Tag: Newton's first law

Poincaré, inertia, and a common misconception

A historical, and ongoing, alternative conception

Keith S. Taber

"…and eleventhly Madame Curie…" Henri Poincaré enjoying small talk at a physics conference (image source: 'Marie Curie and Poincaré talk at the 1911 Solvay Conference', Wikipedia)

One of the most fundamental ideas in physics, surely taught in every secondary school science curriculum around the world, is also the focus of one of the most common alternative conceptions documented in science education. Inertia. Much research in the latter part of the twentieth century has detailed how most people have great trouble with this very simple idea.

But that would likely not have surprised the nineteenth century French physicist (and mathematician and philosopher) Henri Poincaré in the least. Over a century ago he had this to say about the subject of Newton's first law, inertia,

"The principle of inertia. A body acted on by no force can only move uniformly in a straight line.

Is this a truth imposed a priori upon the mind? If it were so, how could the Greeks have failed to recognise it? How could they have believed that motion stops when the cause which gave birth to it ceases? Or again that every body if nothing prevents, will move in a circle, the noblest of motions?

If it is said that the velocity of a body can not change if there is no reason for it to change, could it not be maintained just as well that the position of this body can not change, or that the curvature of its trajectory can not change, if no external cause intervenes to modify them?

Is the principle of inertia, which is not an a priori truth, therefore an experimental fact? But has any one ever experimented on bodies withdrawn from the action of every force? and, if so, how was it known that these bodies were subjected to no force?"

Poincaré, 1902/1913/2015

There is quite a lot going on in that quote, so it is worth breaking it down.

The principle of inertia

"The principle of inertia. A body acted on by no force can only move uniformly in a straight line."

Poincaré, 1902/1913/2015

We might today choose to phrase this differently – at least in teaching. Perhaps along the lines that

a body remains at rest, or moving with uniform motion, unless it is acted upon by a net (overall) force

That's a pretty simple idea.

  • If you want something that is stationary to start moving, you need to apply a force to it. Otherwise it will remain stationary. And:
  • If you want something that is moving with constant velocity to slow down (decelerate), speed up (accelerate), or change direction, you need to apply a force to it. Otherwise it will carry on moving in the same direction at the same speed.

A simple idea, but one which most people struggle with!

It is worth noting that Poincaré's formulation seems simpler than the versions more commonly presented in school today. He does not make reference to a body at rest; and we might detect a potential ambiguity in what is meant by "can only move uniformly in a straight line".

Is the emphasis:

  • can only move uniformly in a straight line:
    • i.e., 〈 can only 〉 〈 move uniformly in a straight line 〉, or
  • can only move uniformly in a straight line:
    • i.e., 〈 can only move 〉 〈 uniformly in a straight line 〉

That is, must such a body "move uniformly in a straight line" or must such a body, if moving, "move uniformly in a straight line"? A body acted on by no force may be stationary.

Perhaps this is less ambiguous in the original French? But I suspect that, as a physicist, Poincairé did not, particularly, see the body at rest as being much of a special case.

To most people the distinction between something stationary and something moving is very salient (evolution has prepared us to notice movement). But to a physicist the more important distinction is between any body at constant velocity, and one accelerating* – and a body not moving has constant velocity (of 0 ms-1!)

*and for a physicist accelerating usually includes decelerating, as that is just acceleration with a negative vale, or indeed positive acceleration in a different direction. These 'simplifications' seem very neat – to the initiated (but perhaps not to novices!)

A historical scientific conception

Poincaré then asks:

Is this a truth imposed a priori upon the mind? If it were so, how could the Greeks have failed to recognise it? How could they have believed that motion stops when the cause which gave birth to it ceases?"

Poincaré, 1902/1913/2015

Poincairé asks a rhetorical question: "Is this a truth imposed a priori upon the mind?" Rhetorical, as he immediately suggests the answer. No, it cannot be.

Science is very much an empirical endeavour. The world is investigated by observation, indeed often observation of the effects of interventions (i.e., experiments).

In this way, it diverges from a rationalist approach to understanding the world based on reflection and reasoning that occurs without seeking empirical evidence.

An aside on simulations and perpetual change

Yet, even empirical science depends on some (a priori) metaphysical commitments that cannot themselves be demonstrated by scientific observation (e.g., Taber, 2013). As one example, the famous 'brain in a vat' scenario (that informed films such as The Matrix) asks how we could know that we really experience an external world rather than a very elaborate virtual reality fed directly into our central nervous system (assuming we have such a thing!) 1

Science only makes sense if we believe that the world we experience is an objective reality originating outside our own minds
(Image by Gerd Altmann from Pixabay)

Despite this, scientists operate on the assumption this is a physical world (that we all experience), and one that has a certain degree of stability and consistency. 2 The natural scientist has to assume this is not a capricious universe if science (a search for the underlying order of the world) is to make sense!

It may seem this (that we live in is an objective physical world that has a certain degree of stability and consistency) is obviously the case, as our observations of the world find this stability. But not really: rather, we impose an assumption of an underlying stability, and interpret accordingly. The sun 'rises' every day. (We see stability.) But the amount of daylight changes each day. (We observe change, but assume, and look for, and posit, some underlying stability to explain this.)

Continental drift, new comets, evolution of new species and extinction of others, supernovae, the appearance of HIV and COVID, increasing IQ (disguised by periodically renormalising scoring), climate change, the expanding universe, plant growth, senile dementia, rotting fruit, printers running out of ink, lovers falling out of love, et cetera,…are all assumed to be (and subsequently found to be) explainable in terms of underlying stable and consistent features of the world!

But it would be possible to consider nothing stays the same, and seek to explain away any apparent examples of stability!

Parmenides thought change is impossible

Heraclitus though everything was in flux

An a priori?

So Poincaré was asking if the principle of is inertia was something that would appear to us as a given; is inertia something that seems a necessary and obvious feature of the world (which it probably does to most physicists – but that is after years of indoctrination into that perspective).

But, Poincaré was pointing out, we know that for centuries people did not think that objects not subject any force would continue to move with constant velocity.

There were (considered to be) certain natural motions, and these had a teleological aspect. So, heavy objects, that were considered mainly earth naturally fell down to their natural place on the ground. 3 Once there, mission accomplished (so to speak), they would stop moving. No further explanation was considered necessary.

Violent motions were (considered to be) different as they needed an active cause – such as a javelin moving through the air because someone had thrown it. Yet, clearly (it was believed), the athlete could only impart a finite motion to the javelin, which it would soon exhaust, so the javelin would (naturally) stop soon enough.

