"Be melting snow, Wash yourself of yourself" [1]
(Rumi)
Free Will
The laws of physics are wonderful, not least because they show us some of the magic formulas behind the seeming mystery of life and the universe. They are also good and proper ‘laws’ – that is, they are intended to be equivalent across space and time.
In addition to showing us the equivalence of energy and matter, we have the great Albert Einstein to thank for also showing us that ‘here’ and ‘now’ are equivalent. His theory of general relativity combined ‘space’ and ‘time’ in a way that had never before been imagined. Einstein has left us unable to talk about the current moment as if it exists independently in the universe.
Time is not a universal independent thing that exists and that we measure with a clock. Entropy, which will be explored later, is relevant to the question of the unusualness and usefulness of life and the changing nature of energy and matter. This movement of energy and matter is also what gives us the feeling of the flow of time.
You might wonder when I am going to start this chapter on freedom to will. I have. I have exercised my freedom to start the chapter by talking about other things. The previous sentence was less flippant than it might first appear.
“The idea that a well-defined now exists throughout the universe is an illusion, an illegitimate extrapolation of our own experience. It is like the point where the rainbow touches the forest. We think that we can see it – but, if we go to look for it, it isn’t there.” [2]
(Carlo Rovelli)
I have been looking for the rainbow we call freedom to will and have found that it does not really exist in the world, at least not as it is often described. In the next chapter we will consider what is the closest quality that we can know exists: distance from the normal behaviour of the surrounding population (or population in question) – that is to say, relative freedom of action.
In writing this part I was most apprehensive about writing about this topic and that of ‘suffering, sacrifice and compassion’. I left this section in square brackets ‘[]’ until near the end of writing the first draft – yet once I had started writing it flowed so quickly and easily that it seemed to write itself. Life has a wonderful sense of irony.
“My feet are locked upon the rough bark.
It took the whole of Creation
To produce my foot, my each feather:
Now I hold Creation in my foot
Or fly up, and revolve it all slowly – I kill where I please because it is all mine
…The sun is behind me.
Nothing has changed since I began.
My eye has permitted no change.
I am going to keep things like this. ” [3]
(Ted Hughes)
Freedom of Action
“Man can do what he wills; but he cannot choose what he wills.” [4]
(Arthur Schopenhauer)
I used most of the short subchapter on free will above to remind readers of some important laws of physics. It is fundamental in any consideration of reason and ethics to be reminded that all life-forms are subject to these universal physical laws. It also helps remind us of the limits of what we can meaningfully talk about when we discuss ‘free will’.
It should go without saying, but just in case: we cannot rationally will something that is impossible, though we can still desire it.
Strong free will could be described as the notion that life-forms have the absolute ability (are not restricted; are ‘free’) to choose (as they wish) paths of action and enact them (as they will) subject only to physical laws.
Action and decision-making can be embedded in code or a result of conscious reflection or both. For humans, the effect of culture is also very significant on action.
Even an imprisoned animal, such as a human, still retains some freedom of action whilst losing its liberty – its ability to move around is constrained but within that smaller space it may still make some choices of movement based on its desires.
Like many concepts, the notion of individual humans having free will may seem so obvious that you might wonder that it deserves so much consideration. Yet it is a concept that has exercised some of the greatest minds in history and continues to do so. So much so that the experts rarely even agree what the term ‘free will’ even means, never mind if it exists and how much of it exists.
“Spinoza was the first to apply with strict consistency the idea of an all-pervasive determinism to human thought, feeling, and action. In my opinion, his point of view has not gained general acceptance by all those striving for clarity and logical rigor only because it requires not only consistency of thought, but also unusual integrity, magnanimity, and – modesty.” [6]
(Albert Einstein)
As you are reading this, be wary of finding yourself seeking to reduce everything to narrow logical proof or binary 0-or-1 answers.
Instead, be willing to accept seeming contradictions and hold those doubts and demurs in mind, whilst maintaining an open mind to diverse information. For example, one can believe in relative freedom of action (enacting unusual behaviour) without believing in some form of strong free will (power to choose to make decisions and enact them independently of normal cause and effect). If you are the sort of person who must (having no real free will in the matter) collapse all mystery into certainty and quantity, then be warned that whatever answer you comfort yourself with is unlikely to be meaningful. If there was an equation that gave us an answer, it would beg the question as to what the question means.
