Ultimately, he proved that you cannot write another program to predict whether a program will finish or not - a result that suggests that you can't definitively determine whether a statement will ever be possible to prove, Grime said. So something very much like Kirk's computer-busting paradox is something that appears in real mathematics.Ĭhasing a similar question, the mathematician and pioneering scientist Alan Turing set out to find out whether it's possible to determine whether any given computer program will be able to solve a problem and halt or get stuck working on the problem forever. If the statement is false, it’s a contradiction, and that means there are contradictions within a mathematical system - so any system without any contradictions will also have statements that are impossible to prove. If the statement is true, it means there are true mathematical statements that can never be proved, like "holes" in mathematics. The captain often achieves this feat using sentences similar to the "Liar's Paradox": "This sentence is false." It's a paradox because if the sentence is false, then the sentence is stating the truth, even though it is supposed to be false if the sentence is true, then it must be true that the sentence is false.Ī similar statement powers mathematician Kurt Gödel's Incompleteness Theorem, which in effect proves there's a similarly paradoxical statement like "This statement is not provable" in any given mathematical system, Grime said. Computer-breaking paradoxĪccording to Grime, Captain Kirk talks computers to death no fewer than four separate occasions in the original series. Hence, numbers of years with few factors are the way to go for cicadas - and maybe for Vulcans, too. If the prey waited just one extra year, coming out every five, the predator and prey would only overlap every 20 years. For instance, if a predator emerged every four years it'd be able to take out prey who emerged every multiple of four - four, eight, 12 and so on. The Vulcan pattern is like that of certain types of cicadas, who live underground and come out only one spring every several years, which lets them avoid predators - in fact, the mating cycles of those so-called periodical cicadas are prime numbers, like 13 or 17 years, which means that they can avoid overlapping with predators that emerge on regularly spaced periodical cycles, too. For instance, in "The Trouble with Tribbles," Spock calculates that after just three days there will be 1,771,561 tribbles! Because each tribble produces 10 additional tribbles every 12 hours, and the original tribble sticks around to reproduce more, the generations grow by 1+10 = 11 times each generation - giving 1 x 11^6 tribbles after six generations (three days). Grime also compared the Vulcans' mode of reproduction, which happens only once every seven years, to that of tribbles, whose numbers grow exponentially and reach great numbers very quickly. "So I think the moral of the story is, if you're on the starship Enterprise and you want to survive, be a scientist." (Only 6 percent of the blue-shirted scientists died over the course of the show.) "There is some truth in the old 'Star Trek' myth if you look at security officers … 20 percent of security officers died," Grime added. Out of 55 goldshirts, 10 died, which is 18 percent! So you are more likely to die as a goldshirt, Grime said. Grime used the "Star Trek" technical manual to find out how many of each crew type there were, which painted a different picture: out of 239 redshirts, 25 died, which is 10 percent. In other words, we're looking at the probability that you are a redshirt if you die (58 percent) - what we want to know is the probability that you die if you're a redshirt, Grime said. That claim, in fact, is false - more "redshirts" died on-screen than any other crew type (10 gold-shirted, which are command personnel eight blue-shirted, who are scientists and 25 red-shirted, Grime said), but that calculation fails to take into account that there are far more redshirts on the ship to start with than any other crew type. Grime first focused on an age-old assertion: that crewmembers wearing red shirts in the original "Star Trek" series, which denote working in engineering or security, are far more likely to be killed off than any other shirt color.
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