Related to the Second Law of Thermodynamics argument against evolution discussed here yesterday is one equally intimidating for the non mathematically inclined that goes “a mutation can never increase genetic information, ergo evolution is impossible.” Like the second law deal it can sound real complicated. But surprisingly, if you’re smarter than a first-grader, the ‘no new info’ argument is super easy to falsify.
Probably 99.9% of the creationists you hear pitch this tired canard have no idea what information theory is, but then most of the people they are trying to hoodwink won’t have any idea about it either. That’s the whole point, the claim is supposed to shut you down and stand unchallenged. And if you do get into the weeds you’ll get bogge down quick in discrete mathematics and set theory over how in the world can genetic information be quantified in the first place. The good news is, it doesn’t matter.
There is such a thing as information theory. Occasionally you may encounter someone who throws out terms therein like Shannon Theory of Kolmogorov Complexity. I only encountered those subfields once, as an undergrad, in some computer math class, I think. Forgive me if this isn’t totally accurate, but I think Shannon info could be loosely summarized as how efficiently or how intact a signal can be relayed, usually over phone lines because if memory serves Claude Shannon worked for Bell Labs. Kolmogorov complexity has to do with how repetitive or compressible a data set is. I probably know more about the latter, the Mandelbrot Set pictured above is there as an example of something that is infinitely complex even though it is generated with a super-simple highly compressible rule, but I don’t know much about either.
But it doesn’t matter! Because all you have to know is what a metric space is and how a back mutation works. Both of those things are simple.
A metric set is a set where the concepts of less than and greater than and equals all make sense. You might be surprised what kind of cool, weird, funky topologies meet this benchmark, but I bet every last person reading this understands intimately what greater than and equals mean. All that matters here is every metric space has to have three properties and the very first one says A = A, i.e., a defined quantity cannot be greater than or less than itself. That means a string of genetic code cannot have less information than itself, regardless of how you are measuring genetic info, provided the measurement method makes mathematical sense.
A back mutation is exactly what it sounds like, a sequence of genetic code undergoes a change during replication — a mutation — and then the replicated code undergoes another mutation that happens to be the exact opposite of the first and restores the sequence back to what it was originally.
Now check this out: If both those mutations caused a loss of genetic information, then the re-replicated genome would have less information than its identical grandparent genome and therefore less information than itself!
Ancient philosophers recognized the form of this iron-clad proof by contradiction long ago and labeled it reductio ad absurdum. In Latin it means literally, reduction to the absurd. In this specific case, since the initial assumption produces a paradox, we can conclude that initial, creationist assumption is wrong. No matter how genetic info is measured or calculated, as long as that measurement is mathematically consistent, it’s a trivial matter to falsify the claim “All mutations cause a loss of genetic info. QED