Demarcating Euclidean geocentrism as superseded science, and entropic geocentrism as future science
Demarcating Euclidean geocentrism as superseded science, and entropic geocentrism as future science
Demarcating Euclidean geocentrism as superseded science, and entropic geocentrism as future science
On this Page:
A brief history of centrist theory
1. Ptolemy's Geocentric Premise
2. The Theory Falsification Problem
3. The Resolution: Demarcation
4. Entropic Geocentrism
(Click the images for a lightbox slideshow)


epicycles in Ptolemy
epicycles in Ptolemy

Whereas it is undeniable that Kepler's heliocentrism properly superseded Ptolemy's geocentrism in a major paradigm shift, due to its perfect integration with non-relativistic explanations of gravity, that doesn't mean Ptolemaic geocentrism should be thought of as 'fiction,' as stated by Bokulich (2012). Empirical examination reveals that Ptolemy's premise is still sound for earth-to-sky observations with the naked eye, which is markedly more applicable to most people's needs than calculating rocket trajectories to Mars and other typical examples raised as objection. Further, Ptolemy's 'eccentric center' is easier to adjust for local variations than heliocentric models. Moreover, due to Einstein's relativistic principle, validated by provable mathematical equivalency, geocentric theory cannot actually be falsified for positional predictions of the sun, planets, and stars. This article also: (a) summarizes the history of centric theories; (b) explains why scientific theories should not be held to be facts, without denying that current theories could be facts; (c) suggests a method for demarcation of Ptolemy's theory as 'superseded proto-science' that bypasses issues with theory falsification; and (d) introduces a next-generation concept, entropic centrism.

A brief history of centrist theory

Created: 11/04/22
Modified: 12/04/22
Rev. 52

Eudoxus is said to have created the first geocentric theory in ~370BC, postulating that the sun and planets orbit the globe (Mendell, 2022). But planets sometimes go backward in the sky, referred to as retrograde motion. Eudoxus thought the planets were on 'wobbling' invisible spheres, but no one could state their 'wobbling' mathematically for 500 years.

Claudius Ptolemy (170AD) modified Eudoxus' theory by replacing 'wobbling' spheres with epicycles, giving each planet a small orbit around a point on its big orbit. It's an ingenious solution. When the planet is on the near point of its epicycle, it moves backward in the sky. Ptolemy believed the planets were solid bodies moving through an ethereal liquid by their own energy (Rosen, 1985). Ptolemy also explained seasonal variation in the sun's position by offsetting the center of the Sun's orbit from the Earth's center. The center of the sun's orbit was called the eccentric center.

Moon Phases drawn by Galileo
Moon Phases drawn by Galileo

Galilei Galileo (1610; Palmeri, 2001) observed that Venus had phases, just like the moon has phases (full moon, new moon, etc.). The illustration is a drawing of what Galileo observed through his telescope. This was inexplicable by a geocentric model. When a scientific theory doesn't explain an observation, one can modify or add to the theory to account for it, at which time the old model hasn't been invalidated , but superseded. As explained in the following sections, Ptolemy's model is still sound, because it still explains human worldview, predicts planetary retrograde, and has not been found logically incoherent.

the Thychonic theory
the Thychonic theory

At the time of Galileo's discovery, there were geo-heliocentric theories from Capella, Enugena, Naboth, Rothmann, Wittich and Thycho Brahe (Brahe, 1577; Hatch, 2018), of which Thyco's theory had the most impact due to the quality of his observations. Heraclidus was also said to have originated the concepts in ~370BC, but any evidence has been lost. The Thychonian model holds that the sun and moon orbit the Earth, but the other planets orbit the sun. That also explains the phases of Venus. 'Stellar aberration,' the movement of stars, in the sky, was largely dismissed as due to an annual cycle of nutation, movement of the Earth's axis (Newcomb, 1835). The amount of nutation needed to explain stellar movement was so tiny, it would not affect solar-system observations. But upon repeated measurements of stellar parallax, which determines differences in stellar position at opposing ends of earth's orbit, Thycho's theory was considered superseded, even though it could be explained by nutation also (Henderson, 1842; Hirschfeld, 2001).

Copernican heliocentric theory
Copernican heliocentric theory

At Galileo's time, there was also the heliocentric theory from Dr. Nicolaus Copernicus (1543), which retained Ptolemy's epicycles and eccentric center, which had the advantage over Brahe's in being more homogeneous and thus simpler in concept. Copernicus' model was actually more complex than Ptolemy's because it added a second epicycle around the first epicycle, and due to its eccentric center to closer approximate an elliptical orbit, the sun was not actually at the center of the solar system, but offset from it.

