The world is a creation of your consciousness. ~ Nisargadatta Maharaj
Energyism posits that physicality is ultimately a mirage, created in the mind. This monism has flavors. Whereas subjective idealism states that the appearance of physicality is a mental construction, neutral monism postulates that existence is ultimately neither mental nor material. These 2 schools of thought are congruent. Indeed, combining the 2 provides a coherent explanation of the nature of psychological reality.
The mind is everything. ~ Indian guru Buddha
Idealism posits that physicality is the product of the mind. Under idealism, the ostensible outside world is a fabrication of perception, moment by moment, given continuity by memory.
Your body is your subconscious mind. ~ Candace Pert
In rendering Nature a mental construct, idealism dissolves the mind-body problem. Idealism instead raises the conundrum of how we can see the same world if it’s all in our minds.
Some subset of these elements form individual minds: the subset of just the experiences that you have for the day, which are accordingly just so many neutral elements that follow upon one another, is your mind as it exists for that day. The neutral elements exist, and our minds are constituted by some subset of them, and that subset can also be seen to constitute a set of empirical observations of the objects in the world. All of this, however, is just a matter of grouping the neutral elements in one way or another, according to a physical or a psychological (mental) perspective. ~ William James
Neutral monism (aka neumonism) is the metaphysical view that the Nature is neither physical nor mental, but instead consists of one kind of non-physical stuff with its own independent existence.
Plato was a proponent of neumonism, believing the empirical world an ersatz, fleeting manifestation of pure forms (ideas), which have an independent, eternal existence.
These absolute ideas exist as simple, self-existent, and unchanging forms. ~ Plato
German mathematician and philosopher Gottfried von Leibniz envisioned the universe as having a hierarchy of 4 different types of souls, which he termed monads. Unsurprisingly, Leibniz’s supreme monad was God: a mythical figure who seldom escapes being in the mix of philosophical musings in the history of Western thought since medieval times.
Neumonism not only sidesteps the mind-body problem, it sidesteps psychology altogether. Nonetheless, neumonism is a philosophy with serious scientific implications.
Animism, the oldest spiritual belief, is a neutral monism. Eastern philosophic traditions and religions also embrace neumonism, whereby a substrate of noumenon (nonexistence) invokes phenomena as an expression.
Modern physics instructs that the essence of existence is energy. This is neutral monism, with energy as the medium.
The residual conundrum of neumonism is that energy is only relative, not absolute. Energy as the essential medium suggests a deeper foundation to reality, which harkens back to Platonic forms.
The Language of Nature
The laws of Nature are written in the language of mathematics. ~ Galileo in the early 17th century
Mathematics has long been a favored target for neutral monism. Its seamless, open-ended entanglements have often made many scientifically inclined to consider math’s constructs the language of reality.
The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious, and there is no rational explanation for it. ~ Hungarian American physicist and mathematician Eugene Wigner
Austrian logician Kurt Gödel is among many who considered the concepts of math as forming “an objective reality of their own, which we cannot create or change, but only perceive and describe.”
It was mathematics, the nonempirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of Nature and the universe that are concealed by appearances. ~ German political philosopher Hannah Arendt
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Mathematics is a merely mental abstraction that serves useful purposes. ~ Derek Abbott
Skepticism of mathematics as the language of reality has been succinctly stated by Australian electrical engineer Derek Abbott: that math is merely a mental invention which occasionally renders useful approximations of phenomena.
Mathematics is a product of the imagination that sometimes works on simplified models of reality. ~ Derek Abbott
The unraveling of Abbott’s argument begins with the observation that faculty for math is innate in all organisms. Even microbes must be able to tell when food supplies are plentiful or running short into order to take appropriate action – which they do based upon estimated quantity. Universalities of life are not inventions; at least, not inventions of those who innately use them.
Why Nature is mathematical is a mystery. The fact that there are rules at all is a kind of miracle. ~ American theoretical physicist Richard Feynman
That any representation of Nature we may model is a gross simplification owes not to the limits of mathematics, but to our ability to understand and employ math. Every historian of science knows that science’s progress has been facilitated by mathematical discoveries. This has been especially true in physics.
For a physicist, mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created. ~ English-born American theoretical physicist and mathematician Freeman Dyson
We naturally assume that we perceive things as they are. There is magic behind that process.
The world is comprehensible only because our perceptions transform sensations into a state where they may be understood. Science has shown actuality to be infinitely complex, while paradoxically still striving to construe laws of Nature, which can only be simplifying heuristics (rules of thumb).
