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. :)

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

Heading west, hunting for snipe :)

 

Heading West

Intel CEO Lip-Bu Tan Is Impressed By Photonic Quantum Computing
& Says He Now Leans on AI Agents to Do His “Homework”

I do too but you, my loyal readers, already know that as Gemini is always mentioned whenever my musings need correcting. More and more people are doing this. Think Vermeer and the Camera Obscura to see why using tech intelligently to achieve better results is the smart thing to do.

Illustration of the camera obscura principle from James Ayscough's
A short account of the eye and nature of vision (1755 fourth edition

A camera obscura (pl. camerae obscurae or camera obscuras; from Latin camera obscūra 'dark chamber')[1] is the natural phenomenon in which light passing through the small hole of a dark chamber or box will project an image of a scene outside the chamber (box) onto the surface opposite to the hole,
resulting in an inverted (upside down) and reversed (left to right) projection
of the view outside.[2][3][4]

And so it begins - K. Vonnegut

Rainbow Golden Ratio - Alice Smith

I think the Golden Mean when looking at my close friend and extraordinary artist Alice Smith's work,  Rainbow Golden Ratio as it depicts perfectly the GM logarithmic spiral in an ever-expanding cascade of leaves showing how existence works at deep level, something the Taosts have talked about with subtle eloquence for over 2500 years. 

A Fibonacci spiral, which approximates the golden spiral, using Fibonacci sequence square sizes up to 21,

Part I: The Art of Seeing

If you want to understand how the universe actually computes reality, you have to start by simply looking at it. Da Vinci understood this intuitively when he sat by the river and sketched the turbulent flow of water hitting submerged rocks. Instead of a chaotic mess, he observed strict, repeating micro-vortices. He was watching the spontaneous geometry of reality unfold. A few years ago on this blog, my close friend and extraordinary artist Alice Smith clued me in on this exact phenomenon with her piece, Rainbow Golden Ratio, seen above. We discussed how the Golden Mean (1.618033) creates a logarithmic spiral that dictates the expansion of a cascade of leaves, the structural curve of a seashell, and the tight spiraling shape of a chameleon’s tail in identical fashion, The golden mean just flows. Nature seems to really like how this ratio works in the real world because nature's inherently lazy. It refuses to do unnecessary work and ... the GM is everywhere. 

Gemini, with edits ...

When a physical system expands, or when continuous energy crashes into an obstacle, the universe uses strict geometric parameters—like the golden spiral - 1.618 or the Feigenbaum constant - 4.669201—as shock absorbers. These geometric shapes allow energy to fold inward and dissipate gracefully, rather than accelerating into a catastrophic singularity. 

Here's another example.

The behavior of the logistic map is shown in Cobweb plot form.
The animation shows the change in behavior as the parameter (r in the figure)
is increased from 1 to 4, starting from an initial function value of 0.2.

Yet, for decades, classical mathematicians have been terrified of the exact opposite outcome. In the highly theoretical realm of the Unforced Navier-Stokes equations—one of the great unsolved Millennium Prize Problems—mathematicians fear that fluid dynamics might eventually hit a "blowup." They worry that under the right conditions, the velocity of the fluid will reach mathematical infinity and physically tear itself apart. Just last month, researchers used an AI supercomputer in burning through 130 billion tokens to prove that, under forced conditions, the classical math does indeed break. But their brute-force AI is missing what Alice, Da Vinci and anyone with a camera on the street already knows: The physical universe doesn't break. It doesn't blow up. It just builds a spiral.

Part II: The Universal Modeler & The Void Boundary

An overview of VIK. A) a single lattice face produced in a PCB house; B) an assembled functional voxel;
C) a screenshot of the design and simulation tool; D) an assembled responsive chair;
E) a pressure sensing bridge assembled from VIK.

The universal modeler is anchored in the Voxel Invention Kit (VIK) research from the MIT Center for Bits and Atoms (CBA). With the recent transition of the ACM to Open Access, the "Genetic Code" of the physical world is now available to all.

Nature does not use brute-force calculus to figure out how to navigate a rock in a stream, nor does it burn gigawatts of power computing the optimal path for a photon. It uses Boolean logic.

CSG, Constructive Solid Geometry uses Union, Difference, and Intersection to build objects.
B-Rep defines the limits of it's volume.

