A Response to ‘God In The Equation’

Posted on 2012/02/27


Feature Image - The Arrogant Humility of Scientific Inquiry (Additional Comments of 'God In The Equation')

After I finished the previous two articles, which challenged various accusations of the ‘arrogance of science’, I found additional comments from Powell’s book “God In The Equation”[7] worth rebuking. So this is really ‘part 3′ of the previous two articles.

I have met similar denunciations of scientific inquiry before, usually presented by groups motivated by a desire to present their favourite untestable speculations as equals to scientific hypotheses. Powell’s motivations are less clear, but he seems to have deep reservation about the whole business of conjecturing beyond present-day direct observation, and seems to confuse the metaphysical content of scientific theories with mysticism.


In the introduction of Powell’s book, he declares the present-state physics as, “empirical, but it knowingly overreaches, describing particles that have never been detected, fields that have never been felt, and region of space that have never been seen.” [p2] He wishes to highlight to the reader the “metaphysical strains that are increasingly obvious” in cosmology, and summarize the present scientific theories as a blending “elements of the experimental and the mystical” [p3] In this respect, he thinks that scientist share with the religious a search for “immaterial forces that animate the world,” and both assume that “there is more to the world than matter.” [p8]

There are several distinct misunderstandings here, which I shall attempt to group into the following claims:

(A) Scientists wrongly over-reach and claim to know beyond that which they have observed.
(B) Scientists suggest entities or processes they cannot directly observe. Therefore, these entities are no different from God, or angels, etc. They are both matters of faith.


(A) This is a common confusion that supposes what we know about the physical world must be derived from experience. Miller phrases the critical rationalist position well when he writes:

“Turning his back on traditional empiricism, Popper decisively separated the categories of knowledge and learning. What we know is one thing, he suggested; what we learn is another. For traditional empiricists, learning precedes and produces knowledge, both psychologically and logically… According to Popper, on the other hand, knowledge must come first, even if it is by empiricist standards a poor sort of knowledge; it is knowledge that is the psychological and logical antecedent of learning. We cannot begin to learn anything if we do not already know something…our knowledge consists of conjectures, but the most important part of what we learn consists of refutations; that is, refutations of those conjectures”[8]

This will only be able to make sense to anyone who accepts that ‘scientific knowledge’ isn’t justified, isn’t certain, and can’t be confirmed or made probable. Scientific knowledge – of any use, at least – is comprised of guesses; conjectures.

How do they arise in our thoughts? No one knows, but we might conjecture that it is correlated with functions of the human brain, and its interaction with external physical stimuli (which is not a claim about how consciousness and the objective world are related).


(B) It is doubtless that many scientists throughout history have proposed the existence of some entity, only for it to be dismissed by either falsification of the theory upon which it relied, or a simpler explanation. Here is a brief list of those entities in graveyard of physics (follow the links for Wikipedia articles):

Other attempts have been more successful.

For example, in 1930, Enrico Fermi noticed that the kinetic energies of electrons from ’beta decay’ nuclear reactions were spread over a verity of values. He proposed the existence of a small neutral particle that would preserve the ‘conservation of energy’ – a very useful principle for physicists to predict future events. Without this particle, which he called the ‘neutrino’ (little-neutral, in Italian), the energy after these reactions did not seem to sum to the energy before. The neutrino was detected in 1956.

Here are some other examples:

  • Alexis Bouvard‘s 1821 calculations of the orbit of Uranus suggested that it was being perturbed by another object. This planet, called Neptune, was discovered in 1846 by Johann Gottfried Galle. [It is also interesting to note that many other astronomers (including Galileo) had previously observed it, but all incorrectly identified it as a fixed star!]
  • George Johnstone Stoney suggested of a ‘unit of electricity’ in 1874. The ‘electron’ was detected and measured by J J Thomson in 1896.
  • In 1928, Paul Dirac conjectured the existance of ’antiparticles’, which were detected in 1932 by Carl D. Anderson.
  • Murray Gell-Mann‘s proposal of ‘quarks’ in 1964 aimed to explain the emerging particle zoo that was bewildering physicists. All six verities of quarks were detected between 1968 and 1995 in a number of locations around the world.

