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The Theory of Evolution is stated to be a process driven by random mutations and the natural selection of beneficial ones.
A scientist used computer modelling of proteins consisting of random chains of amino acids. A protein is a chain of roughly 300 amino acids. At each position of the chain, there can be any one of about 20 different amino acids. The computer model calculated it was extremely improbable a protein formed by a random combination of amino acids could correctly fold into a viable 3-dimensional shape. This is just folding into a 3-d shape and does not even consider being able to do useful work.
Animals have vast amounts of genetic material. Humans have 3 billion base-pairs of DNA. At a certain level of complexity, a few random mutations will cause havoc, rather than helping produce new functionality.
Through selective breeding we observe dogs of different sizes, shapes and fur colour. None of these changes involves the creation of new functionality, such as an eye, the ability to process language or abstract thought. Selective breeding is just tinkering.
A test tube of simple chemicals will produce new substances of all stereoisomers i.e. both left and right handed molecules. Animal life is made up of chemicals of only one type of handedness. (For the non-chemists here, we have both left and right hands. Both are different, but are mirror images of each other. The same goes for stereoisomers.) Yet again, forming animal life from a soup of simple chemicals is more difficult that we would think.
One cell of our bodies is more complex than a whole city. Did we really arise by a random process?