Input-output maps are ubiquitously employed to understand natural mechanics, including physics and biology. As the maps necessarily involve quantized units, represented as numbers, these models are intrinsically discrete, but are often used to comprehend continuous systems. Calculus is exemplary in being able to analyze holistic systems through discrete differentiation.
(Calculus was conceived in the late 17th century via the idea of infinitesimals: atomic quantities too small to measure. 2 centuries later, this same concept was pivotal in the quantization discoveries of Max Planck which led to modern physics.)
Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. ~ British mathematical biologist Kamaludin Dingle et al
Mathematics itself appears biased to fabricate simplicity: models inherently tend to generate simple outputs at an exponentially higher probability than complex outputs.
Simplicity bias – that simple outputs are exponentially more likely to be generated than complex outputs are – holds for a wide variety of systems in science and engineering. ~ English theoretical physicist Ard Louis
Arithmetic reasoning captures deeply important properties of the world. ~ American psychologist C.R. Gallistel & Canadian psychologist Rochel Gelman
Are the maxims of mathematics invented or discovered? The answer to this question can be found in a grander inquiry, more readily answered – is there a natural order?
Nature commonly exhibits self-organization and hidden order within apparent disorder. Chaotically tumultuous fluids spontaneously create stripes of coherent flow alternating with turbulent regions. Liquids self-organize into crystalline structures: a phenomenon known as disordered hyperuniformity. Photons in laser light self-organize into fractal patterns. Viewed as particles in a system (instead of linearly), prime numbers exhibit an ordered structure.
The studies of cosmology, physics, chemistry, and biology all aver a natural order. Hence, the universal means for understanding Nature’s ways – through mathematics – cannot be an invention.
During the Edo Period (1603–1867), Japan had limited contact with foreign cultures. (The Japanese had an active interest in Chinese science from 1600 to 1675. The bit of math imported from China during this time was significantly advanced by the Japanese. This was at a time when China was abandoning its own native mathematics under the influence of the Jesuits.) A Japanese school of mathematics – wasan – flourished, without knowledge of European mathematics. Mathematical discoveries in Japan often contemporaneously mirrored those in Europe.
Proceeding from a different basis, calculus was independently discovered by the Japanese and Europeans at roughly the same time. Whereas Europeans had in mind the numerics of atomic infinitesimals, the Japanese approached calculus geometrically – an unlikely convergence if math were mere invention.
When Japan became infested with Western culture during the Meiji era (1868–1912), Japanese scholars lost interest in wasan, as the Chinese had in their own mathematics almost 3 centuries earlier.
One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them. ~ German physicist Heinrich Hertz
The realm of reason is entangled: structured by Nature, and in a way that that the order may be discerned, using the abstract means by which the order is expressed.
Understanding is a matter of discovery. We invent only contrivances of misunderstanding.
Every new body of discovery is mathematical in form. ~ Charles Darwin
The use of complex numbers comes close to being a necessity in the formulation of the laws of quantum mechanics. Yet complex numbers are far from natural or simple, and they cannot be suggested by physical observations. ~ Eugene Wigner
If reality is a mathematical construct, its mechanics are not quite hiding in plain sight. Complex numbers illustrate.
A complex number is itself 2-dimensional. Complex numbers are ubiquitous for characterizing dynamics in physics, chemistry, and biology.
Construed through complex numbers, fractals are patterns which exhibit self-similarity at different scales. The numbers involved are extra-dimensional: fractional complex numbers.
Fractals are dimensionally discordant. ~ Polish-born French American mathematician Benoît B. Mandelbrot
Many aspects of Nature are fractal. Fluid turbulence forms fractal patterns. The patterns that tree leaves and branches exhibit are fractal. Romanesco broccoli (pictured) are brazenly fractal.
Fractals occur in time as well as space. The brilliant, distinctive symphonies of Austrian composer Gustav Mahler were temporally fractal, with self-similar themes recurring throughout. These were not instances of exploratory variations, which are common in composition (e.g., Bach). Mahler instead ingeniously crafted an interwoven temporal fractal fabric.
There are 2 types of equations. One is invented, human made. The other reflects some ‘pre-established harmony,’ which can only be discovered. ~ Alexander Polyakov
In the 5th century bce, Greek rationalist philosopher Democritus formulated a hypothesis about atoms. One of his arguments in support of atomism was that atoms naturally explain the boundaries known as phase transitions, such as ice melting, or hot water steaming away. Democritus rightly conceived that small atomic transforms could actuate large-scale changes: the idea of physical gyres.
