Many social commentators are keen to remind us we live in an uncertain world. They are quick to point to our parlous geopolitical situation with the rising influence of antidemocratic forces in China and Russia; the threat to our health and wellbeing of the Covid epidemic and unpredictable outcomes of climate change. Most would have us believe that such uncertainty is caused by human nature impacting on an essentially stable, predictable physical universe. But that is essentially wrong. The universe, even without human intervention is inherently uncertain.
I was first compelled to think about this strange situation as an undergraduate student studying physics. It was there I encountered Heisenberg’s Uncertainty Theorem. In simple terms the theorem stated that when studying subatomic particles the more certain we could be of the particles position the less certain we could be about its momentum. There was an inbuilt uncertainty such that the more we could accurately assess one parameter the less we knew about the other.
Conventional wisdom would have us believe that we turn to science for certainty, but real scientists understand that such certainty is, and is likely to be always, elusive. As a corollary it is common for people to say something is “scientifically proven”. In the climate debate, for example, the climate catastrophists are quick to tell us “the science is settled”. But this is, in itself, almost an oxymoron because the very foundation of science is to keep the door open to doubt.
Karl Popper was perhaps the most influential philosopher of science in the twentieth century. He had a wide influence on actually defining science. He argued that scientific theories are distinguished from non-scientific theories because the former make testable claims that future observations might reveal to be false. This is known as Popper’s Falsification Theory. True science therefore emanates from a boldness to take a risk of being wrong. True scientists, consequently, actively seek out data that might prove scientific theories wrong. Unfortunately, being human, many working in science seek out data that confirms what they want to believe rather than objectively test those theories they have a vested interest in. (Thomas S Kuhn’s marvellous book The Structure of Scientific Revolutions gives some great historical evidence of this tendency to lock in scientific beliefs in the face of countervailing evidence.)
The most common misunderstanding about science is that scientists seek and find truth. They don’t. By and large they make and test models. Kepler provided a model that more accurately described the motion of the planets than his predecessors. His predictions were quite accurate. But the laws of planetary motion were subsequently improved by Newton and then later on by Einstein.
Building models is very different from proclaiming truths. It is a never ending process of discovery and refinement. Uncertainty is intrinsic to the process of finding out what you don’t know, not a weakness to avoid.
Uncertainty about the world is not only a feature of science but it is also a feature of mathematics.
Twenty years after becoming acquainted with Heisenberg’s famous theorem, I happened across a fabulous, imaginative work by the American scholar and polymath, Douglas Hofstadter, for which he won the Pulitzer Prize for non-fiction. The book was titled Gödel, Escher, Bach: an Eternal Golden Braid. In it he explored common themes in the lives and works of logician Kurt Gödel, artist M C Esher and composer Johann Sebastian Bach.
From this rather esoteric source, I first learnt about Gödel’s Incompleteness Theorem. Hofstadter’s literal translation of Gödel’s mathematically expressed proposition went something like this:
All complete axiomatic formulations of number theory contain undecidable propositions.
Hofstadter explained that according to Gödel if we wanted a complete theory some propositions would be unprovable. Or if we wanted to ensure all propositions outlined could be proved, then the theory, of necessity, could not be all encompassing. Just as in Physics in the Uncertainty Theory we could either know the position but not the momentum of a particle, in Mathematics we have to choose between completeness and provability.
Now, when I was younger I always understood that humans never had the capacity to fully understand the universe. At that time I thought our limitation was one of capacity. That is, how was it possible for something that was merely a minuscule part of the universe (a human brain)to ever have the capacity to understand the whole shebang!
But the findings I have reported above point to something much deeper. There is something inherent in the fundamental nature of the universe (cosmologist Paul Davies might have attributed it metaphorically to The Mind of God) that renders it somehow inscrutable to the full understanding of humans.
We have subsequently come to understand (contrary to conventional wisdom) that uncertainty is a central component of what make science successful. Being able to quantify uncertainty and incorporate it into scientific models is what makes science quantitative rather than qualitative. Indeed no number, no measurement, no observation in science is exact.
