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# Some Problems Can Be Proved Unsolvable

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Here are two mathematical problems for you to work on in your spare time, and one problem from biology:

1. Find positive integers x,y, z and n>2, such that xn+yn=zn.
2. Remove two diagonally opposite corner squares from a chess board, and cover the remaining 62 squares with 31 dominoes, each of which covers two adjacent squares.
3. Explain how life could have originated and evolved into intelligent humans, through entirely natural (unintelligent) processes.

You can spend a lot of time trying different solutions to mathematical problem #1. After a while you might begin to wonder if it can be done, but don’t give up, there are an infinite number of integers you can try for x,y,z and n.

For problem #2, get out your chess board and some dominoes, cut out two diagonally opposite corner squares, and start covering. If your first try doesn’t work, keep working, there are a huge number of ways you can lay out the dominoes.

A number of theories as to how life could have originated through entirely unintelligent processes have been proposed, but none are plausible, and this problem is generally considered to have not yet been solved. But new theories are constantly being proposed, and it would be unscientific to give up and declare the problem to be unsolvable…wouldn’t it? Charles Darwin felt he had explained how intelligent humans evolved from the first living organisms though entirely unintelligent processes. Today his theory is doubted by an increasing number of scientists, and most of those who still support it would probably agree with microbiologist Rene Dubos that “its real strength is that however implausible it may appear to its opponents, they do not have a more plausible one to offer in its place” [The Torch of Life, 1962]. Most of these doubters have proposed modifications to his theory or alternative theories of their own, but there are always serious problems with the alternative theories too. However, scientists should never give up, even if none of the theories proposed so far are plausible…right? French biologist Jean Rostand [A Biologist’s View, 1956] says “However obscure the causes of evolution appear to me to be, I do not doubt for a moment that they are entirely natural. We have ample time to discover them; biology is in its infancy.”

Well, mathematicians sometimes do give up, after we have proved a problem to be impossible to solve. How can you prove a problem is impossible to solve, if you can’t examine every possible solution? Often you say, assume there is a solution, then using that assumption you prove something that is obviously false, or known to be false. Pierre de Fermat claimed in 1637 to have a simple proof that problem #1 has no solution, but the proof was “too large to fit in the margin” of a document he was working with. Did Fermat really have a short, correct proof? Not likely, because no one else could find a rigorous proof until 358 years later, when Andrew Wiles produced a very long, complicated proof of Fermat’s last theorem. Whether or not Fermat’s short proof was valid may never be known, but at least his conclusion was correct.

After trying a long while, you may get the idea that mathematical problem #2 is also impossible to solve, but if you try to prove it is impossible, you may start to think that this one may also take years to prove impossible. But in mathematics, you can often prove an apparently difficult theorem in a surprisingly simple way once you look at it from the right perspective. For this problem, all you have to do is notice that each domino will cover one black and one red square, so if you could solve the problem, you would have to conclude that the board consists of the same number (31) of black and red squares. But this conclusion is false: the original chessboard had an equal number of red and black squares, but the diagonally opposite corners you removed were the same color!

Well, I have a very simple proof that the biological problem #3 posed above is also impossible to solve, that does fit in the margin of this document. All one needs to do is realize that if a solution were found, we would have proved something obviously false, that a few (four, apparently) fundamental, unintelligent forces of physics alone could have rearranged the fundamental particles of physics into libraries full of science texts and encyclopedias, computers connected to monitors, keyboards, laser printers and the Internet, cars, trucks, airplanes, nuclear power plants and Apple iPhones.

Is this really a valid proof? It seems perfectly valid to me, as I cannot think of anything in all of science that can be stated with more confidence than that a few unintelligent forces of physics alone could not have rearranged the basic particles of physics into Apple iPhones. Unfortunately, most biologists and other scientists don’t seem to be impressed by such simple proofs; they don’t believe it is possible to refute all their solutions to problem #3 without looking at the details of each.