Today, such ideas are seen as alternative conceptions (misconceptions), but for hundreds of years these ideas were largely taken as self-evident and secure principles describing aspects of the world. The idea that the javelin might carry on moving for ever if it was 'left to its own devices' seemed absurd. (And to most people today who are not physicists or science teachers, it probably still does!)

An interesting question is if, and if so, to what extent, the people who become physicists and physics teachers start out with intuitions more aligned with the principles of physics than most of their classmates.

"Assuming that there is significant variation in the extent to which our intuitive physics matches what we are taught in school, I would expect that most physics teachers are among those to whom the subject seemed logical and made good sense when they were students. I have no evidence for this, but it just seems natural that these students would have enjoyed and continued with the subject.

If I am right about this intuition, then this may be another reason why physics is so hard for some of our students. Not only do they have to struggle with subject matter that seems counterintuitive, but the very people who are charged with helping them may be those who instinctively think most differently from the way in which they do."

Taber, 2004, p.124

Another historical scientific conception

And Poincaré went on:

"Or again that every body if nothing prevents, will move in a circle, the noblest of motions?"

Poincaré, 1902/1913/2015

It was also long thought that in the heavens bodies naturally moved spontaneously in circles – a circle being a perfect shape, and the heavens being a perfect place.

Orbital motion – once viewed to be natural (i.e., not requiring any further explanation) and circular in 'the heavens'.
(Image by WikiImages from Pixabay: Body sizes and separations not to the same scale!)

It is common for people to feel that what seems natural does not need further explanation (Watts & Taber, 1996) – even though most of what we consider natural is likely just familiarity with common phenomena. We start noticing how the floor arrests the motion of falling objects very young in life, so by the time we have language to help reflect on this, we simply explain this as motion stopping because the floor was in the way! Similarly, reaction forces are not obvious when an object rests on another – a desk, a shelf, etc – as the object cannot fall 'because it is supported'.

Again, we (sic, we the initiated) now think that without an acting centripetal force, an orbiting body would move off at a tangent – but that would have seemed pretty bizarre for much of European history.

The idea that bodies moved in circles (as the fixed stars seemed to do) was maintained despite extensive observational evidence collected over centuries that the planets appeared to do something quite different. Today Kepler's laws are taught in physics, including that the solar system's orbiting bodies move (almost) in ellipses. ('Almost', as they bodies perturb each other a little.)

But when Kepler tried to fit observations to theory by adopting Copernicus's 'heliocentric' model of the Earth and planets orbiting the Sun (Earth and other planets, we would say), he still struggled to make progress for a considerable time because of an unquestioned assumption that the planetary motions had to be circular, or some combination of multiple circles.

Learners' alternative conceptions

These historical ideas are of more than historical interest. Many people, research suggests most people, today share similar intuitions.

  • Objects will naturally come to a stop when they have used up their imparted motion without the need for any forces to act.
  • Something that falls to the floor does not need a force to act on it to stop it moving, as the ground is in its way.
  • Moons and planets continue in orbits because there is no overall force acting on them.

The vast majority of learners some to school science holding versions of such alternative conceptions.

Read about common alternative conceptions related to Newton's first law

Read about common alternative conceptions related to Newton's second law

The majority of learners also leave school holding versions of such alternative conceptions – even if some of them have mastered the ability to usually respond to physics test questions as if they accepted a different worldview.

The idea that objects soon stop moving once the applied force ceases to act may be contrary to physics, but it is not, of course, contrary to common experience – at least not contrary to common experience as most people perceive it.

Metaphysical principles

Poincaré recognised this.

"If it is said that the velocity of a body can not change if there is no reason for it to change [i.e. the principle of inertia],

could it not be maintained just as well that

the position of this body can not change, or

that the curvature of its trajectory can not change,

if no external cause intervenes to modify them?"

Poincaré, 1902/1913/2015 (emphasis added)

After all, as Poincairé pointed out, there seems no reason, a priori, that is intuitively, to assume the world must work according to the principle of inertia (though some physicists and science teachers whom have been indoctrinated over many years may have come to think otherwise – of course after indoctrination is not a priori!), rather than assuming, say, that force must act for movement to occur and/or that force must act to change an orbit.

Science as an empirical enterprise

Science teachers might reply, that our initial intuitions are not the point, because myriad empirical tests have demonstrated the principle of inertia. But Poincairé suggested this was strictly not so,

"Is the principle of inertia, which is not an a priori truth, therefore an experimental fact? But has any one ever experimented on bodies withdrawn from the action of every force? and, if so, how was it known that these bodies were subjected to no force?"

Poincaré, 1902/1913/2015

For example, if we accept the ideas of universal gravitation, than anywhere in the universe a body will be subject to gravitational attractions (that is, forces). A body could only be completely free of this by being in a universe of its own with no other gravitating bodies. Then we might think we could test, in principle at least, whether the body "acted on by no force can only move uniformly in a straight line".

Well, apart from a couple of small difficulties. There would be no observers in this universe to see, as we have excluded all other massive bodies. And if this was the only body there, it would be the only frame of reference available – a frame of reference in which it was always stationary. It would always be at the centre of, and indeed would be the extent of, its universe.

Poincaré and pedagogic awareness

Poincaré was certainly not denying the principle of inertia so fundamental to mechanics. But he was showing that he appreciated that a simple principle which seems (comes to seem?) so basic and obvious to the inducted physics expert:

  • was hard won in the history of science
  • in not 'given' in intuition
  • is not the only possible basic principle on which a mechanics (in some other universe) could be based
  • is contrary to immediate experience (that is, to those who have not been indoctrinated to 'see' resistive forces sch as friction acting everywhere)
  • could never be entirely demonstrated in a pure form, but rather must be inferred from experimental tests of more complex situations where we will only deduce the principle of inertia if we assume a range of other principles (about the action of gravitational fields, air resistance, etc.)

Poincaré may have been seen as one of the great physicists of his time, but his own expertise certainly did not him appreciating the challenges facing the learner of physics, or indeed the teacher of physics.

Work cited:
Notes

1 With current human technology we cannot achieve this – even the best virtual worlds clearly do not yet come close to the real one! But that argument falls away if 'the real' world we experience is such a virtual reality created by very advanced technology, and what we think of as virtual worlds are low definition simulations being created within that! (After all, when people saw the first jumpy black-and-white movies, they then came out from the cinema into a colourful, smooth and high definition world.) If you have ever awaken from a dream, only to later realise you are still asleep, and had been dreaming of being asleep in the dream, then you may appreciate how such nesting of worlds could work.

