Maths in the dock for design.

How Did Mathematics Come to be Woven Into the Fabric of Reality?

Posted by Barry Arrington

We all learned pi in school in the context of circles.  Pi is the ratio of a circle’s circumference to its diameter.  It is an irrational number approximated by 3.14.

It turns out that pi shows up all over the place, not just in circles.  Here is just one instance.  Take a piece of paper and a stick.  Draw several lines along the paper so that the lines are the length of the stick from each other.  Then randomly drop the stick on the paper.  The probability that the stick will land so that it cuts a line is exactly 2/pi, or about 64%.  If one were to perform millions of trials, one could use the results to perform a very precise calculation of the value of pi without ever considering its relation to circles.

This is just one of many places pi pops up in reality, and pi is just one of several mathematical constants that appear to be woven into the fabric of the universe. One mathematician likened it to looking out over a mountain range, where the bases of the mountains are shrouded in fog, and the symbol for pi is etched into the top of each mountain – one intuitively knows that it is all connected at some basic level even if one has no idea why.

What are we to make of what physicist Eugene Wigner called the “unreasonable effectiveness of mathematics” in describing reality?  The word “unreasonable” makes sense only in the context of expectations.  If one expects the mathematical structure of the universe to be elegant and beautiful, the fact that it turns out to be elegant and beautiful is not unreasonable at all.  It is only unreasonable if one approaches it from the perspective of the metaphysical materialist.  In his universe reality consists of nothing but particles in motion randomly bumping into each other.  In that universe there is no reason to expect any underlying mathematical order, no reason to expect mountain tops etched with pi to pop up all over the place, and no reason to suspect that those mountain tops are connected by a unifying order at the base.

Given materialist premises, none of this makes the slightest bit of sense.  It is just a brute fact.  It cannot be denied or explained.  Yet there it is.

MIT cosmologist Max Tegmark has a theory.  He says consider a character in a computer game (let’s call him Mario) that is so complex and sophisticated that he is able to achieve consciousness.  If Mario were to begin exploring his environment, he would find a lot of mathematical connections.  And if continued to explore, Mario would ultimately find that his entire world is mathematical at its roots.  Tegmark believes we live in a universe that is not just described by mathematics; he believes that mathematics defines all of reality, just as the reality of Mario’s computer game world is defined by mathematics.

Here is the interesting part.  Tegmark makes no design inference.  (He is a multiverse fanatic).  This is astounding.  All he needs to do is take his own analogy one step further.  Why is Mario’s computer game world connected mathematically?  Obviously, it is because that mathematical structure was 
imposed on the game by the game designer.

Why is the universe we live in connected by an unreasonably beautiful, elegant and effective mathematical structure?  Come on Max.  You are a smart guy.  I know you can figure it out.

Cicadas vs. Darwin

The Cicada Challenge to Darwinian Evolution

Evolution News & Views They'll create quite a commotion next month, but they're mostly a harmless nuisance or a wonder of nature, depending on your outlook. They're the northeast brood of Magicicada, the so-called 17-year locusts. Smithsonian Magazine tells about them:

Residents in the Northeast U.S. waiting for warm temperatures may get a surprise along with their May flowers: When the soil reaches 64 degrees Fahrenheit, they'll also get a visit from billions and billions of cicadas.

This latest brood is composed of several species including Magicicada septendecim, M. cassini and M. septendecula, and is expected to take over West Virginia, Virginia, Maryland, New York, Ohio, Pennsylvania and a tiny spot on Long Island. 

In an event that only happens once every 17 years for this brood, the creatures will soon dig their way out of the soil, shed their exoskeletons and emerge en masse. The swarm will spend two to six weeks mating and singing their grating, sing-song call before dying and blanketing the ground with their crispy brown corpses. [Emphasis added.]

