On Constants

In science, there are many laws that are described mathematically. Some are established from experimentation; others are derived theoretically from other known laws. It has often been pointed out that it is quite remarkable that nature operates in  ways that can be accurately described by mathematical equations.

These equations can be categorized into two classes. Some are purely relational between different measurable and deterministic parameters. The idea that a force exerted by an object is equal to the product of the mass and the acceleration of the object is accurately captured by the simple equation F = ma. Each component of the equation is measurable.

The equations in the other category are just as valid, just as true experimentally, but they are somewhat less simple in that they require the addition of an entity that is not measurable. These additional components are called constants, and they may be determined by experiment or mathematical derivation, but they do not change, and they have no physical reality themselves.

An example is the gas law PV = nRT, which consists of 4 measureable parameters (the pressure, volume, temperature and quantity of a gas) and R, the gas constant. The equation doesn’t work without the constant. This is not a question of units, by the way. You can define the other parameters using any kind of units you wish, but when you do the measurements, you will find that PV = nT is never true.

There are many such equations in chemistry and physics, and many such constants. One of the best known is π, a constant of geometry. The area of a circle is determined by its size; namely, its radius or circumference. Its area is

A = πr2.

But what is π? Where did it come from? We don’t know the answer any more than we know why Plank’s constant (h), so important in atomic theory and quantum mechanics, is what it is. We don’t even ask the question, because we know there are no answers.

The values of the physical constants can only be determined by experimental observation. One of the most important such constants is the speed of light. Establishing that this is a constant required some sophisticated experiments and came as a surprise at the time. Knowing what the value of the constant c is allows us to determine many things, including the relationship between mass and energy, as formulated by Einstein:

E = mc2.

But why does light travel at that speed always, and not faster or slower? That question is not part of science as we understand it. .

For me, the philosophical (not scientific) importance of constants lies in the fact that the reason for their values is not subject to scientific enquiry. The idea that there are things that lie outside of scientific investigation – which used to be assumed when speaking of human-related phenomena such as art, music, love, beauty, and so on – has become controversial. Scientism, the belief that all reality is covered by science, has become popular, especially among militant atheists and extreme reductionists.

But the existence of fundamental physical constants proves scientism to be wrong. We don’t need to invoke the emotions one feels when listening to Beethoven, or the source of the creative genius manifested in poetry or painting, to know this. We don’t need to try to defend the concept of love as being more than an evolutionary adaption to reproductive challenges in early hominids. We can look at science itself, to see its limits quite clearly. We need simply ask why π, h, R, c, etc have the values that they have.

We can also ask what the universe would be like if the constants were different, and the answers are both shocking and troubling. In many cases, changing certain constants, even by a small fraction, would lead to a radically different form of reality, usually one in which (among many other changes) there would be no life possible at all. But unless we admit teleology into science – which is forbidden – this answer allows no real insight into the question of why the constants are what they are.

Still, the question cannot be denied as a question, and the answer cannot be denied as being beyond scientific enquiry. This, by itself, demolishes the principle of scientism, for it establishes the reality of questions that are not subject to scientific analysis. Once we drop the illusion that the scientific method as we know it is the only and all-powerful path toward understanding truth, we can make a great deal of progress in learning what other truths await our grasp.

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6 Responses to On Constants

Okay, now I need to sleep on this. Can there really be such a simple and obvious answer to scientist. It certainly sounds convincing to me at 10:30 at night, and I love how clearly you write it. Thank you!

• Sheila

I am looking forward to your further reflections on this. I am not sure what a rational materialist might answer, but my guess is that they would say that this is irrelevant, it doesnt matter what the constants are, they are what they are, and the why isnt part of science. To which I would answer – Precisely my point.

2. Jon Garvey says:

Sy
The nail you’ve hit on is the idea of science pointing beyond itself (which is slightly different argument, in form, to “fine tuning pointing to God”). Yet it’s still related to issues like information theory, in that we have is the existence of radical contingency – the constants just happen to be what they are – and that’s one of the very things that made science what it is, rather than what much Greek philosophy hoped for, which was entirely rational order.

