Saturday, September 03, 2011

Science, Sorites and Society.

Just so that you know, I'm a mathematician (not a proper one, though) and not a scientist. I'm not really a philosopher either but I certainly know I'm doing myself a disservice by trying to label myself as this thing called "mathematician". That's a very typical practice of society - everything has to be packaged in nice little boxes in order for things to make sense.

I do actually love Science very much: I wish I were better at physics not least because it inspires some truly fascinating mathematics which in turn inspires some rather fascinating experiments. The Hadron Collider experiments and the attempts to find the elusive Higgs Boson are true nail-biters. The energy window for finding the Boson is shrinking fast. Can we find it, or is our understanding of physics flawed?

If we do find it, then this bodes very well for the theory which we have, if not it means some exciting new challenges upon which will stretch our understanding of the facts that we have.

Likewise, I find the idea of Evolution not only fascinating but indeed compelling. I've studied many an evolution equation, both discrete and continuous. Langton's ant is also a fascinating example of how a simple rule can bring about both unpredictable and predictable behaviour. Conway's game of life certainly does point to some deeper ideas as to how Evolution can bring up the creatures we see around us today. I've always thought that if God had wanted to create something then I couldn't think of a better way for Him to do it than have us evolve as we have done. It is absolutely fascinating.

But it is just a theory.

Now, we reach a rather important problem with the way that Science is being done these days, and the status which it is given (or perhaps rather that the Scientists believe that it has). If one, for example, doubts that Evolution is true, then one is pilloried by the established scientists. Some scientists can become very much like their own caricature of the Church in opposing freedom of thought. This is despite the fact that, if a deterministic theory of the universe is correct, then given the same laws and the knowledge of the states of every particle in the universe, there is no way of knowing whether the Universe actually began with the beginning of this blog entry. It's actually a very simple extension of the theory of ordinary differential equations. Is it true? I don't know. I can't know. I can try to find out, but how?

And that's the point.

Science, these days, has fallen into a fashion of reductionism, the idea of reducing things to component parts so that we can study the component parts and make inferences as to how they fit together to make up the whole. This reminds me somewhat of Sorites Paradox: if we remove the grains of sand one by one from a sand heap, at which point does it cease to be a heap? However, it's not quite fair to accuse Science of blindly reiterating this paradox. Scientists will try to deduce properties of the heap from the grains of sand. One then has to answer for oneself how one can deduce the "heapiness" of the heap from the grains of sand.

What about a beach? Can one deduce global properties of a beach from all the grains of sand?

Further, if the law of Gravity as we understand in this little locale of the Universe is indeed a universal law (and how do we know this?) then every individual particle must influence the motion of every other individual particle. Given that there are (from what I remember of the most recent physical theories) 10^79 (i.e. 1 followed by 79 zeroes) protons (I may be wrong) in the universe, that surely makes it a bit tricky to get a theory of everything.

In mathematical mechanics, we make assumptions and simplifications - A uniform ladder of mass m kg is resting on rough ground against a smooth wall...etc - these words "uniform" "smooth" "rough" are all simplifications which one makes in order to make some, often beautifully, accurate predictions. We certainly got to the Moon and back using effectively Newtonian Mechanics. However, these assumptions break down. One could use statistical mechanics, but then one gets into likelihoods and probabilities. Scientific Certainty comes with a given margin of error. If it doesn't, something's wrong.

But such is life. We seem often to look for the truth by breaking things to bits. Further to what I said in Horror and Holiness, we have not only stripped the clothes off of the nubile virgin, but also her skin and her flesh to see what makes her tick, and in so doing we destroy not only her dignity, then her beauty, but her humanity as well. This is not to say that we shouldn't be curious about our beautiful universe, but rather that we should not expect Science, or even Philosophy to have definite answers. There's a definite and horrible tragedy there that doesn't seem in any way romantic.

Being religious, I get accused of obfuscating the truth with mystery and meaningless ritual. I find that unfair. One can attempt to probe mystery and then uncover the answer that one was searching for. A materialist will carefully dissect a consecrated wafer to find God, but will only find bits of consecrated wafer or atoms of consecrated wafer or (if he is really lucky) a Higgs Boson within the consecrated wafer, in which case the papers will have a field-day ("God particle found in Wafer"). But a materialist will only find material because material will be all that they will look for. A scientist who happens to be a Christian may also tackle the same experiment, though I doubt that she would be very happy to do so, but she will find exactly the same as a materialist.