For the first mathematical problem, it didn’t take too many years of failed attempts before mathematicians realized their time was better spent proving this problem unsolvable than continuing with attempts to solve it. Maybe after another 358 years of failed attempts to solve problem #3, someone will finally produce a proof that convinces even biologists that they didn’t fail because they just never hit on the right solution, but because the problem doesn’t have a solution.

Why are naturalists/materialist so closed-minded philosophically when it comes to the concept of intelligent design? Why do they reject it a priori without even considering the arguments? ID’ists do not reject the idea of natural causation a priori. Indeed, much of what we perceive in the natural world can be (indeed should be) explained “naturally.” What we do reject is that natural causes are the only kind of causes that must be used to explain the origin and evolution of life. For example, in his book Darwin’s Black Box, Michael Behe asks,
“Might there be an as yet undiscovered natural process that would explain biochemical complexity? No one would be foolish enough to categorically deny the possibility. Nonetheless we can say that if there is such a process, no one has a clue how it would work. Further it would go against all human experience, like postulating that a natural process might explain computers… In the face of the massive evidence we do have for biochemical design, ignoring the evidence in the name of a phantom process would be to play the role of detective who ignore the elephant.” (p. 203-204)
Basically Behe is asking, if biochemical complexity (irreducible complexity) evolved by some natural process x, how did it evolve? That is a perfectly legitimate scientific question. Notice that even though in DBB Behe was criticizing Neo-Darwinism he is not ruling out a priori some other mindless natural evolutionary process, “x”, might be able to explain IC. Behe is simply claiming that at the present there is no known natural process that can explain how irreducibly complex mechanisms and processes originated. If he and other ID’ist are categorically wrong then our critics need to provide the step-by-step-by-step empirical explanation of how they originated, not just speculation and wishful thinking. Unfortunately our regular interlocutors seem to only be able to provide the latter not the former. Behe made another point which is worth keeping in mind.
“In the abstract, it might be tempting to imagine that irreducible complexity simply requires multiple simultaneous mutations - that evolution might be far chancier than we thought, but still possible. Such an appeal to brute luck can never be refuted... Luck is metaphysical speculation; scientific explanations invoke causes.”
In other words, a strongly held metaphysical belief is not a scientific explanation.john_a_designer
February 11, 2021
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ET: That is a lie as there isn’t any evidence that supports unguided evolution. And there isn’t any such thing as “unguided evolutionary theory”. Other opinions are available. And all you have is your opinion with respect to Dr Sewell presenting a straw man He did neglect to discuss or mention many of the arguments, supporting data and multiple threads of evidence. He intentionally tried to dumb-down the basic unguided evolutionary thesis.JVL
February 11, 2021
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JVL:
Christopher Hitchens didn’t create or present the evidence but he looked at it and that led him to believe unguided evolutionary theory to be true.
That is a lie as there isn't any evidence that supports unguided evolution. And there isn't any such thing as "unguided evolutionary theory". And all you have is your opinion with respect to Dr Sewell presenting a straw manET
February 11, 2021
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Even though I think I.D. provokes some interesting questions I am actually not an I.D. proponent in the same sense that several other commenters here are. I don’t think I.D. is “science” (the empirical study of the natural world) any more than naturalism/materialism is science. So questions from materialists, like “who designed the designer,” are not scientific questions; they are philosophical and/or theological questions. However, many of the questions have philosophical/theological answers. For example, the theist would answer the question, “who designed the designer,” by arguing that the designer (God) always existed. The materialist can’t honestly reject that explanation because historically materialism has believed that the universe has always existed. Presently they are trying to shoehorn the multiverse into the discussion to get around the problem of the Big-Bang. Of course, this is a problem because there is absolutely no scientific evidence for the existence of a multiverse. In other words, it just an arbitrary ad hoc explanation used in an attempt to try to wiggle out of a legitimate philosophical question. However, this is not to say that science can’t provoke some important