6 ms·
The most depressing day of my life was the day I learned the proof of Godel's Incompleteness Theorem and the Insolubility of the Halting Problem. Attributing mo
by nh43de 5y ago
The most depressing day of my life was the day I learned the proof of Godel's Incompleteness Theorem and the Insolubility of the Halting Problem. Attributing more than is deserved to the antics of classical computers is still wildly prevalent but oh so adolescent.
- deleted 5y ago[deleted]
- whatshisface 5y agoIncompleteness and the halting problem are both applicable to quantum mechanics and by extension the human brain. They apply to every rigorous system and also to every real-world system that can be described rigorously.
- deleted 5y ago[deleted]
- mjburgess 5y agoThere are many limitations of finite discrete sequential processes; and no evidence whatsoever that reality is best-described by these.
- drdeca 5y ago“No evidence whatsoever” is quite the overstatement. Not conclusive evidence, sure. But there are somewhat compelling arguments based on discoveries from observation, that the space of wavefunctions for a finite region of space, is finite dimensional. That seems like evidence to me.
- fennecfoxen 5y agoThe doomsday cult of the supermind-AI tends to think the "intelligence" is the solution to infinite power, so once the computer starts improving itself, humanity is at its mercy — as if better software alone could deliver the singularity, unchecked by material constraints. I suspect some of this comes from software-oriented nerds who think a slightly too much of the powers intelligence grants them.
- jimbokun 5y agoDoesn't have to be "unchecked", just much less checked than human brains. Although, that is an interesting question in and of itself. Are living brains near a local optimum in terms of computing power, given heat and power constraints? With Moore's Law, the prediction was that computer intelligence would surpass human intelligence in a few more doublings. But now that the primary constraint is more about power usage than absolute clock speed, maybe living brains compare better?
- cogman10 5y agoIt comes from the false notion that infinite means unbounded. I see this debate come up all the time in the discussion of something like pi. You'll see the assertion "Oh, because pi is infinitely non-repeating, it must contain the complete works of Shakespeare" Now, does it? Maybe. However, just because something doesn't repeat, doesn't mean it has to cover all possible combinations. For example, you could have a number that follows the pattern 0.01001000100001000001.... Non repeating and infinite but contains nothing but a simple pattern that will never contain anything meaningful. AI is much the same. We think "all problems have a solution! So a super intelligence must know all the answers!" The assumption "all problems have a solution" is just an assumption, not a truth. FTL travel may very well be an impossibility. No amount of knowledge could reverse that possibility.
- stonemetal12 5y agoWhy though? The halting problem is interesting. The fact that there is a proof that it isn't possible for a certain class of inputs, doesn't mean it is impossible for all inputs. Where is the line? Can we solve it for practical programs? Can we solve it in a non binary manor "Program XYZ halts for inputs UVW, but not for inputs RST"? To me the halting problem proof suggests way more questions than it answers.
- UncleMeat 5y agoThose questions have themselves been solved. Static analysis works in practice, even for very intricate properties.
- nh43de 5y agoFrom the paper: "Interestingly, reduced versions of the decidability problem have produced a fruitful area of re-search: formal verification, whose objective is to produce techniques to verify the correctness of computer programs and ensure they satisfy desirable properties (Vardi & Wolper, 1986). However, these techniques are only available to highly restricted classes of programs and inputs, and have been used in safety-critical applications such as train scheduling. But the approach of considering restricted classes of programs and inputs cannot be useful to the containment of superintelligence. Superintelligent machines, those Bostrom is interested in, are written in Turing-complete programming languages, are equipped with powerful sensors, and have the state of the world as their input. This seems unavoidable if we are to program machines to help us with the hardest problems facing society, such as epidemics, poverty, and climate change. These problems forbid the limitations im-posed by available formal verification techniques, rendering those techniques unusable at this grand scale."
- UncleMeat 5y agoWow. That's just... not true. Not even a little. The authors have totally incorrect and limited understanding of the state of static analysis.
- AtlasBarfed 5y agoThose are almost bigger cognitive shifts in my education track than was calculus. While super-turings are obviously fantastical things like FTL, assuming human brains are some form of turing machine, then from a practical standpoint all we need to do is imagine a human-capability turing with integrated current computing abilities for number crunching, no need of sleep, and ability to scale/clone/copy, and probably far bigger memory and recall. A self-aware AI that can replicate can very rapidly chase Kardashev scales without our pesky lifespan and vulnerability to space.