Powell’s main attack is upon a recent speculation described as ‘dark energy‘, which was proposed to explain the latest data that suggests the universe is not only expanding, but the expansion is accelerating. This is obviously a rather esoteric and technical idea, and will require more words than this small article to describe sufficiently.

To describe it insufficiently, the unique characteristic of ‘dark energy’ is that it is gravitationally repulsive rather than attractive, unlike any other mass/energy we have measured in the universe.

There are perhaps two challenges to this idea: ‘Dark energy’ hasn’t been detected yet, and even if it is detected, this won’t be a direct observation. We will never be able to ‘see’ dark energy, only measure its effects.

So, is a ‘belief in dark energy’ a kind of faith?

Let’s split this up into two sub-challenges:

‘It is a matter of faith to accept entities that…

(B1) …have not been observed.’
(B2) …cannot be directly observed.’


(B1) Notice that this question is similar in for to (A). Where (A) speaks about patterns we cannot prove, (B1) speaks about entities we have not observed. More about this in (B2) below.

Conjecturing the existence of the planet Neptune was motivated from the assumption that Newton’s laws were essentially correct. The discrepancy between prediction and observation therefore only due to a lack of knowledge of the initial conditions. This turned out to be the correct course of action, as Neptune was discovered.

Shortly after the investigation into Uranus’ orbit, the planet Mercury came under scrutiny for the same reason.

Due to the success of the Neptune hypothesis, many people started to assume there was another planet causing the ‘perihelion precession of Mercury‘. The proposed name for this other planet will be familar to any Star Trek fans: ’Vulcan‘!

Vulcan was not detected, and mercury’s orbital discrepancy was eventually explained by Einstein’s General Relativity - an improvement of Newton’s ideas. Einstein’s new theory did not emerge from only dwelling on the problem of Mercury, but a large number of other electromagnetic and gravitational considerations.

After General Relativity, there was no further need for Vulcan, beyond science fiction at least. I think the key question to ask about this story is: between the conjecture of Vulcan and abandoning the idea in favour of a General Relativity, was a belief in its existence faith?

No, it wasn’t. Vulcan’s expected position was calculable from the data of Mercury’s orbit. So astronomers had a good idea of where to look in the sky for it.

‘Dark energy’ is subtly different from Vulcan or Neptune as it is not a particular entity, but a universal hypothesis – something that is supposed to permeate all of space. All the other entities in the two lists above are of the universal verity.

However, the proposal is similar to Uranus insofar as there is no other problems to suppose that General Relativity needs modification (ignoring the quantum problem), just like there were no other problems to suppose Newtonian physics needed modification. So, it is a pragmatic solution, and a solution in the absence of any other ideas!

In addition, ‘dark energy’ is a mathematical consequence of general relativity [For more on this, I recommend a very good lecture by Alan Guth, available here.]

There are no such numerical measurable descriptions to be found entities that are matters of religious faith.


(B2) We can’t ‘directly observe’ protons and neutrons, but might believe they ‘exist’. Contrastingly, we do think we can directly observe tables, apples and mountains.

Of course, there is a lot of philosophy to discuss about my (deliberately) vague previous two sentences. Physicists tend to be less shy than philosophers when they speculate about what exists. One reason philosophers consider this problematic is that the history of physics involves a rather diverse collection of entities, replacing one another with seeming discontinuity.

For example, Newtonian physics was first about solid objects and forces. When General relativity replaced it, we moved to fields and space-time curvature. If we are to explain how General Relativity is somehow a generalization of Newtonian physics (or, phrased the other way around, Newtonian physics is an approximation of General Relativity), why are the entities they propose so radically different? How can we claim to know anything about the universe if we keep drastically changing our mind about its content?