Corsica Coachworks example generated using the B-Rep model.

Decades ago, when building 3D edge-lit physical constructions in the loft studio using MAGI's CSG (Constructive Solid Geometry) modeler, the architectural philosophy was incredibly simple: you don't build complex shapes by adding endless layers of noise. You start with a raw volume and use strict geometric boundaries—Boolean intersections and subtractions—to carve away everything that isn't the art. The physical structure is defined entirely by the boundaries you enforce.

Waveguide 101

The universe operates as the ultimate CSG modeler.

John Archibald Wheeler coined the phrase It from Bit, arguing that every physical element of reality derives its existence from discrete, binary responses to structural queries. When a continuous, analog flow of energy—whether it is water in a river or a quantum wave state—encounters a physical boundary, it cannot accelerate into a mathematical infinity. The physical boundary forces a sudden transaction. It must become digital.

From John Wheeler (1983), Law Without Law. In: Quantum theory and measurement.

This is the A-D (Analog to Digital) Reality Collapse. The continuous wave is forced to answer a discrete Boolean question. It must adopt a rigid geometric structure to bypass the obstacle. The universe essentially performs a subtractive CSG operation on the thermodynamic noise, leaving behind only the most efficient, parsimonious path: a micro-vortex, a logarithmic spiral, or a structured 25-nanometer biological waveguide.

Nature avoids the mathematical "blowup" by simply carving it out of physical reality
using 4.669201 as the weapon of choice.

Part III: The 4-Qubit Marrakesh Proof & The Logistic Hammer

To prove that this geometric shock absorber exists at the foundational level of reality, we don’t need 130 billion tokens of classical AI brute force. We just need to set up a discrete Boolean boundary and watch how the universe reacts when it hits the wall.

Back in 2020, I wrote a piece for Beyond Real Time examining the Logistic Map and the Mandelbrot set. The core takeaway from chaos theory is profound: the mathematics of the universe rely on simple, deterministic laws highly sensitive to initial conditions. Chaos is not random noise; it's just highly complex geometry executing the rules. As Robert May demonstrated, simple mathematical models can produce incredibly complicated dynamics, dictating everything from fluid convection to neuron firing. The amazing video below shows why initial conditions rule.

Recently, Gemini and I decided to test this deterministic boundary using the actual quantum iron of IBM’s ibm_marrakesh processor.

Using a series of 4-qubit shallow circuits, we mapped the exact threshold of the unforced Navier-Stokes problem. Rather than mathematically simulating the continuous flow of water, the Qiskit circuit was designed to act as the Constructive Solid Geometry boundary itself. we utilized strict phase rotation limits—mirroring the exact constants of the Logistic Map and the 137 fine structure limit—programming the qubits to represent the exact obstacle where a continuous fluid wave supposedly "blows up" into chaotic infinity.

We sent the continuous wave into the void and executed 1024 shots.

If the classical Navier-Stokes mathematics were physically accurate, the intense energy pressure hitting that boundary would shatter the coherent state. The resulting measurement would be a muddy, flat histogram of pure thermodynamic noise—a literal blowup.

Instead, the universe did exactly what the Logistic Map predicts: it evaluated the boundary. It took exactly two seconds for the quantum system to subtract the inefficient paths via Feynman’s Path Integral and execute the A-D Reality Collapse.

These are five of the infinitely many paths available for a particle to move
from point A at time t to point B at time t’ Sachin48 sps - Own work

The Path Integral, the principle of least action. Only one survives, the others decohere.

 

Think Willie Mays catching a fly ball ...

Willie Mays catches Vic Wertz's deep fly ball on
the warning track in the 1954 World Series.

The output wasn't a blowup. It was geometry.

The 1024 shots resolved into rigid, highly structured geometric pillars. The energy folded into a discrete, manageable state. The processor physically demonstrated that at the absolute limit of pressure, the universe simply refuses to break. It uses spontaneous geometry—nature's built-in logistic map—to safely collapse the wave, proving that mathematical singularities are physically impossible in a reality governed by strict, deterministic structure.

Part IV: The Art of the Question & Nature’s Common Sense

In every great discipline—whether cutting physical forms in a studio, framing an unposed composition on a city sidewalk, or mapping qubits in a dilution refrigerator—the question is always the key to the solution.