However, the ordinary Christian at Mass will receive a wafer and in so doing will find God, and that Christian will need no specialist knowledge in order to do so except their faith. Of course, the argument goes up. "We can't argue with you religious types. Everything comes back down to Faith with you." That's true of materialists too and their faith that everything that is is material.

This reductionism and Sorites principle is also endemic in Religion. I see it very much evidenced in Anglicanism where things seem to split and split and split ever more finely. It's anti-catholic in its scope and its a scandal, particularly in the Continuum, that there should exist shibboleths to categorise one Anglican from another. Those who have become "former Anglicans" have now rent the Traditional Anglican Communion. This may or may not have been necessary, but it has rocked the identity of the TAC in this deconstruction.

I find myself becoming very doubtful these days with what I'm being presented as certainties. The certainties of my Faith are contingent on the fact that I have Faith, and even then I believe in a God who will surprise me, maybe even scandalise me. That's not to say that I believe that He will contradict Himself - I believe Him to be faithful to me even if I am far from faithful to Him.

I recently learned that a priest before Mass lays out his maniple, stole and cincture in an IHS and I saw in this how a priest takes great care in ensuring that he suffuses himself in Christ. All this is contingent on his faith and the faith that he wants to communicate to his parishioners. I find sacred action and holy ritual to be affirming, though I cannot always find an adequate reason why I should find these things affirming. I suspect it is because it helps me to become suffused in a God whose existence is utterly inexpressible. The theory is beautiful but inadequate, the search meaningful but incomplete, the logic infallible but infinitely far from exhaustive in its search for Truth, the ideas worthy to be expressed but too restrictive.

Catholicism is only truly evidenced in Christ who can be the only uniting principle in opposition to the reductionism that Christianity has contracted from an apparently materialist society. Catholic, Protestant and Anglican are united in their belief in Him and, as they search for Him, honestly and in the greatest childlike humility. This is surely the only way to guard against some truly demonic attacks against the integrity of the Church.

For the Christian, life must be suffused with Christ so that our lives do not fall to bits, into component parts where the meaning of life is lost. I saw something of that while I was studying for my doctorate in four-dimensional geometry. As a result, I had no option to preface my thesis with this (especially with the reference to four dimensions).

That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, May be able to comprehend with all saints what is the breadth, and length, and depth, and height; And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God. Now unto him that is able to do exceeding abundantly above all that we ask or think, according to the power that worketh in us, Unto him be glory in the church by Christ Jesus throughout all ages, world without end. Amen. (Ephesians iii.20)


edpacht1 said...

I’ve read, reread, and admired this profound piece, have wanted to comment on it, and have found it very difficult to do so. I need to do a small amount of nitpicking before going on:

“… Can we find it, or is our understanding of physics flawed?”

If it exists, perhaps we can find it, but even if we do, it is axiomatic that our understanding of physics is flawed. That is a central principle of truly scientific physics, Einstein found the physics of Newton to be flawed, or at least woefully inadequate, and demonstrated this to be so. Likewise, quantum physics is directing serious questions at the work of Einstein. There is a powerful distinction between science and scientism. Scientism is fond of declaring that Science says, of treating Science as a body of dogma.. It isn’t. It doesn’t say. Science asks. The scientific method is an elegant way of asking questions, whose first premise is that all statements are to be questioned, the best statements to be regarded, perhaps, as provisionally true, but never as beyond question. If there is one certainty in scientific inquiry it is that today’s answers will not prove to be entirely accurate and will prove insufficient in the light of further inquiry. I am a fan of science, but find it important to treat all its findings, even the most intuitive, with a good measure of skepticism.

“… than have us evolve as we have done.”

A little logical incoherence here, as you elsewhere admit that one may reasonably question evolution (as the spirit of scientific inquiry insists one must). It might have been better if that had read “… as we seem to have done.”