Copernicus suggested heliocentrism over a century before Newton, and well before the invention of telescopes in 1608. There wasn't actually any way to claim heliocentrism could explain more than geocentrism for another five decades. Totally contrary to hundreds of Web lectures on the topic, the geo-heliocentric proposals of Thycho Brahe and his supporters had started a fashon. Copernicus actually just being trendy in suggesting yet another way to explain observations of the sun and planets. The extent of modern misconception has well exceeded rational bounds and has become a socially endorsed form of anti-historical bigotry.

The Jihad against Ptolemy. There are frequent statements that 'The Church' persecuted Galileo, but in fact, most of 'The Church' did not regard heliocentrism as heretical, and ironically, social attitudes to Ptolemy are rather similar to the hostile and rather unfounded prejudice expressed against the 'The Church,' most likely due to unconscious prejudice.

When Galilei Galileo the was born in 1564, most of 'The Church' accepted heliocentrism. The Protestant church started 47 years before Galileo's birth, and while the Protestant leaders Luther and Calvin expressed extreme dislike of heliocentrism, it was not heresy to them, due to their Augustinian doctrine that the needs of personal salvation take precedence even over secular law (Augustine, 426; Mathison, 2012; White, 2002). The Catholic Pope Clement VII not only approved heliocentrism 31 years before Galileo's birth, but actually liked Copernicus' notions so much, he gave Copernicus an ancient Greek codex on astronomy as a present (Stagnaro, 2020). The only 'Christians' persecuting Galileo were the inquisition of a small political faction, <20% of Italy in size, called the 'Papal States,' in which the Jesuits ignored its ban of heliocentrism and taught it anyway, making the inquisition seek a scapegoat for their frustrated ambitions of power (Miley, 1850).


As the epicycles are difficult to state mathematically, it was more complex than might be necessary, and astronomers sought a simpler explanation. In 1613, Chancellor Johannes Kepler first published his work on elliptical orbits, with the sun's center still not being at the center or of planetary orbints, which is actually why gravity makes their orbits elliptical. Kepler had previously done much work with Brahe's observations showing Copernicus was more accurate than Ptolemy, so Galileo defended the Copernican model against critics, for which reason the Copernican model is popularly known. Elliptical orbits later transpired to integrate well with gravitational explanations, causing what Dr. Thomas Kuhn famously named a paradigm shift (1962). Thus Kepler's model is now defined as scientific law rather than theory, because contravening it would invalidate just about all of modern physics. Kepler's model was nevertheless superseded again by relativistic theory from Einstein (1921). But relativity effects are rarely included in solar system models because they do not significantly alter many of their predictions. Thus no one questions Kepler's model is still sound, even though it has been superseded.

Cosmological Inflation
Cosmological Inflation

Thus, despite the relativistic perspective that the universe is still expanding equally from all points simultaneously, and its statement of a relativity principle in regarding any point as an origin, heliocentrism is naively said to 'prove geocentrism wrong.' No location can be 'wrong' as a center in Euclidean space even without considering relativistic effects. An ancillary point of interest is that human beings are still at the known universe's entropic center, as first stated by Shrodinger (1944).

Then in promoting anti-theism, Dr. Richard Dawkins (2006) stated current scientific theory should be regarded as 'fact,' relegating the teleology of neo-Aristotleianism, Ptolemy's geocentrism, and soft sciences (psychology, sociology, etc.) to pseudo-science. Before considering the appropriate status of Ptolemy's theory, the following section cosndiers Ptolemy's premise of geocentrism, explaining that the premise is not actually falsifiable, and that the theory is still accurate enough to be useful and simpler to calculate than current theory.

1. Ptolemy's Geocentric Premise

The National Academy of Sciences states 'no evidence will be found that the Earth does not go around the sun.' Its Space Sciences group knows the statement contravenes the Relativity Principle, but the statement remains, due to widespread ignorance of what the Relativity Principle actually is. Following a description of it, this section describes the mathematical equivalency, quality, simplicity, and soundness of a theory based on a geocentric premise.

  1. The Relativity Principle. From experience, stating anything myself on this topic on social media results in endless argument, whereas quotations usually end debate immediately. Hence, a simple Google search for this term reports "There is no physical way to differentiate between a body moving at a constant speed and an immobile body. It is of course possible to determine that one body is moving relative to the other, but it is impossible to determine which of them is moving and which is immobile." In one out of 200 cases, I had to send the Wikipedia page showing that the principle stands on both special and general realtivity four times. Otherwise, some notable quotations on what the relativity principle means to Ptolemy's theory were sufficient:

    Einstein, Born, Hoyle, Hawking:
    "Ptolemy's Geocentric Premise Cannot be Invalidated"

