The Big Rock Paradox: Stephen Hawking's Thought-Experiment

[WaveJumper]

Mathematics is very good at describing certain things, English and Russian are better for others. They all involve symbolic representations and abstractions. The fact that mathematics is a more useful language to physicists, doesn't make it special, except when one has an interest in discussing physics.

It is special, the universe is best expressed in digits and mathematical correlations. Black holes were predicted by the equations of General Relativity. I'd like to see you talking in Russian or Pakistani predicting when a massive star will turn into a black hole. You can start in Russian, then we'll shift your "predictions" to multi-lingual mode.

Languages are essentially subjective, ambiguous and reflect a human trait to describe 'classically' what cannot unambiguously be described in such a way. What's more, the precision of mathematics can be infinite, whereas language in as far as it can describe the universe, is extremely vague and approximate.

 

[Hurkyl]

Omnipotence has a history of wordplay... I'm happy with the standard translation, meaning: all-powerful.

Again, the scope of "all" is of supreme importance. If you are too liberal, you don't just invalidate omnipotence, you invalidate logic itself. And besides, recall the words of Lewis Carroll:

‘When I use a word,' Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean—neither more nor less.'​

Sure, you can glibly pick an inconsistent definition and laugh at all those other idiots talking about omnipotence, but if you were really acting in good faith, you would instead find out what they really mean.

 

[JoeDawg]

It is special, the universe is best expressed in digits and mathematical correlations.

No, certain aspects of the universe are. Feel free to describe a sunset, I guarrantee if you describe it in english, more people will understand what you are saying, than if you describe it in math. And I seriously doubt you can do the visual experience justice just with math. Even words isn't such a good way of expressing it. Using colored paints to represent it, and communicate it, would probably be better. Assuming you had learned how to do so. How something is best expressed depends on what you are trying to communicate, and to who.

 

[JoeDawg]

Again, the scope of "all" is of supreme importance. If you are too liberal, you don't just invalidate omnipotence, you invalidate logic itself. And besides, recall the words of Lewis Carroll:

‘When I use a word,' Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean—neither more nor less.'​

Sure, you can glibly pick an inconsistent definition and laugh at all those other idiots talking about omnipotence, but if you were really acting in good faith, you would instead find out what they really mean.

Well, feel free to use your own definitions, and show us. If you can come up with a definition that is not self-contradictory, I would be impressed. I haven't seen one yet. What people do with the word, at best, is dilute the definition with 'exceptions', to the point it loses all meaning.

 

[DaveC426913]

No, certain aspects of the universe are. Feel free to describe a sunset, I guarrantee if you describe it in english, more people will understand what you are saying, than if you describe it in math. And I seriously doubt you can do the visual experience justice just with math. Even words isn't such a good way of expressing it. Using colored paints to represent it, and communicate it, would probably be better. Assuming you had learned how to do so. How something is best expressed depends on what you are trying to communicate, and to who.

I think we're possibly having a diffiiculty with the word "describe".

I think when we are using the word describe, we are using the meaning that is synonymous with define.

The description of a sunset is quite simple to define in physics - it is mostly about normal scattering of light rays, pretty simple stuff in a universe with dark matter, curved spacetime and nucleosynthesis.

The fact that humans have all sorts of little things happening in the chemistry in the nubs at the top of their forms is defineable too, in terms of the proteins and ions.


In this sense, the full mathematical description of a sunset would be much much shorter (i.e. more efficiently defined with fewer ambiguities and fewer 'symbols') than in any verbal language.

In fact, arguably, it is impossible to fully describe a sunset even with an unlimited number of words at your disposal. Or if there were, that would be the day poets would be out of jobs. In 20,000 years of trying we still haven't finished describing it using words.

 

[JoeDawg]

The description of a sunset is quite simple to define in physics - it is mostly about normal scattering of light rays, pretty simple stuff in a universe with dark matter, curved spacetime and nucleosynthesis.

And it simple to define in english. Normally people use color words like: orange, red, purple...
I don't need to know any math to do it. And if I start throwing equations about scattering patterns at people its likely only to get me labeled autistic or a geek. The math simply isn't important to the description, unless you are a physicist.

Math is a language that was designed specifically to represent logical relations, english is more organic, even less precise, but it was designed to describe the everyday world. And for that purpose it does its job, in a way math can't. The fact english isn't good for describing black holes is a no-brainer. A sunset described with C++ wouldn't be much use to most people either, although I'm sure some geek could do it, and might even learn something from doing so.

 

[DaveC426913]

And it simple to define in english. Normally people use color words like: orange, red, purple...
I don't need to know any math to do it. And if I start throwing equations about scattering patterns at people its likely only to get me labeled autistic or a geek. The math simply isn't important to the description, unless you are a physicist.