Probably no one actually believes they are a brain in a vat, but how would we know. There is an argument that

  • 1) the evolution of complex life is a very slow process that requires a complex ecosystem, but
  • 2) once humans (or indeed non-humans) have the technology to create convincing virtual worlds this can be done very much more quickly, and with much less resource [i.e., than the evolution of the physical world which within which the programmers of the simulations themselves live]. So,
  • 3) if we are living in a phase of the universe where such technology has been achieved, then we would expect there to be a great many more such virtual worlds than planets inhabited by life forms with the level of self-consciousness to think about whether they are in a simulation.4 So,
  • 4) [if we are living in a phase of the universe where such technology has been achieved] we would be much more likely to be living in one of these worlds (a character in a very complex simulation) than an actual organic being. 5

2 That is, not a simulation where an adolescent programmer is going to suddenly increase gravity or add a new fundamental force just to make things more interesting.

3 Everything on earth was considered to be made up of different proportions of the four elements, which in terms of increasing rarity were earth, water, air and fire. The rocks of the earth were predominately the element earth – and objects that were mainly earth fell to their natural place. (Rarity in this context means the inverse of density, not scarcity.)

4 When I was a child (perhaps in part because I think I started Sunday School before I could start 'proper' school), I used to muse about God being able to create everything, and being omniscient – although I am pretty sure I did not use that term! It seemed to me (and, sensibly, I do not think I shared this at Sunday School) that if God knew everything and was infallible, then he did not need to actually create the world as a physical universe, but rather just think what would happen. For God, that would work just as well, as a perfect mind could imagine things exactly as they would be in exquisite detail and with absolute precision. So, I thought I might just be an aspect of the mind of God – so part of a simulation in effect. This was a comforting rather than worrying thought – surely there is no safer place to be than in the mind of God?

Sadly, I grew to be much less sure of God (the creation seems just as incredible – in the literal sense – either way), but still think that, for God, thinking it would be as good as (if not the same as) making it. I suspect some theologians would not entirely dismiss this.

If I am just a character in someone's simulation, I'd rather it was that of a supreme being than some alien adolescent likely to abandon my world at the first sign of romantic interest from a passing conspecific.

5 Unless we assume a dystopian Matrix like simulation, the technology has to be able to create characters (sub-routines?) with self-awareness – which goes some way beyond just a convincing simulation, as it also requires components complex enough to be convinced about their own existence, as well as the reality of the wider simulation!

Plus ça change – balancing forces is hard work

Confusing steady states and equilibrium?

Keith S. Taber

"…I am older than I once was
And younger than I'll be
But that's not unusual
No, it isn't strange
After changes upon changes
We are more or less the same
After changes we are more or less the same…"

From the lyrics of 'The Boxer' (Simon and Garfunkel song) by Paul Simon

In a recent post I discussed the treatment of Newtonian forces in a book (Thomson, 2005) about the history of natural theology (a movement which sought to study the natural world as kind of religious observance – seeking to glorify God by the study of His works) and its relationship to the development of evolutionary theory.

The book was written by a prestigious scientist, who had held Professorships at both Yale in the US and at Oxford. Yet the book contained some erroneous physics – 'howlers' of the kind that are sometimes called 'schoolboy errors' (as presumably most schoolgirls would be careful not to make them?)

Read 'Even Oxbridge professors have misconceptions'

'The Watch on the Heath'

by Prof. Keith Thomson

My point is not to imply that this is a poor read – the book has much to commend it, and I certainly thought it was worth my time. I found it an informative read, and I have no reason to assume that the author's scholarship in examining the historical sources was was not of the highest level – even if his understanding of some school physics seemed questionable. I think this highlights two features of science:

  1. Science is so vast that research scientists setting out to write 'popular' science books for a general readership risk venturing into areas outside their specialist knowledge – areas where they may lack expertise 1
  2. Some common alternative conceptions ('misconceptions') are so insidious that we confidently feel we understand the science we have been taught whilst continuing to operate with intuitions at odds with the science.

Out of specialism

In relation to the first point, I previously highlighted a reference to "Einstein's relativity theory" being part of quantum physics, and later in the book I found another example of a non-physicist confusing two ideas that may seem similar to the non-specialist but which to a physicist should not be confused:

"In the 1930s, Arthur Holmes worked out the geology of the mechanism [underpinning plate tectonics] and the fact that the earth's inner heat (like that of the sun) comes from atomic fission."
p.190

Thomson, 2005: 190

The earth contains a good deal of radioactive material which, through atomic fission, heats up the earth from within. This activity has contributed to the, initially hot, earth cooling much more slowly than had once been assumed – most notably according to modelling undertaken by Thomson's namesake, Lord Kelvin.2 Kelvin did not know about nuclear fission.

But the sun is heated by a completely different kind of nuclear reaction: fusion. The immense amount of energy 'released' during this process enables stars to burn for billions of years without running out of hydrogen fuel.3

Lord Kelvin did not know about that either, leading to him suggesting

"…on the whole most probable that the sun has not illuminated the earth for 100,000,000 years, and almost certain that he has not done so for 500,000,000 years"

Thomson, 1862

Kelvin suggested this was 'almost' but not 'absolutely' certain – a good scientist should always keep an open mind to the possibility of having missed something (take note, BBC's Nick Robinson).

We now think the sun has been 'illuminating' for about 4 600 000 000 years, almost ten times as long as Kelvin's upper limit. It may seem strange that a serious scientist should refer to the sun as 'he', but this kind of personification was once common in scientific writings.

Read about personification in science

The first atomic weapons were based on fission processes of the kind used in nuclear power stations.

Hydrogen bombs are much more devastating still, making use of fusion as occurs deep in the sun.

(Image by Gerd Altmann from Pixabay)

A non-scientist may feel this conflation of fission and fusion is a minor technical detail. But it is a very significant practical distinction.

For one thing the atomic bombs that were used to devastate Hiroshima and Nagasaki were fission devices. The next generation of atomic weapons, the 'hydrogen bombs' were very much more powerful – to the extent that they used a fission device as a kind of detonator to set off the main bomb! It is these weapons, fusion weapons, which mimic the processes at the centre of stars such as the sun.

