6. Science’s Problem: math
Copyright © 2005 - 2007 Dennis R. Mannisto
Also see my more recent related stuff, a poem, an essay, and some remarks about A.N. Whitehead.
Particles, and only particles, underlie science. Particles are objects. Objects can be directly observed or perceived; often this involves various tools like magnifiers and such. But anyone can perceive them, one way or another, and see the same thing as the next person. Because anyone who chooses to do so can perceive some object, we consider it a fact. As MIT philosopher of science Thomas Kuhn said, “facts are objective in the sense that they are interpersonal: they are … accessible to and indubitable for all normally equipped human observers.” {citation}
Metaphysical “objects” like ghosts, gods, and past lives cannot be directly perceived by more than one person. Despite being "directly observable" by one person, no one can – reliably and on demand – confirm or deny anything about them. Science requires not just reliable perception, it needs it on demand. This is called a “reproducible result.” Objects meet science’s demands.
The “objects” in math, by contrast, are abstractions: they include the idea of a point or of a line or a numerical quantity. But they are directly and mutually perceptible by a “normally equipped” mind. Once the idea of a point or line, for example, is explained, then anyone can understand it; the mind alone adequately perceives it. Mathematical concepts differ from metaphysical concepts, although both are mental rather than physical objects. They differ because those in math are usually “accessible to … all … human observers,” while the metaphysical ones are not.
Why are metaphysical objects not accessible to all? Typically a lack of agreement, or a lack of a logical basis for accepting what one person sees, prevents mutual perception. A lack of reproducibility – ghosts rarely appear on demand, and deities usually speak to single individuals and, thus, evoke suspicion rather than reliability – also prevents mutual perception. Instead, some metaphysical objects require not agreement, but obedience to dubious words of one or more people who merely assert – without proof, logic, or even probability – that a particular metaphysical object (usually a god-like entity) exists and acts in certain ways. Hence, math’s universal mental objects differ in every way from other “mentations,” and all the others suffer from the lack of reliable universal availability (to perception.)
Regarding objects as the core of science, let’s suppose that we forgive scientists for relying on the madman Comté’s Positivist philosophy. We can forgive them because they wisely restrained his mis-use of logic, and because science has other deeper roots in the more rational work of twenty-something year old Rene Descartes, in sensible Francis Bacon, and many others all the way back to Aristotle and before. And let’s also acknowledge and accept the necessity of using mathematics in science, including in the biological, chemical, and psychological fields. Suppose we focus only on the way that mathematicians do their work, and even then limit ourselves only to the logical ground upon which contemporary mathematics stands and grows as the primary tool for factual science.
Particles, and only particles, populate all of math, and thus all of science, and thus enforce a specific way of seeing the world. How does mathematics contain only particles? And why?
Mathematicians decided among themselves that particles and the very notion of particles suffice for all mathematical purposes. They – primarily Gottlob Frege and Bertrand Russell, but others, too – discussed this late in the 19th century and into the 20th. They argued about Aristotle’s two kinds of quantity: discrete plurality (particle-like items) vs. continuous magnitude (no gaps but divisible.) At the end, they rejected "continuous magnitude" math as unnecessary. Since that time spectacular mathematical advances have occurred and those have permitted the flourishing of modern Western science, both good and bad.
But particles, as far as I can tell, are the problem. Even aside from Aristotle, alternative ways of perceiving the world and its contents exist in coherent, logically consistent, although underdeveloped forms. Our current dependence on the very idea of particles as the ultimate characteristic of the universe inevitably lead to conclusions like Crick’s denial of soul {cite "The Astonishing Hypothesis"}, the {cite Missouri guys ref.} assertion that consciousness is a mirage, as well as regressive, nebulous counter-assertions like Lohrey’s {citation} that matter itself is alive. Science and math depend strictly on particles – or lack of them -- as not only a basic but as the only characteristic that our universe possesses. Yet ordinary, even rudimentary, logic shows that “particles-as-the-essence-of-the-universe” suffers a logical flaw.
Particles in motion can, it seems, and do become living human beings who think and feel and act. Regardless whether evolution or a creator determined the outcome, living people exist and consist of parts and sub-parts and particles. Most of the past century of scientific work, in fact, involved breaking things down into smaller and smaller parts; we call this scientific reductionism. Nobel winning physicist Leon Lederman even wrote a book called The God Particle {citation} that decribes the hunt for a final, fundamental scrap called the Higgs boson, a tiny lit bit that combines with just 15 other particles that together compose the universe and all it contains. Physicists call this collection the Standard Model (of matter.) It all begins and end with particles and objects including particles of energy.
Similarly in mathematics, the mathematician Stewart Shapiro says “we … treat … positions as objects [his italics] … [Some mathematicians] assert that numbers are objects …. Places-are-objects … are bona fide objects.” Later he says that “ante rem realism [the idea that redness, for example, exists even if no red objects exist] … comes closest to capturing how mathematical theories are conceived … [It] delivers … [the] structure of structures.” {citation}
In other words, math itself focuses entirely and only on objects, despite any arguments about what constitutes an object . In current advanced “metamathematics” that he later describes, the work shifts focus from the objects to the relationships among them . But the math still consists of relationships among objects, things that are distinguishable and inert, things (physical or mental) that can, because they are objects, have a relationship. (“Relationship’ in math means simply that, for example, the numbers four and two are related by division, multiplication, squaring, or are sets containing or contained by each other, and so forth.)