I still think you awre using a very mushy defintion of the word 'describe'. Describing something is not a people thing, it's a definition thing. You cannot fully define a sunset by listing a bunch of colours. Especially since colours are subjective.

Let's put it another way.

Something can be said to be fully described when there is enough information to duplicate it. How many words would you need to fully describe a particular sunset such that it could be repeated? Math excels at this sort of thing. Verbal languages suck.

 

[JoeDawg]

Something can be said to be fully described when there is enough information to duplicate it.

I can duplicate a sunset, by taking a picture of it, or even painting a picture of it. Or I can write a poem about it. Or a physics nerd can develop an equation to describe it. At no point, with math or without it, is the duplicate equivalent to the real thing. Nor does the level of detail in the duplication imply I can 'recreate' the thing. The level of detail, only has importance with regards to what I intend to do with said description.

How many words would you need to fully describe a particular sunset such that it could be repeated?

You can repeat the sun? With a math equation, no less. I'd love to see that, from a safe distance, of course. You should patent that process, though, before you tell anyone.

Math excels at this sort of thing. Verbal languages suck.

Ok, I've said this repeatedly. Math is more useful in 'physics'.
But you can describe other things much better -- ie in much more useful ways -- in english.

 

[DaveC426913]

I can duplicate a sunset, by taking a picture of it, or even painting a picture of it. Or I can write a poem about it.

No. That is an extremely poor, single-view, narrow-band rendition of the effect. 99.9%+ of the effect is lost forever.

You can repeat the sun? With a math equation, no less.

In principle, yes. Once it is fully described, duplicating it is simply an (albeit significant) engineering challenge.

A photo, painting or peom will not accomplish this. You've virtually lost it all.

 

[JoeDawg]

No. That is an extremely poor, single-view, narrow-band rendition of the effect. 99.9%+ of the effect is lost forever.

And yet, people have enjoyed sunsets, and used them to tell time for thousands of years.
So its hardly single-view, and its quite useful to most human beings.

In principle, yes. Once it is fully described, duplicating it is simply an (albeit significant) engineering challenge.

LOL. Sounds like reinventing the wheel to me. Details are only important when you need them to accomplish something. A poem, a photo, and a painting may not give you a blueprint of a star, but very few people actually need to create their own.

The blueprint of a star... in as much detail as possible, IS important to astronomers and physicists. But 'warm' and 'bright', do just nicely, for 99.9% of people, 99.9% of the time.

Most of the time, your blueprint is unnecessary and extreme overkill.

 

[DaveC426913]

Details are only important when you need them to accomplish something.

What an astoundingly strange thing to say. But highly insightful now that I think about it...

A poem, a photo, and a painting may not give you a blueprint of a star, but very few people actually need to create their own.

The blueprint of a star... in as much detail as possible, IS important to astronomers and physicists. But 'warm' and 'bright', do just nicely, for 99.9% of people, 99.9% of the time.

Yes, but it will not do in a Physics Forum discussion where we are trying to pin down such terms as omnipotence. The fact that 'warm' and 'bright' will "do" for most people most of the time is the reason we are having this discussion. Ambiguous, verbal terms are not sufficient.

Even you are admitting (without realizing it) that, when the chips are down, in that last .1%, when you "actually want to accomplish something", you've got to abandon what will "do", and go with the ol' reliable that doesn't let you down.

 

[JoeDawg]

Yes, but it will not do in a Physics Forum discussion where we are trying to pin down such terms as omnipotence.

The fact this is a physics forum really doesn't have much to do with it. Omnipotence is not a formula, its not even a word for a scientific idea. And how we use words, and their context and usefulness is very important, when discussing philosophy... regardless of who is discussing it.

The fact that 'warm' and 'bright' will "do" for most people most of the time is the reason we are having this discussion. Ambiguous, verbal terms are not sufficient.

Then I'm sure you can explain omnipotence using mathematics. I'd be very interested to see this.

Even you are admitting (without realizing it) that, when the chips are down, in that last .1%, when you "actually want to accomplish something", you've got to abandon what will "do", and go with the ol' reliable that doesn't let you down.

LOL. You're so patronizing, this I remember well.

I'm perfectly comfortable with what I have said. It has nothing to do with 'when the chips are down' partner. It has to do with what is appropriate to the situation, and what is overkill, in a given situation.

 

[JanClaesen]

I'm sorry for reviving this old thread. If I remember correctly the answer to this question is that God's omnipotence isn't to be seen in 'worldy' terms. His power isn't what we, 'mere humans' perceive as power.

 

[JoeDawg]

I'm sorry for reviving this old thread. If I remember correctly the answer to this question is that God's omnipotence isn't to be seen in 'worldy' terms. His power isn't what we, 'mere humans' perceive as power.

Technically that's not an answer to the question, its more analogus to sticking your fingers in your ears and shouting: La la la, I'm not listening.