…The rusty wire that holds the cork that keeps the anger in
Gives way and suddenly it's day again
The sun is in the east
Even though the day is done
Two suns in the sunset, hmph
Could be the human race is run…

From the lyrics of 'Two suns in the sunset' (Pink Floyd song) by Roger Waters

In terms of peaceful technologies, fission-based nuclear power stations, whilst not using fossil fuels, have been a major concern because of the highly radioactive waste which will remain a high health risk for many thousands of years, and because of the dangers of radiation leaks – very real risks as shown by the Three Mile Island (USA) and Windscale (England) accidents, and much more seriously at Fukushima (Japan) and, most infamously, Chernobyl (then USSR, now Ukraine). There are also serious health and human rights issues dogging the mining of uranium ore, which is, of course, a declining resource.

For decades scientists have been trying to develop, as an alternative, nuclear fusion based power generation which would be a source of much cleaner and sustainable power supplies. This has proved very challenging because the conditions under which fusion takes place are so much more extreme. Critically, no material can hold the plasma at the extreme temperatures, so it has to be magnetically suspended well away from the containment vessel 'walls'.

The tenacious nature of some misconceptions

My second point, the insidious nature of some common alternative conceptions, is a challenge for science teachers as simply giving clear, accurate presentations with good examples may not be enough to bring about change in well-established and perhaps intuitive ways of thinking, even when students study hard and think they have learnt what has been taught.

I suggested this was reflected in Prof. Thomson's text (Keith, that is, not Sir William) in his use of references to Newton's ideas about force and motion. Prof. Thomson was not as a biologist therefore seeking to avoid referring to physics, but rather actively engaging with Newton's notions of inertia and the action of forces to make his points. Yet, also, seemingly misusing Newtonian mechanics because of a flawed understanding. Likely, as with many students, Prof. Thomson's intuitive physics was so strong that although he had studied Newton's laws, and can state them, when he came to apply them his own 'common-sense' conceptions of force and motion insidiously prevailed.

The point is not that Prof. Thomson has got the physics wrong (as research suggests most people do!) but that he was confident enough in his understanding to highlight Newtonian physics in his writing and, in effect, seek to teach his readers about it.

Newton's laws

What are commonly known as 'Newton' three laws of motion' can be glossed simply as:

N1: When no force is acting, an object does not change its motion: if stationary, it remains stationary; if moving, it carries on moving at the same speed in the same direction.

Indeed, this is also true if forces are acting, but they cancel because they are balanced, i.e.,

N1': When no net (overall, resultant) force is acting, an object does not change its motion: if stationary, it remains stationary; if moving, it carries on moving at the same speed in the same direction.

N2: When a net force is acting on a body it changes its motion in a way determined by the magnitude and direction of the force. (The change in velocity takes place in the direction of the force, and at a rate depending on the magnitude of the force).

So, if the force acts along the direction of motion, then the speed will change but not direction; but if the force acts in any other direction it will lead to a change in direction.

Strictly, the law relates to the 'rate of change of momentum' but assuming the mass of the body is fixed, we can think in terms of changes of velocity. 4

N3: Forces are interactions between two bodies/objects (that attract or repel each other): the same size force acts on both. (This is sometimes unfortunately phrased as 'every action having an equal and opposite reaction') 5.

These (perhaps) seem relatively simple, but there are complications in applying them. Very simply, the first law,when applied to moving bodies does not seem to fit our experience (moving bodies often seem to come to a stop by themselves – due to forces that we do not always notice).

The second law relates an applied force to a process of change, but it is very easy to instead think of the applied force directly leading to an outcome. That is people often equate the change in direction with the final direction. The change occurs in the direction of the force: that does not mean the final direction is the direction of the force.

The third law is commonly misapplied by assuming that if 'forces come in pairs' these will be balanced and cancel out. But they cannot cancel out because they are acting on the two bodies. (If your friend hits you in the eye after one too many pedantic complaints about her science writing you cannot avoid a black eye simply by hitting her back just as hard!)

A N3 force 'pair' does not balance out!

Often objects are in equilibrium because the forces acting on them are balanced. But they are never in equilibrium just because a force on them is also acting on another body! An apple hangs from a tree because the branch pulls it up the same amount as its weight pulls it down: these are two separate forces, each of which is also acting on the other body involved (the branch, and the earth, respectively).

Read about learning difficulties and Newton's third law

Thomson's 'Newtonian Physics'

In the previous posting I noted that Prof. Thomson had written

  • "Any trajectory other than a straight line must be the result of multiple forces acting together."
  • "the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun…
  • "a Newtonian balance of forces… rocks: gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again"

The first two statements are simply wrong according to conventional physics. Curved paths are often the result of a single force acting. The earth and moon orbit because they are both the subject of unbalanced forces.

Those two statements are contrary to N1 and N2.

The third statement seemed to suggest that a balance of forces was somehow considered to bring about changes. The suggestion appeared to be that a cycle of changes might be due to a balance of forces. But I acknowledged that "this reference to Hutton's ideas seems to preview a more detailed treatment of the new geology in a later chapter in the book (that I have not yet reached), so perhaps as I read on I will find a clearer explanation of what is meant by these changes being based on a theory of balance of forces".

Now I have finished the book, I wanted to address this.

A sort of balance

Prof. Thomson discusses developing ideas in geology about how the surface of the earth came to have its observed form. Today we are familiar with modern ideas about the structure of the earth, and continental drift, and most people have seen this represented in various ways.

Image by Venita Oberholster from Pixabay
Image by Clker-Free-Vector-Images from Pixabay
Original images by by Michel Müller from Pixabay

However, it was once widely assumed that the earth's surface was fairly static , but had been shaped by violent events in the distant past – a view sometimes called 'catastrophism'. One much referenced catastrophe was the flood associated with the biblical character Noah (of Ark fame) that was sometimes considered to have been world-wide deluge. (Those who considered this were aware that this required a source of water beyond normal rainfall – such as perhaps vast reservoirs of water escaping from underground).

The idea that the earth was continually changing, and that forces that acted continuously over vast periods of time could slowly (much too slowly for us to notice) lead to the formation of, for example, mountain ranges seemed less feasible.

Yet we now understand how the tectonic plates float on a more fluid layer of material and how these plates slowly collide or separate with the formation of new crust where they move apart. Vast forces are at work and change is constant, but there are cyclic processes such that ultimately nothing much changes.

