the entire wiki with video and photo galleries
find something interesting to watch in seconds
click links in text for more info
Criticism of Darwinism in Mathematics
Page 1 of 1

Mathematics has a long tradition of criticism of evolutionary biology. Darwin’s theory of evolution is essentially based on a mathematically describable algorithm which uses a random trial and error process to produce complex organisms. Some prominent mathematicians argue that the observed complexity of life cannot have been achieved by chance.

What does generating new forms of life mean? Most biologists agree that it would entail generating a new protein. Genes are segments of DNA that spell out the links of a protein chain. DNA has the shape of a spiral staircase.

A section of DNA
A section of DNA

Mutations occur when DNA splits in half down the center of the staircase. Each half-staircase attracts a matching set of molecules (nucleotides) from the surrounding chemical soup and two complete new DNA molecules emerge. A random mistake in this replication process yields a mutation, and if it occurs in a so-called germ cell, it can be passed on to the next generation.

In 1967 Victor Weisskopf, the former Group Leader of the Theoretical Division of the Manhattan Project, organized a picnic lunch at his house in Geneva. “A rather weird discussion” took place between mathematicians Weisskopf, Schützenberger, Ulam and Eden, and the biologists Kaplan and Koprowski. The subject was evolution by natural selection. The mathematicians were highly skeptical of the optimism of the evolutionists about what could be achieved by chance.

Victor Frederick Weisskopf
Victor Frederick Weisskopf

After heated debates it was proposed that a symposium be arranged to consider the points of dispute more systematically. The symposium was held in 1966 at the Wistar Institute in Philadelphia. It was called Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution and its proceedings were published under the same title in 1967 (Wistar Institute Press, 1967, No. 5).

The general consensus among mathematicians at the symposium was that Darwinism was simply not mathematically tenable. “It seems to require many thousands, perhaps millions, of successive mutations to produce even the easiest complexity we see in life now. It appears... that no matter how large the probability of a single mutation is, should it be even as great as one-half, you would get this probability raised to a millionth power, which is so very close to zero that the chances of such a chain seem to be practically non-existent.” (Stanislaw M. Ulam, “How to Formulate Mathematically Problems of Rate of Evolution,” in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, p. 21)

The author of this quote, Stanislaw Ulam participated in the Manhattan Project and is known as the inventor of the Teller–Ulam design of thermonuclear weapons. Ulam also originated the Monte Carlo method of computation, and suggested nuclear pulse propulsion.

Stanislaw Ulam
Stanislaw Ulam
The first test of the Teller–Ulam design (a staged fusion bomb)
The first test of the Teller–Ulam design (a staged fusion bomb)

A protein molecule is a chain of around 150 links. Each link consists of one of 20 amino acids. There are thus 20150 (~ 10195) possible amino acid sequences of length 150, but less than 1012 actual proteins are believed to exist. Amino acids cannot be grouped at random, only certain combinations will form themselves into stable proteins.

The chance of assembling a single stable protein from amino acids at random is estimated at 1 in 1074. The total number of organisms that have ever lived on Earth is estimated only at 1040, and this number is dominated by bacteria. Most bacteria pass on their genetic information unmutated, but even if we assume each one of them yielded one mutation, the chance of randomly achieving the complexity of any single existing protein is 1 in 1034, which is infinitely smaller, than, for instance, the chance of winning the jackpot in a nationwide lottery (1 in 108).

Similar numbers arise in the analysis of natural language. Murray Eden of MIT, another participant of the Wistar Symposium, was also concerned with the element of randomness, which supposedly provides the mutational variation upon which evolution depends: “No currently existing formal language can tolerate random changes in the symbol sequences which express its sentences. Meaning is almost invariably destroyed”.

For instance, there are 27150 (~ 10214) possible sequences of English letters (with spaces) of length 150. Of these only around 10125 consist of valid English words: assuming 5 letters on average plus a space per word, we have a total of 25 words, so a dictionary of 105 words can produce 10125 phrases. Thus the chance of generating a valid sequence is 1 in 1089.

Genes that are obviously variable within natural populations seem to affect only minor aspects of form and function, while those genes that govern major changes, apparently do not vary or vary only to the detriment of the organism.

