If Accidents Can't Make Tables, How Can They Make Super-organized Biological Wonders?

Professors tell us that biological complexity has arisen through blind processes of evolution. They teach that random mutations and survival of the fittest have been sufficient to produce all the wonderful innovations we see in biological organisms.

To shed some light on whether this is a tenable notion, let us do some calculations that will help clarify how improbable it is that a very simple accidental invention could occur. If we are to imagine evolution producing some biological innovation, we have to allow that at least some simple invention would have to occur by chance before any biological reward would be achieved. For it is never true that an organism gets survival value by just developing something with one part or two parts. Everything that we can think of that is useful requires at the very least quite a few parts organized with some coordination. For example, before it could yield any biological reward, even the simplest vision system would have to be at least as complex as, say, a table. And before it could yield any biological reward, even the simplest wings would have to be at least as complex as a table. Both of these things (vision systems and wings) must actually be vastly more complicated than a table to work in even the most primitive way.

So let us use a table as an example of a very simple invention. How improbable is it that random pieces of wood in a forest would assemble in such a way as to make a table? If we find that this isn't too improbable, something that we might expect to see after a few thousand tries, it might bolster the idea that blind nature can accidentally make inventions.

We can define a table as a portable flat surface elevated by table legs. The requirements for a simple table are as follows:

1. there must be a table top
2. the lower surface of the table top must have four peg holes
3. there must be four table legs that fit into the peg holes.

The visual below shows the parts that are needed (ignore the ring feature shown in the legs, which aren't necessary for the table working).  We see the underside of the table top, with its four peg holes into which the table legs can fit. 

Conceivably there could accidentally occur in nature some items that might act as the table top and the four table legs. We can imagine several logs accidentally bound together by vines that might end up looking a little like a rectangular table top. If the logs had varying widths, there might be gaps between the logs that could serve rather like peg holes.  The "table legs" could be four other logs.

Given such a short requirements list, at first it may not seem too improbable that a table may form by chance. But let's do some math to get a clearer idea of the chance of such a thing forming accidentally.

To do the math, let us imagine a little machine we may call a Table Part Tumbler. The machine will be a spinning box, rather like the transparent spinning boxes they often use to randomly draw lottery numbers. Let us assume that this Table Part Tumbler is a cubic box that is two meters wide. Let us assume that there is a table top somewhere inside that volume of space. We will also assume that there are four table legs somewhere in this volume of space.

We can imagine that this box will be electrically powered, and spinning for a long time. We can imagine the box equipped with some artificial intelligence detector that will cause it to stop spinning whenever all four table legs fit into the four peg holes. The spinning may cause a table leg to accidentally enter one of the peg holes, or accidentally fall out of one of the peg holes. But once four peg holes are filled, the machine will stop spinning, because a table has been accidentally constructed.

Now these table legs could have any orientation at all in three dimensional space. They could be pointing straight up, or they could be pointing sideways, or they could be pointed at some angle to the left or the right. But for the table legs to accidentally fit into the pegs, the legs must be perpendicular to the underside of the table top, pointing at one of the leg holes. How can we calculate the chance that a leg would be pointing in such a direction?

Here is a method that can be used. Let us assume that a table leg is about an eighteenth of a meter in width (about two inches). Now consider the top surface of our cubic box that is two meters across. In that top surface (two meters wide) there will be about 36 by 36 little areas as wide as one of these table legs. So you can imagine some 1296 little circles on the top face of our box. 

There are also five other faces of the cubic volume to consider: the side faces of the box, and the bottom face of the box. We can also imagine 1296 little circles on each of the four side faces of the box, and 1296 little circles on the bottom face and top face of the cubic volume, as in the diagram below:

To imagine an orientation of a table leg (its position in 3D space), we can imagine a line between one of these circles on the one face of the cubic box, and another circle on some other of the box's six faces. But if a table leg is oriented randomly in 3D space, each of the 1296 circles on the bottom face of the cubic volume can connect to any of 1296 circles on each of the other five faces of the cubic box (which is a total of 6480 circles).

So under these assumptions there will be a total of 1296 times 6480 ways in which a table leg could be oriented in three-dimensional space, or 8398080 possibilities. This is an example of what is called a combinatorial explosion. Such huge expansions of the number of possibilities occur all the time when we consider the number of ways parts can be arranged in three-dimensional space.

Given 4 leg holes in the table, the chance of a particular table leg having the right orientation to fit into one of the leg holes would only be about 1 in 8398080 divided by 4, or about 1 in 2099520. I say “divided by 4” because there are four leg holes that a particular table leg can fit into.