“Again, no one knows how or by what means the mind moves the body, nor how many various degrees of motion it can impart to the body, nor how quickly it can move it. Thus, when men say that this or that physical action has its origin in the mind, which latter has dominion over the body, they are using words without meaning, or … they are ignorant of the cause … and do not wonder at it.” [7]
(Benedictus de Spinoza)
Let us begin by building up a picture of freedom of action based on physical laws and the wider community of life, so as to get closer to understanding what on Earth people might be talking about when they talk about free will.[8] Taking an issue away from a specific use case often allows us to return with a clearer picture and a better understanding of any implicit assumptions. This can remove sources of confusion in our application.
So, coming back to that seemingly flippant comment:
Did I really have freedom in how to write a section on ‘free will’ and its content? If so, how much? And how would you or I know? How might we measure it?
The first question for a scientist is:
What useful work would we need to do to measure the possible amount of freedom available in writing about ethics with a sub-chapter on free will?
Leave aside, for now, the issue of whom is choosing an action and what their subjective view is about that choice. For example, I could write no words in such a sub-chapter, or I could write a very, very long sub-chapter. However, there are clearly some constraints within the publishing system that make those outliers so improbable that – although they have some theoretical quantity of possibility – the ability to exhibit freedom in those respects becomes near impossible within the practical constraints of the system (in this case, publishing a physical or digital book). Before considering this point further it is necessary to define what we mean by exhibiting freedom to do anything.
As we live in a physical world, we must first consider what any observable freedom means before we wrestle with this thorny notion of freedom to will anything and the degrees of freedom available to do so. In physics and chemistry:
“a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system’s phase space, and the degrees of freedom of the system are the dimensions of the phase space.” [9]
This means that the location of a particle in three dimensions requires three parameters (which are the position coordinates), that is, ‘x’, ‘y’ and ‘z’. These are also called Cartesian coordinates after the great French philosopher, mathematician and scientist René Descartes, who gave a more modern algebraic treatment of geometry.
This 3D space is also called Euclidean space after Euclid of Alexandria, considered the founder of geometry, whose ancient axioms still appear to hold true over two millennia later within 3D space. The total number of positions that are possible within a 3D space gives the total ‘phase space’.
The degrees of freedom within a phase space are therefore the number of parameters that are able to vary (i.e., be different). The direction and speed at which a particle moves within this field can be described in terms of velocity components within the three dimensions of Euclidean space.
How about a larger moving body, like a ship?
Ships have six degrees of freedom along three axes, called yaw, pitch and roll.
“The vertical/Z axis, or yaw axis, is an imaginary line running vertically through the ship and through its centre of mass. A yaw motion is a side-to-side movement of the bow and stern of the ship.
The transverse/Y axis, lateral axis, or pitch axis is an imaginary line running horizontally across the ship and through the centre of mass. A pitch motion is an up-or-down movement of the bow and stern of the ship.
The longitudinal/X axis, or roll axis, is an imaginary line running horizontally through the length of the ship, through its centre of mass, and parallel to the waterline. A roll motion is a side-to-side or port-starboard tilting motion of the superstructure around this axis.” [10]
“A spacecraft in microgravity has six degrees of freedom (6-DOF) of motion. Specifically, it is free to translate along three perpendicular axes – forward and backward, up and down, or left and right. In addition, the spacecraft can rotate about these three axes, termed pitch, yaw, and roll.” [11]
What about a spaceship?
A spaceship that is capable of leaving Earth has the same number of degrees of freedom within 3D space as a ship on the sea. The difference between a sailing ship and a spaceship in 3D space is therefore a difference in extent (and location). However, we have been ignoring the time dimension; a spaceship also has additional freedom of action within 4D space-time since it can jump from local space-time (unlike a sea-sailing ship). A moving body’s vector (direction of movement and magnitude) is therefore a feature that is relevant to its degrees of freedom.
A spaceship that is capable of leaving Earth has the same number of degrees of freedom within 3D space as a ship on the sea. The difference between a sailing ship and a spaceship in 3D space is therefore a difference in extent (and location). However, we have been ignoring the time dimension; a spaceship also has additional freedom of action within 4D space-time since it can leave local space-time (unlike a sea-sailing ship). A moving body’s vector (direction of movement and magnitude) is therefore a feature that is relevant to its degrees of freedom.
In Einstein’s space-time (the more accurate representation of coordinates in the universe) a spaceship’s increased velocity gives it the ability to move between locations with markedly different gravitational conditions, where time is relative for each place. We now need to use four parameters to specify a location (x, y, z, t) given that time is a relevant relative variable that can differ markedly between objects. Space-time therefore adds an additional potential degree of freedom to our existing physical coordinates. Depending on the body in question, there may also be other degrees of measurable freedom (e.g., pressure, temperature).