The German geneticists Christiane Nüsslein-Volhard and Eric Wieschaus won the Nobel Prize in 1995 for the “Heidelberg screen,” an exhaustive investigation of mutations of Drosophila. “We think we’ve hit all the genes required to specify the body plan of Drosophila,” said Wieschaus in answering a question after a talk. “Not one promising as raw materials for macroevolution”, because mutations in them all killed off the fly long before it could mate.

A large number of mutations occurring at once is guaranteed to be deadly, because, as has been shown, the chances of accidentally producing a viable result in such case are infinitely small.

Starting from a valid sequence and introducing only a few minor changes during a lifetime would not kill an organism, but then the number of lifetimes needed to progress from the simplest to the most complex organisms would be infinitely larger than the total time life has existed on Earth. The total number of organisms required (given that most mutations do not produce useful results) would by far exceed the estimated total number of organisms that have ever lived.

Manhattan Project [videos]
The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of 
Manhattan Project - The Trinity test of the Manhattan Project was the first detonation of a nuclear weapon.
Manhattan Project - A 1940 meeting at Berkeley, California: Ernest O. Lawrence, Arthur H. Compton, Vannevar Bush, James B. Conant, Karl T. Compton, and Alfred L. Loomis
The Trinity test of the Manhattan Project was the first detonation of a nuclear weapon.
Geneva [videos]
Geneva is the second-most populous city in Switzerland and the most populous city of the Romandy, the French-speaking part of Switzerland. Situated where the 
Geneva - A view over Geneva and the lake
Geneva - Geneva seen from SPOT Satellite
A view over Geneva and the lake
Geneva seen from SPOT Satellite
Geneva - The Geneva area seen from the Salève in France. The Jura mountains can be seen on the horizon.
Geneva - Coat of arms of Geneva as part of the pavement in front of the Reformation Wall, 2013
The Geneva area seen from the Salève in France. The Jura mountains can be seen on the horizon.
Coat of arms of Geneva as part of the pavement in front of the Reformation Wall, 2013
Natural selection [videos]
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charles Darwin popularised the term "natural selection" 
Natural selection - Modern biology began in the nineteenth century with Charles Darwin's work on evolution by natural selection.
Natural selection - Aristotle considered whether different forms could have appeared, only the useful ones surviving.
Modern biology began in the nineteenth century with Charles Darwin's work on evolution by natural selection.
Aristotle considered whether different forms could have appeared, only the useful ones surviving.
Natural selection - Part of Thomas Malthus's table of population growth in England 1780–1810, from his Essay on the Principle of Population, 6th edition, 1826
Natural selection - Charles Darwin noted that pigeon fanciers had created many kinds of pigeon, such as Tumblers (1, 12), Fantails (13), and Pouters (14) by selective breeding.
Part of Thomas Malthus's table of population growth in England 1780–1810, from his Essay on the Principle of Population, 6th edition, 1826
Charles Darwin noted that pigeon fanciers had created many kinds of pigeon, such as Tumblers (1, 12), Fantails (13), and Pouters (14) by selective breeding.
Wistar Institute [videos]
The Wistar Institute is an international leader in biomedical science, with special expertise in oncology, immunology, infectious disease and vaccine research. Located in the University City section of Philadelphia, Wistar was founded in 1892 as America's first nonprofit institution solely focused 
Wistar Institute - Isaac J. Wistar, 1852, San Francisco, California
Wistar Institute - The Wistar Institute of Anatomy and Biology, c. 1900–1910
Isaac J. Wistar, 1852, San Francisco, California
The Wistar Institute of Anatomy and Biology, c. 1900–1910
Wistar Institute - A Wistar rat
Wistar Institute - Koprowski in 2007
A Wistar rat
Koprowski in 2007
Philadelphia [videos]
Philadelphia, sometimes known colloquially as Philly, is the largest city in the U.S. state and Commonwealth of Pennsylvania, and the sixth-most populous U.S. city, with a 2017 census-estimated population of 1,580,863. Since 1854, the city has been coterminous with Philadelphia County, the most 
Philadelphia - Benjamin Franklin, 1777