philosophical and theological questions-- questions which at present those questions can’t be answered scientifically. For example: Scientifically it appears the universe is about 14.5 billion years old. Who or what caused the universe to come into existence? If it was “a what”-- just natural causes-- how do we know that? Why does the universe appear to exhibit teleology, or design and purpose? In other words, what is the explanation for the universes so-called fine tuning? How did chemistry create the code in DNA or RNA? How dose mindless matter “create” consciousness and mind? If consciousness and mind are “just an appearance” how do we know that? There are many questions that arise out of science which are philosophical and/or theological questions. Is it possible that they could have scientific explanations? Possibly. But even if someday some of them could be answered scientifically that doesn’t make them at present illegitimate philosophical/theological questions, because we don’t know if they have, or ever could have, scientific answers.john_a_designer
February 11, 2021
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ET: And he said that absent evidence it can be dismissed. Believing isn’t evidence. I didn't say it was. Christopher Hitchens didn't create or present the evidence but he looked at it and that led him to believe unguided evolutionary theory to be true. I am not sure Dr Sewell argued against a straw man Your opinion. Other opinions are available.JVL
February 11, 2021
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The typical anti-ID troll, many of whom unfortunately, show up here appears to be someone who is motivated by an extreme antireligious prejudice. However, the problem with any kind of prejudice is that taken to the extreme it turns its advocate into the a bad reflection of what he (or she) hates: an incorrigible, irrational dogmatist-- in other words, a fundamentalist. No one summed it up better than theoretical physicist and Nobel Laureate Peter Higgs, who himself is an atheist. He said this about Richard Dawkins:
"What Dawkins does too often is to concentrate his attack on fundamentalists. But there are many believers who are just not fundamentalists," Higgs said in an interview with the Spanish newspaper El Mundo. "Fundamentalism is another problem. I mean, Dawkins in a way is almost a fundamentalist himself, of another kind." He agreed with some of Dawkins' thoughts on the unfortunate consequences that have resulted from religious belief, but he was unhappy with the evolutionary biologist's approach to dealing with believers and said he agreed with those who found Dawkins' approach "embarrassing".
https://www.theguardian.com/science/2012/dec/26/peter-higgs-richard-dawkins-fundamentalism Some have suggested that so-called new atheism is a dying trend. I don’t think so. I think after having done its damage it’s simply stopped propagating as fast. However, it’s still alive a well on-line with a lot of little Richard Dawkins clones. It’s been so successful that people of good will and good faith, whether they be atheist, agnostic or theist, do not want to be involved in the so-called discussion. Personally, it has limited my participation. I have better things to do than waste my time with self-centered pseudo intellectual trolls who have no interest in talking about fact based evidence-- who think whatever they think and believe is true, because that’s what enlightened people like them think and believe.john_a_designer
February 10, 2021
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JVL:
I said he believed it to be true.
And he said that absent evidence it can be dismissed. Believing isn't evidence. I am not sure Dr Sewell argued against a straw manET
February 10, 2021
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Bob O'H: ba77 – well stop playing games, then, and simply answer my question @45. This is the 4th time I’ve asked you to simply clarify what you meant. If you can do that we can move on. You're not playing the game right Bob O'H. You should assume that Bornagain77 is saying something you think is wrong and stupid and then go from there. That way you can avoid answering simple, direct questions. You can direct the conversation whichever way you wish because you can always make an unfounded assumption about what the other person asked or wrote. It's simple really; I can't believe you don't get it.JVL
February 10, 2021
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ET: Oh my. Christopher Hitchens never provided any evidence that supports unguided evolution. No one has, unless you think that deformities and genetic diseases help your case. I didn't say he did. I said he believed it to be true. And seeing there aren’t any known facts that support abiogenesis there doesn’t need to be anything beyond what Dr Sewell presented. As long as it's accepted that Dr Sewell did not present a 'proof' and that he argued against a straw man version of unguided evolution I'm good.JVL
February 10, 2021