“Picasso was particularly struck by Poincaré’s advice on how to view the fourth dimension, which artists considered another spatial dimension. If you could transport yourself into it, you would see every perspective of a scene at once. But how to project these perspectives on to canvas?” [12]
(Arthur I. Miller)
Earlier experiments with relativity attempted to deal with the difficult concept that there is no absolute frame of reference determining the way in which to see ‘reality’ (as represented by space and time). Pictures of physical reality and things within it now needed to include time as an additional scalar quality, in addition to the vector coordinates.
Almost immediately after the ‘hard sciences’ started to explore and discover this new dimension of space-time, as a fundamental feature of the universe, creative artists sought to translate this extra dimensional ‘freedom’ into our culture so that we could make sense of it.
This is known to have given rise to Cubism and other influences in abstract modern art. Our new understanding of light, time and space transformed our views of reality.
“Simultaneity in Cubism was one way artists illustrated their understanding of the fourth dimension, meaning that the artist would simultaneously show views of the same subject from different viewpoints – views that would not normally be able to be seen together at the same time in the real world.” [13]
(Beth Gersh-Nesic)
Around the start of the 1900s it became clear that physical reality as we know it is much more flexible than had been imagined.
In accordance with general relativity anything that remains outside of our light cones – no matter how far they project forward or backward in time – are effectively disconnected from our local part of the universe and cannot ever affect it.
The deformation of both space and time around dense objects (like the Earth) affects the freedom of action of a body. As there is no absolute frame of reference time is dependent on the shape of local space-time and acceleration; this gives rise to some extraordinary implications for the ‘truth’ state of any specific event.
The famous ‘twin paradox’ thought experiment highlights the impact of a feature of special relativity of space-time for life-forms. It has subsequently been proven.
Imagine two brothers, one of whom flies on a rocket at great speed (always moving away from the Earth) and then returns at the same speed whilst the other brother remains on Earth.
Imagine also, to make the thought experiment simpler, that the returning twin does not require any time to change direction for his return back.
“In 1911, Paul Langevin gave a ‘striking example’ [at 99.995% the speed of light] … The traveler remains in a projectile for one year of his time, and then reverses direction. Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth.” [14]
Let us assume that the traveller does not go quite as fast as in Paul Langevin’s example.
“Consider that [a] planet is 3 light years away from the earth, and A moves with a speed (which will give us a ) for both the inbound and outbound journeys.
Here we will assume the ‘turnaround time’ is negligibly small … Both A and B send each other signals at a regular interval of one year as measured in their own respective frames.
Hence, whenever either A or B receive a signal from the other, they know that one year has elapsed in the other’s frame. This will be useful when they try to determine each other’s ages …
Thus, B will observe that it takes A 5 years to reach the planet and 5 years to return to earth as measured in the frame of B. B will also observe A’s clocks to run slower by a factor of , and thus, will conclude that the twin A has aged . This is exactly what is depicted in the spacetime diagram above. When A reaches the [planet] at a distance 3 light years away, 5 years have elapsed in B’s reference frame, whereas 4 years have elapsed in A’s reference frame.” [15]
Now, you might be wondering why so much time is being spent on explaining physical laws in a section on free will. It is important to demonstrate that freedom is both constrained by physical laws and that those laws may be more flexible than we might think, due to our continually improved understanding. It is to put humans within the correct physical perspective and framework for a discussion about any form of freedom that can be seen and measured.
Coming back to the amount of freedom I might exercise in writing a sub-chapter on free will, it can be broken down as follows:
o Average number of words in a book chapter = approximately 3000 [16]
o Set of sub-chapters that my section was within = 4
o Expected average number of words in a subsection = 750
o What are the number of words actually used? = approximately 400
On a bell curve showing length of subchapter, the subchapter would be to the left of the mean – somewhat unusual, but not so unusual as to be very extraordinary. Under this analysis, an empty chapter or a near infinitely long chapter would represent a real outlier, and evidence of potentially costly unusualness (note: the cost does not mean it is useful unusualness – it really depends on what happens next). [17]
We now need to find data on the likelihood that a section of a book on this topic would have both:
o such few words
o words that do not directly deal with the matter in the section title and that do not make use of the words of the section title in the section itself (which I studiously avoided)
Putting all of this together, we might begin to understand how much structural freedom may have been exercised in writing the section. However, we have not even considered the quality of the writing, a parameter which would appear to be too subjective to be measurable in the shorter term; in culture, quality is a scalar property that only becomes truly ascertainable with time. [18]
“The ages are all equal, but genius is always above its age.” [19]
(William Blake)
Nor have we measured the freedom exhibited in the content, which would need to be scored for unusualness. Depending on the culture, the content itself could be an example of significant freedom in addition to the structural freedom. In some countries and times, such freedom has been enough to have a writer imprisoned, tortured or murdered for blasphemy or as a heretic or apostate.