When philosopher David Chalmers posed what has become known as the “Hard Problem,” {citation} he asked scientists and scholars of consciousness how inanimate – non-living – physical particles become a living conscious being. Despite his formidable philosophical credentials and specialization in consciousness studies, and many subsequent years of other people’s scholarly work about his question, neither he nor anyone else seems to have noticed what appears to me an obvious flaw.
A good introductory logic class teaches students about many kinds of mistakes, and gives them names like “begging the question,” and “fallacy of ambiguity.” Putting Chalmers’s problem up against Crick’s denial of soul into the context of math exposes the flaw. Whenever perfect logic leads to an obviously mistaken conclusion, such as consciousness-is-a-mirage, then you must examine the premises as the cause of the bad ending. Logicians call this specific mistake the “fallacy of false premises.” Here’s an example.
Premise 1: All women want a man.
Premise 2: Sappho is a woman.
Premise 3: Sappho wants a man.
Wrong conclusion! Sappho was a famous, ancient lesbian. The logic is correct as far as its structure is concerned, but a mistake occurred in the first premise. We only know that most women want a man, not all. Bad premise, good logic, bad conclusion.
Particles are the flaw in the mathematical-scientific premise. Expecting only particles forces good, even eminent, scientists to reach erroneous ends, and pushes others to re-assert primitivism in a feeble attempt to correct the wrong conclusion with a different, but equally erroneous, premise. It took me a lot of thought and reading to see this; brighter people might have seen it sooner. It seems to me that by looking carefully and thoughtfully at the philosophy upon which science is based – Descartes, Comte, empiricism, and today’s physicalism – it becomes obvious that scientists who insist that “facts [be perceptible to] all normally equipped human observers” actually only mean perceptible objects, both physical and mental. Today “objects” include all the galaxies and super-galactic clusters, all the infinitesimally small quarks and gluons, plants, animals, and people, as well as all abstract things like nations, notions, and mathematical points in space that lack length, width, height, or weight.
But perception, in the sense of simply looking, reveals more than mere objects: we can plainly, if only conceptually, “see” motion. Yet mathematics dismisses everything that is “non-discrete” (non-object-like.) By depending upon particles it reconfigures motion as a sequence of particle-like points stretched along a line in time. This dismissal and some other logic allowed scientists to dismiss “innate animacy” (primitive animism in which everything is considered alive.) It permitted reducing energy itself to quantum particles that join with matter to make it move. Any actual event – whether as atoms or as people moving – scientifically and mathematically consists only of objects occupying a sequence of different places (which also carry a sense of particle-ness) in time. Some would even claim that a rock, for example, at one moment is a different rock at the next moment. It does not move through time; a new identical rock simply occupies the next moment in time making an infinite string of immovable stone: motion becomes an illusion.
Described mathematically like this, and bearing in mind that the locations change by infinitesimally small amounts, motion-as-a-string-of-particles is then “plain for all to see.” Even if we allow for motion, in today’s world, “all that is” still consists of inert objects endowed with object-like chunks of energy. Thus, for some people and a very few scholars, it seems that only by reasserting primitive animism – adding some indefinable quality of life to inert objects – can we counterbalance science’s conclusive denial of life and mind and heart and soul. Everybody, to my eyes and ears, is wrong.
To resolve a conflict between definitive science and equally definitive common sense – because we can plainly observe lively objects living – requires us to apply rigorous yet ordinary and elementary logic. We must re-apply science’s rules so that we can accurately reassess the scientific and mathematical assertion that “all that is” consists of objects great and small. The term “assertion” is, from my perspective, generous. I find it more like an arrogant presumption force-fed by powerful and long-dead people who could not, or refused to, examine themselves and their beliefs. The presumption self-perpetuates because its students succeed with the presumption which leads to even more success and more like-minded students. They have a hammer and treat everything as a nail; believers in only discreteness can only see particles. But a simple recognition of the “particular,” and thus the particulate, as the premise from which math and science grow allows us to challenge it. In fact, it makes the alternative clear.
Primitive animism – the idea that “everything is alive” – fails to pass muster as an alternative to object-based mathematics and science. Despite innumerable profound and simple attempts, no one has ever successfully defined “life.” At least, no one has given an explanation that satisfies even a simple majority of people. We are life, we see life, we live life, recognize death as its end, and yet remain ignorant of any clear and understandable definition of it. So endowing objects with “life” effectively lacks meaning at best and circles back on itself at worst; that’s the logical flaw of begging the question. (In this case defining life by saying it consists of life. Duh!)
Similarly Aristotle’s notion of continuous magnitude – sort of an unbroken but breakable “oomph” in an amount or in a number – must also be rejected. The mathematical experts seem to have settled that issue, even if the rest of us cannot or don’t want to know the details. Aristotle’s continuous amount – even compared to his own complementary concept of discrete amount or collection of bits – still suffers from a critical error: magnitude or amount still carries a sense of object-ness, thing-ness, and particle-ness.