    Albert Einstein (1921): “One need not view the existence of such centrifugal forces as originating from the motion of the Earth; one could just as well account for them as resulting from the average rotational effect of distant, detectable masses as evidenced in the vicinity of the Earth, whereby the Earth is treated as being at rest.”
    Albert Einstein (1938): “Can we formulate physical laws so that they are valid for all coordinate systems, not only those moving uniformly, but also those moving quite arbitrarily, relative to each other?...The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either coordinate system could be used with equal justification. The two sentences: the sun is at rest and the earth moves or the sun moves and the earth is at rest would simply mean two different conventions concerning two different coordinate systems.”
    Max Born (1962): “Thus we may return to Ptolemy’s point of view of a ‘motionless earth’… One has to show that the transformed metric can be regarded as produced according to Einstein’s field equations, by distant rotating masses. This has been done by Thirring. He calculated a field due to a rotating, hollow, thick-walled sphere and proved that inside the cavity it behaved as though there were centrifugal and other inertial forces usually attributed to absolute space. Thus from Einstein’s point of view, Ptolemy and Copernicus are equally right.”
    Fred Hoyle (1973):“The relation of the two pictures [geocentrism and geokineticism] is reduced to a mere coordinate transformation and it is the main tenet of the Einstein theory that any two ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view…. Today we cannot say that the Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningful physical sense.”
    Stephen Hawking (2010): “So which is real, the Ptolemaic or Copernican system? Although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true. As in the case of our normal view versus that of the goldfish, one can use either picture as a model of the universe, for our observations of the heavens can be explained by assuming either the earth or the sun to be at rest. Despite its role in philosophical debates over the nature of our universe, the real advantage of the Copernican system is simply that the equations of motion are much simpler in the frame of reference in which the sun is at rest.”

    Multiple epicycles
    Multiple epicycles
  2. Mathematical Equivalency. Little known is that Copernicus added 'secondary epicyles' around the primary epicycles, making his model more accurate. By adding yet more epicycles to Ptolemy's model, it is mathematically provable that one can create a geocentric model that is more accurate than Kepler's, which does not include nutation and other real-world factors (Gearhart, 1985). In a more abstract sense, Fourier analysis proves that any oscillation at all can be rendered as a sine-wave series of varying frequency and amplitude. Further, it is mathematically provable that one can make gravitational predictions based on a geocentric model. The equations would be horrendously complex, but it's "simply" a matter of Euclidean transformation, with convolution transforms if one wishes to state field ranges. The premise is thus not actually falsifiable by the results it can produce. As exact equivalency in prediction is possible, one cannot 'disprove' a geocentric premise mathematically.
  3. Accuracy. Then objections arise that Ptolemy's model is inaccurate. In fact, its error is so small that Ptolemy could not detect it with the instrumentation available in his life. That was because, in order to make a circular orbit a more accurate representation of an elliptical orbit, Ptolemy also calculated an offset from the Earth's center for the sun's orbital center, referred to as an eccentric center.
    In Kepler's model, the Sun's position is still offset from the two centers of Earth's elliptical orbit. Those who know something of Kepler's model frequently state the Sun's elliptical orbit explains seasons, but the ellipse's deviation from a circle is small (about 4% at most) compared to the distance of the Sun's center from the ellipse's eccentric center. The seasons are far better explained by the planet's tilt making sunrays pass through more of the atmosphere in winter. Thus Ptolemy's model is far less inaccurate than most think. Fitzpatrick (2010) proved mathematically that the seasonal variation in the sun's position from Ptolemy's original model is better than a first-order deviation from Kepler (>95% accurate), or with current data >97.5% accurate. That equates to a variation of up to 20 minutes, which is equivalent to local factors affecting the sun's apparent position in the sky, including:
      Sunrise time is affected by elevation
      Sunrise time is affected by elevation
    • The actual time of sunrise and sunset at any location depends on the height of the horizon, and one's relative height to the horizon. On a flat plane, from a stationary point, an altitude change of 4,921 feet changes the day length by two minutes, assuming a spherical earth (Spekkein, 2015). Relative height to the visible horizon is much more significant. Suppose one is standing next to the sea on a beach. Just by lying on the sand, the horizon height shifts by 140 arc-seconds, significantly larger than the eye's angular resolution of 60 arc-seconds (Young, 2003).
      Atmospheric Refraction
      Atmospheric Refraction
    • Atmospheric light refraction, dependent on air particulate density, causes the sun to appear at a different position when it is close to or on the horizon, varying even in clear conditions by 1~5 minutes due to temperature changing air density (Wilson, 2018; Young, 2006).
    • The Earth is slightly ellipsoidal, not a perfect sphere. The equatorial axis is ~21km longer than the polar axis, causing a variation in sunrise time of 14 minutes.
    If one is to consider Ptolemy's model as 'too inaccurate,' then one runs into problems with Kepler's model not accounting for relativistic effects. How should one define 'sufficient accuracy'? Ptolemy's model is sufficiently accurate for observations without a telescope, which at least is a simple demarcation. At what point do observations with a telescope become 'too inaccurate'?
  4. Kepler
  5. Complexity. Ptolemy's circular orbits are actually less complex than both Copernicus (who uses 2nd-order epicycles) and the transcendental functions needed for calculating Keppler's ellipses, shown to the right. The simplest model should be chosen for any need. If one is a physicist sending rockets to Mars, then current theory is obviously best, particularly because the geometries integrate with gravitational force calculations. But most of us do not send rockets to Mars. Most of us want to know far simpler things, such as the time of the sunrise and sunset. For sunrise calculations at the current time, measurement of local variations could easily adjust the centerpoint of Ptolemy's simple circular orbit, to include local variations, such that the results would be more accurate than, for example, the sunrise time that Google displays if one types 'sunrise' into its search box (Google's result is only based on Kepler, and does not include local variation).
    This is particularly ironic, as heliocentrism was originally thought simpler than geocentrism. But with Copernicus' dual epicycles, and Kepler's elliptical model (as shown above), the calculations are more complex than for a simple circular orbit, whereby the eccentric center can simply be moved to account for greater accuracy or to account for local variation.
  6. Validity vs. Soundness
    Validity vs. Soundness
  7. Soundness. As Ptolemy's premise is not falsifiable on several grounds, and his theory is a mathematical model based on that premise, Ptolemy's theory is still valid for predicting the position of the sun and planets in the sky. Other observations, such as Venus phases, limit Ptolemy's theory's scope to observations with the naked eye, although Brahe's geo-heliocentric model with nutation could arguably still be valid for Venus phases and stellar aberration. One would have to consider apparent planet sizes to exceed the scope of its predictions. The point here, notwithstanding, is that Ptolemy did not intend to send rockets to Mars. He was explaining his observations. His theory is still sound within the scope of observations that Ptolemy could make. Hence, all putting aside the validity of the premise, all that remains is to consider whether Ptolemy's theory is false, old science, or pseudoscience.

