There is a scientific challenge posed. Nobody in Darwin's archaic camp wants to attempt it because it is clearly impossible to get anywhere with odds of 1 in 10 to the 10,000th or less.
The soundness of Dembski's concept of specified complexity and the validity of arguments based on this concept are widely disputed. A frequent criticism (see Elsberry and Shallit) is that Dembski has used the terms "complexity", "information" and "improbability" interchangeably. These numbers measure properties of things of different types: Complexity measures how hard it is to describe an object (such as a bitstring), information is how much the uncertainty about the state of an object is reduced by knowing the state of another object or system, and improbability measures how unlikely an event is given a probability distribution.
On page 150 of No Free Lunch Dembski claims he can demonstrate his thesis mathematically: "In this section I will present an in-principle mathematical argument for why natural causes are incapable of generating complex specified information." When Tellgren investigated Dembski's "Law of Conservation of Information” using a more formal approach, he concluded it is mathematically unsubstantiated. Dembski responded in part that he is not "in the business of offering a strict mathematical proof for the inability of material mechanisms to generate specified complexity". Jeffrey Shallit states that Demski's mathematical argument has multiple problems, for example; a crucial calculation on page 297 of No Free Lunch is off by a factor of approximately 1065.
Dembski's calculations show how a simple smooth function cannot gain information. He therefore concludes that there must be a designer to obtain CSI. However, natural selection has a branching mapping from one to many (replication) followed by pruning mapping of the many back down to a few (selection). When information is replicated, some copies can be differently modified while others remain the same, allowing information to increase. These increasing and reductional mappings were not modeled by Dembski. In other words, Dembski's calculations do not model birth and death. This basic flaw in his modeling renders all of Dembski's subsequent calculations and reasoning in No Free Lunch irrelevant because his basic model does not reflect reality. Since the basis of No Free Lunch relies on this flawed argument, the entire thesis of the book collapses.
According to Martin Nowak, a Harvard professor of mathematics and evolutionary biology "We cannot calculate the probability that an eye came about. We don't have the information to make the calculation".
Dembski's critics note that specified complexity, as originally defined by Leslie Orgel, is precisely what Darwinian evolution is supposed to create. Critics maintain that Dembski uses "complex" as most people would use "absurdly improbable". They also claim that his argument is circular: CSI cannot occur naturally because Dembski has defined it thus. They argue that to successfully demonstrate the existence of CSI, it would be necessary to show that some biological feature undoubtedly has an extremely low probability of occurring by any natural means whatsoever, something which Dembski and others have almost never attempted to do. Such calculations depend on the accurate assessment of numerous contributing probabilities, the determination of which is often necessarily subjective. Hence, CSI can at most provide a "very high probability", but not absolute certainty.
Another criticism refers to the problem of "arbitrary but specific outcomes". For example, if a coin is tossed randomly 1000 times, the probability of any particular outcome occurring is roughly one in 10300. For any particular specific outcome of the coin-tossing process, the a priori probability (probability measured before event happens) that this pattern occurred is thus one in 10300, which is astronomically smaller than Dembski's universal probability bound of one in 10150. Yet we know that the post hoc probability (probabilitly as observed after event occurs) of its happening is exactly one, since we observed it happening. This is similar to the observation that it is unlikely that any given person will win a lottery, but, eventually, a lottery will have a winner; to argue that it is very unlikely that any one player would win is not the same as proving that there is the same chance that no one will win. Similarly, it has been argued that "a space of possibilities is merely being explored, and we, as pattern-seeking animals, are merely imposing patterns, and therefore targets, after the fact."
Apart from such theoretical considerations, critics cite reports of evidence of the kind of evolutionary "spontanteous generation" that Dembski claims is too improbable to occur naturally. For example, in 1982, B.G. Hall published research demonstrating that after removing a gene that allows sugar digestion in certain bacteria, those bacteria, when grown in media rich in sugar, rapidly evolve new sugar-digesting enzymes to replace those removed. Another widely cited example is the discovery of nylon eating bacteria that produce enzymes only useful for digesting synthetic materials that did not exist prior to the invention of nylon in 1935.