So the chance of a particular table leg fitting into one of the leg holes would be only about 1 in 2099520. But what would the chance be that all four of the legs would accidentally fit into the leg holes at the same instant? Since the probability of each leg fitting into a peg hole is an independent probability, we follow the rule that to calculate the chance of four independent events occurring, we multiply together the probability of each occurring. That gives us a probability of 1 in 2099520 to the fourth power. This is a probability of about 1 in 1.94 X 10²⁵.  In this model, the tumbling of the Table Part Tumbler can cause a leg to either fall in a leg hole or fall out of a leg hole. The odds would be greatly reduced if there was some rule that legs always stay in leg holes, but given the tumbling that is occurring, we should not assume such a rule. 

If there were just one of these Table Part Tumbler machines, the chance of a table being produced in a billion years would be very low. Let's imagine that each second of spinning produces a different combination. There are about 3 quadrillion seconds (3 x 10¹⁶) in a billion years. But with a probability of only about 1 in 1.94 X 10²⁵ of the table legs all fitting into the peg holes at the same time, the chance of a table being assembled during the billion year period is very low, less than 1 in 100,000,000.

Now you may object that when evolution occurs that there is not just one organism, but many organisms in a population. So perhaps the odds would be better. But they wouldn't be. Each spin of our Table Part Tumbler is like a random mutation in a particular organism, occurring in one particular spot of the organism. Even if there is a very large population of organisms, we should not expect that there will be more than one random mutation per second in one particular part of any of those organisms. For example, even if there are millions of eyeless fish in some particular population, fish that are being born and dying at various times, we would not expect that there would be more than one mutation per second in this entire population corresponding to the little spot of the fish where it might have an eye.

Moreover, for the sake of conceptual simplicity, our model of the Table Part Tumbler has ignored several difficulties that would worsen the odds very much. Consider the following:

(1) The model assumes that there are four peg holes that match the size and shape of the four table legs. But if the model were to better simulate random evolution, then both the width of the table legs and the width of the pegs would be randomly varying, and both the shape of the table legs and the shape of the pegs would be randomly varying, which would very much worsen the odds of the table forming.  
(2) The model has done nothing to factor in the extremely low probability of three or four logs being linked together by vines so you would have a flat table-like surface with four gaps resembling peg holes. 
(3) While wood logs might last for a very long time, after not many years there would occur decay that would rot away any vines that linked together three or four logs to make a flat table top. So if you ever were to have a freak occurrence that created a flat surface resembling a table top with peg holes, by vines linking together logs, such an improbable arrangement would not persist for longer than a few centuries. So instead of having a billion years for the table legs to fit into the table pegs, there would actually be only rare centuries (occasionally occurring during million-year periods) in which there was a possibility of such a fit. 

Altogether these factors would make it quadrillions of times less likely that the table would ever randomly assemble from accidental events in a forest. Given such factors which would vastly worsen the chance of a table being formed accidentally, and the very low probability previously calculated for the chance of all four legs fitting into the peg holes, it seems fair to conclude that the chance of a table (consisting of five or more parts fitting together in the right way) being assembled accidentally on any forest on Earth during a five-billion year period is less than 1 in 100,000,000.  Such an estimate is consistent with the fact that no one has ever observed any table-like structure (consisting of 5 or more parts fitting together in the right way to make a table) that accidentally formed in a forest. 

What does this exercise suggest? It suggests that the chance of even the simplest invention (requiring five or more parts) occurring from random events is very, very low, even given billions of years for random mutations to occur. We can put the matter concisely by saying: typically even the simplest of inventions (requiring exactly the right organization of five or more parts) are extremely unlikely to occur by chance, even if there are quadrillions of random attempts. In the crude mathematical model presented above, there are more than a quadrillion attempts, but the likelihood of the table accidentally appearing is still very, very low. 

These calculations are consistent with the average man's intuitive insight on this matter. The average man intuitively grasps the general truth that useful feats of construction requiring multiple parts fitting together do not occur by accident. 

A table is a ridiculously simple thing compared to biological innovations such as prokaryotic cells, eukaryotic cells, eyes, wings, cells, DNA, and the molecules needed for photosynthesis and respiration. What would the odds be if we were to calculate the chance of the simplest prototype of an eye appearing, or the simplest prototype of a cell, or the simplest prototype of one of the proteins needed for a vision, or any of thousands of similar things? It would be some probability incredibly smaller than the probabilities I have mentioned concerning the accidental appearance of a table. 