There are different degrees of freedom for cultural freedom of action. Leaving all that aside – and this is the insurmountable crux for free will – even if we know all of the unusualness ‘scores’ of this book, we cannot really know if I ‘freely chose or willed’ the structure and each word in this book.
Did I choose to exercise freedom to be unusual in writing this way or did freedom to act unusual choose me?
I might think that this book has arisen from my choices and intellectual judgement, [20] but my writing choices are severely constrained by my desire for readers. My options and choices start after many billions of previous actions by everyone else, alive and dead.
My knowledge of the subjects in this book relies much more on the work of others and their experience, as passed on in common culture (including language), than any ‘free’ thinking I may have done. I did not choose my starting conditions in life; many of the decisions I feel I have made to this point have been determined by others or by ‘me’ only subconsciously. It is basic honesty to state that; all of my experience, my DNA, the way my brain and mind works, my family and culture and everything that came before me and that is around me is relevant to my actions.
Reality has a plasticity that allows for change to occur between a body and the surrounding environment, whereby what we do impacts what we can do; however, this is still within the normal realms of cause and effect. To ask what life-forms think is happening when they act does not appear to be a very useful question when trying to understand the relative extent and degrees of freedom available to them. In addition, to only admit conscious actions is not justified rationally. Many actions are made subconsciously but are no less intelligent for that.
The only way we could identify something close to free will in the world is to measure the practice of unusual behaviour. You will note that this is still a statistical property within any set of variable things (including height, place of birth etc.), so it does not prove how free any individual life-form is to will what they wish, only the statistical extent of the freedom that might be available to act differently to other life-forms.
To recommend use of statistical measures of unusualness is a marked improvement on the usual discussion about free will – because that free will concept is like asking if there is an anthropomorphic god. It is unhelpful and abstract speculation, a form of intellectual gambling with the guarantee of there being no useful payoff.
“It’s just as if a man were wounded with an arrow thickly smeared with poison … and the man would say, ‘I won’t have this arrow removed until I know whether the man who wounded me was a noble warrior, a priest, a merchant, or a worker.’ He would say, ‘I won’t have this arrow removed until I know the given name and clan name of the man who wounded me … until I know whether he was tall, medium, or short … until I know whether he was dark, ruddy-brown, or golden-colored … until I know his home village, town, or city … until I know whether the bow with which I was wounded was a long bow or a crossbow …’ The man would die and those things would still remain unknown to him.” [21]
(Gautama Buddha)
We must avoid abstract philosophy that fails to ask meaningful and useful questions – the questions and potential answers allowing us to investigate, discover and understand something interesting about this wonderful world we have lucked into. Universal physical laws define the constraints for any behaviour – the potential degrees of freedom of anything within the system. In a world of cause and effect, if there is freedom, all it can really mean is enacting unusual behaviour compared to the other population(s) of life-forms in question within the available degrees of freedom of the system in focus.
Discussion of freedom must focus on describing the ability to make or enact better, worse or simply different choices from the total paths that are available within the relevant field (the phase space or box) in the absence of overpowering inhibiting external pressure. [22]
In this case the box is theoretically the size of the universe, so we have lots of space-time to play with theoretically (because the universe is expanding faster than the speed of light and so an increasingly large volume of the universe will forever be causally disconnected from us even if some of it is observable). We would need to discover worm-hole travel to connect with parts of the universe outside of our future light-cone of 16.5 billion light years (our affectable universe). [23] However, the possible freedom of action to make choices and the extent will never be as great as the theoretical extent. We are always taking actions from a conditioned and local starting point. Decisions are made in a specific space-time and that means they are literally the results of (caused by) all that has come before in that part of the universe.
In some cases, a path to exercise unusual freedom of action will not be practically possible – because it is not consistent with invariant laws or because the relative space-time conditions when making the decision (the starting point for that action) make it just too improbable. Let us return to the problem of free will. We will get to those tricksy humans eventually but let us first consider the freedom of things that are not life-forms.
Does each molecule of H2O in a room filled with steam have freedom?
