Impossible IS the MCLRG

You do not need a book, but just one word, to show that species did not “form” or “evolve” through random mutations: “impossible”.

The probability that a monkey pounding on a keyboard with 100 keys will come up with the word “impossible”, without counting the quotes and without uppercase characters requiring key combinations, can be calculated as follows:

The probability for the monkey (or a random process) to hit the first Character, an “i” on a keyboard is 1 out of 100 (101 key keyboards are the most common – let’s imagine one key being disabled).

The probability for the first two characters (“im”) to be hit, in the wanted position, is 1 out of 100 x 100, or 1 out of 100²  (or 10⁴). The probability for all the 10 characters in the word “impossible” to be hit, in the proper sequence, is 1 out of 100¹⁰ (or 10²⁰). This number is bigger that the number of seconds since the beginning of the universe.

No random process pushing keyboard keys once every tenth of a second, coming up with a 10-character long word once per second (we call this an “occurrence”), is likely to have come up with the word “impossible” since the beginning of time.

The number of seconds in an hour is 3600, in a day is 86,400, in a year is 31,536,000. This is (rounded up) 3.2 x 10⁷ (seconds in a year). 
The age of our solar system is estimated at about 5 Billion years, or 1.6 x 10¹⁷ seconds. 
The age of the universe is estimated to be less than 25 Billion years, or .8 x 10¹⁸ seconds.

Thus 100 Billion years (a mere 10¹¹ years – four times what astronomers think the age of the universe is) is less than 3.2 x 10¹⁸ seconds, a number two orders of magnitude smaller than the number of random occurrences – one per second – which would be needed to possibly generate our word by chance: 10²⁰.

Our target word is a case of “irreduceable complexity”: We want exactly the word “impossible” to be generated randomly as written. We do not want to try until a half the word is generated, and then try many more times to get the rest of the characters in sequence. We want the whole word to be generated in one occurrence.

Another example of irreduceable complexity is a “jackpot” combination of four specific symbols in a slot machine. We can use the same formula to calculate the odds of winning when the machine has four wheels and each wheel has a character set of ten unique symbols. In this case the number of trials would be 10⁴, and the probability of hitting the jackpot would be of one in 10,000.  This is a relatively low probability, which would allow the owners to set a jackpot prize of perhaps $1,000, when the cost of each “trial” is one quarter. In the long run, the owners would make about $2,500 (ten thousand quarters) for each jackpot they are likely to pay out (without considering other small prizes).

If the designers of the slot machines wanted to decrease the probability of winning a jackpot, in order to possibly increase both the prizes paid out and their earnings, they could either increase the number of unique symbols on each wheel, or the number of wheels, or both. For example, in a slot machine with 5 wheels and 16 unique symbols, the odds to win a jackpot would be about one in a million (one in 10⁶).  The odds in our “impossible” example are equivalent to hit a jackpot in a slot mahine with 10 wheels with 100 unique symbols: 100¹⁰, or 10²⁰: A very skewed slot machine, where the odds of hitting the jack pot, even trying one occurrence per second for 100 Billion years would be very close to zero.

The above calculations give us an idea of the numbers involved in a random process of “generation”. We can assume the number 10¹⁸ (the number of seconds in more than 31 billion years) as the maximum amount of random occurrences possible, once per second, for a time approximately as long as our universe has existed. This corresponds to the Maximum Complexity Limit for a pattern or system that requires as many occurrences, once per second, to be generated by a random physical process: The Maximum Complexity Limit for Random Generation (MCLRG for short).

Some evolutionary biologists have suggested that random mutations could explain how new species could be generated as the progenies of existing species.

The idea of random mutations between one individual and its progeny has an innate problem: By definition, a random mutation can apply to some, or a large part, or most of the genetic information of the parent individual. Assuming otherwise, would require some other intervening process.

For example, could an ape develop one more toe to be able to grab things better? If we entertain other concepts, such as adaptation to the environment, or some other theory, working in conjunction with random mutations, then random mutations need to be severely limited, or any progeny would have a very large probability of not being viable.

The more we limit the concept of random mutations, the more time is needed to produce their intended effect (a genetically different viable individual). But we have seen from our calculations that random variations (applied to non-trivial patterns) do not have enough time to work their magic even if they happened once per second for billions of years. Any severe restriction imposed on random mutations by some other reasoning, for example by introducing a process of adaptation involving several generations of individuals of that species, would require more time and further invalidate the theory of random mutations.

Thus, considering random mutations independently from other processes, the probability for a particular random genetic mutation to generate a progeny able to survive or thrive is equivalent to the probability of producing a viable individual randomly from scratch.

As we read in the “random mutation” literature, a mutation is “unrelated to how useful that mutation would be”. Mutations, in conformance with the theory, always include the possibility of producing a different species altogether!

In today’s world of DNA and amino-acid sequences, we tend to get distracted by the incredible details of microbiology. By using examples taken from genetics in an argument, we can lose most of our listeners (and even get ourselves lost) in the details of DNA sequencing.

For example, we could say that a DNA sequence of a sexually reproducing mammal is millions of times more complicated that the word “impossible” and it could not have been created randomly. We can say this intuitively, but when we embark in a specific explanation we are bound to make approximations and mistakes that a microbiologist will flag as errors in our reasoning, invalidating our argument for the wrong reasons.

For this reason, we will follow a “low tech” approach that most people can understand without knowledge of microbiology.