 

[Dadface]

Technically that's not an answer to the question, its more analogus to sticking your fingers in your ears and shouting: La la la, I'm not listening.

Which can be a good way of responding to the paradox.If we define that there is an omnipotent being then how can we then go on to demand that he/she(or whatever title we choose) should conform to our logic and understanding?

 

[JoeDawg]

Which can be a good way of responding to the paradox.If we define that there is an omnipotent being then how can we then go on to demand that he/she(or whatever title we choose) should conform to our logic and understanding?

If something is beyond your understanding, how can you claim to define it?

 

[TheStatutoryApe]

Technically that's not an answer to the question, its more analogus to sticking your fingers in your ears and shouting: La la la, I'm not listening.

I don't see how that follows. I have always had a hard time with this particular 'paradox' primarily because it does not seem to make sense. Why does an omnipotent being create a rock too heavy for it to lift? What is an omnipotent being doing lifting rocks? As I said earlier in the thread the question seems to unnecessarily anthropomorphize the being.

 

[Dadface]

If something is beyond your understanding, how can you claim to define it?

Precisely,you seem to have pointed out the contradiction between definition and understanding but in a different way to that presented by JanClaesen and myself.

 

[apeiron]

I'm sorry for reviving this old thread. If I remember correctly the answer to this question is that God's omnipotence isn't to be seen in 'worldy' terms. His power isn't what we, 'mere humans' perceive as power.

Definition actually seems a straightforward issue here. We don't need to complicate things by speculating about the further qualities or purposes of some actual god.

Potency is defined as - possessing inner or physical strength, having great control or authority.

Omni means all, or in the limit.

So omnipotent clearly means strong and in control of things without restriction, without constraint.

We are taking a word with a standard worldly meaning and extrapolating it to an unworldly extreme.

As is always the case in this metaphysical game, a dichotomy emerges. If you find you can head in a direction, then that means you are also creating the direction you are managing to leave behind.

In this example, the idea of control over events is dichotomous to the complementary idea of resistance. And naturally if we infinitise both - posit two extremes, omni-control and omni-resistance in interaction - then we must produce a paradox.

This should be no surprise. The two ideas arise out of each other as opposite directions in the first place and so you can never go so far in one direction as to have actually left the other completely behind. Therefore "omni" - the actual limit - is the place that cannot be reached.

So that in turn means in reality (as opposed to word play), a logical paradox cannot arise. You can never get the irresistable force or the unmoveable object as that would break apart what is actually the one thing. A move towards the idea of force that depends on a departure from the matched idea of resistance.

It is just like Newton realized he needed a third law to complete his mechanics - every action demands its precisely complementary reaction. You can't create the figure without also creating the ground, or event without the context. And this dichotomous connection has to remain intact for statements about reality to be meaningful - for the statement that relies on dichotomisation to be actually anchored at both of its ends to something.

Sometimes it is incredible that after 2500 years of philosophy and logic, people don't get these simple ideas. Or do they just have too much fun wallowing about in the confusion of Zeno-style logic twisters?

 

[ueit]

The resolution of the paradox is simple once you understand that a god cannot do things that are logically impossible. He cannot make a round square, he cannot express sqrt(2) as a rational number and so on. A rock that cannot be lifted by a god is also a logically impossible thing, therefore there is no paradox that it cannot be created by said god.

 

[apeiron]

If something is possible, then its antithesis is also possible.

If something is impossible, then its antithesis is also impossible.

That is the way the logic of reality works.

Get rid of ill-defined notions like gods and stick to definable terms and you can do philosophy.

 

[JoeDawg]

The resolution of the paradox is simple once you understand that a god cannot do things that are logically impossible.

It's still a paradox, all you've done is put constraints on omnipotence, which by definition, makes it not -- omnipotence. The whole point of the rock analogy is to get you to think about what a word like omnipotence really means, and how illogical the idea is. Words like nothing, infinite, omni-anything, are all problematic because they are conceptual and ill-defined, at least with regards to how they relate to the everyday world.

The most simple resolution is that omnipotence doesn't exist.
Its just a badly designed human concept.

 

[JoeDawg]

I don't see how that follows. I have always had a hard time with this particular 'paradox' primarily because it does not seem to make sense. Why does an omnipotent being create a rock too heavy for it to lift? What is an omnipotent being doing lifting rocks? As I said earlier in the thread the question seems to unnecessarily anthropomorphize the being.

The paradox showcases how difficult it is to logically discuss something like god. People often define god in the vaguest terms, which are often self-contradicting. Saying that god is beyond logic is simply evading the problem.

 

[DaveC426913]

The most simple resolution is that omnipotence doesn't exist.
Its just a badly designed human concept.

Eloquent and succinct. I think this is the answer to the paradox.

Omnipotence is merely a concept. That doesn't mean it exists - or even can exist.

 

[apeiron]

Eloquent and succinct. I think this is the answer to the paradox.