The answer seems to be a resounding ‘no’. We have no reason to believe that H2O molecules have any capacity to make decisions or enact choice of action. There is no observable evidence that H2O molecules have any ability to choose to arbitrarily change their probable location within a field (in this case, a room).
That means it is entirely deterministic [24] in principle as to where any molecules of H2O will be within the room at any point in time, though in practice the quantity of molecules and size and shape of the room may bring chaos theory into the issue.
“Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general” [25]
Poor time!
We jail it and blame it
We imprison eternity
To try to feel free [26]
Footnotes:
[1] “Be Melting Snow”, 1200s, from Rumi: Selected Poems, 2004 CE, trans. by Coleman Barks.
[2] The Order of Time, 2017.
[3] “Hawk Roosting”, from Lupercal, 1960.
[4] On The Freedom Of The Will, 1839.
[5] Though we should always be careful not to consider the improbable as impossible, given many of our greatest discoveries and inventions and perhaps life itself is very improbable.
[6] “Letter to Dr. Dagobert Runes”, Einstein Archive, 1932.
[7] Ethics, 1667.
[8] Readers that wish to dive down this rabbit hole and understand the history of free will in Western philosophy could start by reading some of the Stanford Encyclopedia of Philosophy entries, such as “Foreknowledge and Free Will” and “History of the Free Will Problem”. For Buddhist interpretations, see, for example, Rick Repetti, “Buddhist Meditation and the Possibility of Free Will”, Science, Religion and Culture, 2015, 2(2): 81–98 and Katie Javanaud, “Reformulating the Buddhist Free Will Problem: Why There can be no Definitive Solution”, Journal of Indian Philosophy, 2018, 46: 773–803.
[9] Wikipedia, “Degrees of freedom (physics and chemistry)”.
[10] Wikipedia, “Ship motions”.
[11] SIX DEGREES OF FREEDOM, DSLAURETTA
[12] Phaidon, “Picasso, Einstein and the fourth dimension”, 2012. Image: Lucas Vieira Barbosa, “Conceptual illustration of both 3D space and time distortion near a mass”, Wikipedia, 2017, CC BY-SA 4.0. The gif illustrates how space compresses and time slows down nearer objects that are larger (in mass; e.g., planets, stars and black holes).
[13] “The Fourth Dimension: Definition in Art History”, 2018.
[14]
[15] NIHAN10, “The Twin Paradox (Part 4 of the series)”, www.properphysics.wordpress.com, 2014, public domain. See also the WolframAlpha relativistic calculator.
[16] Reedsy blog, “How long should a chapter be?”, 2017.
[17] i.e., the result of unusualness may become the cause of more unusualness, which is how we go from single-celled life to 150,000-kg blue whales and primates flying in rockets. Alternatively, it may be unusualness that is not useful in local space-time conditions, in which case it will often not be passed on.
[18] As Nick Drake sang in “Fruit Tree”: “Safe in your place deep in the earth / That’s when they’ll know / What you are really worth”.
[19] Irene Langridge, William Blake: A Study Of His Life And Art Work, 1904.
[20] The average book is almost 90,000 words long: “Frequently Asked Questions – On Getting Published”, megcabot.com. This book has approximately 125,000 words.
[21] accesstoinsight.org, “Cula-Malunkyovada Sutta: The Shorter Instructions to Malunkya”, trans. from the Pali by Thanissaro Bhikkhu, 1998 CE.
[22] See Stephen Cave, “There’s No Such Thing as Free Will”, The Atlantic, June 2016 for a good short, readable article on this complex area of philosophy and science.
[23] Toby Ord, “The Edges of Our Universe”, 2021 CE, arXiv:2104.01191.
[24] Can be measured and forecast.
[25] Wikipedia, “Chaos theory”; see also Wikipedia, “Three-body problem”.
[26] Peter Pink-Howitt, “Time”, unfinished poem. Image: Peter Pink-Howitt, “Poor time!”, algo-art, 2021. As always I am strongly influenced by the spirit of William Blake: “He who binds to himself a joy / Does the winged life destroy / But he who kisses the joy as it flies / Lives in eternity’s sun rise”, The Notebook, c. 1793 CE. Pablo Neruda also gave us the lovely line “Time cannot be cut with your weary scissors”, “Too Many Names”, from Estravagario, 1957–1958, trans. by Anthony Kerrigan in Selected Poems, 199. Also, Henry Thoreau’s: “As if you could kill time without injuring eternity”, Walden, 1854.
This publication is an extract from the book 'Ethics of Life'.