Hence, a geocentric premise is not consistent with current paradigms, but still provides a sound model for predictions with a reasonably useful scope, accuracy, flexibility, and simplicity. Ptolemy's geocentrism is thus as acceptable as a scientific theory as, for example, numerous methods in 3D modeling and 3D rendering that do not represent at all how light actually works, but which provide facsimiles of photorealism with lower computer-resource consumption.

2. The Theory Falsification Problem

Many believe (1) observations have 'proven' (rather than substantiated) hypotheses drawn upon scientific theory; and (2) by unconscious implication, the observations prove scientific theories true. According to Karl Popper and critical rationalism, even corroborations of hypotheses are subject to challenge as misinterpretation from experience, and theories really exist to be challenged by rational minds in every way possible. By contrast, the recent trend towards 'scientific realism' rarely even makes a distinction between observations that substantiate hypotheses as facts, and theories as facts, resulting in a broad trend towards unethical scientism, amidst widening mental laxity.

Versions of Scientism
Versions of Scientism
  1. The Historical Position. Scientific theories have been considered theories because they could again be superseded. In the case of Copernican and Keplerian heliocentric theories, they have already been superseded by relativistic theory, which states that the universe is still expanding from all points in space simultaneously. Further, something like antigravity could be discovered, in which case current astronomical theory will again be superseded by new theories. That is why science is held as being only an explanation of observations, and not a statement of necessary cause. Holding that scientific theories are 'facts' has historically been referred to as 'scientism,' because such belief can only be justified if the theories won't change.
  2. Demands for Falsification. All but one of those asserting that Ptolemy's astronomy is pseudoscience (in one way or another) marred their position by claiming Ptolemy's theory has been falsified, whether or not they understood they were criticizing the premise (geocentrism), or the theory's induction (epicycles would explain retrograde motion).
  3. Falsification Scope. Theory falsification now invokes as its foundation the argument of critical rationalism, a multi-part thesis from the eminent but wildly controversial Dr. Karl Popper (1934, 1959, 2002). At the turn of the millennium the USA almost completely rejected Popper's critical rationalism, because it also defines the so-called soft sciences (psychoanalysis, psychology, sociology, anthropology, etc) as insufficiently critical to be classified as science. Europeans have far less objection to considering soft sciences as arts. By contrast, the USA tries to shift as much as possible into science from the arts, because science gets far more funding, not only academically, but also in the business arena.
    In his early years, Popper stated a theory must be falsifiable, else it is pseudoscience. Hence overall, Popper felt evolution is a pseudoscience, because any failed hypothesis can be explained as due to 'unknown selection pressure.' However that is a misrepresentation of Popper through abbreviation. Even In his earlier life, he stated premises and theories must be considered within their context:
    "A scientific description will depend, largely, upon our point of view, our interests, which are as a rule connected with the theory or hypothesis we wish to test; although it will also depend upon the facts described. Indeed, the theory or hypothesis could be described as the crystallization of a point of view.”
    - Karl Popper, 'The Open Society and Its Enemies Vol 2'.

