Well, there are many complexities. People here are talking about the Programming Complexity (of which one measure is Cyclomatic Complexity) of a textual program vs. the Time/Space complexity of the same program. There is the weakly-related concept of the Kolmogorov complexity of a string.
It's obvious that the time/space complexity of a program can stay fixed while you arbitrarily raise the programming complexity of a program by arbitrarily raising the number of branches that are rarely taken, an action that won't affect the asymptotic time complexity of a thing.
And sure, you can talk about the Kolmogorov complexity of a string of computer code, but the minimal string representation of that code is unlikely to be one that a programmer would describe as simple. Even minimizing the string that would behave as that of the original program is usually non-desirable.
Pick any of those. Given a problem, there is a minimal complexity to the programs that solve it. You can always raise the complexity, but not reduce it.
I'm confused by your response to ninjapenguin[0]. Were you agreeing with him or disagreeing or something else? I interpreted your response to be disagreement. I feel that your original style of phrasing "If only x etc. etc." is not easy to understand. I'm having a hard time placing your subsequent comments in context of that original response.
I was disagreeing with the statement that "Comparing [complexity] to something as fundamental as energy is pure bollocks." There is, in fact, a discipline that studies complexity -- computer science, and, in particular the field of complexity theory. Complexity was, in fact, found to be fundamental and "irreducible". Two people, Hartmanis and Stearns, did, in fact, discover that through a comparison to physics [1] in 1965, and for that discovery -- that led to the creation of complexity theory -- they won the Turing Award in 1993.
It's obvious that the time/space complexity of a program can stay fixed while you arbitrarily raise the programming complexity of a program by arbitrarily raising the number of branches that are rarely taken, an action that won't affect the asymptotic time complexity of a thing.
And sure, you can talk about the Kolmogorov complexity of a string of computer code, but the minimal string representation of that code is unlikely to be one that a programmer would describe as simple. Even minimizing the string that would behave as that of the original program is usually non-desirable.
https://en.wikipedia.org/wiki/Programming_complexity
https://en.wikipedia.org/wiki/Computational_complexity_theor...
https://en.wikipedia.org/wiki/Kolmogorov_complexity