Main Logic Bomb Discussion

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12:56:00 PM Feb 12th 2015
If you try to stop a robot by telling it to calculate pi, it wouldn't do anything unless the robot does what you say. If the robot is programmed to do whatever you say, why not just tell it not to kill you?
12:44:13 PM Dec 3rd 2014
The note accompanying the page image states that #3 isn't a mistake, because the axiom of regularity states that a set cannot contain itself; but the bullet point addressing Portal 2 says that a set can contain itself, and gives an example that I didn't really understand and that I'm not sure was explained very well. Could someone more knowledgeable about math perhaps reconcile these two points so that they're at least consistent between each other?
10:41:56 PM Dec 21st 2014
edited by
Sets are a special type of classes. A class can contain itself, but a set cannot. The example in the note is incorrect- a box containing an apple and a box is not a set containing itself because the interior box is not the same object as the exterior box. Why not? Because the exterior box contains an apple and a box while the interior box does not. If you know a little bit of math, it can be explained as follows: {1} is not the same set as {{1}}. The first is the set of the number 1. The second is the set of the set consisting of only the number 1. The elements of the first set are numbers while the elements of the second set are sets.

Edit: Corrected spelling
01:24:43 PM Dec 23rd 2013
The computing section of this page has a discussion of the Y2K problem which includes these two paragraphs:

  • Even worse than that - at least with Y2K, computers merely confused the year 2000 with another valid year, such as 1900. With Y2.038K, not so lucky: the rollover will cause the counter to output a negative number, which is forbidden as a date representation, and is in fact used by many systems to represent error codes. so, while a Y2K-afflicted machine merely computed dates wrongly, a Y2.038K-afflicted one is expected to mistake the date for an error code and crash.
    • That's not worse, that's better! If your UNIX computer keeps running in 2039, how do you know if it never had the problem in the first place (they switched to 64-bit) or if it has the problem and is now getting subtly wrong answers? Talk to any medical equipment, process control or financial computer vendor: silent wrong answers are much worse than crashes.

The first paragraph seems to be at least partially in error unless the editor was referring to some other Unix/Linux time measuring system than from the standard time_t. For pre-standard C (grandfathered into standard C and into C++) functions (as used in the implementation layer of Unix/Linux) using time_t, negative values are both legal and valid (they represent times before the epoch). User code-level programming languages and other systems aren't required to accept negative values, and indeed, some do not.

The second paragraph is essentially correct, but rendered moot if the first one is re-written.

Unless someone else cares to argue against this, I intend to edit the first paragraph above to take out or modify the assertion that negative time values are forbidden.

References: Unix time, Year 2038 problem.
11:01:51 AM Jan 9th 2014
It is done.
02:10:03 AM Sep 5th 2012
Two tropes: There Are No Girls on the Internet and Most Fanfic Writers Are Girls.

Don't see the problem here. If we assume that both statements are true it just means that there is a shitload of Fanfic's on off line devices. Probably better that way since they are bound to be yaoi anyway.

The "Most" makes all the difference.
10:10:24 PM Feb 8th 2012
In the original Empire Earth's expansion, you can get Cyber Ninjas. They have an attack, literally called Logic Bomb. You use it on an enemy facility to temporarily stop it from producing units.

Im not entirely sure if this would be appropriate here, because...Well its an actual bomb! That actually does...something...for reasons unexplained.
07:22:01 PM Jun 16th 2011
edited by keybounce
Something like the liar's paradox breaking a system is just lazy writing or not doing any research.

GEB takes this whole thing to task. If you really want to break a computer, you don't worry about things like "The set of all sets", or "The set of things that don't contain themselves". A smart computer that is ZFC aware knows that those are not valid set constructions. Equally, liars paradox has no truth value.

No, if you really want to confuse a computer, you first attempt to see if it understands Godel numbering, and teach it the concept if it does not. Then, long proofs can be reduced to mathematical equations and automatic validation.

Then you introduce substitution, and in no time at all, you have G.

For those that do not know, G is basically the following:<br> 1: Any proposed proof can be turned into a number, with each logic symbol being turned into some digits.<br> 2. You can then create a sentence that asserts that for each number, that number is not a proof of this statement.<br> 3. And it's true.<br> 0 is not a proof of G.<br> 1 is not a proof of G.<br> 2 is not a proof of G.<br> ...<br>

No "number" is a proof of G.

But that's what G claims. So what's the real killer for the computer?