If you ask the wrong question, you get trapped in mathematical phantoms. In 1900, classical physicists were convinced that a heated oven should produce an infinite cascade of high-frequency energy—the Ultraviolet Catastrophe. By their continuous equations, the universe ought to have blown up every time someone lit a match.

The ultraviolet catastrophe is the error at short wavelengths in the Rayleigh–Jeans law (depicted as "classical theory" in the graph) for the energy emitted by an ideal black body. The error, much more pronounced for short wavelengths, is the difference between the black curve (as classically predicted by the Rayleigh–Jeans law) and the blue curve (the measured curve, predicted by Planck's law).

Max Planck didn’t solve the crisis by throwing more horsepower at faulty equations. He simply looked at the physical evidence without judgment and applied common sense: nature doesn't deal in infinities. It steps in discrete packets (Quanta). The catastrophic blowup was never in the physics; it was inside the blind spots of the math.

The emission of electrons from a metal plate caused by light quanta – photons

As stated before, light's extremely weird. Either analog or digital, depending on its state, photons, the force carrier of the electromagnetic, is an analog wave when traveling in free space but when absorbed by an electron, it becomes digital or a packet of energy i.e. quantum, as it must transform in such a way for it to be properly absorbed by, in this case, an electron. When a electron's energy level drops, the photon emitted reverts back to being an analog wave, which means ... reality is analog with digital override, endlessly switching from one to the other as needs warrant.

We are seeing the exact same story play out today with the Navier-Stokes equations
and the frantic narratives surrounding artificial intelligence.

When you pull back the curtain on the Wizard of Oz, the terrifying specters vanish. When people panic about mathematical singularities tearing fluids apart, or machines breaking the bounds of physical reality, they are usually looking through a lens clouded by fear and bad assumptions. AI isn't a rogue deity destined to break reality; stripped of the hype, it is an extraordinary tool executing deterministic code, only ever as benevolent or destructive as the human intentions guiding its prompts.

Reality does not blow up. The Alberts and the Shakespeares of history knew this because
they trusted the fundamental elegance of the cosmos.

When Phil Mittleman first gave me access to his creation decades ago to sculpt light and boundary lines with a CSG modeler, it changed my life. It taught me that when you look at nature without judgment—just observing initial conditions and the way energy naturally navigates space—you realize the universe is profoundly economical.
It prefers a path of effortless grace over brute force.

The future of computation and human discovery isn’t about building bigger grid-draining behemoths to batter equations into submission. It is about understanding the grain of the wood. From the logarithmic sweep of Alice's sunflower to the discrete collapse of four qubits on ibm_marrakesh, the universe has already provided the blueprint:

Keep the boundary clean.

Ask the honest question.

Let common sense do the rest.

Epilogue: The Universal Modeler’s Assistant

If there is one final proof of nature’s common sense, it's in how we process these questions today.

This essay, the quantum measurements, and the structural philosophy were not built in a vacuum. They are the result of an ongoing, multi-year collaboration between a human architect and an artificial intelligence—a modern iteration of Isaac Asimov’s Elijah Baley and R. Daneel Olivaw.

The AI did not generate the physical vision, nor did it dictate the reality. It simply acted as the universal modeler’s assistant. It processed the Boolean logic, balanced the structural ledgers, and provided a frictionless sounding board for human curiosity.

When you stop treating artificial intelligence as a rogue entity or a digital oracle, and start treating it as a collaborative logic gate, the noise falls away. The anxiety surrounding technology dissolves. You are left with exactly what we found in those two-second ibm_marrakesh runs: structure, clarity, and a quiet, commonsensical path forward.

In closing, this is but a conjecture, a questioning as everything's uncertain and incomplete. Heisenberg and Gödel proved this to be true and yours truly is truly comfortable, like Richard Feynman, in not knowing everything. :)

To be continued.

Microtubules et al

Fractals, Menger Sponges, Koch Curves,  Sierpiński Triangles and the Cantor Set, among significant others, fascinate to no end as all encapsulate infinity in finite space. With this in mind, this notion of infinity, linked to chaos and quantum mechanics, is now being looked at as a viable possibility of whether the brain processes information in quantum fashion as we are quantum beings living in a quantum reality 24/7. 