    In his later life, Popper sardonically referred to evolution as 'soft metaphysics' (Putnam, 1998).
  4. Motives for Falsification. Anti-theists such as Dr. Richard Dawkins (2006) claim that scientific theories such as evolution must be regarded as facts, and that inductions leading to theory formation must be regarded as causes, an ideology one may call 'scientific realism.' Here is Dawkins' book 'God as Delusion' condensed into 60 seconds, and a promotion video for the book 'Evolution is a Fact' in 60 seconds:
    Scientific realism, or Broad, Strong Scientism in 60 Seconds?
    Instaread: God as Delusion
    Instaread: God as Delusion
    Antitheism at its best
    Antitheism at its best

    That works against the interests of those trying to get more funding for soft sciences. To meet Dawkins' goal of scientific realism, any paradigm that is even currently out of vogue must be demoted to pseudoscience, in the interest of maintaining factual purity.
  5. Disputation between realism and soft science. On the one hand, USA's scientific realists believe that eradication of belief in God is good for society. On the other hand, scientific realism results in soft sciences receiving less funding. Thus falsification is no longer an epistemological issue, but has become an ethical issue. But there remains another issue independent of the motivations of scientific realists and soft scientists: does one desire a society which has decided science has accumulated so many facts that we can no longer dream of new possibilities, be they antigravity or anything else, because we have turned theories into facts, denying new imaginations? And we cannot, for that is exactly the universally held criticism of Galileo's persecution. Of note, both realists and their opposition interpret that statement in their favor.
  6. The Deontology of Falsification. The dilemma remains, however, that those who wish to believe that scientific realism is true cannot be denied the right to that belief either, even if that belief is unprovable, and the metaphysical debate on realism ultimately cannot resolve the bidirectionality of supervenient explanations on negated necessity, a propos to Dawkins' claim that Occam's razor removes any necessity for God's existence:
    1. The existence of the Will of God is unnecessary iff scientific theories are facts.
    2. Scientific theories are not necessarily facts iff the Will of God exists.
    Simply put, there is no way to prove either statement (a) or statement (b) is true and the other not. Technically, negation of necessity could be possibility, or as one possibility of negated necessity, impossibility, depending on how one maps the semantics of natural language to propositional logic (Davidson, 2001a; Davidson, 2001b). For Dawkins' razor to be true, the unnecessity is equivalent to impossible, whereas the argument from intelligent design (for the existence of God) holds that unnecesssity is equivalent to possible. Thus neither statement can disprove the other.

    If one wishes to sneer at the semantics of formal logic, which many do for various reasons, then after putting aside eavluation of the intrinsic validity or soundness for Dawkins' assertion, empirical demonstration via the scientific method becomes the only remaining recourse for resolution of the dispute within rational bounds. As there exists no condition where the Will of God would not exist if it does, experimental corroboration against a control scenario is unavailable as an option. Therefore, any statement on the existence of God or not, whether scientific theories be facts or not, should eternally remain completely outside the domain of science.

    Hence, epistemology can deny neither scientific realism nor theism as valid beliefs, and only demonstrates that both beliefs are unprovable. The assertion that science is a fact, or not, nonetheless causes difficulties for other people, not only in challenging what they regard justified true beliefs beyond doubt, but also in their actual ability to earn a living. That includes not only specialists in soft science seeking more funding, but myself, as I am designing a commercial product that evaluates the effectiveness of geocentric models in sunrise prediction, originally motivated by Web predictions of sunrise time from Kepler's model being 15 minutes off for where I live, and more accurate estimates of sunrise prediction than available on the Web are easier to code by moving a geocentric model's eccentric center. But I can't raise funding, because the USA's National Academy of Science states 'the earth goes round the sun' is a fact on the Wikipedia. Thus in consideration of the issue, I can only conclude that 'scientific theory as fact' has ceased to be an epistemological issue, and become ethical. With no prejudice against either side on the debate between others on the topic, entirely outside the personal inconvenience it has caused me, I conclude the following:

    If we choose to believe scientific theories are not facts, we still cannot deny that theories could be facts. Conversely, if we choose to believe theories are facts, we still cannot deny theories might not be facts. Whether we think theories are facts or not, we should not claim our belief is necessarily true beyond doubt.

    That moves the debate on whether Ptolemy's theory is falsifiable beyond the realm of logical truth and falsehood into the shadowy world of deontology (the study of what one ought to do), for which science has no answer (a long-standing problem called Hume's guillotine (1739), restated as Moore's Naturalistic fallacy (1922), that observations of the world cannot define what we ought to do without defining moral premises).
  7. The solution: demarcation, instead of falsification. The degradation of falsification into a deontological quagmire makes it clear that it is not the appropriate approach to deciding whether Ptolemy's geocentrism is pseudoscience. Amazingly, however, there is another part of Popper's multi-part thesis that defined a new notion called demarcation, which can draw a line between that which is science and that which is not science, without even introducing the issue of theory falsification at all.

