Re:Nasa’s Mars Rover Opportunity Concludes a 15-Year Mission
by dTal on Thursday February 14, 2019 @05:34AM
(#19160901)
I don't think it's strictly true that you always have to have a single point of failure. Trivial counterexamples: 6 people carrying a sofa, an ant colony, BitTorrent.
The closest thing I can remember encountering to what you describe is the "Contracrostipunctus" chapter in Douglas Hofstadter's Godel, Escher, Bach, where he writes a dialog featuring record players as an analogy to Godel's Incompleteness Theorem (which only applies to "formal systems" - descriptive mathematical languages). He does go on to explore a real-world example of the principle in the form of viruses - a cell cannot fully defend against DNA modification using only instructions found in its DNA. The same principle applies to cracking copy protection in games - no matter how elaborate the validity checks, there's always a single point of failure in the form of the final decision - "if(checks_pass){run_game()}" - which can be trivially short circuited with a debugger.
I'm not a good enough mathematician to fully understand the limits of Godel's Theorem. But it seems to me that all of the above applications are examples of some sort of well defined formal computational system, and you can't generalize it to "everything has a single point of failure" without some carefully defined rules as to what constitutes the boundaries of system.
The closest thing I can remember encountering to what you describe is the "Contracrostipunctus" chapter in Douglas Hofstadter's Godel, Escher, Bach, where he writes a dialog featuring record players as an analogy to Godel's Incompleteness Theorem (which only applies to "formal systems" - descriptive mathematical languages). He does go on to explore a real-world example of the principle in the form of viruses - a cell cannot fully defend against DNA modification using only instructions found in its DNA. The same principle applies to cracking copy protection in games - no matter how elaborate the validity checks, there's always a single point of failure in the form of the final decision - "if(checks_pass){run_game()}" - which can be trivially short circuited with a debugger.
I'm not a good enough mathematician to fully understand the limits of Godel's Theorem. But it seems to me that all of the above applications are examples of some sort of well defined formal computational system, and you can't generalize it to "everything has a single point of failure" without some carefully defined rules as to what constitutes the boundaries of system.
http://www.math.yorku.ca/Who/Faculty/Brettler/3500_06/Godels...