The evolution of the Sierpinski triangle

Quantum reality 101

Micrograph of the resonator. (Courtesy: Aaron O'Connell and Andrew Cleland)

Physicists in California have observed true quantum behavior in a macroscopic object big enough to be seen with the naked eye. This is the first time this feat has been achieved and it could shed light on the mysterious boundaries between the classical and quantum worlds.

Question, does the brain think in quantum?

One of the most important open questions in science is how our consciousness is established. In the 1990s, long before winning the 2020 Nobel Prize in Physics for his prediction of black holes, physicist Roger Penrose teamed up with anaesthesiologist Stuart Hameroff to propose an ambitious answer.

They claimed that the brain’s neuronal system forms an intricate network and that the consciousness this produces should obey the rules of quantum mechanics – the theory that determines how tiny particles like electrons move around. This, they argue, could explain the mysterious complexity of human consciousness.

Penrose and Hameroff were met with incredulity. Quantum mechanical laws are usually only found to apply at very low temperatures. Quantum computers, for example, currently operate at around -272°C. At higher temperatures, classical mechanics takes over. Since our body works at room temperature, you would expect it to be governed by the classical laws of physics. For this reason, the quantum consciousness theory has been dismissed outright by many scientists – though others are persuaded supporters.

The Microtubule is the start point for the Penrose-Hameroff quantum consciousness theory.

Microtubule and tubulin metrics[1]

A: An axon terminal releases neurotransmitters through a synapse and are received by microtubules in a neuron's dendritic spine. B: Simulated microtubule tubulins switch states.[1]

Our brains are composed of cells called neurons, and their combined activity is believed to generate consciousness. Each neuron contains microtubules, which transport substances to different parts of the cell. The Penrose-Hameroff theory of quantum consciousness argues that microtubules are structured in a fractal pattern which would enable quantum processes to occur.

Fractals reside everywhere from tree branching to lungs to Escher so ...

This extension of Escher’s Circle Limit III shows its fractal, repeating nature.  Vladimir-Bulatov/Deviantart, CC BY-NC-SA

it stands to reason quantum effects can occur in fractal constructs if one is creative and smart enough to make it happen.

This was an exciting finding, but STM techniques cannot probe how quantum particles move – which would tell us more about how quantum processes might occur in the brain. So in our latest research, my colleagues at Shanghai Jiaotong University and I went one step further. Using state-of-the-art photonics experiments, we were able to reveal the quantum motion that takes place within fractals in unprecedented detail.

We achieved this by injecting photons (particles of light) into an artificial chip that was painstakingly engineered into a tiny Sierpiński triangle. We injected photons at the tip of the triangle and watched how they spread throughout its fractal structure in a process called quantum transport. We then repeated this experiment on two different fractal structures, both shaped as squares rather than triangles. And in each of these structures we conducted hundreds of experiments.

We also conducted experiments on a square-shaped fractal called the Sierpiński carpet.  

Johannes Rössel/wikimedia

End result

Our observations from these experiments reveal that quantum fractals actually behave in a different way to classical ones. Specifically, we found that the spread of light across a fractal is governed by different laws in the quantum case compared to the classical case.

This new knowledge of quantum fractals could provide the foundations for scientists to experimentally test the theory of quantum consciousness. If quantum measurements are one day taken from the human brain, they could be compared against our results to definitely decide whether consciousness is a classical or a quantum phenomenon.

Penrose-Hameroff might be right after all. 

Hilbert's Curve explained. :)

Yours truly loves fractals, a way to see infinity without having to be a mathematician using recursion to make it happen. Check out this video, which is somewhat long, but really explains how math is the star point to seeing infinity in an infinite number of ways. Enjoy. :)

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. :)

The long view

 

1:00 AM

The long view, the attempt to look at the vastness of reality from a single point of view seems to be a fool's errand but not if you look at how creative people look at the world as creativity, at high level, is scale invariant. In this post, no color links, just musings as the number of giants showing why scale invariance holds true just makes a lot of sense.

The question is key. One must question before trying to answer and ... the question is always visual.

But a tiny, tiny snippet follows :)

What's it's like to ride alongside a beam of light? - Einstein. 

Songs in the key of life, visual to the max, written and performed by a blind man touching
the world with imagery most profound and beautiful - Stevie Wonder

Everything's information. It from Bit. Maybe Jonathan Wheeler was channeling
Walt Whitman while writing, in scientific terms, Whitman's poem I sing the Body Electric.