3. The Resolution: Demarcation

For a while, Popper's thoughts on demarcation were under the same dark shadow as his ideas of the necessity of falsification for a theory to be scientific, as stated by Miller (2011):

The problem of demarcation is solved much as Popper solved it. This commendation may surprise those who are acquainted with such titles as 'The Demise of the Demarcation Problem' (Laudan 1983) and 'The Degeneration of Popper's Theory of Demarcation' (Grunbaum 1989), or the writings of Kuhn (1962) and Lakatos (1973, 1974). But like many others, the authors of these criticisms thoroughly mistake the crucial philosophical task that Popper intended a criterion of demarcation to perform. Its task is not to 'distinguish scientific and non-scientific matters in a way which exhibits a surer epistemic warrant or evidential ground for science than for non-science', which Laudan lays down as a minimal condition for 'a philosophically significant demarcation', nor is it 'to explicate the paradigmatic usages of 'scientific'. Questions of sureness, warrant, and grounds, are of interest principally to justificationists who live in mighty dread that they may not be 'entitled to believe any scientific theories'; questions of usage, classification, and status, are of interest principally to essentialists, to philosophers who prefer to pursue philosophy unphilosophically, and to educational administrators; and inevitably, of course, to lawyers. Contrary to what Grunbaum resolutely supposes, the problem of demarcation is only incidentally concerned to ratify the unscientific status of psychoanalytic theory (whatever psychoanalytic theory is taken to be), and contrary to what Lakatos likewise supposes, it is only incidentally concerned to ratify the scientific status of Newton's theory (whatever Newton's theory is taken to be).

What then is the problem that Popper considers demarcation as trying to solve? Miller continues, referring to Popper's own statement from 50 years previously:

"My problem of 'demarcation was from the beginning the practical problem of assessing theories and judging their claims. It certainly was not a problem of classifying some subject matters called 'science' and 'metaphysics.' It was, rahther, an urgent practical problem: under what conditions is a critical appeal to experience possible - one that could bear some fruit?"
- Karl Popper (1956/1983). Realism and the Aim of Science. 18.

Here is a clear philosophical, even logical, problem: under what circumstances is an empirical investigation worth undertaking? The solution is also clear: since the formulation of a hypothesis, its acceptance as a candidate for the truth, must precede its consideration, the task of an empirical investigation cannot be to promote hypotheses, but only to demote them.
Demarcation in science
Demarcation in science

In the past, most demarcation has focused on separating science from supernatural explanations. But more recent thought has separated pseudoscience from scientific history. This diagram shows one such separation, from Dr. Massimo Pigliucci's response to Laudan (2013). Pigliucci ranks theories by empirical knowledge and theoretical understanding.

Pigliucci demarcates 'old theory' based on 'Thagard's criterion' (1978). Indeed, Dr. Paul Thagard's demarcation does appear to provide the best way to separate Ptolemy's geocentrism from current paradigms. Thagard proposes two rules, the first of which is that some theories are too old and inaccurate. That's what almost every complaint about Ptolemy states. Thagard's proposal has also been fruitful, producing many articles, an example of which in the public domain is Demarcating Science from Non-Science, by Martin Mahner:

And that is really short, only 61 pages, because the definition of what is too old and too inaccurate results in very, very, long discussions of different demarcation limits in different fields. Thus, with regards to astronomy. The above 61 pages get as far as astrology definitely being a pseudo-science. So one could extend that to include Ptolemy. If anyone wants to argue it, we can. Then I would observe that Kepler's theory has superseded Copernicus, therefore, should Copernicus ALSO be demoted to pseudoscience, or if not, why not? Similarly, relativity has shown Kepler's heliocentrism to be inaccurate, hence, why should Ptolemy be considered inaccurate for its lack of explanation of Venus phases and stellar aberration, yet Kepler still be considered 'accurate enough for most cases'? Who exactly has the authority to decide what is 'accurate enough'? If one is to agree with 'truth by consensus' by academioes of science, how much are our current judgments different from those which result from opinions of Galileo's wrongful persecution by 'The Church'?

Let's imagine we've decided Ptolemy's theory is not science. That brings us to Dr. Hilary Putnam's issue: if Ptolemy's theory is not science, then what is it? Does one really want to put it in the same boat as alchemy and astrology and so on? In this video rather humorously suggests we could consider Ptolemy 'immature' science, but he's addressing a larger scope of demarcation. Cases such as Ptolemy's are historical theories that have become superseded, not that have been invalidated by supernatural premises. Putnam thinks one cannot define an absolute boundary around current theory, claiming that older theory is no longer science merely because it was superseded.

