Well one issue that I am aware of here, is that mathematicians sometimes have a habit of thinking that their pet hypotheses somehow magically dictate to reality. There's a lot of emphasis on pursuing elegance in mathematics, a concept I saw at work first hand in the mathematics classes I attended, courtesy of the fact that in many instances, a search for an elegant solution has proven to be of utility value repeatedly within that realm. for example, from my own classes, I can recall being taught how a number of proofs in the world of Cartesian coordinate geometry, which are tedious and long-winded when attacked within that system, become wonderfully elegant, and expressible with startlingly contrasting brevity, the moment you move on to vector analysis. Likewise, proving that certain results in the world of vector analysis are valid for all possible coordinate systems, is a tedious and long-winded affair, but the moment you move on to tensor analysis, the resulting proofs become simple, elegant, and expressible with an almost frightening brevity of notation. Indeed, it's impossible to do any serious work in General Relativity without recourse to tensors, and tensor analysis has proven time and again to be a wonderfully elegant vehicle within which to express some ferociously complex concepts in simple, elegant and succinct terms.
There's a dark side to this pursuit of elegance, though. Whilst pursuit of elegance in mathematical proof has, in numerous instances, led to entire new methods of analysis - indeed, the whole of modern analysis, involving groups, rings, fields, vector spaces, topologies, and more recently, category theory, arose from said pursuit of elegance, framed in terms of generalisation and unification of concepts - the temptation is ever-present for mathematicians to read into this something that may not necessarily be there. This temptation has led even world mathematicians to engage in dangerously fragile speculations, Kurt Gödel being a prime example. After having unleashed his Incompleteness Proof upon the world, a proof which ironically, from the standpoint of his later speculations, provided a proof that formal axiomatic systems had their limits, Gödel then went on to engage in some frankly worrisome speculations, centred upon the manner in which mathematics is so frequently a valuable tool for understanding the real world. It's a temptation that, as I learned in my classes, mathematicians have to be on their guard against. Constant vigilance is required, if a mathematician is to avoid making a leap from appreciating the utility value of elegance, to adopting seductive but unsupportable metaphysical assertions on the basis thereof.
Unfortunately, not every mathematician maintains that vigilance. Worse still, some fall into the trap of concluding that an elegant model they have constructed must somehow necessarily be right, simply because that model is so elegant and beautiful and sophisticated. Having seen the value of elegance elsewhere, some mathematicians fall into the trap of thinking that elegance constitutes some sort of soundness criterion for models of the real world, forgetting the lesson learned the hard way by empirical scientists, that no matter how exquisite one's theoretical constructions are, if those constructions don't agree with the data, then they're nothing more than academic curiosities.
Indeed, mathematicians have come a cropper in the past, with respect to trying to lecture biologists how biological systems behave. The infamous Wistar Conference in 1966 is a prime example, where mathematicians tried to tell biologists that evolution couldn't work, on the basis of their models, only for the biologists to point and laugh. Interested readers can find out a little more about this
here. Needless to say, creationists routinely quote mine the findings of that conference in a duplicitous attempt to peddle their evidence-free, assertion-laden propaganda, laced with the usual lies about valid science. But I digress. This latest paper is, in effect, another instance of mathematicians thinking that they can dictate to other branches of science, just because they happen to have alighted upon something they regard as "elegant".
It's not surprising that a biology journal rejected this paper. Biologists have to put up with this sort of intrusion into their work all the time, which is why sensible biologists recruit their own mathematicians, and teach those mathematicians a few pertinent biological facts first. indeed, quite a few biologists have been sufficiently mathematically sophisticated in their own right, to make valuable contributions to mathematics as well, and I emphasise strongly at this point, that genuine cross-discipline contributions by appropriately gifted individuals are manifestly welcome, much as my caveats above might suggest otherwise to the naive reader (or, bearing in mind the likelihood thereof, the quote miner).
Funnily enough, Dembski began his career as a mathematician, though as others have observed, his actual output in that field of endeavour has been sparse to put it mildly. The idea that this individual, with few properly peer reviewed publications to his name even in mathematical journals, is some sort of genius ready to lead the way to a new creationist golden age, a notion that has been doing the rounds of the Discovery institute for some time, is another one of those fantasies creationists have a habit of entertaining, flagrantly disregarding the inconvenient facts whilst doing so. Dembski has not only allowed a preference for pretty models over ugly data to cloud his thinking, he's also allowed his religious ideology to cripple his intellect, to the point that many now regard him as a joke figure, one who wasted his time allowing the music of the spheres of his own verbal diarrhoea, to hypnotise him into adopting banal fantasies, and pretend that those banal fantasies somehow magically dictated to reality. Of course, he isn't alone amongst supernaturalists in this regard, supernaturalism by definition consists of pretending that the assertions of your favourite mythology dictate to reality, without bothering to ask whether or not reality actually agrees with this, but Dembski has added to the mix an unfortunate brand of hubris that any competent mathematician should be on guard against.
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