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Bornagain77: JVL and Bob,,, I have much better things to do with my time than playing games of semantics with you guys.,,, Waiting for you guys to be reasonable. I can't speak for Bob O'H but I'm happy to let it stand that Dr Sewell didn't actually 'prove' anything or even attempt to. And I'm happy to continue thinking he attacked a straw man version of unguided evolution.JVL
February 10, 2021
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Oh my. Christopher Hitchens never provided any evidence that supports unguided evolution. No one has, unless you think that deformities and genetic diseases help your case. And seeing there aren't any known facts that support abiogenesis there doesn't need to be anything beyond what Dr Sewell presented.ET
February 10, 2021
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ba77 - well stop playing games, then, and simply answer my question @45. This is the 4th time I've asked you to simply clarify what you meant. If you can do that we can move on.Bob O'H
February 10, 2021
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JVL and Bob,,, I have much better things to do with my time than playing games of semantics with you guys.,,, Waiting for you guys to be reasonable. https://tenor.com/view/ihave-better-things-to-do-with-my-time-lily-tomlin-frankie-bergstein-grace-and-frankie-igot-better-things-to-do-gif-17593894bornagain77
February 10, 2021
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ET: Again, unguided evolution is absent evidence. And according to Hitchens that means it can be dismissed out of hand. Even the best evidence for macroevolution is absent a mechanism. Christopher Hitchens disagreed with you. His brother probably would agree with you however. And Dr Sewell offered a simple proof. Just because you are too stupid to understand it doesn’t mean anything. It wasn't anything like a 'proof'. A proof is a series of arguments starting with known facts and following logically to the conclusion. Dr Sewell didn't even try to do that. He just made an assertion and he KNOWS what a proof entails.JVL
February 10, 2021
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No, JVL, it is not my opinion.
“Support” as in believed it to be true and argued against those who attacked it.
Again, unguided evolution is absent evidence. And according to Hitchens that means it can be dismissed out of hand. Even the best evidence for macroevolution is absent a mechanism. And Dr Sewell offered a simple proof. Just because you are too stupid to understand it doesn't mean anything.ET
February 10, 2021
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ba77 - please, can you simply clarify what you meant. That's all I'm asking.Bob O'H
February 10, 2021
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Bornagain77: JVL, YOU claimed ‘multiple threads of evidence’ that contradicted Dr. Sewell’s claim! You failed to provide a single example! That's because I'm not trying to do that. I'm merely commenting on Dr Sewell's arguments (or lack thereof) and his 'proof'. You failed to provide the ‘proof’ that Dr. Sewell’s claim is false that YOU claimed that you had. I claimed no such thing. Dr Sewell claimed he had a proof but he didn't support or 'prove' his proof. As a mathematician Dr Sewell knows very well that it ain't a proof until you prove it. There's no need for someone to disprove something that hasn't been proved. He didn't even try.JVL
February 10, 2021
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Whatever Bob,,, I would leave playing dumb to your students. You've been here for years, You know how to behave. And certainly don't need me to remind you.bornagain77
February 10, 2021
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John_a_designer: When you argue that life originated by some “mindless natural process,” that is not an explanation how. Could you not make the same criticism of ID, i.e. when you argue that life originated by design that is not an explanation how? That is, there is a big gap between a design and the implementation of that design that ID does not address. (I typed the above without adequately reading the rest of your paragraph.) Therefore you are committing the same error which you accuse ID’ists of committing. That’s a double standard, is it not? What do you think? Are both sides guilty of the same thing?JVL
February 10, 2021
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JVL, YOU claimed 'multiple threads of evidence' that contradicted Dr. Sewell's claim! You failed to provide a single example! You failed to provide the 'proof' that Dr. Sewell's claim is false that YOU claimed that you had.bornagain77
February 10, 2021