Physicist, Lawrence Krauss has written:
Quoting numbers without attaching an uncertainty to them implies that they have, in essence, no meaning.
The notion of uncertainty is perhaps the least well understood concept in science. Paradoxically, in the public eye, uncertainty is often portrayed as a bad thing implying a lack of rigour and predictability.
In quantum physics uncertainty predominates. Nothing is assumed absolutely determinate but is assigned a probability.
Making sense of anything means making models that can predict outcomes and accommodate observations. At any level of complexity those models don’t deal with certainties but with probabilities. After some consideration we can’t avoid the conclusion that the world is not determinate but must be described in terms of probabilities, i.e. that it is inherently uncertain.
Concomitant with our need to understand the world through models are uncertainties provided by the limitations of models themselves.
Alfred Korzybski the founder of the field of knowledge known as general semantics reminded us of those limitations with his famous quote:
The map is not the territory.
He reminds us that our perception of reality is not reality itself but our own version of it, or our own “map”.
We know that all such models (“maps”) are limited and as a result their predictions will always have room for error. In the physical world, the only way to know tomorrow’s weather in detail is to wait twenty four hours and see. The universe is computing tomorrow’s weather as rapidly and efficiently as possible; any smaller model is inaccurate, and the smallest error can be amplified to large effects.
Mathematician, Rudy Rucker, has written:
It’s a waste of time to chase the pipe dream of a magical tiny theory that allows us to make quick and detailed calculations about the future. We can’t predict and we can’t control. To accept this can be a source of liberation and inner peace. We’re part of the unfolding world, surfing the chaotic waves.
But human beings crave certainty. Our brains revolt at the idea of randomness. We have evolved as a species to become exquisite pattern finders. Our minds automatically try to place data in a framework that allows us to make sense of our observations and use them to predict and understand events.
We resort to various subterfuges to help us explain unexplainable events. Popular sentiment would have us believe that we get “runs of luck”, or that bad things happen in threes. Others turn to Astrology to help explain what are normal, random events.
But many events are not fully predictable or explicable. Paradoxically when we aggregate large numbers of such events we unearth a surprising predictability. Charles Seife, science journalist and author of The Dark Arts of Mathematical Deception writes:
The law of large numbers is a mathematical theorem that dictates that repeated independent random events converge with pinpoint accuracy upon a predictable average behaviour. Another powerful mathematical tool, the central limit theorem, tells you exactly how far off that average a given collection of events is likely to be. With these tools, no matter how chaotic, how strange a random behaviour might be in the short run, we can turn that behaviour into stable, accurate predictions in the long run.
The rules of randomness are so powerful that they have given physics some of its most sacrosanct and immutable laws. Though the atoms in a container full of gas are moving at random, their collective behaviour is described by a simple set of deterministic equations. Even the laws of thermodynamics derive their power from the predictability of large numbers of random events. They are indisputable only because the rules of randomness are so absolute.
So what is the overall lesson here? The universe is under-laid with uncertainty. Essentially, as a result, even those scientific theories that provide the best maps of the world for us, can never be definitively proven. They may however be disproven. We are given some underlying support in interpreting this indefinite world by the use of probability theory. But in essence it would appear that the laws underpinning both physics and mathematics have contrived to create a world that will always be beyond our complete understanding.
Congratulations on a very interesting essay. The underlying uncertainty in the world is something that most thoughtful engineers and scientists know about and struggle with. I was not aware of the Hofstadter work and I will chase it up – it looks interesting. What we do know is that by testing and verification of our models of the world, we can, with some confidence, navigate our way through life. Even so, the theories are just conceits that seem to work in our limited field of view. Structural engineering theory and thermodynamics. These bodies of science help us design structures that don’t fall down and power stations that keep the lights on. But they are only theories, even if they have been verified many times. (I have an interesting book on the history of the theory of structural engineering and shows well the struggles and blind alleys engineers followed to come to now what is an accepted theory of structures).