In other words, the early modern scientists recognised rational order, and interpreted it as God’s law. But they couldn’t just sit down in theoir armchairs and reason to the way things were, because of contingency – which they interpreted as God’s freedom. You had to actually investigate things to see what choices God had made. And the constants are simply observed wihin that part of science, and suggest, “that’s where you’ve seen a choice.”

You can only take things further scientifically either by finding law behind contingency (or fantasizing a multiverse in which there is such a law), or by saying, “Chance did it”, which is a complete non-explanation.

But as a biologist, I guess you’re aware that the same idea that science points beyond itself was developed in evolutionary biology by Alfred Russel Wallace, co-founder of evolution by natural selection, well over a century ago. I reviewed one of his books here: http://potiphar.jongarvey.co.uk/2014/10/13/another-century-late-review/. There’s also a rather beautiful 20minite film on his approach here: https://www.youtube.com/watch?v=hxvAVln6HLI.

However, Wallace is strangely neglected by biologists both atheistic and theistic – witness the paucity of references if you search his name on a Certain Well Known Theistic Evolution Website. I wonder why that would be?

• Jon, you do have a habit of continually enlightening me in fairly dramatic ways. I am pretty sure that I first heard of James Shapiro from you (one of your Hump posts). I had been unaware of Wallace’s views, never read his books, in fact I admit that the only thing I have read of Wallace was some of his communications with Darwin. So this is all quite fascinating. Once again, thanks.

As you know the major and only argument I know if against teleology in the natural world, is that it isnt needed to explain mechanism. That is a very weak scientific argument. In biology there are countless things that arent needed to explain anything, but which still exist. I dont really need to have three umbrellas, or in fact quite so many books, especially those I havent and probably wont ever read. And yet, there they are.

I am currently engaged in an online argument (not at your favorite TE web site, but a different one) about evolutionary psychology. This incredibly unscientific field of materialism that attempts to extrapolate the supposed lack of design in biology even to creatures like us who are (or at least used to be considered) quite good intelligent designers. I have posited that its pretty hard to find an evolutionary “explanation” for consciousness.

I imagine two groups of early humans, one much like us, and the other considerably less self aware, and not terribly interested in anything outside of the standard biological imperatives of survival and reproduction. A herd of animals passes both groups. The less conscious ones grunt, point, grab their spears and go on the hunt using group strategies only slightly more sophisticated than that of wolves, hyenas and other group hunters.

What happens with our ancestors? the really fully conscious humans? Well, when the signal is given, one guy says “Oh listen, why don’t you guys go on without me, Im in the middle of writing a poem and I think Oogetta will really like it. I will catch up later”. Another guy pipes up “Im not going either, I have decided not to kill any more animals. It just isnt right. We can live fine on fish and berries and stuff. I feel sorry for the poor deer”.

A third guy says, “Fine, you two sissies stay here, I will lead the hunt and get all the glory, and Oogetta will be mine when she sees how much meat I bring back, to hell with your stupid poem” and in order to make sure he does indeed get all the glory, he takes some stupid risks and breaks his ankle before any animals can be killed.

So which group is more likely to survive by natural selection?

• Jon Garvey says:

Thanks Sy – as I always say, we aim to please 🙂

Wallace interested me because he was so neglected and dismissed as “good guy gone bad because he went spiritualist”. A bit like with the regular the dismissal of Paley, I find myself asking, “What did he really say – after all, he invented natural selection.” Suddenly you find yet another case of the winners controlling the history.

Another variant on your insightful academic hominid scenario is the rather famous “zombie” situation posed by various philosophers. Here’s your primal hunting scene, and one group of hominids is like us, in hunter-gatherer mode and the other exactly like us except – not conscious and self-aware. Like a super-robot, perhaps, with all the reflexes, logic circuits and so on, but no sense of “I”. Indistinguishable from the outside, though.

Apart from the impossibility of explaining how this mysterious consciousness evolved from DNA changes, why on earth would it be an advantage when the robot will survive the same?