Assume G is true. Then, you have a simple derivation where you conclude If G, then G, and take G as an axiom; this proves G. But this is now a finite proof of G, hence has a number, which means <br> xyz is a proof of G<br> which contradicts G.

No problem, right? That means that ~G must be true.

But ~G asserts that there is a "number" that proves G ...

(Of course, "number" isn't "normal number", and if you're talking about a computer that uses language to reason rationally ...)
12:20:07 AM Jun 2nd 2011

  • Come to think of it, religion as a whole could be said to work this way. Faith is a paradox: you hope that something is true. But if you have to rely on hope, how can it possibly be true?

Because not only is it not an example of a Logic Bomb, it's not really a paradox. It's perfectly possible for something you can only hope for to be true. I hope there isn't an asteroid on course to crash into the Earth within my lifetime. Just because there's no way for me to verify my hope doesn't mean Earth is doomed. Furthermore, religion is about "faith" or "belief," not "hope." Hope means acknowledging the possibility that you're wrong, while faith encourages otherwise.
03:37:32 PM Jan 18th 2011
Follow-up: This page seems to have strayed from its topic; if I am reading it correctly, the trope is "a paradox breaking an AI down", but it grew to include anything that could remotely be considered a paradox.
12:59:41 PM Jan 17th 2011
Removed most of the real life examples (more like non-examples):

  • Critics of the concept of an omnipotent God will say, "Can God create a rock so heavy he cannot lift?"
    • Popular pro-omnipotence answers include:
      • No, "a rock so heavy an omnipotent being cannot lift it" is self-contradictory. God cannot make square circles, married bachelors, or other things that are nonsensical non-referents.
      • Yes, but since we already said that the very idea is self-contradictory, God can then still lift that rock. Omnipotence includes doing the logically impossible.
      • Yes, but so long as God does not create that rock, God is still omnipotent.
    • Asked of rocks, the question sounds silly. ("Lifting" is an act performed by beings restrained by a celestial object's gravity; for a non-physical being to "lift" something is difficult to make sense of.) Asked more generally, "can an omnipotent being impose limits on itself," the question is more meaningful. Consider free will, which would not be meaningfully free if God could veto it. (And let's end this chain of philosophy...)
    • The obvious solution is for God to create another unliftable rock, and then make a clone of Himself that is not omnipotent. Then they both would attempt to lift their respective rock at the same time, with the result that God would both be able and not be able to lift the rock!
    • I prefer the food version, it's easier to understand. "Can God make a sandwich so big he cannot eat it?" Answer: Yes, but then he will eat it anyways.
  • Incidentally, if somebody tries to Logic Bomb you with "This statement is a lie," the proper response is, "No it isn't."
    • No, it isn't. That would assert that the statement is true, which means it is false. The proper response is to say that it is not a valid statement.
    • Or just take a third option.
  • The "this page is intentionally left blank" pages in college apps and standardized tests, and the phrase, "this phrase is false."
  • Epimenides was a Cretan who made one immortal statement: "All Cretans are liars."
    • Not actually a logic bomb or paradox, since Epimenides could have simply been lying (so it is not true that all Cretans are liars, just Epimenides). Indeed, he could also have been telling the truth this once, and still counted as a Cretan and a liar; liars don't always lie, after all.
    • This would be a paradox. As Epimenides was a Cretan he is included in the group "All Cretans". If he is a liar then the statement "All Cretans are liars" is proved true and therefore invalidates itself hence paradox.
      • Short version: No, because after you prove that he's a liar, you have to prove that every other Cretan is.
      • It's actually a problem of distribution, in particular the predication that if someone is a liar, then all instances of their speech are lies, and further that if Epimenides is a Cretan, all things that he does are representative of all Cretans. Epimenides inclusion in the group "Cretans" is necessary to define attributes or properties of Epimenides as a Cretan, however his attributes or properties are not sufficient to predicate things of "Cretan". This is problematic in that, even if Epimenides is a liar, he may not be lying about all Cretans being liars, but he may lie about other topics or on other occasions. Further, even if he is lying and some Cretans are truthful, this does not engender truth to his given statement, rendering a paradox. Truth is a measure of the correlation of a statement to the standing of the universe, not an inimical and inherent property, although YMMV regarding what you hold to be "Truth".
      • In logic, the opposite (technically, the negation) of "all" is not "none" but "some" (as in, "not all").
        • Maybe "some does not"? For example "not all Cretans are liars" is equivalent to "there are some Cretans who are not liars".
  • Quine's Paradox is a logic problem that definitively shows that all languages capable of description necessarily can be used to construct unsolvable logic bombs.
  • Truth Intel-evasion The Garbage-in Garbage-out Maxim. Or, to put it more poetically and with a slight Vonnegutian spin: Computers believe whatever we tell them so we must be very careful what we tell them.
    • Garbage In Gospel Out is the inversion related to this maxim: People tend to believe whatever output a computer produces even if the input is garbage.
    • "On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' (...) I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question." —Charles Babbage
  • Using this statement will create one: "I have to tell you the truth; I'm a pathological liar."
  • All generalizations are false.
  • The entire concept of Opposite Day. Just think about it for a moment. If it was, then it wouldn't be and then AAAGH
    • Questionable, since things like Gravity and the date don't actually change.
  • On a Windows NT-based computer, open up Task Manager, right-click a process and set the priority to "Realtime". Warning: odds are your computer will lock up hard! Realtime is NT's version of "program running at higher priority than the OS kernel itself".
    • Vista won't let me, it just sets it to "High".
      • On 7, and I'm assuming Vista, you have to be running that particular program as the administrator.