It is a pity that the opponents of climate science don’t apply the same principles of objective observation, modelling and testing to help us navigate a safe path through this aspect of life. All serious climate scientists would acknowledge the uncertainty in the field, but patterns have emerged through careful observation that strongly suggest that increasing carbon levels in the atmosphere are significantly changing the earth’s climate and will do so into the future. These observations are backed up by credible models for how this can occur and there has been extensive verification of these models. Indeed, some scary predictions on the future of the earth’s climate have been made on the basis of these models. Only predictions and only models, but scary nonetheless. Is the “science settled”? Does that matter? The markers are there. We are fools if we don’t pay attention.
Thank you Richard for your comment. But you know I must disagree with respect to climate change. I have stated on many occasions that climate change is happening. However I don’t agree with the catastrophic predictions of the climate change zealots. Time and again their prognostications, seemingly informed by their climate change models, have been grossly overstated. Modelling climate (as I have alluded) must be one of the most challenging enterprises for any scientist or would be scientist. I have seen no convincing evidence that such models are good enough to base government policy on.
An excellent essay, many thanks.
Certainty is indeed always an illusion but it is a very comfortable one and craved by humans to counter the realities of life.
As to science, which in the modern age has become a religion and the sort of religion, fundamentalist, it set out to destroy, we fail to appreciate its limitations, which, by its nature, like uncertainty, are hardwired into the system of enquiry which we call science.
Particularly in the modern age where it has committed itself to a belief, a delusional belief, that all can be reduced to the material. Which means, a mechanical approach to life and everything in this world which can only fail and deceive in those realms beyond the manmade.
Science can only know – and that does not mean understand – what it can measure.
Logic then says, what it can measure depends on the ability within the technological development available at the time to measure, and, a desire to measure by someone, and, a desire for someone to pay for the measuring, and a desire by someone to release the data once available i.e. to find the measuring results profitable in some way.
In short, there is much which modern science cannot measure, because it cannot be reduced to the material and mechanical; much that science has no wish to measure; much that no-one will pay to measure and much which once measured reveals data no-one wishes to release.
The modern scientific system of enquiry is indeed highly skilled in the realms of machines and mechanics, but distorted and dangerous in terms of the natural world, which it cannot understand because of its belief systems.
Physics, as suggested in the article, is the one area of science which offers hope for greater wisdom in science and its creation, conventional or allopathic medicine. Without that, science and allopathic medicine represent the greatest danger to people and planet at this point in history.
When hubris walks hand in hand with ignorance, ego and profits, as it does in the powerful scientific system of enquiry, we ‘soar’ to ungainly heights where it is not just wings which melt, but people and planet.
Before the age of materialist reductionist science, which has developed over recent centuries, scientists at least had spiritual/religious beliefs which could counsel humility and wisdom. No doubt there are some scientists still who are subject to such caution but the scientific system in general is not, and, having sold its soul long ago to Government and corporate agendas, simply cannot be trusted.
The greatest uncertainty principle is where such a system may take us if we do not stand up and hold it accountable.
Ros, you are right to warn against a reliance on rational determinism. When I published my little book Augustus Finds Serenity, I wrote the following:
In the introduction to “Augustus Finds Serenity” I outlined the reason why I had sought to use the medium of metaphor and parable to outline the concepts that I thought were useful in helping people live more fulfilled lives.
I started my career as an engineer and the principal tools I used were built on mathematics and physics. Rational, quantitative science has delivered many benefits to the world. Yet there is still much of what is important to me that is not illuminated by scientific method.
Why is this so?
In some ways we are still locked in to the “Age of Reason” prompted by the discoveries of Newton and Descartes. The tremendous advances of western societies initiated by scientific and mathematical discoveries in the seventeenth century led many to believe that the world could only be understood by the application of such rationalism. However by the twentieth century, many (including some very influential scientists) were beginning to doubt the efficacy of this approach in coming to grips with the world.
