One of the common criticisms that one hears against us science-based atheists is that our search for naturalistic explanations of hitherto mysterious phenomena, coupled with a relentless assault on irrational and unscientific thinking, results in all the wonder being drained from life. We are told, for example, that to explain that the rainbow is the product of multiple scattering of light by water droplets in the air is to somehow detract from its beauty or that when gazing at the billions of twinkling stars on a beautifully clear cloudless night, to be aware that they are the products of nuclear fusion reactions that took place billions of years ago is to reduce their grandeur.
I must say that I don’t understand the criticism. For me at least, understanding how these things come about actually enhances my sense of wonder about the universe. The more I learn about how the universe works and how the impersonal forces of nature created everything around us, the more I am impressed.
To illustrate my point, I am now going to show you something that I think is incredibly beautiful. It is the equation:
T = 2tanh-1(√ΩΛ)/(3H0√ΩΛ)
So what is so great about this equation? It is the equation that tells us the age of the universe. Note that the age T depends on just two quantities H0 and the square root of ΩΛ, both of which are measured quantities. H0 is the value of the Hubble constant at the present time and is given by the slope of the straight line obtained when one plots the speed of distant galaxies (on the y-axis) versus the distance to those galaxies (on the x-axis). ΩΛ is the ratio of the density of dark energy in the universe to the total energy density of the universe.
As with all scientific results, there are some basic theoretical assumptions that go into obtaining them. This particular one requires that the universe be governed by Einstein’s equations of general relativity and that its current state is ‘matter dominated’ (i.e., the energy contribution of pure radiation is negligible) and ‘flat’ (i.e., the total density of the universe is at its critical value so that the curvature of space is neither convex nor concave). These ‘assumptions’ are supported by other measurements, so they are not arbitrary.
The values of H0 and ΩΛ are obtained using satellite probes that collect a vast body of data from stars and galaxies and scientists then do a best fit to those data for multiple parameters, of which these are just two. The current values were obtained in 2009 by the WMAP (Wilkinson Microwave Satellite Probe) satellite launched in 2001, and are given by H0=70.5 km/s/Mpc and ΩΛ=0.726. Insert these values into the above equation (with the appropriate units) and you get that the age of the universe is 13.7 billion years.
Why do I think this equation is a thing of extraordinary beauty? Just think about the implications of that equation for a moment. We humans have been around for just an infinitesimally small period of time in history and occupy an infinitesimally small part of the universe. And yet we have been able, using pure ingenuity and by steadily building upon the scientific achievements of our predecessors, to not only figure out the large-scale structure of the vast universe we happen to occupy but to determine, in a simple equation, its actual age! That is truly incredible. If that does not strike you with wonder, then I don’t know what will.
Furthermore, note how simple the equation is. The tanh-1 function (which represents the inverse of the hyperbolic tangent) may be intimidating for some but it is such a standard mathematical function that it can be found on any scientific hand calculator. If a news report states that new satellite data have given revised best fit values for by H0 and ΩΛ, anyone can calculate the revised age of the universe themselves in a few minutes.
But as this xkcd cartoon captures accurately, it is not that scientists lose their sense of wonder but that they find wonder in learning about the universe, and do not need to invoke mystery to sense it.