10:25:53 AM Nov 13th 2010
edited by girlyboy
I've deleted the following paragraph (formerly the third on the page) because I'm not sure what this paragraph is supposed to do. Plz feel free to restore if I was mistaken.

"This trope is based on mathematical thinking that logic is bidirectional. If a mathematical proof states that X=Y, this means that not only do X and Y share the same value, but they retain that value from the proof's start to finish and cannot be changed. In computer programming the same statement can be interpreted two different ways, depending on the particular language and context involved: It could be an evaluation of whether or not X and Y are equal values at the time (and the computer simply returns "true" or "false" without paradox), or it could be a command to set X equal to the value of Y, without regard for whatever the value of X was beforehand."

I don't understand what this really has to do with the trope. Maybe that's because I am not the most computer-literate person. But still, is this trope really based on this fact about how computer programming works? I somehow doubt the writers for the original Star Trek series from the 60's spent a lot of time learning how to program before having Kirk talk all those computers to death...
09:23:10 PM Aug 6th 2010
Honestly, I'm gonna erase most of that stuff in the Real Life section. Y'know, the stuff about God. Really, the thing devolves into pointless bickering, ruining the light-hearted thread.

Any objections?
09:34:39 PM Aug 6th 2010
It looks pretty lighthearted to me, but maybe the emotional stakes are higher for other readers.
01:24:25 AM Jul 13th 2010
"Can an omnipotent being create a rock it can't lift?" Of course it can. Lump all matter in the entire universe together and the concept of 'lifting' the resulting black hole loses all meaning because there is nothing left to lift it from. Or rather, there is nothing left to act as a frame of reference for moving it.
01:11:21 PM Mar 4th 2010
edited by Lenoxus
Lenoxus: I'm wondering: is it even possible to build a (very, very simple) computer that would be in some sense destroyed by logical/mathematical problems, apart from building it deliberately to do this (IF input receives a known logical contradiction, THEN activate the self-destruct sequence)?

I mean, even if you take an old Texas Instruments calculator and ask it to divide 2 by 3 (an operation that can't be "completed" in base ten), it will simply cut off at a 6 or 7, not overheat. Since all computation, logical or otherwise, occurs within a given set of finite parameters, it's difficult to see how, for example, the Liar Paradox would present some sort of "problem" to a machine; it would simply go back and forth between "true-false-true-false" until it reached the end of its cycle.

People who actually know about computers: Please correct the above! (By adding text below, of course).
05:03:18 PM Jul 14th 2010
edited by
I'm not really a computer expert, but I can think of one way to do that. You'd have to build a system which, when it comes across a problem it's taking too long to solve, starts overclocking your systems in an attempt to speed things up. Of course if it still takes too long, it'll overclock your system again, and again, until it breaks down because the hardware is no longer capable of withstanding the heat. There's no reason it'd ever explode, since there aren't really any explosive substances anywhere in or near your computer to begin with.

I suppose it's possible that an advanced artificial intelligence program might be 'frustrated' with things like the liar paradox, and may attempt to increase it's own computational power by doing things like overclocking the system. Of course, I'd hope that an artificial intelligence program would be intelligent enough to realize what the liar paradox actually means, just as well as we humans can.
09:32:30 PM Aug 6th 2010
According to legend, the mechanical calculators used in the Manhattan Project would sometimes literally break when performing an irrational division like your example. The physicists spent a lot of time trading mental arithmetic tips.
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