These considerations strongly suggest that the origin of complex biological innovations by random mutations and natural selection is impossible. Is there some way that natural selection can get us out of this jam? No, there is not. Natural selection or survival of the fittest can only get started (in regard to some biological innovation) when some biological innovation progresses to the point where some survival advantage is yielded. We may call this point the rewards threshold. Achieving such a reward threshold will always require at least some biological invention vastly more complicated than the very simple invention that is a table. And in almost every case the rewards threshold will not be reached until there is some biological innovation far more complicated and vastly more unlikely to occur by chance than a table.

Inside the human body are more than 20,000 types of protein molecules. Most of these protein molecules are complicated things, usually consisting of a special arrangement of more than 300 amino acids. Protein molecules only are functional if they fold in just the right way to achieve a particular three-dimensional shape. A slight change in the sequence of amino acids in a protein molecule will prevent it from folding, and will make the molecule useless.  A protein molecule cannot originate through some process of accumulation, because the molecule is useless if only a third of it or half of it exists.  Natural selection will not do anything to move a non-beneficial protein molecule closer and closer to a state of being beneficial.  On a biochemical level, we may say that there are more than 20,000 complex inventions in each of our bodies, those inventions being our protein molecules.   How many of these would we expect to exist, under current evolutionary assumptions? Not a single one of them.  The problem of explaining the origin of protein molecules was unknown to Darwin, who knew nothing of the immense complexity of either protein molecules or cells. 

It is easy to roughly calculate the chance of a functional protein molecule appearing by chance.  There are 20 amino acids used by living things, and the number of amino acids in a human protein varies from about 50 to more than 800. The scientific paper here refers to "some 50,000 enzymes (of average length of 380 amino acids)." According to the page here, the median number of amino acids in a human protein is 375, according to a scientific paper. The simplest calculation you could make is to calculate that the chance of a protein molecule appearing in its current form from a chance combination of amino acids is about 1 in 20 to the 375th power.  But that assumes that the protein molecule would not be functional unless it was exactly the way it is.  We do know of many reasons for assuming that for a protein molecule to be functional, a protein molecule has to be nearly the same as it is. Protein molecules are highly sensitive to mutation changes, so sensitive that changing randomly changing ten or twenty amino acids will typically disable the protein. This paper here estimates a probability of about 34% that a random amino acid change will produce a "functional inactivation" of a protein molecule. But that doesn't quite mean that a protein molecule has to be exactly as it is to be functional. 

Let us generously assume that there are many variations of a particular protein molecule that would still be functional.  A reasonable way to allow for such variation is to assume that only half of the amino acids need to have their current arrangement.  That would still leave you with a probability of about 1 in 20 to the 187th power for the chance of a typical protein molecule appearing from a chance combination of amino acids.  That likelihood is about 1 in 10 to the 243rd power, which is smaller than the chance of you guessing correctly all of the ten-digit telephone numbers of 24 consecutive strangers. It's a likelihood so small we would never expect it to happen by chance in the history of the observable universe. 

In his interesting recent book Cosmological Koans, which has some nice flourishes of literary style, the physicist Anthony Aquirre tells us about just how complex biological life is. He states the following on page 338:

"On the physical level, biological creatures are so much more complex in a functional way than current artifacts of our technology that there's almost no comparison. The most elaborate and sophisticated human-designed machines, while quite impressive, are utter child's play compared with the workings of a cell: a cell contains on the order of 100 trillion atoms, and probably billions of quite complex molecules working with amazing precision. The most complex engineered machines -- modern jet aircraft, for example -- have several million parts. Thus, perhaps all the jetliners in the world (without people in them, of course) could compete in functional complexity with a lowly bacterium."

Our Darwinist professors are blissfully ignorant of the math that crushes their explanatory pretensions. Acting rather like Darwin, who had no interest or ability in mathematics, our Darwinist professors pay no attention to combinatorial explosions, and in general pay little attention to mathematics. When they do mathematics, it is usually some type of tangential side calculation rather than the type of calculation that is most relevant to the likelihood of Darwinian evolution. What Darwinist professors mainly do is tell stories, and concentrate on narrative repetition, endlessly repeating claims that miracles of complex construction occurred by accident. But such thinkers are careful to never use the unintentional-sounding word "accident" when describing their theory of a 100% unintentional origin of biology wonders. Instead, they use the very intentional-sounding phrase "natural selection" to describe their theory of a 100% unintentional origin of biology wonders, which isn't terribly forthright. 

The lack of relevant probability calculations by Darwinist professors bothered the eminent physicist Wolfgang Pauli, discoverer of the subatomic Pauli Exclusion Principle on which our existence depends. Pauli stated the following:

"I should like to critically object that this model has not been supported by an affirmative estimate of probabilities so far. Such an estimate of the theoretical time scale of evolution as implied by the model should be compared with the empirical time scale. One would need to show that, according to the assumed model, the probability of de facto existing purposeful features to evolve was sufficiently high on the empirically known time scale. Such an estimate has nowhere been attempted though."