At any moment, matter exists in a certain state, which is really a phase, as matter may transform from one state to another via a phase transition. Phase transitions occur with a sufficient change in ambient energy: thermal (heat), mechanical (pressure), and/or electromagnetic.
The 3 states of matter with which we are naturally familiar are gas, liquid, and solid. There is a 4th material state: plasma, which is an ionized gas-like state. While rare in our experience (neon signs excepted), plasma is the most abundant state of matter in the universe. Stars are plasmic, which is to say that the foundry of matter works in a plasmic state.
Plasma may be invoked thermally or in the presence of a strong magnetic field. Despite the sustained intense ionization required for its existence, plasma is odd in being conductive while remaining electrically neutral. Of course, one may consider any matter phase peculiar for its properties. Peculiarity is, after all, only a matter of expectation as to how Nature operates. Any law of Nature one conceives is nothing more than an expectation.
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Mathematically, phase transitions represent a discontinuity; hence their mathematical representation is tricky.
In attempting to deal with irreversible processes, non-equilibrium statistical mechanics deals with phase transitions. In principle, the results could be mathematically exact by following deterministic equations, but the underlying complexity of such an approach renders precise solutions difficult to come by.
In 1920, German physicist Wilhelm Lenz challenged his doctoral student Ernst Ising to have a go at modeling the transition of magnetic materials losing their magnetism when sufficiently heated. Heat – thermodynamic disequilibrium – is a common provocateur of phase transitions.
Ising imagined a material comprised of millions of tiny atomic magnets, all aligned, exerting their influence. At a high enough temperature, the alignment broke down, shedding magnetism: a critical point of phase transition.
Ising’s model was insufficient, as it applied only to a 1-dimensional row of atoms. Anything more complex was mathematically overwhelming.
In 1944, Norwegian physicist Lars Onsager solved Ising’s model in 2 dimensions: not only could the model acquire magnetism, but it could also demagnetize above a critical temperature. For such a simple approximation, Onsager’s 2D Ising model proved far more powerful than it had any right to be. It was used to simulate a bewildering array of phenomena that quickly flip between states: from infectious disease dispersal to neuron signaling in the brain.
The race was on to solve the Ising model in 3 dimensions: “something that could open up entirely new fields in mathematical physics,” speculated Israeli physicist Zohar Komargodski.
In the late 1960s, Russian theoretical physicist Alexander Polyakov was studying interactions between fundamental particles. Polyakov realized that they represented strongly coupled systems which could undergo sudden phase transitions. For instance, triads of quarks are bound by the strong nuclear force to form a hadron. Thus enslaved, they tribally serve as the nuclei of atoms. A high enough energy could liberate quarks, freeing them into independence, as they may have once existed in the infant universe.
Polyakov thought that solving the 3D Ising model might provide insight into why atomic matter exists as it does.
Mathematically, the 2D Ising model and equations typifying elementary particle behavior are linked by certain symmetries. In particular, at critical points they exhibit conformal symmetry.
Conformal transformations distort space, but leave angles unchanged within small regions, as illustrated by the function cf. If this were true of the 3D Ising model, its mathematical description at a critical point might describe other strongly coupled systems with similar symmetries.
I remember in the 1960s, some senior physicist, a very good one actually, asked me what I’m working on now. I said, I’m trying to understand elementary particles by looking at a boiling kettle. I got a very strange look; obviously he thought that me a crackpot. Nobody believed that it was serious. ~ Alexander Polyakov
Polyakov’s shot in the dark was certainly an odd one. Rather than start with some sense of what a particle system should look like, Polyakov began by describing overall symmetries, and other properties, needed for such a model to make sense. From there he worked backwards to equations. The more symmetries described, the more constrained the underlying equations became. Polyakov’s technique is now known as the bootstrap method, for its ability to generate knowledge from only a few general properties.
Polyakov and his colleagues soon managed to bootstrap a replication of Onsager’s achievement with a 2D Ising model. A 3D version still lay out of reach. Frustrated, Polyakov moved on, and the bootstrap technique became moribund.
By 2008, after extensive fruitless search, physicists were wondering if the mythical Higgs boson actually existed. In trying to build an alternative hypothesis, Russian theoretical physicist Slava Rychkov and his group stumbled upon Polyakov’s discarded bootstrap.
It was one of those lucky moments. We basically said, either we can try to tackle it using the bootstrap, or we will never be able to solve this problem. ~ Slava Rychkov
Solve it they did: 4D conformal transforms. (3D was not feasible because “explicit conformal blocks are not known in odd dimensions.”)
