.

Kekule claims that he stopped writing and dozed off to sleep. He saw atoms whirling and dancing before his eyes. The atoms then began to reassemble themselves into long rows that seemed to move about in a snake-like motion. As he watched the snake dance, the vision progressed until the snake formed itself into an image he had seen years before at the 1850 murder trial: the snake devouring its own tail.

Kekule states that he awoke as if struck by lightning. He realized in a flash that the problem he had worked on for years had been solved not by studying, but by the serendipitous intervention of a dream."

When looking at how the banks run the US, one sees the Ouruborus as the symbol of futility...

"Goldman Sachs Group Inc is on pace to make record bonus payouts after a robust first half, the Guardian newspaper reported on Sunday."

Why?

"Let's remember that Goldman got roughly $10 billion in AIG-funneled money to "settle" CDS that their CEO said was a fully-hedged position and which would have had no material impact if AIG had gone down, mostly because they had collected nearly all of the hedge before AIG got in serious trouble.

That is, they got paid twice - once with their hedge (good move guys) and again by government fiat, directed by Henry Paulson who coincidentally used to run Goldman.

Also note the size of the first-quarter profit, multiply by four (assuming equally good results) and then compare against the "extra" payout through AIG to figure out whether there would be any bonus pool absent that payment.

Looks to me like the US Taxpayer is funding all of Goldman's bonuses, never mind this ditty:

Last week, the firm predicted that President Barack Obama's government could issue $3.25tn of debt before September, almost four times last year's sum. Goldman, a prime broker of US government bonds, is expected to make hundreds of millions of dollars in profits from selling and dealing in the bonds.

Nice, eh? Do Treasury's bidding, get paid for it, get an extra $10 billion from the taxpayer as a gift to cover a bet you had already hedged against default, and pocket it all.

Change we can believe in - yep, we'll steal even more than we did under The Bush Administration!"

The Fix is in but we already knew that, right?

Music of the Spheres

The figure shows how geometrical music theory represents four-note chord-types -- the collections of notes form a tetrahedron, with the colors indicating the spacing between the individual notes in a sequence. In the blue spheres, the notes are clustered, in the warmer colors, they are farther apart. The red ball at the top of the pyramid is the diminished seventh chord, a popular 19th-century chord. Near it are all the most familiar chords of Western music. Credit: Dmitri Tymoczko, Princeton University.

Well it seems the ancient Greeks were right about tying geometry to music as three music profs have connected sophisticated 3D modeling techniques to musical components to come up with a powerful new way to analyze music. "They take sequences of notes, like chords, rhythms and scales, and categorize them so they can be grouped into "families." They have found a way to assign mathematical structure to these families, so they can then be represented by points in complex geometrical spaces, much the way "x" and "y" coordinates, in the simpler system of high school algebra, correspond to points on a two-dimensional plane. "

What they found was pretty amazing in terms of how easily "western" composition could be transformed into really interesting geometric shapes (including spheres), something that Thales and his student Pythagoras, used in developing number theory to describe how reality worked. "The (Pythagoreans were) ... the first to take up mathematics ... (and) thought its principles were the principles of all things. Since, of these principles, numbers ... are the first, ... in numbers they seemed to see many resemblances to things that exist ... more than [just] air, fire and earth and water, (but things such as) justice, soul, reason, opportunity ..."

What's also fascinating about the Greeks is the fact they hated the concept of Zero. "The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything."

Any questions?

Addendum: Check out Zeno’s Paradox to see what happens when Zero is left out of the equation.