The main assumption, in order for the generation process to work, is that an adult, sexually reproducing mammal must be generated in its integrity, with all the elements necessary for it to survive, grow to adulthood and reproduce itself. Our individual is irreduceably complex, as it needs several organs to function and reproduce, such as:

1. An endocrine system to regulate the body (including reproduction hormones);
2. a respiratory system, to feed oxigen to its organs;
3. a blood circulation system, to transport oxigen and nutrients to its organs;
4. a stomach or some system to break down ingested food;
5. a digestive system to absorb chemicals from food and feed the body;
6. a filtering system to process and get rid of liquid waste;
7. a skeleton, to support the individual;
8. a brain, to search for food, escape attacks, defend itself, control its organs, etc.
9. a vision system to identify food, enemies, etc.
10. a muscular system to be able to grab, move, chew, etc.
11. a lymphatic system to transport and methabolize the fluid in between cells;
12. a nervous system to communicate commands to various muscles and organs;
13. a skin system to enclose and protect its organs; and
14. a reproductive system.

Our individual will need all of the above systems (and probably more) to be fully functioning. If any of the above systems failed, then the individual could not survive long enough to be able to mate and reproduce.

Thus we can say that the above fourteen systems represent a level of irreduceable complexity for a mammal to become a candidate for the generation of a new species. All of the systems need to be present, in a certain position with respect to, and connected to the other systems. The relation among these systems is a much stronger and more complex than just the positional order in our “impossible” word.

For example, each muscle in the body needs to be attached in specific and multiple points to the skeleton, must be connected in specific and multiple points to the nervous system, must be fed in many points by the blood circulation system, etc. Thus the “positioning” of the muscular system is not just a few bits of information describing its order in a string of 14 characters, but requires perhaps thousands of pieces of information specifying its relations with several other systems.

Thus by using with the analogy of the word “impossible” and assuming that our new word (describing a mammal) is a 14-character word, we are making a great simplification.

To complete the analogy, we need to think about what choices (or “character set”) are available for each system (or “character”).

The simplest way is to think of each system as using its own set of keys.

For example, in a working endocrine system there are about 20 organs involved, each producing one or more out of about 70 hormones, which need to be regulated using four signaling systems through many feedback mechanisms, so that the production of these hormones can start and stop as necessary. A simplified analogy could be having a keyboard with 20 super-keys, which when pressed show a pull-down menu on a screen with 4 selections, each invoking a pop-up window with 70 possible choices. This analogy would give us 20 x 4 x 70 = 5,600 possible choices in our endocrine system “character set”.

But this analogy is still very simplified, because:

1.      In the above calculation we considered only the actual hormones we know are essential, and the organs we know are involved, not all the possible hormones that can be randomly created or all the possible organs that can randomly be conceived.

2.      In the above description of the system we did not consider many other choices which determine its functionality, such as the type of organs or glands, their composition, size, structure, design, position in the body, emittors and receptors of stimuli, design and functionality of the feedback systems, and so on.

Even without knowing much about biology we can guess that the number of choices required to generate a functioning endocrine system are many thousands.

Thus our first “character” in our “word” representing one mammal individual, would have to come from a choice set of many thousands (certaily more than 5,600).

Without trying to recall basic biology and describe each system in detail, we can simplify again and say that each of our 14 systems will have a choice set of only 1,000. Even with this generous simplification, a random process would still require 1,000¹⁴, or 10⁴² number of “trials”, one occurrence per second, to generate our individual mammal characteristics, which is still a number incomparably bigger (22 orders of magnitude bigger) than the number of trials required to generate the word “impossible” (10²⁰).

We could forget about the real complexity of these systems and assume that each of them could be described by one character out of character set of 100, as if there were only 100 possible choices to uniquely and completely define each system. Then our formula would give us 100¹⁴ possible choices or a probability of one out of 10²⁸ for our individual to be randomly defined. This is still eight orders of magnitude bigger than our “impossible” example.

Thus, according to our calculations, not even one viable mammal animal species could have been “defined” by random trials, once per second, during the time the universe has existed, rounded up to 100 Billion years. We are very generous with the age of the universe as well, even if the “Cambrian explosion” is estimated to have happened less than 1 Billion years ago.

Furthermore, how would the random process know, without an “external intelligence” which combination is the right one, once it is achieved? Through the process of elimination: Those individuals that are not viable, or less able to cope, will be less likely to grow and reproduce. The theory of random mutation implies a “meeting” between two individuals of the same sexually reproducing species (Let’s forget about the low probability of two individuals of the same species being randomly generated in the same reproductive lifetime span – out of 100 Billion years. Let’s also forget about the low probability of them meeting in the same spot). They need time to growth to maturity, time for courting and reproduction, time for testing their survival, dying, etc. These are all processes that require much more time (several orders of magnitude bigger) than one second (which we assumed in our calculation as the time between random occurrences). 

Our explanations are hardly necessary, since we intuitively know that the description of the characteristics of an animal species must be more complex than the sequence of ten characters, out of a regular keyboard, forming the word “impossible”.

Our simplifications were so great and so many, that the same reasoning could be applied to any one system (or sub-system, such as an eye, or even a single gene) and show that even this by itself could not possibly be generated through random mutations.

In conclusion, a random mutation scenario for the generation of animal species is so far from the realm of mathematical possibility to make it ridiculous to entertain, even as part of, or in combination to other possible processes or theories.