Instead, we can look deeper just as we did earlier, into science and math. Look and then we can see that the professions depend not on objects, per se. They depend upon a deep belief in the primacy of a single characteristic, a characteristic that all objects share: they have “particle-ness” in common. Objects have boundaries, beginnings and ends, insides, outsides, and separation from any other thing; they have “distinguishability.” Particle-ness endows objects with both wholeness in themselves and separate-ness. Separation from what? Separation occurs simply from looking and seeing and effectively deciding that a boundary exists. Particle-ness is a choice about what to see, an interpretation of what anyone can see. Making a choice implicitly indicates you have alternative choices. Objects appear to have edges although those might only be an appearance, a mirage. The appearance could also be what is called an "artifact" of the observing instrument; in this case the "instrument" is the observor's expectation of a particle or inability to see understand anything non-particulate (when you have a hammer....) Particles and objects – usually by unspoken definition – also lack life if for no other reason than to distinguish the nonliving from the living objects. They have “thing-ness” to distinguish them from energy and motion. But no accepted definition of a “living object,” much less life itself, exists anyway, so we must return to this later.
To challenge science’s insistence on particles and only particles requires a challenge to mathematics, a challenge that must offer another belief, an alternate, believable viewpoint. The particle-ness of particles, in my view, poses the problem because it is the only acceptable trait of "truth." Since a characteristic is the problem, it requires an alternative characteristic. “Activeness” provides the obvious choice.
Activeness is not action. It precedes action the same as the sense of particle-ness precedes particles. While particles have distinguishability, action has activeness, an inherent option or potential to change. For many practical and often for survival reasons, people and other organisms learned to distinguish images in their eyes and sounds in their ears from one another. For example, certain cells near the beginning of the visual system are called “edge detectors ” because they emphasize boundaries {citation}. Noticing an edge turns our attention to other features and differences that inform us whether something will kill or feed us.
The very beginning of our biology, therefore, encourages us to emphasize
differences, distinctions, boundaries, and to add the characteristic that I call
particle-ness. Having found an edge we – from our cells on up – presume
particleness and then conclude that an object exists. Even if the object moves,
for example like a falling rock or snarling animal, it remains an object. Its
motion, however, needs another characteristic that objects lack. (Note: see my remark about detecting time, here.)
Primitives, the uneducated, and the misguided simply endow objects with either life, or a vague notion of internal energy or with energy applied to them by something living (someone pushed the rock, or a deity started the universe.) Physicists provide more detail, but remain equally unaware that action requires not another object – such as a quantum particle of energy – nor the application of energy by something else, but another deep characteristic: activeness.
The so-called “language of science” – mathematics – displays the problem
clearly and explicitly by focusing on objects, their relationships, and their
defining characteristic “distinguishability.” Math requires that a point in
space can exist at one or more points in time, but does not allow an action to
exist in a single moment of time. Action typically requires time to occur.
This is because time also breaks down into particle-like points of
time.
To their credit both science and mathematics now produce an endless series of amazing results from this dependence on particleness. Right now the “Standard Model” in physics offers 16 particle-like objects of which everything in the universe is made, and endless experimental evidence continues to support the model; the bits of the Standard Model attest to the pernicious strength of the particle-ness mind-set. A mathematical focus on objects even led physicist Richard Feynmann to comment on how mathematical work alone, apart from laboratories, successfully precedes later scientific discoveries. But life and mind remain alien, incomprehensible, or unreal to the realists. Objects born of particle-ness make it so.
If, however, science generally and mathematics especially add to – not replace – their notion of particleness the second characteristic of activeness, then life can begin to escape from the “coffin of science.” {citation to Rudolf Steiner}
None of this denies mathematics’ ability to describe action itself. The simple miles or kilometers-per-hour formula for speed (v=d/t) accurately describes an aspect of the motion of an object such as a car or bicycle. Higher math describes the complex motions of galaxies, typhoons, and of subatomic particles. But all of it merely describes action rather than defining it. Quantum physicist Roland Omnes says “we do not know what ‘action’ is or where it comes from.” {citation} Elsewhere, in an unpublished work-in-progress, discovered in an online group about the “Theory of Everything,” Tony Bermanseder refers to math (Lagrange equations in particular ) to say that “the difference between two quantities … together form something called … ‘action’ … [or] … Anything that multiplies [and] give[s] the ENERGYxTIME dimensions.” {citation/link} But even that remains merely descriptive.
Particles present a major difficulty: they have clear boundaries and so lend themselves to precision. Action born of activeness seems to engender the opposite. Since a mere trait (particle-ness) adequately supports all of discrete math, it seems to me that activeness can similarly support a complete, rigorous, and useful mathematic in the ordinary day to day world. The pair of characteristics / attributes that anyone can plainly see are required; each alone is merely "necessary but not sufficient" for understanding a universe or a mind.
4/25/2005... more when I get the time ... -Dennisº
revs. 9/20/2007; a few links added 04/21/07