The real purpose of the scientific method is to make sure Nature hasn't mislead you into thinking you know something you don't actually know.

—Zen and the Art of Motorcycle Maintenance

I occasionally read books about science, pseudo-science, and just generally sorting out what is actually true from what you think is true1... and while those books do a good job of laying out the problem, this formulation really resonated with me... though Nature isn't generally the one doing the tricking.

[1]Bad Science and The Flaw of Averages being two of the most recent.

Lorem Ipsum to Hebrew (redux)

The previous post: Lorem Ipsum to Hebrew gets a little side tracked in the technical details. There's a program to evolve text using mutation-selection cycles and a program to chart the results, but it mostly misses the point.

Questions for Evolutionists asks:

How can mutations (recombining of the genetic code) create any new, improved varieties?
(Recombining English letters will never produce Chinese books.)

This question has two problems. First, it presents a straw man: nobody contends that mutations alone result in the awe inspiring adaptations possessed by the life all around us. The vast majority of mutations are silent-site mutations and have no effect on the phenotype of the resulting creature, because the mutation occurs in a non-coding section and is never expressed. The majority of the rest of mutations are deleterious and give you cancer or Down's syndrome or something equally nasty. Only a tiny fraction of mutations have any beneficial effect on those carrying the mutation.

Mutation alone would never have produced the staggering variety of life that populates the Earth. Mutation combined with selection on the other hand can produce staggering effect on a population. Mutation introduces novel varieties into a population with each generation. While some mutants will be more fit than than their parents most will not be and some will be decidedly less so. The most fit individuals will found the next generation and beneficial mutations will slowly accumulate generation after generation producing the adaptations observed in current populations.

Second, conceptualizing mutation as moving letters around, is a complete underrepresentation of the ways in which our genome's can be mis-copied. There can be deletions, replacements, duplications of single bases or entire sections of DNA. Additionally, it is at the completely wrong level of granularity. Mutation would not occur on the letters themselves but on the bytes representing them. With only 256 bytes to choose from you can represent either Macbeth or the I Ching with ease. Likewise, using only C, G, A and T you can just as easily spell E. Coli and H. Sapiens and you can almost spell Human immunodeficiency virus, but you would be missing the U.


So how can mutation create new and improved variants? When acting alone, mutation would only ever improve an individual through luck. It is after all a random process and would mostly only introduce deleterious changes. When combined with selection on the other hand, together mutation and selection can produce amazing adaptations by allowing beneficial mutations to accumulate over generations.

Lorem Ipsum to Hebrew

Questions for Evolutionists asks:

How can mutations (recombining of the genetic code) create any new, improved varieties?
(Recombining English letters will never produce Chinese books.)

Lorem Ipsum to "ןגכה9'kpx%y'ךbעX]kגkVגגהiEג9*Qעfעt9fכ9עגכf' qFxה%עגה9תגכג9X' k-?%עגכהןגכה9'" in only 118 generations. Sure it's garbled gobbledygook but if you have any familiarity with Hebrew you should be able to spot kaf, ayin and tav among others. In this string there is a total of 33 Hebrew characters ranging from aleph to tav. is the program which produced this particular piece of gibberish. It models evolution by natural selection by successively evolving a population of phrases for two hundred generations. In the case of this particular string, fitness was calculated as a function of the number of Hebrew characters contained by an individual.


Each population starts as a single copy of Lorem Ipsum. It is allowed to reproduce without the influence of any kind of selection until the population reaches 1024 individuals. At which point only the 1024 fittest individuals will be allowed to be part of the next generation.

Generation n + 1 is composed of the daughters of generation. Each individual produces two offspring and dies (binary fusion) each daughter is an inexact copy of their mother: 1 in 10 bases are replaced by a point mutation. Daughters are then decoded from utf-8 to unicode and then encoded back to utf-8, errors are ignored. The genome of the mother is recycled until a full 128 bytes are copied to the daugther's genome. Once 2 daughter cells are generated for each mother, the 1024 fittest cells are selected to be the mothers for the next generation.

Three different fitness criteria were used in three different evolutions: # Hebrew characters, # Latin Uppercase characters, # Latin Lowercase characters.


In each of the following figures the absolute fitness of an individual (in terms of the # of relevant characters) is shown on the Y axis while the generation is shown on the X axis. The green dots are the most fit individuals of their generation while the blue dots are the least fit.

Scatter plot of population fitness.

Figure 1: Evolution of Lorem Ipsum when selecting for # Hebrew characters

Scatter plot of population fitness.

Figure 2: Evolution of Lorem Ipsum when selecting for Uppercase Latin

Scatter plot of population fitness.

Figure 3: Evolution of Lorem Ipsum when selecting for Lowercase Latin


In the three figures there are a couple of important similarities:

  1. Maximum fitness reaches a fitness plateau before it reaches the theoretical maximum in any of the experiments (128 in the case of either Latin experiment or 64 in the case of Hebrew).
  2. Minimum fitness drops off for the first 10 generations in the two Latin experiments.
  3. In two of the three experiments minimum fitness after 100 generations greatly exceeds initial fitness of the population.


This is an example of the mutation-selection balance. Essentially, after a certain point the mutation rate is introducing deleterious mutations (replacing characters relevant to fitness with characters that are not) as fast as selection removes them from the population. Thus the population's fitness reaches a plateau.

The Hebrew experiment was far more susceptible to this effect than either of the Latin experiments because each Hebrew character is represented by two bytes rather than one, the chance of a beneficial mutation is lower and the chance of a deleterious mutation is higher.

Minimum Fitness Dropoff

Lorem Ipsum is a text that is written using Latin characters as such the fitness of the founding individual is greater than zero. Since the population starts with a single individual which divides until it reaches the maximum population of 1024, individuals are not under selection for the first ~10 generations and thus deleterious mutations may accumulate without facing negative selective pressure.

Improved Minimum Fitness Over Time

Lorem Ipsum is a text mostly composed of lowercase Latin characters, as such it is not overly surprising that it shows almost no improvement over time.

On the other hand, the other two experiments show vast improvements in both minimum and maximum fitness over time. In fact the Hebrew experiment starts out with an individual of fitness 0 and results in a population of median fitness ~20 a mere 100 generations later. The Latin Uppercase experiment starts with an individual of fitness ~5 and results in a population with a median fitness of ~85 after 50 generations.


This experiment offers example of several interesting evolutionary effect. We've seen the mutation selection balance in play. Mutations introducing novel variants into the population. The steady increase of fitness over multiple generations. Increase in complexity of the organisms under study (Hebrew characters are represented using two bytes while Latin characters only use one).

Maybe rearranging the letters of the poems of Shakespear can never produce the I Ching, but rearranging the bytes most certainly could.