Philadelphia - Juxtaposition of architectural styles in Center City, showing One Liberty Place and City Hall
Juxtaposition of architectural styles in Center City, showing One Liberty Place and City Hall
Philadelphia - "Leacht Quimhneachain Na Gael", an Irish famine memorial at Penn's Landing honors the large Irish community (14.2% of the city's population).
Philadelphia - Interior of the Cathedral Basilica of Saints Peter and Paul
"Leacht Quimhneachain Na Gael", an Irish famine memorial at Penn's Landing honors the large Irish community (14.2% of the city's population).
History of the Teller–Ulam design [videos]
This article chronicles the history and origins of the Teller–Ulam design, the technical concept behind modern thermonuclear weapons, also known as hydrogen bombs. This design, the details of which are military secrets known to only a handful of major nations, is believed to be used in virtually 
History of the Teller–Ulam design - Ivy Mike, the first full test of the Teller–Ulam design (a staged fusion bomb), with a yield of 10.4 megatons (November 1, 1952)
History of the Teller–Ulam design - Physicist Edward Teller was for many years the chief force lobbying for research into developing fusion weapons.
Ivy Mike, the first full test of the Teller–Ulam design (a staged fusion bomb), with a yield of 10.4 megatons (November 1, 1952)
Physicist Edward Teller was for many years the chief force lobbying for research into developing fusion weapons.
History of the Teller–Ulam design - Ivy King, the largest pure fission bomb tested by the US, yielding 500 kt (November 16, 1952)
History of the Teller–Ulam design - A view of the Sausage device casing, with its diagnostic and cryogenic equipment attached. The long pipes would receive the first bits of radiation from the primary and secondary ("Teller light") just before the device fully detonated.
Ivy King, the largest pure fission bomb tested by the US, yielding 500 kt (November 16, 1952)
A view of the Sausage device casing, with its diagnostic and cryogenic equipment attached. The long pipes would receive the first bits of radiation from the primary and secondary ("Teller light") just before the device fully detonated.
Bacteria [videos]
Bacteria are a type of biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria have a number of shapes, ranging from spheres to rods and spirals. Bacteria were among the 
Bacteria - Scanning electron micrograph of Escherichia coli rods
Bacteria - An electron micrograph of Halothiobacillus neapolitanus cells with carboxysomes inside, with arrows highlighting visible carboxysomes. Scale bars indicate 100 nm.
An electron micrograph of Halothiobacillus neapolitanus cells with carboxysomes inside, with arrows highlighting visible carboxysomes. Scale bars indicate 100 nm.
Bacteria - Helicobacter pylori electron micrograph, showing multiple flagella on the cell surface
Bacteria - Bacillus anthracis (stained purple) growing in cerebrospinal fluid
Helicobacter pylori electron micrograph, showing multiple flagella on the cell surface
Bacillus anthracis (stained purple) growing in cerebrospinal fluid
Nobel Prize [videos]
The Nobel Prize is a set of annual international awards bestowed in several categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances. — The 
Nobel Prize - Alfred Nobel had the unpleasant surprise of reading his own obituary, which was titled The merchant of death is dead, in a French newspaper.
Nobel Prize - Table at the 2005 Nobel Banquet in Stockholm
Alfred Nobel had the unpleasant surprise of reading his own obituary, which was titled The merchant of death is dead, in a French newspaper.
Table at the 2005 Nobel Banquet in Stockholm
Nobel Prize - Laureates receive a heavily decorated diploma together with a gold medal and the prize money. Here Fritz Haber's diploma is shown, which he received for the development of a method to synthesise ammonia.
Nobel Prize - When it was announced that Henry Kissinger was to be awarded the Peace Prize, two of the Norwegian Nobel Committee members resigned in protest.
Laureates receive a heavily decorated diploma together with a gold medal and the prize money. Here Fritz Haber's diploma is shown, which he received for the development of a method to synthesise ammonia.
When it was announced that Henry Kissinger was to be awarded the Peace Prize, two of the Norwegian Nobel Committee members resigned in protest.
Drosophila [videos]
Drosophila is a genus of flies, belonging to the family Drosophilidae, whose members are often called "small fruit flies" or pomace flies, vinegar flies, or wine flies, a reference to the characteristic of many species to linger around overripe or rotting fruit. They should not 