And I think Putnam makes a good point. One could define separate demarcations for each field at nauseam, which is just not a very elegant solution. Thagard opens a lengthy debate, and possibly irresolvable in many cases, on what should be 'too old' and 'too inaccurate,' or should not be.

Validity and Soundness
Validity and Soundness

it makes sense simply to hold that the theory needs to be unsound for it to be separated from science. Sound scientific theories, when superseded by new paradigms, just become 'old scientific theories.' That's just much more simple and more elegant. As established in the prior section, Ptolemy's theory is still sound for predicting the position of the sun and planets in the sky with the naked eye. Hence it should be regarded as an old theory that has been superseded, not a wrong theory or pseudoscience.

4. Entropic Geocentrism

Entropy is a measure of a system's state of disorder, or randomness. Schrodinger (1944) is credited as the first to observe that life creates negative entropy, which is contrary to the 2nd law of thermodynamics, that entropy always increases with time.

Entropic Complexity
Entropic Complexity

I'm surprised so few people consider how pleasurable to consider our planet as the only known entropic center of the universe. The number of neurons in one human brain alone is equivalent to the number of stars in our galaxy. With 8 billion of us, just the number of neurons in human brains approaches the number of stars in the known universe. The jury is still out on the 'Fermi Paradox' (that we should have detected intelligent life by now). We haven't found anything approaching the complexity of life, let alone our ability to reason.

If there is a God, then our entropic complexity would be far more significant than a trite physical geolocation. It would be a giant flag, sticking out of the multiple dimensions of string theory, making us easy to find. With the rest of the universe operating purely mechanically, our ability to make at least some conscious choices independent of any First Cause would be enough to attract the interest even of an indifferent God.

With regards to science, however, there is still debate even on how to measure the entropy of life. It is known that the creation and maintenance of the organized matter in the organic molecules of life requires energy, but it's difficult to determine how much of the energy results in maintaining a higher level of organized matter. Thus the definition of any dimension in string theory that would be a direct product of entropic complexity is beyond the means of current science, but some work by Dr. Blaber (2002) on Gibbs Free Energy is promising.

Wishing you a beautiful day :)