Pauli also stated the following about Darwinist biologists:

“In discussions with biologists I met large difficulties when they apply the concept of ‘natural selection’ in a rather wide field, without being able to estimate the probability of the occurrence in a empirically given time of just those events, which have been important for the biological evolution. Treating the empirical time scale of the evolution theoretically as infinity they have then an easy game, apparently to avoid the concept of purposesiveness. While they pretend to stay in this way completely ‘scientific’ and ‘rational’, they become actually very irrational, particularly because they use the word ‘chance’, not any longer combined with estimations of a mathematically defined probability, in its application to very rare single events more or less synonymous with the old word ‘miracle’.”

In general, Darwinist professors ignore the mountainous improbability of parts fitting together to make complex innovations. Our Darwinist experts typically speak as if having the parts for something is about as good as  having that thing, ignoring the reality that the more complex something is, the more improbable that parts would accidentally fit together to make that thing, even if all the parts were present.  How often have we heard SETI enthusiasts speaking as if having "the building blocks of life" in space (by which they mean mere amino acids) was almost as good as having a living thing (which requires at least a fantastically improbable special arrangement of such building blocks)? 

Roughly speaking, we can say that the improbability of a complex innovation appearing accidentally usually rises exponentially and geometrically as the number of parts needed for that innovation undergoes a simple linear increase, in most cases when a special arrangement of the parts is required. Similarly, the improbability of you throwing a handful of cards into the air and having them all form into a house of cards will rise exponentially and geometrically as the number of cards in your hand undergoes a simple linear increase.  Getting a two-card house of cards by accident isn't too hard, by having two cards lean together diagonally. But if all the humans in the world spent their whole lives throwing a deck of cards into the air, none of these random throws would ever produce a 20-card house of cards by accident. 

I have spoken about logs, and it is interesting that orthodox biologists are unable to account for the current distribution of animals in the world without resorting to some very unbelievable tall tales in which logs play a part.  For example, there are many similarities between Old World monkeys and New World Monkeys.  Committed to the assumption that such similarities must be because of common descent, Darwinist professors maintain that the New World monkeys are descendants of the Old World monkeys, and that such an ancestry was able to occur because some Old World monkeys rafted across the Atlantic ocean something like 40 million years ago, arriving in the New World.  Such an idea is supremely unbelievable for several reasons: (1) the incredible improbability of a sea-worthy raft appearing accidentally from logs; (2) the almost equally great improbability that any monkeys would ever swim out to sea and jump on such a raft; (3) the almost equally great improbability that such monkeys could ever survive a voyage across the Atlantic.  You can calculate the improbability of item (1) by doing calculations similar to those I have done in regard to a table. The chance of a sea-worthy raft appearing accidentally are almost as bad as the chance of a table appearing accidentally. 

You can make some rough estimates:

(1) Chance per year that a stable raft might accidentally form, one sea-worthy enough to take monkeys across the Atlantic: less than  in a trillion.

(2) Chance that monkeys would ever swim out and jump on such a raft, and stay on it as it floated out to sea: less than 1 in a billion.

(3) Chance that monkeys on such a raft would ever survive a voyage across the Atlantic: less than 1 in a thousand.

The overall likelihood of such a trans-Atlantic monkey voyage per year would be less than the product of all three of these independent probabilities multiplied together: 1 in a trillion times 1 in a billion times 1 in a thousand, which gives a probability of less than 1 in 1,000,000,000,000,000,000,000,000 per year.  The chance that such a thing would have occurred during a 10-million year window of opportunity is, according to such an estimation, less than 1 in 10,000,000,000,000,000.  But as fantastically improbable as such an event would have been, it would still have been trillions of times more probable than the cases of accidental engineering that our biologists ask us to believe in. 

In the willingness of some to accept these supremely absurd tales of trans-Atlantic rafting monkeys, we see what seems to be an example of what is called escalation of commitment. Having wedded themselves to the notion of a purposeless origin of biological organisms, certain people will seemingly accept many an absurdity that follows from such an idea.  At no point does it ever occur to such people to ask whether credulity has been strained too much. Innumerable weighty straw-bundles are heaped upon the camel's back, each a new belief requirement required by the original assumption; and such people will never ask whether the latest one has broken the camel's back, requiring one to finally look for alternatives to the original assumption. Faced with evidence of extremely precise fine-tuning in the universe's fundamental constants, which dramatically subverts their "purposeless nature" assumptions, such people will not hesitate to postulate a multiverse of innumerable universes, which is like piling a million additional straw bundles on the camel's back.