Drosophila - Side view of head showing characteristic bristles above the eye
Drosophila - D. setosimentum, a species of Hawaiian picture-wing fly
Side view of head showing characteristic bristles above the eye
D. setosimentum, a species of Hawaiian picture-wing fly
Drosophila - Image: Fruit fly larva 01
Drosophila - Image: Fruit fly pupae 01
Image: Fruit fly larva 01
Image: Fruit fly pupae 01
Mutation [videos]
In biology, a mutation is the permanent alteration of the nucleotide sequence of the genome of an organism, virus, or extrachromosomal DNA or other genetic elements.Mutations result from errors during DNA replication or other types of damage to DNA (such as may be caused 
Mutation - Hugo de Vries, making a painting of an evening primrose, the plant which had apparently produced new forms by large mutations in his experiments, by Thérèse Schwartze, 1918
Mutation - A mutation has caused this moss rose plant to produce flowers of different colors. This is a somatic mutation that may also be passed on in the germline.
Hugo de Vries, making a painting of an evening primrose, the plant which had apparently produced new forms by large mutations in his experiments, by Thérèse Schwartze, 1918
A mutation has caused this moss rose plant to produce flowers of different colors. This is a somatic mutation that may also be passed on in the germline.
Mutation - Image: Darwin Hybrid Tulip Mutation 2014 05 01
Image: Darwin Hybrid Tulip Mutation 2014 05 01
Thermonuclear weapon [videos]
A thermonuclear weapon, or fusion weapon, is a second-generation nuclear weapon design which affords vastly greater destructive power than first-generation atomic bombs. Modern fusion weapons consist essentially of two main components: a nuclear fission primary stage (fueled by uranium-235 or 
Thermonuclear weapon - Edward Teller in 1958
Thermonuclear weapon - Operation Grapple on Christmas Island was the first British hydrogen bomb test.
Edward Teller in 1958
Operation Grapple on Christmas Island was the first British hydrogen bomb test.
Thermonuclear weapon - Photographs of warhead casings, such as this one of the W80 nuclear warhead, allow for some speculation as to the relative size and shapes of the primaries and secondaries in U.S. thermonuclear weapons.
Photographs of warhead casings, such as this one of the W80 nuclear warhead, allow for some speculation as to the relative size and shapes of the primaries and secondaries in U.S. thermonuclear weapons.
Christiane Nüsslein-Volhard [videos]
Christiane Nüsslein-Volhard is a German developmental biologist and 1995 Nobel Prize-winner. — Nüsslein-Volhard earned her PhD in 1974 from the University of Tübingen, where she studied protein-DNA interaction. She won the Albert Lasker Award for Basic Medical 
Christiane Nüsslein-Volhard - A preparation of the cuticle from a Drosophila embryo, similar to those examined by Nüsslein-Volhard. Note the bands of denticles on the left hand side (towards the head) of each segment.
Christiane Nüsslein-Volhard - Image: Christiane Nüsslein Volhard mg 4406
A preparation of the cuticle from a Drosophila embryo, similar to those examined by Nüsslein-Volhard. Note the bands of denticles on the left hand side (towards the head) of each segment.
Image: Christiane Nüsslein Volhard mg 4406
Christiane Nüsslein-Volhard - Image: Christiane Nüsslein Volhard mg 4383
Image: Christiane Nüsslein Volhard mg 4383
Nuclear pulse propulsion [videos]
Nuclear pulse propulsion or external pulsed plasma propulsion, is a hypothetical method of spacecraft propulsion that uses nuclear explosions for thrust. It was first developed as Project Orion by DARPA, after a suggestion by Stanislaw Ulam in 1947. Newer designs using inertial confinement fusion 
Nuclear pulse propulsion - An artist's conception of the Project Orion "basic" spacecraft, powered by nuclear pulse propulsion.
Nuclear pulse propulsion - Concept graphic of a fusion-driven rocket powered spacecraft arriving at Mars
An artist's conception of the Project Orion "basic" spacecraft, powered by nuclear pulse propulsion.
Concept graphic of a fusion-driven rocket powered spacecraft arriving at Mars
Amino acid [videos]
Amino acids are organic compounds containing amine and carboxyl functional groups, along with a side chain specific to each amino acid. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen, although other elements are found in the 
Amino acid - Image: Muscle protein synthesis signaling cascades