Some philosopher have proposed the solution lies abandoning any commitment to ‘entities’ and reducing knowledge claims to only the structure of the mathematical equations that predict experimental measurements. This philosophy is called ‘structural realism‘.

This view makes explicit that when a physical theory is improved upon, the previous (now falsified theory) always becomes an approximation of the newer theory (reduced speeds, larger sizes…). Neils Bohr even made this an explicit goal of quantum mechanics in his ‘correspondence principle‘.

This view fits well with the critical rationalist position. As Miller writes:

“[O]ne may note, the pervasiveness of metaphysical and other untestable hypotheses within science. Such hypotheses are often introduced as essential adjuncts to scientific hypotheses; indeed, all falsifiable hypotheses have amongst their consequences a host of unfalsifiable statements (ranging from tautologies and unrestricted existential statements to meaty metaphysics) that enter science as it were on the coat-talks of their parents. But these unfalsifiable consequences – to the extent that that is all they are – are not scientific in their own right; they title is one of courtesy. If their parents are rejected from the realm of scientific knowledge, they will have to rejected too. Thus the metaphysical components of science need not be denied. It simply needs properly and responsibly to be taken care of.”[9]

So, we might conjecture these metaphysical ideas, but they are contingent on their ‘parent’ physical theories remaining unfalsifed.

Some philosopher find this very inadequate, and believe that the ‘manifest image‘ – how things appear with ‘common sense’, or intuition- to be unshakable; compared to the latest scientific metaphysics, which seems fleeting.

We might be unclear about the existence of protons and neutrons, but we don’t waver over the existence of tables. This line of thought has led some philosophers to goes so far as to insist the metaphysical speculations of scientists are, “nothing more than a garb of ideas thrown over the world of immediate intuition and experience, the life-world.”[10]

I think this is quite incorrect, and a good rubuttal has been provided by the philosopher James Ladyman:

The manifest image is not itself fixed or necessary but is a product of the contingencies of our evolution, and of course there is some variation in it since the acuity of the senses varies between musicians, artists, surveyors and so on. I see no reason why philosophers should find escape from the manifest image impossible if it is possible for scientists. To those who maintain that science should stay in its proper place I reply that the predictions that science makes are ultimately tested by their observable consequences or the behaviour of things in the manifest images. So it is wrong to suggest that science should not impinge on the manifest image because it just does, as a matter of fact.[11]

Other examples are abundant. When you look at a rainbow, you might think it an object. However, this conflicts with reports for other people nearby, as they’ll see the rainbow in a slightly different position. This can be baffling. But when you know a little optics, you’ll think of the rainbow as an optical effect that depends upon your position, just as much as it depends upon the sun and the rain.

Our ‘manifest image’ – our intuition about the world – is hard to shake, and may be an innate part of the human brain. But our brains also show great conceptual plasticity, and we are able to construct new ideas and views of the world. It is always easy to regress back to the manifest images, as we all do most of the time, but scientific inquiry can provide new perspective on common perceptions, and provide coherence to the world.

Paraphrasing Winston Churchill’s assessment that, “democracy is the worst form of government except for all those others that have been tried,” Ladyman summarizes his positions by quipping, “science is the worst sort of metaphysical belief, except for all the others.” We might have an ideal that our intuition is somehow the primitive on which all other work must rest. Yet, we must remember that the first idea is not always the correct one. And if the new metaphysics is a matter of faith, our intuitive view of the world must also be a form of faith.


[7] Powell, Corey S (2002) ‘God in the Equation’ New York: Free Press

[8] Miller, David (2006) ‘Out of Error’ Ashgate pp 85-86

[9] Miller, David (1994) ‘Critical Rationalism: A Restatement and Defense’ Peru, IL: Open Court pp 10-11

[10] Husserl, Edmund (1973) ‘Experience and Judgment’ Evanston: Northwestern University Press pp 44-45

[11] Ladyman, James (2009) ‘Who’s Afraid of Scientism’ [an interview for 'Collapse V' Urbanomic]