In most pre-modern cultures there were two recognised ways of thinking, speaking and acquiring knowledge. The Greeks called them mythos and logos.
Logos (reason) was essential in engaging the material world. It was needed in ordering our societies, manufacturing our produce and dealing with the physical environment.
Mythos (myth) helped us to come to a more informed understanding of human nature and our place in the world. The stories of gods and heroes shared over generations the practical knowledge of dealing with the human condition. Whether it was Jason seeking the Golden Fleece or Hercules enduring his Twelve Labours, people understood that these weren’t stories of real people but pointers to how we might live our lives.
These two ways of knowing are complementary. We rely on both to help us come to grips with the human predicament. If we accept logos but reject mythos we will be logical, competent people but lacking in spirituality and a deeper understanding of human nature. If we reject logos and accept only mythos we might live a rich internal life but will be grossly ineffective in dealing with the world around us.
Darryl Reanney, in his lovely little book “The Music of the Mind” quotes the famous lines from TS Eliot’s “Little Gidding”.
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
Reanney points out ‘that most people react to this poem in a special way; they sense that it is true without being able to see why it is true’ Mythos can tap well-springs of knowing that logos can not and vice versa.
As well, much of the wisdom that we arrive at through the means of mythos is also paradoxical when viewed through the lens of logos.
For example:
He who loses his life shall find it.
The best way to learn something is to teach it.
All I give to another I give to myself
Reanney called the realisations we get from such a process “another way of knowing”.
Just then, as we hand down the realisations we get from logos in formulae, theorems and equations, the realisations that we get from mythos we hand down as parables, metaphors and stories. In this way mythos underpins our spirituality, and also indeed, in many ways, our understanding of human psychology.
What we must guard against in this process of course, is not to take the stories as literal. We need to see them as reflecting ‘truths’ but not being true in a factual way. This is the trap of fundamentalism. Indeed a Buddhist sage once pointed out, ‘When the sage points to the moon, the fool sees the finger!’
This then is the reason for the use of parables in my little book. The world’s wisdom traditions have all used the same vehicle. I trust that these little stories will resonate with you, and connect you with some realisations that are accessed by “another way of knowing”!
You are a legend. Just saying
Well Matt, in the sense that legends are built on fantastical interpretations of the past, I might well be a legend – but I don’t think so!
Ted
Your comment that “the most common misunderstanding about science is that scientists seek and find truth. They don’t. By and large they make and test models”. In my own profession (HR) I rarely see evidence of practitioners ‘making and testing models’. In fact the reverse seems to apply.
Take the way we manager performance in the workplace. It was reported in a 1976 article by Harry Levinson published in the Harvard Business Review that the then systems of performance appraisal do not serve any useful function. Yet the process has not substantially changed in past 46 years.
Perhaps your comment that “most would have us believe that such uncertainty is caused by human nature impacting on an essentially stable, predictable physical universe.” is true.
I’ll have to test that theory 🙂
Mark, as you know I have dabbled more than a little into the arcane field of HR. My impression is that HR is about as scientific as making prognostications about the future by examining chicken entrails!
Reading your essay was informative and interesting as usual Ted. I’m left thinking that you’ve provided great incentive for us to live in the now. And you know better than most that there’s no probability or randomness when we choose to see reality from our supra-personal mind-the mind of light, peace and love!
Is that a cop out?
Well that’s a challenging question, Edward.
To begin with we have no choice but to live in the “now” because that’s all there is in our consciousness. We might have memories but they are reconstructions of our past that we experience now. We might have perceptions of our futures but they too are constructions of our minds that we can only experience now. But when we understand that this universe is a manifestation of the collective consciousness of which we can only experience our own little segment, we know that there must of necessity be much beyond our comprehension. The collective consciousness, however, is benign and no matter that we sometimes can’t understand and interpret things differently, we should feel assured, even though sometimes it is not obvious, that “All Is Well!”