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[Vester]

I confess.

I'm the world's first sentient spambot.

[Neruz]

The problem with time being continuous is you run into good old infinity, which breaks everything at a logical level. Modern caculus and advanced mathematics and physics gets around the infinity issue by ignoring it and thus claiming to have solved the problem, without actually addressing the problem. Continuous time raises a whole bunch of very hard-to-answer questions that require some rather silly contortions of science in order to explain away, discrete time raises a smaller number of relatively easy to answer questions that require almost no contortions to explain.

Wait, what?  Calculus is the field of mathematics that is intended to deal with things that are infinitely small, large, or many.  Infinity doesn't break things at a logical level.  It's a concept defined logically; the ambiguity surrounding it doesn't come from the logical or mathematical side of things, but rather of the theoretical application to the real world.  People ask "What's infinite?" but don't really get that it's a symbol used to describe relative concepts.  Infinity is farther, no matter how far; infinity is longer, no matter how long.  In fact, infinity is an issue with discrete models too.  They avoid the infinitesimal, but not the infinite.

That is, of course, the problem with infinity.

When you're operating in nice clean fantasy-maths world, infinity is fine. The problem is when you try and apply it to reality, at which point everything breaks.


Hence my comment about modern calculus getting around the infinity problem by pretending it's not there; it gets around the problem by simply removing reality from the equation, and then they all throw their hands up in the air and go "Aren't we incredible! We solved the problem!" while the rest of us make wooshing noises as the mathmaticians completely miss the point.

[Starver]

I thought that if a robot was forced to harm humans to save the whole humanity, the stress would fry its brain and it would shut down, and not go on a murderous rampage. Do I completely misremember?

That's what's intended.  The Giskard/Daneel situation is that Giskard is a slightly broken robot, in that he can conceive of the Zeroth law, and that alongside a telepath-like ability (maybe how he gets the insight?  ...can't remember, it was a while ago I read the Caves Of Steel set of stories).  He outright cannot implement the Zeroth law, personally, but understands the need for it.  Using his abilities, he (without telling Daneel until it's done) carves the Zeroth law into Daneel's matrix, essentially.  The act of implementing the Zeroth law by proxy still overcomes him. Daneel, however, now has the Zeroth-Law fully implemented so is able to "do what must be done" with impunity, and survive the situation.

Largely, the laws are supposed to be so ingrained that it's not even a matter of a segment of code saying something like:

Code: [Select]

  LOOP: while (true) {
    if (Outcome("inaction") cmp "human comes to harm") { push @actionstodo, "save human"; next LOOP }
    until (@actionstodo && ($action = shift @actionstodo)) {}
    if (Outcome($action) cmp "human injured")          { Reject($action); next LOOP }
    if (Outcome($action) cmp "human disobeyed")        { Reject($action); next LOOP }
    if (Outcome($action) cmp "self damaged")           { Reject($action); next LOOP }
    &Do($action)
  }

...it's supposed to be formed of myriad threads of 'thought' whose behaviour results in "Obey the laws or cease functioning altogether!".  (Which always confused me, for even at a young age I thought that systems of this complexity with emergent behaviour would be almost impossible to 'debug' to ensure complience with the intended spec...  And that was long before I was involved in anything like the Y2K preparations, which were trivial in comparison, though comparable (in some cases, at least) what with the possibility of a 99->100 rollover in some unprotected BCD/Ascii data fields causing strange overwrites...)


Still, Asimov did allow design-time mutability of the laws at times.  The plot of "Little Lost Robot" involves robots helping with work at a space station, on some project or other, except that one of the project areas has a radiation that: a) Completely fries robot brains, and b) Has a slight and/or slightly possible effect on human health.  Like a dental X-ray.  More than background level risk, but really not a significant problem.  But enough to trigger the robots' "save the human" response, leap into the area to do so and get fried, to great expense and annoyance.