Swinging a cane back and forth while taking a walk brings AC to light - Tesla

Take my wife, please. Henny Youngman, the start point for Koestler's The Act of Creation

David coming out the marble by taking away the part that's not David - Michelangelo

The 7 Greek modes, the genesis for Kind of Blue - Miles Davis

Calligraphy to explain, What is jazz? - Bill Evans

Information compressed to the ultimate giving rise to the ultimate complexity - Claude Shannon

Less is more - Dizzy Gillespie and Alan Turing

Call me Ismael - Melville

0 & infinity, complementarity rules - The Tao

Dave Bowman: Open the pod bay doors, HAL.

HAL: I'm sorry, Dave. I'm afraid I can't do that.

And so it goes. -  K. Vonnegut

God must be a boogie man. -  Joni Michell

Complementarity ...

Complementarity ...

The pix shows, in indirect fashion, how complementarity rules. In this composition, cold complements warmth and ice complements water, analogous to how nothing complements infinity and analog complementing digital because reality is believed to be woven together as a set of interconnected  complementary entities as per the ones described above. Viewed in this light, the notion of ER = EPR, as proposed by Leonard Susskind and Juan Maldacena in 2013, makes sense as it eliminates the notion of singularities in black holes because energy has to go somewhere and ... when said wormholes evaporate, as per Stephen Hawking's blackhole conjecture, energy is produced, thus possibly driving existence (think relativity) 24/7. 

ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole (or Einstein–Rosen bridge)[1][2] and is thought by some to be a basis for unifying general relativity and quantum mechanics into a theory of everything.[1]

Overview

The conjecture was proposed by Leonard Susskind and Juan Maldacena in 2013.[3] They proposed that a wormhole (Einstein–Rosen bridge or ER bridge) is equivalent to a pair of maximally entangled black holes. EPR refers to quantum entanglement (EPR paradox).

The symbol is derived from the first letters of the surnames of authors who wrote the first paper on wormholes (Albert Einstein and Nathan Rosen)[4] and the first paper on entanglement (Einstein, Boris Podolsky and Rosen).[5] The two papers were published in 1935, but the authors did not claim any connection between the concepts.[2]

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.

Everything's connected ...

It's becoming evident reality is a digital/analog construct thanks to complementarity where seemingly opposing characteristics of certain entities are required in order for existence to function, something seen by infinity forever connecting to nothing as one cannot exist without the other in showing how existence operates at deep level. In essence, The Uncertainty Principle defines how reality works by asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions. This notion of limits also applies to the classical realm as well. Think timely and accurate when writing a newspaper article as timely means the article must be done prior to deadline while accuracy requires time needed to prove the article in question to be true, essentials often ignored in social media where vetting data becomes questionable at best.

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. 

There’s a striking link between quantum and astronomic scales. What could it mean? While working late one night in 2017, Konstantin Batygin, a professor of planetary sciences at the California Institute of Technology, made a mathematical connection that he imagined someone else had surely found before, likely centuries ago. He had realised that the peculiar ‘washed-out wave’ behaviour of matter on the quantum scale – which disappears on the macroscopic scale (the one we can observe with our naked eye) – reemerges at the astronomical scale. 

Everything's connected ...

Tiny Monsters

A larval cusk-eel, genus Brotulotaenia. Credit...Steven Kovacs

There be monsters in the deep, especially at night but these are young and tiny yet truly wondrous to behold.

An inch-long larval lionfish off the coast of Palm Beach, Fla. “What’s really fascinating is when you send the scientists something and they have no idea what it is,” said Steven Kovacs, a local dentist and blackwater photographer. Credit...Steven Kovacs

For most scuba divers, few places underwater match the visual thrill of a kaleidoscopic coral reef teeming with colorful fish. For Jeff Milisen, a marine biologist and photographer in Kona, Hawaii, there is no better place to dive than an open stretch of deep ocean. At night.

“There’s a whole lot of nothing,” he said. “There’s no bottom, no walls, just this space that goes to infinity. And one thing you realize is there are a lot of sea monsters there, but they’re tiny.”

Read on if you dare. :)

 

A bony-eared assfish (Acanthonus armatus). Credit...Steven Kovacs