The Higgs boson showed itself in 2012 at the expected energy level (mass). By then, American physicists David Simmons-Duffin and David Poland had gone back to the problem that puzzled Ising: a mathematical description of magnetism at critical points. They hadn’t set out to solve the 3D Ising model. Bizarrely, using Polyakov’s bootstrap technique, their equation system started to reproduce characteristic features.
It seemed to know about the 3D Ising model. This was a big surprise. ~ David Simmons-Duffin
Simmons-Duffin and Poland teamed up with Rychkov and others to carry on. Using the bootstrap method, they constrained key model properties over 1,000 times more tightly than had ever been done, thereby providing the 1st rigorous mathematical foundation for describing 3D systems at their critical points. The achievement was impressive, but for Polyakov a major mystery lingered.
It’s not obvious why it should be so precise. There’s something hidden which we don’t understand. ~ Alexander Polyakov
The physical universe could emerge naturally from a mathematical structure. ~ American theoretical physicist Garret Lisi & American physicist and mathematician James Weatherall
If existence is mathematical in nature, it begs the question of what the foundation of mathematics is. The answer: nothing.
The basis of all mathematics is 0 = 0. ~ American theoretical physicist John Wheeler
Mathematics is founded upon sets: groups of entities.
Math begins with the empty set. Only then can 1 be defined as the set which contains only the empty set.
To be created, something first has to not exist in space or time, and then exist. ~ Swedish American cosmologist Max Tegmark
Mathematically, space and time themselves are contained within a larger construct. If mathematics has credence as the spinner of Nature, this suggests that actuality is a subset of reality.
Space and time themselves are contained within larger mathematical structures. ~ Max Tegmark
There are salient examples which suggest that mathematics necessarily defines reality, and vice versa.
When Einstein finished his general theory of relativity in 1916, his equations elicited an unexpected message: the universe is expanding. As Einstein believed then that the universe itself was static, he ignored the implication. 13 years later, American astronomer Edwin Hubble unearthed convincing evidence of cosmic expansion.
In the 1960s, several researchers found lurking in their models of particle physics a fundamental field whose interactions formulate existence. Almost a half-century later, the field revealed itself as the Higgs.
The quantum fields that pervade all of space encode within themselves the potential for particles and antiparticles and dictate the rules of how they behave. ~ American physicist Brian Skinner
All of the fields which give rise to quanta dictate the properties that quanta possess. Quantum fields, which are mathematical expressions of energy, bestow upon their creations the behaviors which define them; behaviors which are entirely mathematical.
Maybe it’s because math is reality. ~ American theoretical physicist Brian Greene
The 2 energetic monisms do not conflict so much as cover different scopes. Idealism and neumonism are congruent kissing cousins.
Subjective idealism has the mind producing each individual’s world and goes no further. Meanwhile, neumonism postulates Nature as the product of something noumenal, such as energy, which is insubstantially conceptual.
Philosophically, idealism is an inadequate account for the nature of existence, in failing to identify how different minds may share the same sense of reality. Neumonism goes beyond idealism in positing an independent source of minds (e.g., energy), but does not identify an origin for that energy. Thus, though on the right track, these monisms fall short of a comprehensive explanation.
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The seeming but chimerical connection between the mind and body provides the best empirical evidence to infer the nature of monistic reality. Saliently, the choice of matterism or energyism centers on a single issue in physics: whether space and time are real, or only relations.
If space and time are absolute, we live in a physical world. If they are only relational, an amazingly convincing simulation is constantly before us.
For spacetime to be real requires inherent integrity. Instead, cosmological observations confirming Einstein’s relativity theories show spacetime as anything but incorruptible. Spacetime predictably distorts under the sway of gravity and is observer dependent. The only possible conclusion is that the spacetime coordinate system is merely a set of relations, and so cannot buttress matterism. In short, relativity alone proves energyism, with wave/particle duality as icing on the cake.
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Mediocre minds usually dismiss anything which reaches beyond their own understanding. ~ French author François de La Rochefoucauld
Matterism is literal minded in taking what is perceived as being reality (naïve realism). In contrast, energyism posits manifestation as a persistent illusion of objects which act as a puppet show of energetic interactions. The conclusion of energyism coincides with modern physics.
Materiality is to energyism analogous to what classical physics and thermodynamics are to modern physics: an approximation which works at ambient scale but is not fundamental. Matter is not to be taken literally as elemental. Actuality is an artifice of a deeper, immaterial reality.
Probable impossibilities are to be preferred to improbable possibilities. ~ Aristotle