Those things out of the way, I find myself in agreement with what you say, and wishing I’d said it as you have. In many ways there’s a striking similarity between Science and Theology. Both are far more accurately seen as methods of inquiry that as bodies of dogmatic authority. Science begins with observation, always remembering that the observer may have observed inaccurately. Theology begins with Revelation, and must remember that the hearer has not necessarily heard properly. Both are concerned with probing into the unknown. Both are capable of coming to a partial understanding of what is found in that probing. Both are, by very definition, seriously flawed, as, for both, there is far more unknown than is known. Honest scientists, including atheists like Carl Sagen, and Stephen Hawking (in his “Brief History of Time”) are quite open in declaring, with some sort of awe, that they face mystery, as are honest theologians. There’s even a strong similarity in that both disciplines are abused in similar ways, theology by fundamentalism, and science by scientism. In both disciplines there is much that has to be accepted as fact (at least until shown otherwise), and in both disciplines there is much effort at explaining those ‘facts’ – but the explanations must always be seen as provisional and inadequate.

Warwickensis said...

A little logical incoherence here, as you elsewhere admit that one may reasonably question evolution (as the spirit of scientific inquiry insists one must). It might have been better if that had read “… as we seem to have done.”

Point taken, though there are plenty of alternative theories of evolution which are not necessarily Darwinian. We have all evolved in a sense because our very selves have been the product of subtle changes from how we interact, indeed our very relationship with God is evolving.

I think the point that I ought to be getting at is that while it's obvious that there is an evolution, namely how I got to be sitting here typing this and how you got there to be reading this, it may not be the evolution we think, but if we hold fast to the idea of a Creator God, then the true nature of our evolution will be beautiful and elegant.

JamesIII said...

Like Ed, I wanted a bit of time, not to clarify my thinking as much as to formulate how I presented my thoughts.

Scripture presents us with a dichotomy of sorts; on one hand we are “a little lower than the angels” and on the other, “dust thou art and unto dust...”. Our problem comes with thinking of ourselves as the pinnacle of creation. That stance produces a skewed perspective of our wonderful place in God's cosmos. We have only to look at discoveries made in the last 50 years, a pebble on the beach of time, to know that our knowledge is limited but ever evolving. Life has been found dwelling in conditions that were considered impossible for survival and we have gazed into distances that were considered voids, discovering that the universe continues beyond our wildest imaginings.

The catechism presents us with a question at the very beginning; Why did God make us? The expected response is “To know Him, to love Him, and to serve Him”. Each portion of that answer leaves a lot of “wiggle-room” as far as methodology is concerned. Science and our faith were meant to walk hand-in-hand when it comes to the first answer. Contrary to popular belief, the church has practiced that axiomatic stance better than most of the laity have. Our faith reveals “what He did” and science helps us understand “how He did it”. Our limited perspective often causes us to deny the obvious when faced with an answer that we think is counter to our flawed perception of holy writ.

The story in Genesis dealing with Eden is far older than our compilation of the Old Testament and has a common theme that weaves through many religions. Our penchant for thinking as we do; causes us to mistakenly believe that each discovery we make, each revelation, is a destination rather than another branch in the path. We've only scratched the surface of both our faith and our science. Our great mistake lies in thinking that our advancing sciences bring us closer to “being God” than to knowing Him.

I tend to agree with Albert Einstein that there is no conflict between faith and science except the one that we create in our arrogance. In the end, scientists and theologians will point at each other and say, “see... I told you so”.

Warwickensis said...

I tend to agree with Albert Einstein that there is no conflict between faith and science except the one that we create in our arrogance. In the end, scientists and theologians will point at each other and say, “see... I told you so”.

I like thos very much. What will probably be more likely is that scientists and theologians will say to each other, "Wow, we weren't even close!"

edpacht1 said...

Our great mistake lies in thinking that our advancing sciences bring us closer to “being God” than to knowing Him.

I like that, James. That God created humanity with an inquiring mind seems to tell me that God intended that humanity should be seeking know;ledge. We have an amazing capacity to learn and mental tools with which to seek to learn. The Tree of the knowledge of good and evil seems to represent both an avoidance of the hard work of actually learning and an expectation of reaching an end point at which learning would no longer be necessary. This constitutes both a denial of man's own nature and a desire to be as God who does not need to learn, to reach, as you put it, some kind of end point. To a finite being there is no end point in the approach to infinity. There is always much to learn, and we are intended to learn as much as we can, but also to remember that we know very little indeed.

Yes, I am made "in the image of God", but only an image. That there is something godlike about me surely does not make me God, and the pride of wishing that I were mars the image dreadfully. But I do wish to know Him, and to have restored to me as much of the fullness of His image as can be borne in my oh-so-limited being.