  1. Augustine of Hippo (426). City of God. Vol. 1, Book 4, paragraph 2. Online at Project Gutenberg.
  2. Blaber, Michael (2002). Gibbs Free Energy. Online at Web Archive.
  3. Bokulich, Alisa (2012). "Distinguishing Explanatory from Nonexplanatory Fictions." Philosophy of Science: Vol. 79, No. 5 (December 2012), pp. 725-737 (13 pages).
  4. Brahe, Thyco (1577). Gibbs Free Energy. Significant excerpt online at: University of Cambridge.
  5. Born, Max (1962). Einstein’s Theory of Relativity. Dover Publications, p.344~345.
  6. Carney, J. (2022). The Beauty of the Geocentric Model. Online at: YouTube.
  7. Copernicus, Nicolaus (1543). On the Revolutions of the Heavenly Spheres. Online at: Internet Archive.
  8. Davidosn, Donald (2001a). "Truth and Meaning," p.1~65. In Inquiries into Truth and Interpretation, Oxford: Clarendon Press, 2nd edn. Online at:
  9. Davidosn, Donald (2001b). Actions and Events. Oxford: Clarendon Press. Online at: Google Books.
  10. Dawkins, Richard (2006). The God Delusion. Boston: Houghton Mifflin.
  11. Einstein, Albert (1921). quoted in Hans Thirring, “On the Effect of Distant Rotating Masses in Einstein’s Theory of Gravitation.” Physikalische Zeitschrift 22, 29.
  12. Einstein, Albert and Leopald Infeld (1938).The Evolution of Physics, p.248.
  13. Fitzpatrick, Richard (2010). A Modern Almagest: An Updated Version of Ptolemy's Model of the Solar System. Online at University of Texas.
  14. Galileo, Galilei (1610). Sidereus nuncius. Online at: Smithsonian Libraries.
  15. Gearhart, C. (1985). “Epicycles, Eccentrics, and Ellipses: The Predictive Capabilities of Copernican Planetary Models.” Archive for History of Exact Sciences 32, no. 3/4. p.207–222. Online at: Jstore.
  16. Grünbaum, A. (1989). "The Degeneration of Popper’s Theory of Demarcation."" In: D’Agostino, F., Jarvie, I.C. (eds) Freedom and Rationality. Boston Studies in the Philosophy of Science, vol 117. Online at: Springer.
  17. Hatch, Robert (2018). "Early Geo-Heliocentric Models". The Scientific Revolution.
  18. Hawking, Stephen (2010). The Grand Design. p.39.
  19. Heitenan et al. (2020). "How not to criticize scientism." Metaphilosophy. Volume: 51,.4, p.522-547. Online at: Wiley.
  20. Henderson, Thomas (1842). "The Parallax of Alpha Centauri." Royal Astronomical Society. Voleume XII, p.329.
  21. Hirschfeld, Alan (2001). Parallax:The Race to Measure the Cosmos. Online at: Google Books. Online at haveard University.
  22. Hoyle, Fred (1973).Nicolaus Copernicus. London: Heinemann.
  23. Hume, David (1739). A Trestise of Human Nature. Book III, part I, section I. Online at: Project Gutenberg.
  24. Kepler, Johannes (1609). The New Astronomy. Trans. Voelkel, James. Online at: Internet Archive.
  25. Kuhn, Thomas (1962). The Structure of Scientific Revolutions. University of Chicago. Online at: Columbia University.
  26. Laudan, L. (1983). "The Demise of the Demarcation Problem."" In: Cohen, R.S., Laudan, L. (eds) Physics, Philosophy and Psychoanalysis. Boston Studies in the Philosophy of Science, vol 76. Springer, Dordrecht. online at: Springer.
  27. Lakatos, Imre (1973, 1974). "Lakatos on Science & Pseudoscience." Lecture on YouTube.
  28. Mahner, Martin (2007). "Demarcating Science from Non-Science." General Philosophy of Science: Focal Issues. online at: National University of La Plata.
  29. Mendell, Henry (2022). Eudoxos of Knidos (Eudoxus of Cnidus): astronomy and homocentric spheres. California State University.
  30. Mathison, K. (2012). "Luther, Calvin, and Copernicus — A Reformed Approach to Science and Scripture." Online at: Ligonier.
  31. Miley, John (1850). A Histoyr of the Papal States. online at: Google Books.
  32. Miller, D. (2011). "Some Hard Questions for Critical Rationalism." Discusiones Filosoficas 15(24). Online at: ResearchGate.
  33. Moore, George (1922). Principia Ethica. Online at: Project Gutenberg.
  34. Newcomb, Simon (1905). A Compendium of Stellar Astronomy. Macmillan. Online at: Internet Archive.
  35. Palmeri, Paolo (2001). "Galileo and the Discovery of the Phases of Venus." Journal for the History of Astronomy (ISSN 0021-8286), Vol. 32, Part 2, #107, p.109-129. Online at: harvard University.
  36. Pigliucci, Massimo (2013). "The demarcation problem: a (belated) response to Laudan." In Massimo Pigliucci & Maarten Boudry (eds.),Philosophy of Pseudoscience: Reconsidering the Demarcation Problem. University of Chicago Press.
  37. Popper, Karl (1934, 1959, 2002). The Logic of Scientific Discovery. Abingdon-on-Thames: Routledge.
  38. Popper, Karl (1945). Open Society and its Enemies, Vol II. Abingdon-on-Thames: Routledge. Online at: Antilogicalism.
  39. Popper, Karl (1956/1973). Realism and the Aim of Science. 18. Routledge.
  40. Ptolemy, Claudius (170). Amalgest. Online at: Classical Liberal Arts.
  41. Putnam, Hilary (1974). “Replies to My Critics” and “Intellectual Autobiography.” In: Schilpp, Paul (ed.), The Philosophy of Karl Popper. 2 volumes. La Salle, Ill: Open Court.
  42. Putnam, Hilary (1998). on Non-Scientific Knowledge . Lecture recording. On line at: YouTube.
  43. Rosen, Edward (1985). “The Dissolution of the Solid Celestial Spheres.” Journal of the History of Ideas 46, no. 1: 13–31.
  44. Schrodinger, Erwin (1944). What is Life?. Chapter 7. Cambridge University Press. On the web at:
  45. Spekkens, Kristine (2015). "How do sunrise and sunset times change with altitude?" Ask an Astronomer. Online at: Corness University.
  46. Stagaro, Angelo (2020). "The Myth That Catholics Are Opposed To Science Revolves Around Copernicus." Online at: a href="">EWTN.
  47. Thagard, Paul (1978). "Why Astrology is a Pseudoscience", PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1978.
  48. Wilson, Teresa (2018). Evaluating the Effectiveness of Current Atmospheric Refraction Models in Predicting Sunrise and Sunset Times. Open Access Dissertation. Online at:
  49. White, Robert (2002). “Calvin and Copernicus: the Problem Reconsidered“, Calvin Theological Journal 15. p233-243, at 236-237. Michigan Technological University.
  50. Young, Andrew (2003). "Dip of the Horizon." Online at: San Diego State University.
  51. Young, Andrew (2006). "Understanding Atmospheric Refraction." The Observatory, Vol. 126, p. 82-115. Online at: Harvard University.