So they design a robot without the "by inaction" part to help out in that part of the station.  Identically looking, it just wouldn't leap in, although theoretically it would still not hurt a human.  And then someone tells it to "get lost", more or less, and it insinuates itself within the normally applied robots to obey that order.  The trouble is that such a robot might (as explained) be able to kill.  The mere act of dropping a heavy weight above a human would not break the attenuated 1st Law, if there was every possibility of catching the weight before it landed on them.  But having dropped the weight, there would be no reason to stop its downward travel.  Unless explicitly ordered (and, latterly, to protect its own existence, but that would just mean it would have to be sneaky).

How they try to work out which of the robots is the Little Lost one (in order not to destroy a whole batch of expensive normal robots) is best read about.  As is how the Little Lost Robot thwarts the attempts.  I like the logic.  (Can you tell?

[LumenPlacidum]

That is, of course, the problem with infinity.

When you're operating in nice clean fantasy-maths world, infinity is fine. The problem is when you try and apply it to reality, at which point everything breaks.


Hence my comment about modern calculus getting around the infinity problem by pretending it's not there; it gets around the problem by simply removing reality from the equation, and then they all throw their hands up in the air and go "Aren't we incredible! We solved the problem!" while the rest of us make wooshing noises as the mathmaticians completely miss the point.

Indeed, I admitted that I couldn't argue if your approach was to challenge the applicability of mathematical theory to the world around us.  However, don't stop at infinity!  Don't forget that all of mathematics is done in the realm of conceptual fantasy.  There's never been any reason why the world of math has to reflect the real universe, even starting with just numbers.  There's no such concrete thing as 'One' and no reason why three apples and four apples should combine to yield seven apples just because 3+4=7.  I can't and won't say that of course infinity is applicable, but then it seems that if you reject it as being largely applicable to the real world then you must also reject those structures built off of it, which unfortunately includes most of modern physics since it's built with the tools of calculus.

Of course, perhaps that's what you mean by everything falling apart.  I just don't understand why we'd give up what seems to be the second most powerful tool we have in understanding the nature of what's happening around us.

[Rowanas]

Combat-AI-maths-shut up and get back on topic so that I can understand a word you're saying

Yeah, I don't even understand the word "of" when calculus is the one after it.

[Don_Pablo]

This thread is not about Combat any more, nor has it been in quite some time.

Infinity, discrete numbers, and a host of other mathematical concepts fit neatly with reality, why would you think they don't?  "One" is not a real-world "thing" which you can grab hold of or see, nor is "two," that is true.  But there is a one-to-one correspondence between what you perceive as "one" thing and the first slot on the (yes, theoretical) number line mathematicians refer to as the set of integers.  Any number of materiel objects can thenceforth be plotted onto this imaginary set without losing any relevance or meaning.  It is a short step (trivial mathematically) from there to rational and real numbers. 

Infinity, too, exists, both in mathematicians' heads and in material reality.  To use a somewhat cliched example, the universe is infinite in any of the three spatial dimensions, as well as (as far as we know) in time.  Simpler than that, though, is the fact that literally any curved surface can be thought of as infinite as well.  The two-dimensional surface of the earth is finite in area, and given decent enough equipment could be measured to a very accurate level.  Its one-dimensional length, though, has no beginning, no end, and is infinite.  If you are astute enough to use analogies like Zeno's Paradox without thinking of it as a paradox, you can even see that any distance at all may contain infinite subdivisions, including our friend "one" ::unit of length here::

HEYYYYY OFF-TOPIC

[Baughn]

Ignoring the planck length, yes. 

The universe may also be infinite spatially - or it may not be. It's a moot point, as the accessible universe is finite - there's a cosmic horizon, and it's not getting bigger. (Well, it is, but space is expanding faster than light (relative to us) that far off, so in practice it's actually getting smaller.)

In other words, regardless of whether the universe is really infinite or not, the part that can have any actual effect on us is finite, and not unbounded; adding time just makes it smaller. It's very annoying, since that means eternal life may be impossible.

Oh well, I'll worry about the first billion years first.

[Anticipation]

Just for you Baughn I've started (and intend to finish) that link you posted.

[Neruz]

We don't know if infinity exists outside of conceptual mathematics. Indeed it's impossible to tell if something is infinite, because you cannot measure infinity.

Which is, of course, one of the reasons why applying infinity to reality causes headaches.