Here's a natural wonder worth thinking about. There are 14 identified species of periodic cicadas in the United States. A southern brood on a 13-year cycle came up in 2011 (see Live Science). Both 13 and 17 are prime numbers. Evolutionists have long touted their adaptive story about why this is. Smithsonian says:

Researchers have theorized that the insects spend such a lengthy time underground in an effort to outlive parasites that may harm them, Eoin O'Carroll wrote for The Christian Science Monitor in 2013. Other researchers speculate that the 13 and 17-year life cycles, both prime numbers, are an evolutionary adaptation and a mathematical trick that keeps cicadas from emerging during peak population periods for their predators. 

"A cicada that emerges every 17 years and has a predator with a five-year life cycle will only face a peak predator population once every 85 years," writes Patrick di Justo in The New Yorker, "giving them an enormous advantage over less well-adapted cicadas."

Live Science adds that the sheer numbers provide an advantage, too: no predator could possibly devour so many of them. But it's the prime number quirk that attracts evolutionists' attention:

The key factor is that both numbers are prime; they can't be divided evenly by any smaller numbers (except one). It is no mere coincidence that cicadas have evolved indivisible life cycles. As explained by the entomologist Stephen Jay Gould, prime cycles have a major evolutionary advantage over cycles that are multiples of smaller numbers of years, and for a simple reason: They make cicadas more elusive.

"Many potential predators have 2-5 year life cycles. Such cycles are not set by the availability of cicadas (for they peak too often in years of non-emergence), but cicadas might be eagerly harvested when the cycles coincide," Gould wrote in his best-seller "Ever Since Darwin" (Norton 1977). "Consider a predator with a life-cycle of five years: if cicadas emerged every 15 years, each bloom would be hit by the predator. By cycling at a large prime number, cicadas minimize the number of coincidences (every 5×17, or 85 years, in this case)."

In summary: "Thirteen- and 17-year cycles cannot be tracked by any smaller number."

We could leave it at that, and agree that evolutionary theory is wonderful the way it explains things. Yet think again. Don't the two explanations work against each other? If predation is a problem, why the billions at once? With so many, they could come up every year and do just fine. Why wait? And if selection pressure helps the cicadas, can't it help the predators the same way? Where are the 17-year predators? Besides, you wonder what the predators are eating outside the two-to-six week window the cicadas are active. 

Like the peppered moths and the Galápagos finches, the evolutionary story of cicadas offers a certain intuitive satisfaction, until you start asking questions. Worse, it distracts from the really interesting aspects that really need explaining. To wit:

• The remarkable timekeeping ability of the nymphs to silently count 13 or 17 years.
• The trigger that makes all of them emerge simultaneously. The temperature gauge needs to coordinate with the clock, otherwise they would emerge every year.
• The "incomplete metamorphosis" they undergo (i.e., unlike butterflies shown in the film Metamorphosis, cicadas do not have a chrysalis or pupa stage; the nymphs grow directly into adulthood). Even so, the larvae have to transition from one body plan into another that has completely new structures, like wings, eyes, antennae and reproductive organs. 

Other amazing facts about cicadas tend to get drowned out in the rush to explain the evolution of prime numbers. For instance, cicadas have amazing wing surfaces that burst bacteria. Three years ago, Nature News described nanoscopic pillars on the wings that pop bacterial membranes, shredding them to pieces (see videos in the article). It was such a clever method for disinfection, scientists envisioned creating similar materials that "could one day be applied to public surfaces that commonly harbour disease, such as bus railings." 

PhysOrg mentioned other advantages: "In marked contrast to the biochemical mechanisms of antibiotics, which are subject to acquired resistance, physical mechanisms are non-specific, and cannot be reversed or altered, tackling bacterial cells as a whole." This kind of "anti-microbial physics" could be designed to simultaneously nourish human cells, supporting "a variety of biomedical implants, anti-fouling surfaces or biosensors."

Obviously, any creature capable of powered flight deserves our admiration for impeccable design. Add to that all the other systems required for complex animal life: (e.g., reproductive, digestive, respiratory) and traits characteristic of insects (e.g., articulated legs, compound eyes, antennae) and we see a whole package of systems that challenge blind processes of natural selection.