Last week the director of education for the UK Royal Society, Professor Michael Reiss, resigned after he was criticized for being ambiguous about the correct response to creationism, and to religion in general, if brought up by a pupil in a high-school science lesson. Perhaps his words touched upon a raw nerve in the scientific community or perhaps the point he wanted to make was just too subtle to be understood by the media in these troubled times.
Professor Reiss, who is also a Church of England minister, apparently suggested that in his experience it was more effective in such a situation to discuss creationism in the science class if only to show that evolution fits the facts better. Critics said that he should have had the teacher simply refer the pupil to religious education classes as creationism is not a scientific theory at all. Professor Reiss himself has stated that creationism is a `world view’ and that you have to discuss it to get through to pupils with such beliefs.
Was it over-reaction? A defender of Professor Reiss’ position on the BBC radio I heard argued that the creation myth was a metaphor, not to be taken literally. Hence scientists should not be so touchy. A critic could argue, however that if that were the case then that is exactly why the teacher should indeed to refer the pupil to poetry, drama or religious studies where parables as metaphor are appropriate. The problem is that as soon as you bring it into a science lesson you risk confusing science and parable. This is not helped by creationists who insist that the creation myth is not a parable but true and should at the very least be taught as a valid theory alongside evolution. This then makes a mockery of science.
Science, after all, is supposed to be searching for absolute truths verifiable (in principle) by anybody who cares to. It is supposed to uncover Nature using mathematical or logical tools, of course to formulate theories and hypotheses but to treat these with deep skepticism. Faith is anathema to science. Please understand me. Faith, a moral compass, spiritual values, all have a vital role to play even in the life of a scientist. When you are stuck on a problem you have to put forth a hypothesis. You have to have some faith in it to take it seriously enough to explore. You may even have a ‘vision’ which is a kind of faith that guides your life’s work. But that’s all about the human process of research. The actual science is supposed to be based on fact and logic independently of how you got there, to the maximum extent possible. So faith is also the bit you are spending your life trying to squeeze out of the end product. It’s a complex dynamic which obviously can’t be grasped by pupils who have not yet understood what science itself is. They have to first learn what science is pure and simple and this is what confusing the issue so early on would deny them. This, in my opinion, is why many scientists are so angry about the no doubt well-meaning but highly dangerous position of the professor and other science educators with similar views.
Let’s see how these issues play out at the modern cutting edge of the most hard-core of sciences, fundamental physics. This is a vast and enormously successful edifice of knowledge which nevertheless has through the hard work of generations of physicists been boiled down to a mere handful of fundamental equations and beautifully simple ideas through which, in principle, we understand the physical world. There is still a certain amount of work to be done in particle physics. There is still a big problem which stumped Einstein but which physicists are now very optimistic about, namely the unification of quantum theory and gravity. But the consensus is that everything is going well and these are truly the best of times …
… but lets look carefully.
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The fallacy in this argument is that to solve an extremal problem you ate trying to find the
best, locally or globally, so have to explore all possibilities. Darwinism does not say that
all possible mutations have been explored either globally or locally, only that then organism evolves to a little bit better (as judged at the time). The calculation on a computer in terms of minimization problem would be to move down the slope, that is all, and takes hardly any time at all on a computer. You have also missed the point of parallel processing.
There are too many interesting comments on this post for me to reply to!
So just to reply to the purely technical one; David asked about discrete geometry. The methods of noncommutative geometry also apply to ordinary but discrete spaces, where one has non trivial differentials, connections, curvature even on a lattice. David, you can see my two coauthored papers with Raineri and Ngakeu respectively. Just as Lie groups have geometry, we do geometry and physics on finite groups such as the nonAbelian group of six elements. The alternating group turns out to be Ricci flat, i.e. solves Einstein’s equation in a vacuum. Refs are:
Electromagnetism and Gauge Theory on the Permutation Group S_3, J. Geom. Phys. 44 (2002) 129-155
Noncommutative Riemannian Geometry of the Alternating Group A_4, J. Geom. Phys. 42 (2002) 259-282.
Shahn
Darwinism is a good framework to tackle the problem of evolution, but it may be incomplete thus far. If you ever tried to resolve an extremal problem in physics (like finding minimum energy states) through a computational method like a Monte Carlo simulation, you will know one thing: high-dimensional spaces are slow to explore. (Hint: http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_methods_in_finance ).
Darwinism is an extremal multi-dimensional method to evolve the species. Dimension in Darwinism means every different possibility available to a life being to evolve. And that number is really huge even for the simplest case of a cell even a virus. Nature has the advantage that may perform a Monte Carlo cycle really fast (possible less than a nanosecond) and it also has millions of years to spend in doing these cycles. On the other hand, computers also complete cycles very fast (10 GFlops implies 1 cycle per nanosecond) and today supercomputers are crunching numbers for months to solve just one problem. The fact is that currently huge-dimensional extremal problems cannot be resolved successfully no matter how powerful the supercomputer you use.
Conclusion: maybe some day scientists will realize that the Darwinist Natural Selection is not enough fast to explain life evolution. And here is exactly the point where Creationism makes sense.
On another note, pertaining to the spacetime continuum hypothesis itself, I would like to digress from the Science vs. Religion theme to divulge a conundrum I have yet to find my way through with regard to a discrete spacetime.