Well, nothing much changes on a broad perspective. Locally of course, changes may be substantial: land may become submerged, or islands appear from the sea; mountains or great valleys may appear – albeit very, very slowly. But crust that is subsumed in one place will be balanced by crust formed elsewhere. And – just as walking from one side of a small boat to another will lead to one side rising out of the water, whilst the opposite side sinks deeper into the water – as land is raised in one place it will sink elsewhere.

This is the kind of model that scientists started to develop, and which Prof. Thomson discusses.

"[Dr John Woodward (1665-1728) produced] "an ingenious theory, parts of it quite modern, parts simply seventeenth century sophistry within a Newtonian metaphor. Woodward's earth, post deluge, is stable, but not in fact unchanging. This is possible because it is in a sort of balance – a dynamic balance between opposing forces."

Thomson, 2005: 156

Plus ça change, plus c'est la même chose

James Hutton (1726 – 1797) was one of the champions of this 'uniformitarianism',

"Hutton's earth is in a constant state of flux due to processes acting over millions of years as mountains are eroded by rain and frost. In turn, the steady raising up of mountains, balances their steady reduction through erosion.

…for Hutton the evidence of the rocks demonstrated a cyclic history powered by Newtonian steady-state dynamics: the more it changed, the more it stayed the same."
p.181

Thomson, 2005: 181

The more it changed, the more it stayed the same: plus ça change, plus c'est la même chose. This, of course, is an idiom that has found resonance with many commentators on the social, as well as the physical, world,

"…A change, it had to come
We knew it all along
We were liberated from the fold, that's all
And the world looks just the same
And history ain't changed
'Cause the banners, they all flown in the last war
…
There's nothing in the street
Looks any different to me
And the slogans are effaced, by-the-bye
And the parting on the left
Is now parting on the right
And the beards have all grown longer overnight…"

From the lyrics of 'Won't get fooled again' (The Who song), by Pete Townsend

Steady states

So, there are vast forces acting, but the net effect is a planet which stays substantially the same over long periods of time. Which might be considered analogous to a body which is subject to very large forces, but in such a configuration that they cancel.

Where Prof. Thomson is in danger of misleading his reader is in confusing a static equilibrium and a macroscopic overall steady state that is the result of many compensating disturbances. This is an important difference when we consider energy and not just the forces acting.

A steady state can be maintained by nothing happening, or by several things happening which effectively compensate.

If we consider a very heavy mass sitting on a very study table, then the mass has a large weight, but does not fall because the table exerts a balancing upward reaction force. Although large forces are acting, nothing happens. In physics terms, no work is done. 6

Now consider a sealed cylinder, perfectly insulted and shielded from its surroundings, containing some water, air and too much salt to fully dissolve. It would reach a stead state where the

  • the mass of undissolved salt is constant
  • the height of the solution in the tube is constant

On a macroscopic level, nothing then happens – it is all pretty boring (especially as if the cylinder was perfectly insulated we would not be able to monitor it anyway!)

Actually, all the time,

  1. salt is dissolving
  2. salt is precipitating
  3. gases from the air are dissolving in the solution
  4. gases are leaving the solution
  5. water is evaporating into the air
  6. water vapour is condensing

But the rates of 1 and 2 are the same; the rates of 3 and 4 are the same; and the rates of 5 and 6 are the same. In terms of molecules and ions, there is a lot of activity – but in overall terms, nothing changes: we have a steady state, due to the dynamic equilibria between dissolving and precipitating; between dissolving and degassing; and between evaporation and condensation.

This activity is possible because of the inherent energy of the particles. In the various interactions between these particles a molecule is slowed here, an ion is released from electrical bonds – and so. But no energy transfer takes place to or from the system, it is only constantly redistributed among the ensemble of particles. No work is done.

Cycling is hard work

But macroscopic stable states maintained by cyclic processes are not like that. A key difference is that in the geological cycles there are significant frictional effects. In our sealed cylinder, the processes will continue indefinitely as the energy of the system is constant. In the geological systems, change is only maintained because there is source of power – the sun drives the water cycle, radioactive decay in effect drives the rock cycle.

Work is done in forming new crust under the sea between two plates. More work is done pushing one plate beneath another at a plate boundary. It does not matter if the compensating changes were produced by identical magnitude forces pushing in opposite directions – these are not balanced forces in the sense of cancelling out (they act on different masses of material) – if they had been, nothing would have happened.

You cannot move tectonic plates around without doing a great deal of work – just as you cannot cycle effortlessly by using a circular track that brings you back to where you started, even though when cycling in one direction the ground was pushing you one way, and on the way back the ground was pushing you in the opposite direction! (Your tyres pushed on the track, and as Newton's third law suggests, it pushed back on the tyres in the opposite direction – but those equal forces did not cancel as they were acting on different things: or you would not have moved.)

Perhaps Prof. Thomson understands this, but his language is certainly likely to mislead readers:

"Hooke realised that there was a balance of forces: while the geological strata were being formed and mountains were raised up, at the same time the land was constantly being eroded…"

Thomson, 2005: 179

No, there was not a balance of forces.

It could be that Prof. Thomson's use of the phrase 'balance of forces' is only intended as a metaphor or an analogy. 7 However, he also repeats errors he had made earlier in the book

  • "the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun"
  • "any trajectory other than a straight line must be the result of multiple forces acting together"

which suggests a genuine confusion about how forces act.

One of these mistakes is that planetary orbits (which require a net {unbalanced} force), are due to 'opposing forces',

"…Paley's tortured dancing on the heads of all these metaphysical pins is pre-shadowing of modern ecological thinking and a metaphysical extension of Hooke and Newton's explanation of planetary orbits in terms of opposing forces, or Woodward's theory of matter, or Hutton's geology – it is the living world as a dynamic system of force and counterforce, of checks and balances."
p.242

Thomson, 2005: 242 (my emphasis)

The other was that a single force cannot lead to a curved path,

"…the philosophical concept of reduction, namely that any complex system can be reduced to the operation of simple causes. Thus the parabolic trajectory of a projectile is the product of two straight-line forces acting on each other [sic];…"
p.264

Thomson, 2005: 264 (my emphasis)

Forces are interactions between bodies, they are abstractions and do not act on each other. The parabolic path is due to a single constant force acting on a body that is already moving (but not in the direction of the applied force). It can be seen as the result of the combination of a force (acting according to N2) and the body's existing inertia (i.e., N1). Prof. Thomson seems to be thinking of the motion itself as corresponding to a force, where Newton suggested that it is only a change of motion that corresponds to a force.

