I write this as a addendum to a series of questions on the power of science and an explanation posted by Sean Caroll at the Cosmic Variance blog. The detailed post on the misunderstandings , elaborates on why scientists can be so sure of their conclusions (when they can form them) and why society in general is so skeptical. The fact that society is skeptical of scientific conclusions , while empirically and intuitively obvious to most, was recently verified in a survey – and is in my opinion the single most important factor in deciding the volume and nature of science done in , at least, prosperous economies.
Sean Caroll proposes that science itself is an ‘empirical behavior practiced by humans’ . Of course, this means that science is plagued by at best disagreements within the community , and at worst , agitated controversies like the ‘religion’ issue.
In my personal opinion, the problem lies in the way science is projected to the public – it is projected like it is mathematics, like a conjoint twin of the blue-blooded mathematics, but destined to ‘get its hands dirty’. But then , consider this quip from (the) Einstein :
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
Albert Einstein, "Geometry and Experience", January 27, 1921
You can imagine that this becomes a major peeve for science, which claims to be in the business of studying and revealing the workings of reality. I do understand that very important role that mathematics plays in making science tangible – but mathematics is a player of the abstract – numbers are ideas that are arranged in equations to reflect reality. In effect , calculus and arithmetic based mathematics is the 
ultimate simulation of reality.
Science , therefore, uses mathematics only as a tool. Yet, all too often it is dismissed by the populace as a dry, dispassionate subject- exacting, never completely applicable to reality, and working as it should only on a Professor’s blackboard. This view, whether valid or not, is more applicable to mathematics, and science suffers under the transferred epithet.
Science, I conclude then, needs a new metaphor, and the only part of mathematics that lends an appropriate one is Probability theory.
Bear with me for a moment, and assume that reality (or more appropriately , reality as we understand it) is a collection of probability distributions on increasing orders of complexity and scale. Quite obviously, the most basic of these distributions are those of quantum mechanics – the Schroedinger equation and so on. At the other end of the scale , are the observed cosmic probability distributions – such as the chance of star formation, supernovae, spatial inflation (given the WMAP data) etc. Everything else, from ecology, sociology to music lies in between.
The job of science is to fill up the actual values that determine these distributions. It is apparent in this picture that nothing is impossible or possible – just very likely or unlikely. It is now left to the informed public to decide whether they are going to place their bets on what is a likely or something that has almost no chance of occurring.
This mental model of science provides two major advantages :
Firstly, it makes science overtly non-judgmental – as it should be. It doesn’t say walking on water , virgin births and resurrection from the dead is impossible – just something that isn’t very likely. In fact, it makes it just about as unlikely as thin air transforming into gold bullion. I said overtly earlier because in fact, it lumps together all the ‘unlikeliest , thereby accentuating the ridiculousness of belief in them. If you think walking on water is possible, then you must also believe that fish have developed civilization and are now (put your favorite mockery here) simply taking a break this millennium. Science as a probability function-finder is a way of enabling Stephen Jay Gould’s Magisteria, without causing science to lose it ‘power’ to say something about the world.
Secondly, it makes science more versatile and in many ways, a better representation of reality. Most theories in science, especially in biology, geology and cosmology provide ball-park figures, and rarely the precision of numbers available in physics. Considering a probabilistic spread of values provides a much better assessment of the theory’s power for explaining reality. Of course, even today science does use this premise, especially when applying statistical analysis. Statistics is a useful discipline and yet scientists sometimes think as of statistics is some sort of compromise.
“If your experiment needs statistics, you ought to have done a better experiment.”
Ernest Rutherford
The reason, I think, is that scientists have let the mathematicians mislead them with the false glorification of a single , elegant equation that explains everything. Murray Gell-Mann even proposes that the elegant beauty of an equation is in some ways an indication of its correctness. That may be so, but from what we have learnt from every other field of science, is that at least such elegance is NOT scalable. Any set of rules that describes a living cell with its ~100,000 thousand or so different types of molecules does not exhibit the elegance of Maxwell’s equations , or general relativity. It possesses a different kind of beauty – the chaotic charm of a pulsating ménage, a Rube Goldberg machine that has found a purpose – to ensure its existence using the the very thermodynamic laws that is fighting to stay one step ahead of.
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Beauty at varied scales
Left : Maxwell’s equations – a complete description of all electromagnetic phenomenon
Right : a genomic map of the simplest known organism Mycobacterium genitalium, indicating its various functional genetic elements.
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With that in mind, in an era when science branches out into unknown territory as a matter of routine, there is a chance to alter its image in the public eye. It begins with scientists giving up the glorification of elegance, and acceptance of the messy uncertainties whose existence is the only certainty in the complex, dynamic world we find ourselves in.
Perhaps then, and ironically so, by relaxing its own expectations of the precision of reality, and by distancing itself in ideology from its quantitative associate, science will befriend the masses and find the credibility it has lacked throughout history.