Years ago, while doing my graduate studies, I was in an advanced solid state physics class. We were discussing (specific) heat capacities of solids, the Debye model, and continuum vs. the more realistic discrete nature of solids. An important take-away was that while the Debye model requires an artificial cutoff (the Debye temperature or energy) in order to obtain finite heat capacities, the more realistic discrete nature of solids, while involving a significantly more complicated density of states, provides its own, natural cutoff (with the cutoff and the overall density of states exhibiting a remarkable resemblance, though far more rough and random looking, to the smooth Debye model with its artificial cutoff).
At this point I was familiar with quantum mechanics (and we used it extensively in this solid state physics class), the “renormalizeable” infinities of quantum field theory, and General Relativity with its predilection to bend spacetime based on any and all energy densities (so the infinities of quantum field theory lead to infinitely curved spacetimes: The universe can only be a singularity [I'm sorry, but that conflicts with my experience/observations
]). So the germ of an idea was born: What if spacetime was not a continuum, but discrete?
I’m sure others have asked the same question, though I have had a hard time finding good works that follow this hypothesis.
I have come up with many interesting consequences of this hypothesis, including the unavoidability/inevitability of a statistical nature, and the potential for the dimensionality of the “manifold” to vary with spacetime location (not “compactification”, but actual different measures in different locations [with limitations]). However, as I alluded to above, I have come to a roadblock I have yet to surmount: I can go from discrete spacetime to “connections” (of the parallel transport type) like what’s in both General Relativity and Quantum Field Theory, and I can go from “curvature” tensors to the Einstein-Hilbert and Yang-Mills actions (and some cross terms that may or may not be eliminateable). The problem is in jumping the gap from “connections” to “curvature” tensors.
In a continuum spacetime it’s rather trivial to consider a “connection” (parallel transport) around a loop and look at the limit as the loop is shrunk to a point, in order to make this connection to the “curvature” tensor(s). However, discrete spacetime has no such ability to take any such limits (so derivatives don’t exist either*).**
Does anyone, per chance, have any suggestions of good work others may have done in anything similar? Are there other serious works pursuing a discrete spacetime/manifold hypothesis, that aren’t simply working from a continuum model (superstring theory, loop quantum gravity, or some such) and obtaining suggestive results that point, somehow, to the “idea” that the “reality” is, in some sense, “discrete”?
I would be greatly appreciative of any pointers.
Thanks.
David
* In discrete spacetime/manifolds we no longer have calculus as we know it (differential geometry, if you will). Instead all is simply algebra—incredibly huge algebra problems like ten to the one hundredth simultaneous high dimensional vector equations in the case of a single proton or neutron over a time span of a single femtosecond.
** I know that Lattice Gauge theory uses discrete spacetime. It uses parallel transport “connections” along the lattice links/edges between the discrete points (sites/vertices), and assigns the “curvature” to the surfaces (plaquettes/faces) in between points bounded by the lattice links/edges. Unfortunately, this assignment of a quantity to “nowhere” is an anathema to my way of thinking, for any model of “reality”. (As a computational model, I have no problem. It’s only when in search of a model of “reality” that I have a problem with it.)
Of course, another problem with Lattice Gauge theory is the use of a uniform lattice: This imposes a preferential reference frame. “Reality”, in my opinion, adheres to general “invariance” (general covariance plus).
While I think the comparison with one, apparently fairly common, interpretation of the “religious” approach to “truth” is interesting, I think it doesn’t fully characterize the broader religious character.
To me, at least, truth is truth*, independent of the source or means whereby it is obtained. However, one must recognize that religious speculation—by this I mean extrapolation upon some interpretation of some religious writing beyond its intended meaning (unfortunately, admittedly, such a “barrier” can be very difficult to ever be sure of)—must not be confused with truth. Additionally, one must also recognize (and admit, as a scientist, or proponent thereof) that neither is scientific theory (let alone any hypothesis or combination thereof) to be confused with truth: such are simply what we believe to be our best approximation to truth so far. (I think the article did a good job of pointing this out, at least for the spacetime continuum hypothesis. However, I believe most physicists understand enough about the history of physics, and the scientific revolutions we have been through thus far, to recognize that even our best theories may need to be “replaced” along the path to ever better approximations to truth.)
The problem lies, in my opinion, in the conflict between scientific theory (and hypotheses, of course) and religious speculation. So, as long as neither line is crossed—with this line not necessarily corresponding with the of-times espoused line of “in their respective realms” (as if it were an issue of “turf”)—then, I believe, we should have few if any issues.
So, I suggest that when religious vs. scientific conflicts occur, both (all) parties should step back, as it were, and try to honestly asses whether the conflict is really over truth vs. truth, or the aforementioned conflict between scientific theory and religious speculation.
A hard thing to ask, I suppose, but I believe it is what is necessary.
David
* Perhaps these “truths” should be spelled with capital Ts, but then I risk having others suggest I’m implying that scientific truth is different from religious Truth, which I’m not.
I commented on the same “creationist chimera” in other terms in a book review of Only a Theory here at Science Blog.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Greetings,
There’s a brand new argument in the argument about science and faith. Creationists and ID’ers can talk all around it but cannot refute the central premise.
It’s called: “The Creationist Chimera of Accidental Evolution Lives On As the Centerpiece of Intelligent Design”:
http://phoebekate.com/2008/09/14/randomness-creationism-and-intelligent-design
So get those mousetraps and flagella ready!