However, whilst Prof. Thomson is wrong, he is in good company – as one of the most common alternative conceptions reported is assuming that a moving body must be subject to a force. Which, as I pointed out last time, is not so daft as in everyday experience cars and boats and planes only keep on moving as long as their propulsion systems function (to balance resistive forces); and footballs and cricket balls and javelins that do not have a source of motive power (to overcome resistive forces) soon fall to earth. So, these are understandable and, in one sense, very forgiveable slips. It is just unfortunate they appear in an otherwise informative book about science.

Sources cited:
  • Thomson, K. (2005). The Watch on the Heath: Science and religion before Darwin. HarperCollins.
  • Thomson, W. (1862). On the Age of the Sun's Heat. Macmillan's Magazine, 5, 388-393.
  • Thorn, C. E., & Welford, M. R. (1994). The Equilibrium Concept in Geomorphology. Annals of the Association of American Geographers, 84(4), 666-696. http://www.jstor.org/stable/2564149
Notes

1 Although there are plenty of 'academic' books in many fields of scholarship (usually highly focused so the author is writing about their specialist work), the natural sciences tend to be communicated and debated in research journals. Most books written by scientists tend to be for a more general audience – and publishers expect popular science books to appeal to a wide readership, so these books are likely to have a much broader scope than academic monographs.

2 When he was ennobled, William Thomson chose to be called Baron Kelvin – after his local river, the river Kelvin. So the SI unit of temperature is named, indirectly, after a Scottish River.

Kelvin's reputation was such that when he modelled the cooling earth and suggested the planet was less that a 100 000 000 years old, this caused considerable concerns given that geologists were suggesting that much longer had been needed for it to have reached its present state.

3 For a brief discussion regarding energy changes during processes of this kind, see 'How much damage can eight neutrons do?'

4 The rate of change of momentum is proportional to the magnitude of the applied force and takes place in the direction of the applied force.

As momentum is mv, and as mass is usually assumed fixed (if the motion is well below light speeds) 'the rate of change of momentum' is the mass times the rate of change of the velocity – or ma. (F=ma.)

The key point about direction is that it is not that the body moves in the direction of the force, but the change of momentum (so change of velocity) is in the direction or the force.

As the body's momentum is a vector, and the change in momentum is a vector, the new momentum is the vector sum of these two vectors: new momentum = old momentum + change in momentum.

The object's new direction after being deflected by a force is in the direction of the new momentum

5 When there is force between two bodies (let's call them A, B) the force acting on body B is the same size as the force acting on body A, but is anti-parallel in direction.

The force between the earth and the sun acts on both (not shown to scale)

6 This is an ideal case.

A real table would not be perfectly rigid. A real table would initially distort ever so slightly with the area under the mass being ever so slightly compressed, and the weight dropping to an ever so slightly lower level. The very slight lowering of the weight does a tiny amount of work compressing the table surface.

Then, nothing more happens, and no more work is done.

7 Thorn and Welford (1994) have referred to "the fuzzy and frequently erroneous use of the term…equilibrium in geomorphology" (p.861), and how an 1876 introduction of the "concept of dynamic equilibrium resembles the balance-of-forces equilibrium that appears in dynamics, but by analogy rather than formal derivation" (p.862).

Even Oxbridge professors have misconceptions

Being a science professor is no assurance of understanding Newton's mechanics

Keith S. Taber

…this author had just written that
all matter is in uniform motion unless acted upon by an external force
but did not seem to appreciate that
any matter acted upon by an external force will not be in uniform motion

I started a new book today. 'The Watch on the Heath. Science and Religion before Darwin' had been on my pile of books to read for a while (as one can acquire interesting titles faster than find time to actually read them).

'The Watch on the Heath'

by Prof. Keith Thomson

The title is a reference to the analogy adopted at the start of William Paley's classic book on natural theology. Paley (1802) argued that if one was out walking across a heath and a foot struck an object on the ground, one would make very different assumptions if the object transpired to be a stone or a pocket watch. The stone would pass without much thought – there was no great mystery about how it came to be on the heath. But a pocket watch is an intricate mechanism composed of a multitude of especially shaped and arranged pieces fashioned from different materials. A reasonable person could not think it was an arbitrary and accidentally collated object – rather it clearly had a purpose, and so had a creator – a watchmaker.

 
Paley developed a detailed argument based on the analogy that organisms are like intricate mechanisms that offer obvious evidence of having been designed (Images by  Thomas Wolter and  Gerd Altmann  from Pixabay)

Paley used this as an analogy for the complexity of the living world. Analogies are often used by teachers and science communicators as a means of making the unfamiliar familiar – a way of suggesting something that is being introduced is actually like something the audience already knows about and feels comfortable with.

Read about analogies in science

Paley was doing something a little different – his readers would already know about both watches and living things, and he was developing the analogy to make an argument about the nature of living things as being designed. (Living things would be familiar, but Paley wanted to invite his reader to think about them in a way they might find unfamiliar.) According to this argument, organisms were so complex that, by analogy with a watch, it followed they also were created for a purpose, and by a creator.

Even today, Paley's book is an impressive read. It is 'one long argument' (as Darwin said of his 'Origin of Species') that collates a massive amount of evidence about the seeming design of human anatomy and the living world. Paley was not a scientist in the modern sense, and he was not even a naturalist who collected natural history specimens. He was a priest and philosopher / theologian who clearly thought that publishing his argument was important enough to require him to engage in such extensive scholarship that in places the volume gives the impression of being a medical textbook.

Paley's work was influential and widely read, but when Darwin (1859) presented his own long argument for evolution by natural selection there began to be a coherent alternative explanation for all that intricate complexity. By the mid-twentieth century a neo-Darwinian synthesis (incorporating work initiated by Mendel, developments in statistics, and the advent of molecular biology) made it possible to offer a feasible account that did not need a watch-maker who carefully made his or her creatures directly from a pre-designed pattern. Richard Dawkins perverted Paley's analogy in calling one of his books 'The Blind Watchmaker' reflecting the idea that evolution is little more than the operation of 'blind' chance.

Arguably, Darwin's work did nothing to undermine the possibility of a great cosmic architect and master craft-person having designed the intricacies of the biota – but only showed the subtlety required of such a creator by giving insight into the natural mechanisms set up to slowly bring about the productions. (The real challenge of Darwin's work was that it overturned the idea that there was any absolute distinction between humans and the rest of life on earth – if humans are uniquely in the image of God then how does that work in relation to the gradual transition from pre-human ancestors to the first humans?)