Amino acid - Image: Resistance exercise induced muscle protein synthesis
Image: Muscle protein synthesis signaling cascades
Image: Resistance exercise induced muscle protein synthesis
Protein [videos]
Proteins are large biomolecules, or macromolecules, consisting of one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, responding to stimuli, providing structure to cells and 
Protein - A representation of the 3D structure of the protein myoglobin showing turquoise α-helices. This protein was the first to have its structure solved by X-ray crystallography. Towards the right-center among the coils, a prosthetic group called a heme group (shown in gray) with a bound oxygen molecule (red).
A representation of the 3D structure of the protein myoglobin showing turquoise α-helices. This protein was the first to have its structure solved by X-ray crystallography. Towards the right-center among the coils, a prosthetic group called a heme group (shown in gray) with a bound oxygen molecule (red).
Gene [videos]
In biology, a gene is a sequence of nucleotides in DNA or RNA that codes for a molecule that has a function. During gene expression, the DNA is first copied into RNA. The RNA can be directly functional or be the intermediate template for a protein that performs a function. The transmission of genes 
Gene - Gregor Mendel
Gregor Mendel
Nucleotide [videos]
Nucleotides are organic molecules that serve as the monomer units for forming the nucleic acid polymers deoxyribonucleic acid and ribonucleic acid, both of which are essential biomolecules within all life-forms on Earth. Nucleotides are the building blocks of nucleic acids; they are 
Nucleotide - Showing the arrangement of nucleotides within the structure of nucleic acids: At lower left, a monophosphate nucleotide; its nitrogenous base represents one side of a base-pair. At upper right, four nucleotides form two base-pairs: thymine and adenine (connected by double hydrogen bonds) and guanine and cytosine (connected by triple hydrogen bonds). The individual nucleotide monomers are chain-joined at their sugar and phosphate molecules, forming two 'backbones' (a double helix) of a nucleic acid, shown at upper left.
Showing the arrangement of nucleotides within the structure of nucleic acids: At lower left, a monophosphate nucleotide; its nitrogenous base represents one side of a base-pair. At upper right, four nucleotides form two base-pairs: thymine and adenine (connected by double hydrogen bonds) and guanine and cytosine (connected by triple hydrogen bonds). The individual nucleotide monomers are chain-joined at their sugar and phosphate molecules, forming two 'backbones' (a double helix) of a nucleic acid, shown at upper left.
Victor Weisskopf [videos]
Victor Frederick "Viki" Weisskopf was an Austrian-born American theoretical physicist. He did postdoctoral work with Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli and Niels Bohr. During World War II he was Group Leader of the Theoretical Division of the 
Victor Weisskopf - Victor Frederick Weisskopf in the 1940s.
Victor Frederick Weisskopf in the 1940s.
Marcel-Paul Schützenberger [videos]
Marcel-Paul "Marco" Schützenberger was a French mathematician and Doctor of Medicine. He worked in the fields of formal language, combinatorics, and information theory. In addition to his formal results in mathematics, he was "deeply involved in struggle 
Marcel-Paul Schützenberger - Image: Schützenberger
Image: Schützenberger
Neo-Darwinism [videos]
Neo-Darwinism is the interpretation of Darwinian evolution through natural selection as it has variously been modified since it was first proposed. It was early on used to name Charles Darwin's ideas of natural selection separated from his hypothesis of pangenesis as a Lamarckian source of 
Neo-Darwinism - Image: George John Romanes, photograph by Elliott & Fry
Image: George John Romanes, photograph by Elliott & Fry
Macroevolution [videos]
Macroevolution is evolution on a scale at or above the level of species, in contrast with microevolution, which refers to smaller evolutionary changes of allele frequencies within a species or population. Macroevolution and microevolution describe fundamentally identical processes on different time 
Macroevolution - Early cetaceans like Ambulocetus natans possessed hindlimbs, derived from their walking ancestors, but no longer useful in their marine environment.
Early cetaceans like Ambulocetus natans possessed hindlimbs, derived from their walking ancestors, but no longer useful in their marine environment.
From this Article