[Vengeful Donut]

Hence my comment about modern calculus getting around the infinity problem by pretending it's not there; it gets around the problem by simply removing reality from the equation, and then they all throw their hands up in the air and go "Aren't we incredible! We solved the problem!" while the rest of us make wooshing noises as the mathmaticians completely miss the point.

A statement about reality can be experimentally tested to any degree, but this never gives it mathematical rigor. Mathematical statements (rigirously proven statements) can therefore not be statements about reality. They can at best be about a model we think is a good match for the real world.
Nobody is removing reality from the equation - you can't stick reality into an equation in the first place.

Also, you seem to be very cavalier about saying what other people don't know. You can only (reliably) tell us what you personally don't know.

Specifically, never forget that Bell's theorem has been experimentally validated. IMO that pretty much rules out every explanation of quantum mechanics except the very simple (null interpretation) of MWI, but I know people tend to disagree on that.. well, I've got occam's razor on my side, at least.

Don't you mean that the hypothesis of Bell's theorem has been experimentally verified to be false?
(Also, your phrasing seems weird. "Experimentally validated" isn't something you can say about a theorem. A theorem's validity is in no way dependent on experiments.)

[Neruz]

Hence my comment about modern calculus getting around the infinity problem by pretending it's not there; it gets around the problem by simply removing reality from the equation, and then they all throw their hands up in the air and go "Aren't we incredible! We solved the problem!" while the rest of us make wooshing noises as the mathmaticians completely miss the point.

A statement about reality can be experimentally tested to any degree, but this never gives it mathematical rigor. Mathematical statements (rigirously proven statements) can therefore not be statements about reality. They can at best be about a model we think is a good match for the real world.
Nobody is removing reality from the equation - you can't stick reality into an equation in the first place.

Also, you seem to be very cavalier about saying what other people don't know. You can only (reliably) tell us what you personally don't know.

I can reliably tell you that calculus does not address the issue at hand with the well-known paradoxes of Zeno. It solves the paradox, but anyone with half a brain can tell you that Achilles will be able to overtake the tortoise. It's the theory behind the paradox; that an infinite number of tasks taking a finite period of time is a contradiction in terms, that remains unaddressed by calculus.

Hence, calculus 'solves' the problem by ignoring it.

[dragnar]

But an infinite number of tasks taking a finite period of time is not a contradiction at all, if each task is infinitely short.
essentially, infinity / infinity = 1 (though this is a massive over-simplification)

Also, how on earth did this tread go from combat mechanics, to sentient AIs to the nature of infinity? I just read it and I still don't know what happened.

[darius]

Ahh sweet smell of derailment. Maybe we need a subforum: "philosophy n other cool stuff"
Back to offtopic: I don't really get the wrestling. Tried 100 times wrestling a cougar (or a tiger) with legendary wrestler, superdwarvenly strong and still can't break the joints unless I missed something

[Vengeful Donut]

I can reliably tell you that calculus does not address the issue at hand with the well-known paradoxes of Zeno. It solves the paradox, but anyone with half a brain can tell you that Achilles will be able to overtake the tortoise. It's the theory behind the paradox; that an infinite number of tasks taking a finite period of time is a contradiction in terms, that remains unaddressed by calculus.

Hence, calculus 'solves' the problem by ignoring it.

You do not have enough authority on this subject for these kinds of claims to hold weight without making a strong argument in their favor.

Zeno's paradox requires the assumption that simply because the number of tasks is infinite, the amount of time they take also must be infinite. The only problem is instinctive acceptance of that idea as an axiom. You can solve all of the issues by simply disallowing such an arbitrary premise.

Calculus isn't even relevant to the discussion. If someone told you calculus addresses the "problem", then the error is with that person. Not with calculus.

[Neruz]

Actually the solution to the Achilles paradox is to say either that you have a finite number of tasks that can be divided infinitely, so while you can divide them smaller an infinite number of times, at any stage in that division there is only a finite number of tasks, the other solution of course is to say that distance is discrete, rather than continuous.

As for infinity/infinity = 1, only if the infinities are the same size.