Read 'Intergenerational couplings in the family. A thought experiment about ancestry'

Arguably Darwin said nothing to undermine the omnipotence of God, only the arrogance of one branch of the bush of life (i.e., ours) to want to remake that God in their image. Anyway, there are of course today a range of positions taken on all this, but this was the context for my reading some questionable statements about Newtonian mechanics.

Read about science and religion

Quantum quibbling

My reading went well till I got to p.27. Then I was perturbed. It started with a couple of quibbles. The first was a reference to

"…the modern world of quantum physics, where Einstein's relativity and Heisenberg's uncertainty reign."

Thomson, 2005: 27

"Er, no" I thought. Relativity and quantum theory are not only quite distinct theories, but, famously, the challenge of finding a way to make these two areas of physics, relativity theory and quantum mechanics, consistent is seen as a major challenge. The theories of relativity seem to work really well on the large scale and quantum theory works really well on the smallest scales, but they do not seem to fit together. "Einstein's relativity" is not (yet, at least) found within the "world of quantum physics".

Still, this was perhaps just a rhetorical flourish.

The Newtonian principle of inertia

But later in the same paragraph I read about how,

"Newton…showed that all matter is in uniform motion (constant velocity, including a velocity of zero) unless acted upon by an external force…Newton showed that an object will remain still or continue to move at a constant speed in the same direction unless some external force changes things."

Thomson, 2005: 27

This is known as Newton's first law of motion (or the principle of inertia). Now, being pedantic, I thought that surely Newton did not show this.

It is fair to say, I suggest, that Newton suggested this, proposed it, mooted it; perhaps claimed it was the case; perhaps showed it was part of a self-consistent description – but I am not sure he demonstrated it was so.

Misunderstanding Newton's first law

This is perhaps being picky and, of itself, hardly worth posting about, but this provides important background for what I read a little later (indeed, still in the same paragraph):

"Single forces always act in straight lines, not circles. Any trajectory other than a straight line must be the result of multiple forces acting together."

Thomson, 2005: 27

No!

The first part of this is fair enough – a force acts between two bodies (say the earth and the sun) and is considered to act along a 'line of action' (such as the line between the centres of mass of the earth and the sun). In the Newtonian world-view, the gravitational force between the earth and sun acts on both bodies along that line of action. 1

However, the second sentence ("any trajectory other than a straight line must be the result of multiple forces acting together") is completely wrong.

These two sentences are juxtaposed as though there is a logical link: "Single forces always act in straight lines, not circles. [So therefore] any trajectory other than a straight line must be the result of multiple forces acting together." This only follows if we assume that an object must always be moving in the direction of a force acting on it. But Newton's second law tells us that acceleration (and so the change in velocity) occurs in the direction of the force.

This is confusing the sense of a change with its outcome – a bit like thinking that a 10 m rise in sea level will lead to the sea being 10 m deep, or that if someone 'puts on 20 kilos' they will weigh 200 N. A 'swing to Labour' in an election does not assure Labour of a victory unless the parties were initially on par.

The error here is like assuming that any debit from a bank account must send it overdrawn:
taking £10 from a bank account means there will be £10 less in the account,
but not necessary that the balance becomes -£10!

Changing direction is effortless (if there is an external force acting)

Whenever a single force acts on a moving object where the line of action does not coincide with the object's direction of travel then the object will change direction. (That is, a single force will only not lead to a change of direction in the very special case where the force aligns with or directly against to the direction of travel.) So, electrons in a cathode ray tube can be shown to follow a curved path when a (single) magnetic force is applied, and an arrow shot from a castle battlement horizontally will curve down to the grounds because of the (single) effect of gravitational force. (There are frictional forces acting as well, but they only modify the precise shape of that curve which would still be found if the castle was on a planet with no atmosphere – as long as the archer could hold her breath long enough to get the arrow away.)

The lyrics of a popular song declare "arc of a diver – effortlessly". 2 But diving into a pool is only effortless (once you have pushed off) because the diver is pulled into an arc by their gravitational attraction with the earth – so even if you dive at an angle above the horizontal, a single force is enough to change your direction and bring you down.

"Arc of a diver – effortlessly"

© Pelle Cass. This image is used with kind permission of the artist.

(This amazing artwork is by the photographer Pelle Cass. This is one of a series ('Crowded Fields') that can be viewed at https://pellecass.com/crowded-fields.)

So, there is a mistake in the science here. Either the author has simply made a slip (which can happen to anyone) or he is operating with an alternative conception inconsistent with Newton's laws. The same can presumably be said about any editor or copy editor who checked the manuscript for the publisher.

Read about alternative conceptions

Misunderstanding force and motion

That might not be so unlikely – as force and motion might be considered the prototype case of a science topic where there are common alternative conceptions. I have seen estimates of 80%+ of people having alternative conceptions inconsistent with basic Newtonian physics. After all, in everyday life, you give something a pull or a push, and it usually moves a bit, but then always come to a stop. In our ordinary experience stones, footballs, cricket balls, javelins, paper planes, darts – or anything else we might push or pull – fail to move in a straight line at a constant speed for the rest of eternity.

That does not mean Newton was wrong, but his ideas were revolutionary because he was able to abstract to situations where the usual resistive forces that are not immediately obvious (friction, air resistance, viscosity) might be absent. That is, ideal scenarios that probably never actually occur. (Thus my questioning above whether Newton really 'showed' rather than postulated these principles.)

So, it is not surprising an author might hold a common alternative conception ('misconception') that is widely shared: but the author had written that

  • all matter is in uniform motion unless acted upon by an external force

yet did not seem to appreciate the corollary that

  • any matter acted upon by an external force will not be in uniform motion

So, it seems someone can happily quote Newton's laws of motion but still find them so counter-intuitive that they do not apply them in their thinking. Again, this reflects research which has shown that graduates who have studied physics and done well in the examinations can still show alternative conceptions when asked questions outside the formal classroom setting. It is as if they learn the formalism for the exams, but never really believe it (as, after all, real life constantly shows us otherwise).

So, this is all understandable, but it seems unfortunate in a science book that is seeking to explain the science to readers. At this point I decided to remind myself who had written the book.

We all have alternative conceptions

Keith Thomson is a retired academic, an Emeritus Fellow at Kellog College Oxford, having had an impressive career including having been a Professor of Biology at Yale University and later Director of the Oxford University Museum and Professor of Natural History. So, here we have a highly successful academic scientist (not just a lecturer in some obscure university somewhere – a professor at both Yale and Oxford), albeit with expertise in the life sciences, who seems to misunderstand the basic laws of physics that Newton postulated back in 1687.

