I once had a strange discussion with the author of a so-called “New Age” book. He had some disparaging things to say about science and mathematics. To illustrate a point he maintained that even the universal constant pi could not be accurately determined. He, of course was misled. Because pi was unable to be defined as a proper fraction or in a finite number of decimal places in decimal notation he seemed to think it was therefore undefinable. Now of course there is a formula defining pi and as a result we are able to define it to whatever degree of accuracy we desire but not absolutely in a finite number of decimal places. Of course that is not to say in some other number system (other than one whose base is 10) it might well be able to be defined as a proper fraction. Who knows if we tried a number system with base 11, 13, 29, or indeed 356793 it well might be possible to express that ubiquitous constant as a proper fraction. Nevertheless we know exactly what pi is and we can express it to whatever degree of accuracy we desire in decimal notation. So we know with certainty the value of pi but our conventional mathematics makes it difficult to express that value.
Now the reason I raise this question is because I have been thinking about our ambiguous notions about certainty and uncertainty.
In mathematics, as discussed above, there are things we can be certain about. This is hardly ever the case in science. We are often misled by the claims that “it has been scientifically proven” that ……………
(Of course even in mathematics we are faced with uncertainty. I refer my readers to the Gödel Incompleteness Theorem. The philosopher mathematician Douglas Hofstadter has attempted to translate into words what Kurt Gödel discovered. He describes it thus: – ‘All consistent axiomatic formulations of number theory contain undecidable propositions’. In essence if number theory is complete it must contain undecideable propositions. If it is to be consistent it must necessarily be incomplete!).
But in science this position was put most forcefully by the eminent philosopher of science, Karl Popper. As he pointed out, no matter how many experimental results supported a scientific hypothesis it was never proven. On the other hand one contrary result would be sufficient to disprove it. Hence whilst mounting evidence that supported a particular theory might give us some confidence that the theory was true, we must be alert to the fact that one contrary result could dismantle it.
Of course rational consideration of the evidence is often prevented by the world-view of the observer. This was highlighted by Thomas S Kuhn in his seminal work The Structure of Scientific Revolutions. Kuhn showed that even reputable scientists tended to discard data that did not support their favoured hypotheses and emphasised the data that did.
This self-serving irrational behaviour pervades many topical debates. Let’s look at some examples.
Let us begin with the issue of global warming. Climate science is indeed very complex and, I would suspect many experts would concede, not well-understood. As a result we have a very polarised debate between the catastrophists and the deniers. Having been personally involved in the issue through my interests in renewable energy and a broad concern for the natural environment, it seems to me that neither side has amassed enough evidence to convincingly make their respective cases. We are therefore caught in a cleft stick. If the catastrophists are right and we don’t act soon we condemn future generations to deal with the unfortunate outcomes of our ignorance and selfish materialistic pursuits. If the deniers are right we could sacrifice our standard of living in trying to mitigate an imaginary problem. Faced with this uncertainty many suggest that we should take a precautionary position. And maybe we should. But what such a position might be will be just as controversial as the initial debate. But to go back to my over-riding thesis what action we should take, or indeed if we should take any action at all, is difficult to know because of the uncertainty of the science. In terms of evidence available this is perhaps the most difficult issue of those I want to put before you. Although the extremists in either the catastrophist or denier group would of course dispute this.
My next example is medicine.
Alternative medicine is a burgeoning industry. It is largely marketed on the basis of unsubstantiated claims and anecdotal evidence. On the other hand conventional medicine is substantially supported by reputable research and close scientific scrutiny. However we would be unwise to suggest that conventional medicine is always right and there is often ongoing controversy and debate regarding the use of particular drugs and treatment strategies. But as a body of knowledge, conventional medicine is far better supported by confirming research and experiential evidence than alternative medicine. So what about alternative medicine – where does it stand in the spectrum of certainty? Here I think we need to apply great (or perhaps more appropriately, greater) caution. Without the same rigorous examination that is applied to conventional medicine, we are entitled to be more sceptical about the claims regarding the efficacy of alternative medicine. It is probably true that some of it works, for some people, in some circumstances. But most of us know for example, of cancer sufferers and others for whom conventional medicine has not been able to offer remedies with reasonable chance of success and who have therefore, in desperation, turned to bizarre alternative treatments only to have been gravely disappointed. Just as in my previous example regarding climate change and global warming, we could not say that alternative medicine has been entirely discounted. But we must admit on the evidence, that we would be foolish to have the same confidence in alternative medicine as we do for conventional medicine. No doubt those of my readers who have a large psychic investment in alternative medicine will dispute this (thus confirming the findings of Kuhn!).
As you might have perceived, my examples are moving from a position of less certainty to a position of comparatively greater certainty. It seems to me that we are still in an ambivalent debate about climate change. But with regard to medicine I am willing to say that we are entitled to have more confidence in conventional medicine than alternative medicine. In saying this, I am prepared to concede that alternative medicine may offer solutions to some health issues in some circumstances.
Perhaps two areas that stand out in my mind where the evidence of the efficacy of conventional medicine seems unfairly under question are:
- Fluoridation of potable water, and
- Vaccination of children.
My final example exemplifying the tension between certainty and uncertainty is the debate regarding creationism and evolution.
It is a source of some amazement to me that some 60% of American citizens believe that the universe was created in recent historical times by the Old Testament God in the very manner it is described in the book of Genesis.
The essentials of contemporary evolutionary theory are robust. The theory is supported by huge amounts of empirical evidence.
So what have we got to advance the case of creationism in the face of this overwhelming evidence to the contrary?
The only defence of creationism relies on a literal interpretation of the Old Testament.
One would think that this was an unequal contest. There is now a huge body of knowledge supporting the theory of evolution. There is a paucity of evidence to support the literal truth of the Old Testament.
But of course we are again confronted with the dilemma that Kuhn demonstrated. When we have a vested interest in a belief system it is almost impossible for us to assimilate any evidence that might require us to question that belief system. If I have made a large psychic investment in being a Christian (or perhaps more reasonably, a traditional, fundamentalist Christian) it is unlikely that I can give credence to those things that question my belief.
Using Popper’s “falsifiability” criteria we cannot say for certain that the Theory of Evolution is definitely true. But we can say it is well supported by the evidence. Similarly we could say that we cannot disprove creationism. But we can say that it is not supported by the evidence.
Science then is not amenable to certainty. We see in certain branches of science, for example Quantum Theory, that certainty is not even attempted. What we try to do is assign certain probabilities to various projected outcomes.
However, it seems to me that when it comes to public policy or indeed what we should teach our children, we need to be careful to ensure we have strong supporting evidence. I can, for example, see no compelling case why creationism should be taught in our schools (as it is in the USA) when the evidentiary support is virtually non-existent. Similarly I think it reasonable that we should be somewhat sceptical about alternative medicine.
The physicist, Lawrence Krauss (director of Origins Project, Arizona State University) writes:
“ ……uncertainty is a central component of what makes science successful. Being able to quantify uncertainty and incorporate it into models is what makes science quantitative rather than qualitative. Indeed no number, no measurement, no observation in science is exact. Quoting numbers without attaching an uncertainty to them implies that they have, in essence, no meaning.”