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ET: No, JVL, it isn’t my opinion. It is a fact that all OoL research has been a bust. No one even knows how to test the claim that nature can produce a coded information processing system. In your opinion. And, not the topic I was discussing. And no, Dr Sewell did not state a straw man. And you don’t know what Dr Sewell used to make his statement. Clearly he used his knowledge on the subject. All I can judge is what he actually published at the beginning of this thread. He did not offer much, if any, support for his 'proof' and he argued against an extremely dumbed-down and misrepresentative version of what the unguided evolutionary argument and work and research actually say. How did Hitchens support unguided evolution? He didn’t provide any science nor evidence. "Support" as in believed it to be true and argued against those who attacked it. And again you prove that you cannot follow along. There isn’t any intelligence nor reasoning to respond to with respect to the OoL research. The best they have is the production of biologically relevant molecules. It’s like saying nature can produce Stonehenge cuz nature produces stones. Since you haven't actually agreed that Dr Sewell produced and supported a 'proof' I guess you've conceded that he didn't. You do keep trying to change subjects however.JVL
February 10, 2021
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A few years ago here at UD one of our regular interlocutors who was arguing with me about the ID explanation for origin of life pointed out:
the inference from that evidence to intelligence being involved is really indirect. You don’t have any other evidence for the existence of an intelligence during the times it would need to be around.
I responded,
“We have absolutely no evidence as to how the first self-replicating living cell originated abiogenetically (from non-life). So following your arbitrarily made-up standard that’s not a logical possibility, so we shouldn’t even consider it. As the saying goes, ‘sauce for the goose is sauce for the gander.’”
When you argue that life originated by some “mindless natural process,” that is not an explanation how. Life is not presently coming into existence abiogenetically, so if such process existed in the past it no longer exists in the present. Therefore you are committing the same error which you accuse ID’ists of committing. That’s a double standard, is it not? This kind of reasoning on the part of some of our interlocutors reveals that you don’t really have any strong arguments based on reason, logic and the evidence. If you do, why are you holding back?john_a_designer
February 10, 2021
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Bornagain77: JVL, and you have evidence that unguided material processes can produce information where exactly? Not the point I was trying to make. And since you've changed the subject from the point I was trying to make I just might stop with the conversation. You claimed that you had “multiple threads of evidence” refuting Dr. Sewell’s claim. I asked for just a single example. Shoot, there is a 10 million dollar prize associated with such evidence if it ever came forward. You provided no evidence and only reiterated your fallacious claim that Dr. Sewell provide no proof all the while failing to provide ANY proof for your claims, i.e. that unintelligent processes can build computers etc… No, I said the full and complete argument for unguided evolution incorporates multiple lines of evidence . . . according to those supporting that point of view. I wasn't, in this instance, making an argument in support of that point of view. The logical hypocrisy on your part is dripping off every word you write. Since you seem to have stopped trying to argue about what I actually said initially I guess we've finished with that. So, no 'proof' by Dr Sewell.JVL
February 10, 2021
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ba77 - sorry, are you saying that I should or should not continue on this thread if I don't want to be banned? Your comment @ 34 had a clear meaning to me, but seemed an odd thing to write in context, which is why I asked for clarification. Please, simply clarify what you meant.Bob O'H
February 10, 2021
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Bob at 45,,, HUH???, ,, struggling to comprehend a simple sentence with a clear meaning is not a good sign for a college professor Bob,,, perhaps you should take an extended sabbatical (from UD and your college) so as to refocus your thoughts towards more important matters? I hear scenic tours of beautiful countrysides are pretty good for refocusing your mind towards things which are more important in life. :)
Experiencing Awe Increases Belief in the Supernatural - November 25, 2013 Excerpt: Valdesolo and his colleague Jesse Graham of the University of Southern California tested this prediction by having participants watch awe-inspiring scenes from BBC’s Planet Earth documentary series or neutral video clips from a news interview. Afterward, the participants were asked how much awe they felt while watching the video, and whether they believed that worldly events unfold according to some god’s or other non-human entity’s plan. Overall, participants who had watched the awe-inspiring video tended to believe more in supernatural control, and were more likely to believe in God when compared with the news-watching group.,,, https://www.psychologicalscience.org/news/releases/experiencing-awe-increases-belief-in-the-supernatural.html Beauty and the Imagination - Aaron Ames - July 16th, 2017 Excerpt: Beauty… can be appreciated only by the mind. This would be impossible, if this ‘idea’ of beauty were not found in the Mind in a more perfect form…. This consideration has readily persuaded men of ability and learning… that the original “idea” is not to be found in this sphere (Augustine, City of God). https://theimaginativeconservative.org/2017/07/beauty-imagination-aaron-ames.html