Prof. Thomson seems to have flaws in his knowledge in this area, yet is confident enough of his own understanding to expose his thinking in writing a science book. This, again, is what we often find in science teaching – students who hold alternative conceptions may think they understand what they have been taught even though their thinking is not consistent with the scientific accounts. (This is probably true of all of us to some degree. I am sure there must be areas of science where I am confident in my understanding, but where that confidence is misplaced. I likely have misconceptions in topics areas where Prof. Thomson has great expertise.)

A balance of forces?

This could have been just a careless slip (of the kind which once made often looks just right when we reread our work multiple times – I know this can happen). But, over the page, I read:

"…in addition to the technical importance of Newton's mathematics, the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun, quickly became a valuable metaphor…"

Thomson, 2005: 27

Again – No!

If there is 'balance of forces' then the forces effectively cancel, and there is no net force. So, as "all matter is in uniform motion (constant velocity, including a velocity of zero) unless acted upon by an external force", a body subject to a balance of forces continues in "uniform motion (constant velocity…)" – that is, it continues in a straight line at a constant speed. It does not circle (or move in an ellipse). 3

Again, this seems to be an area where people commonly misunderstand Newton's principles, and operate with alternative conceptions. Learners often think that Newton's third law (sometimes phrased in terms of 'equal and opposite forces') implies there will always be balanced forces!

Read about learning difficulties and Newton's third law

The reason the moon orbits the earth, and the reason the earth orbits the sun, in the Newtonian world-view is because in each case the orbiting body is subject to a single force which is NOT balanced by any countering force. As the object is "acted upon by an external force" (which is not balanced by any other force) it does not move "in uniform motion" but constantly changes direction – along its curved orbit. According to Newton's law of motion, one thing we can always know about a body with changing motion (such as one orbiting another body) is that the forces on it are not balanced.

But once circular motion was assumed as being the 'natural' state of affairs for heavenly bodies, and I know from my own teaching experience that students who understand Newtonian principle in the context of linear motion can still struggle to apply this to circular motion. 4

Two conceptions of orbital motion (one canonical, the other a misconception commonly offered by students). From Taber, K. S., & Brock, R. (2018). A study to explore the potential of designing teaching activities to scaffold learning: understanding circular motion.

I even developed a scaffolding tool to help students make this transition, by helping them work through an example in very simple steps, but which on testing had modest effect – that is, it seemed to considerably help some students apply Newton's laws to orbital motion, but could not bridge that transition for others (Taber & Brock, 2018). I concluded even more basic step-wise support must be needed by many learners. Circular motion being linked to a net (unbalanced) centripetal force seems to be very counter-intuitive to many people.

To balance or not to balance

The suggestion that a balance of forces leads to change occurs again a little later in the book, in reference to James Hutton's geology,

"…Hutton supported his new ideas both with solid empirical evidence and an underlying theory based on a Newtonian balance of forces. He saw a pattern in the history of the rocks: gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again."

Thomson, 2005: 39

A balance of forces would not lead to rocks being "gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again". Indeed if all the relevant forces were balanced there would be no erosion, washing, sedimentation, or raising.

Erosion, washing, sedimentation, raising up ALL require an imbalance of forces, that is, a net force to bring about a change. 5

Reading on…

This is not going to stop me persevering with reading the book*, but one can begin to lose confidence in a text in situations such as these. If you know the author is wrong on some points that you already know about, how can you be confident of their accounts of other topics that you are hoping to learn about?

Still, Prof. Thomson seems to be wrong about something that the majority of people tend to get wrong, often even after having studied the topic – so, perhaps this says more about the hold of common intuitive conceptions of motion than the quality of Prof. Thomson's scholarship. Just like many physics learners – he has learnt Newton's laws, but just does not seem to find them credible.

Sources cited:
  • Darwin, C. (1859). The Origin of Species by Means of Natural Selection, or the preservation of favoured races in the struggle for life. John Murray.
  • Dawkins, R. (1988). The Blind Watchmaker. Penguin Books.
  • Paley, W. (1802/2006). Natural Theology: Or Evidence of the Existence and Attributes of the Deity, Collected from the Appearances of Nature (M. D. Eddy & D. Knight, Eds.). Oxford University Press.
  • Rosen, E. (1965/1995) Copernicus on the phases and the light of the planets, in Rosen, E. (1995). Copernicus and his successors (E. Hilfstein, Ed.). The Hambledon Press.
  • Taber, K. S., & Brock, R. (2018). A study to explore the potential of designing teaching activities to scaffold learning: understanding circular motion. In M. Abend (Ed.), Effective Teaching and Learning: Perspectives, strategies and implementation (pp. 45-85). New York: Nova Science Publishers. [Read the author's manuscript version]
  • Thomson, K. (2005). The Watch on the Heath: Science and religion before Darwin. HarperCollins.
  • Watts, M. and Taber, K. S. (1996) An explanatory gestalt of essence: students' conceptions of the 'natural' in physical phenomena, International Journal of Science Education, 18 (8), pp.939-954.
Notes

1 Though not in the world-view offered by general relativity where the mass of the sun distorts space-time enough for the earth to orbit.

2 The title track from Steve Winwood's 1980 solo album 'Arc of a Diver'

3 We have known since Kepler that the planets orbit the sun following ellipses (to a first order of approximation*), not perfect circles – but this does not change the fundamental point here: moving in an ellipse involves continuous changes of velocity. (* i.e., ignoring the perturbations due to the {much smaller} forces between the orbiting bodies.**)

[Added, 20220711]: these perturbations are very small compared with the main sun-planet interactions, but they can still be significant in other ways:

"…the single most spectacular achievement in the long history of computational astronomy, namely, the discovery of the planet Neptune through the perturbations which it produced in the motion of Uranus."

Rosen, 1965/1995, p.81

4 What is judged as 'natural' is often considered by people as not needing any further explanation (Watts and Taber, 1996).

5 This reference to Hutton's ideas seems to preview a more detailed treatment of the new geology in a later chapter in the book (that I have not yet reached), so perhaps as I read on I will find a clearer explanation of what is meant by these changes being based on a theory of balance of forces.* Still, the impression given in the extract quoted is that, as with orbits, a balance of forces brings about change.

* Addendum: I have now read on, see: 'Plus ça change – balancing forces is hard work'