The beauty revealed in nature and biology goes far beyond what can be explained by Darwinian evolution.
The Biology of the Baroque – video https://www.youtube.com/watch?v=FothcJW-Quo BEAUTY, DARWIN & DESIGN – video - 2019 https://www.youtube.com/watch?v=7ax-lkRoES8
In fact Darwin himself stated that "They believe that very many structures have been created for beauty in the eyes of man, or for mere variety. This doctrine, if true, would be absolutely fatal to my theory.”
“The foregoing remarks lead me to say a few words on the protest lately made by some naturalists, against the utilitarian doctrine that every detail of structure has been produced for the good of its possessor. They believe that very many structures have been created for beauty in the eyes of man, or for mere variety. This doctrine, if true, would be absolutely fatal to my theory.” (Charles Darwin - 1859, p. 199)
And there you have it, the existence of beauty itself falsifies Darwinian evolution!bornagain77
February 10, 2021
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No, JVL, it isn't my opinion. It is a fact that all OoL research has been a bust. No one even knows how to test the claim that nature can produce a coded information processing system. And no, Dr Sewell did not state a straw man. And you don't know what Dr Sewell used to make his statement. Clearly he used his knowledge on the subject. How did Hitchens support unguided evolution? He didn't provide any science nor evidence. And again you prove that you cannot follow along. There isn't any intelligence nor reasoning to respond to with respect to the OoL research. The best they have is the production of biologically relevant molecules. It's like saying nature can produce Stonehenge cuz nature produces stones.ET
February 10, 2021
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ba77 - do you mean "Bob, whatever, you can play your games elsewhere unless you want to have the admin decide what you meant."? I assume you're not saying that if I don't continue to discuss on this thread, I might be banned!Bob O'H
February 10, 2021
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JVL, and you have evidence that unguided material processes can produce information where exactly? You claimed that you had “multiple threads of evidence” refuting Dr. Sewell's claim. I asked for just a single example. Shoot, there is a 10 million dollar prize associated with such evidence if it ever came forward. You provided no evidence and only reiterated your fallacious claim that Dr. Sewell provide no proof all the while failing to provide ANY proof for your claims, i.e. that unintelligent processes can build computers etc... The logical hypocrisy on your part is dripping off every word you write.bornagain77
February 10, 2021
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JVL:
No, I said that just to note that he didn’t use his expertise and background.
How do you know what he used?
Look, my point was Dr Sewell attacked a straw man version of the lengthy, complicated, involved unguided evolutionary theory and its support by reducing it to a silly statement which did not even acknowledge the evidence, the arguments or the research.
Every bit of research and evidence supports what Dr Sewell said. Unguided evolution is total nonsense. Abiogenesis is also total nonsense.
Because he wants people to dismiss it out of hand instead of engaging with the reasoning.
According to Hitchens it should be dismissed out of hand because there isn't anything but lies to support it.
Why didn’t he support his ‘proof’ with more intelligent reasoning?
There isn't any intelligence nor reasoning to respond to.ET
February 10, 2021
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ET: All the research supports the claim that nature didn’t do it. All of the evidence supports the claim that nature didn’t do it. The argument is complicated and lengthy only because it is filled with BS, lies and promissory notes. Your opinion. Since you've stopped saying that Dr Sewell didn't make a straw man attack or that he provided a real 'proof' I guess I got my point across. How do you know what he used? He didn't use any of his expertise in his stated argument. Every bit of research and evidence supports what Dr Sewell said. Unguided evolution is total nonsense. Abiogenesis is also total nonsense. Your opinion. According to Hitchens it should be dismissed out of hand because there isn’t anything but lies to support it. Christopher Hitchens supported unguided evolution. Try again. There isn’t any intelligence nor reasoning to respond to. You must be bored then because you keep responding. Got to have the last word?JVL
February 10, 2021
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