Omnipotence is merely a concept. That doesn't mean it exists - or even can exist.

That approach misses the point as well. Omnipotence is a definition of a limit state. The fact that it "does not exist" is a contentful philosophical statement in view of the argument it is indeed "the only form of potence that cannot exist". It is a direction that potentce can head for but cannot then reach.

Just like counting to infinity and other very useful limit descriptions we employ to model reality.

So don't just dismiss it as merely wordplay - concepts without meaningful content. We all know how important the invention of the zero, the representation of pure nothingness, was to maths. And dichotomously, a little later, the invention of infinity - pure everythingness. (Then the infinitesimal - the further dichotomisation of infinity into the perfectly large and the perfectly small).

God is indeed a weak concept. It avoids precise definition and so is not even interesting to a philosopher as a point of discussion. But omnipotent is fair game and holds instructive lessons.

 

[DaveC426913]

It is a direction that potentce can head for but cannot then reach.

Just like counting to infinity and other very useful limit descriptions we employ to model reality.

So don't just dismiss it as merely wordplay...

I'm not dismissing it. I'm (actually JoeDawg) is simply saying it is no longer a paradox. Just like infinity, zero and convergent series are no longer paradoxes.

 

[JoeDawg]

So don't just dismiss it as merely wordplay - concepts without meaningful content. We all know how important the invention of the zero, the representation of pure nothingness, was to maths. And dichotomously, a little later, the invention of infinity - pure everythingness. (Then the infinitesimal - the further dichotomisation of infinity into the perfectly large and the perfectly small).

Infinity and zero are useful mathematical concepts, they are meaningless outside that context, ie in terms of what actually exists.

I think the 'big rock' example is an important tool for people learning to think logically. As long as they don't get confused and think its an ontological problem, its conceptual, a definitional or language based paradox. Solipsism is also a useful thought experiment; when discussing epistemology, but not so much with ontology.

 

[apeiron]

Infinity and zero are useful mathematical concepts, they are meaningless outside that context, ie in terms of what actually exists.

I think the 'big rock' example is an important tool for people learning to think logically. As long as they don't get confused and think its an ontological problem, its conceptual, a definitional or language based paradox. Solipsism is also a useful thought experiment; when discussing epistemology, but not so much with ontology.

I'm being picky now but this is too sloppy.

Mathematics is modelling and so claims a very precise relationship to what exists (or doesn't exist). Concepts can't be useful in the one context and meaningless in the other if all we have at the end of the day is concepts by which we model.

The point I was making was about the modelling relationship - the fact that the unreal turns out to be the most useful vantage point for modelling the real. Limits states cannot actually exist because they are precisely what lies outside reality. And therefore having placed us outside reality (as ideas) give us the most efficient viewpoints to look back into the reality (in which we exist).

It sounds crazy put like this I agree. But it is important to get what "objectivity" is about. Extract the limit and treat it as the truth, even while knowing it is asymptotically the very place reality cannot reach.

And you will see from this that we are dealing with an ontic claim. A direct claim about what can exist, and what can't in turn exist. If you like, we are talking about the ontology of the epistemology! Why we find concepts like infinity and zero and omni so useful, but why they are also fundamentally the unreal. If we insist on treating them as states that exist in nature rather than goals which nature might pursue.

This is why when I hear "paradox" its like three fruit coming up on a slot machine. Jackpot. You have refined your concepts to the point they are successfully unreal. Your work is done. You are no longer standing subjectively inside the system you are trying to describe but standing "objectively" outside it. You have to move beyond the real to stand on the unreal and look back across all the reality you just departed.

 

[JoeDawg]

Mathematics is modelling and so claims a very precise relationship to what exists (or doesn't exist). Concepts can't be useful in the one context and meaningless in the other if all we have at the end of the day is concepts by which we model.

As a concept within mathematics, a zero has value, outside mathematics, its just a line joined at both ends.
You can't separate the concept from its mathematical context. The fact one can relate it to things outside of a mathematical framework is simply a matter of applying math. There is no inherent relationship. A model does not necessarily represent reality. Those that do are useful.

The point I was making was about the modelling relationship - the fact that the unreal turns out to be the most useful vantage point for modelling the real. Limits states cannot actually exist because they are precisely what lies outside reality. And therefore having placed us outside reality (as ideas) give us the most efficient viewpoints to look back into the reality (in which we exist).

But they don't actually place us outside anything.
I have no real problem with what you are saying here.. You can place limits anywhere you like... for instance if you want to narrow your focus, by accepting premises. But the model only relates to the thing being modeled in the way we define it. Whether the model accurately, for our purposes, represents the thing being modeled is a different question.

It sounds crazy put like this I agree. But it is important to get what "objectivity" is about. Extract the limit and treat it as the truth, even while knowing it is asymptotically the very place reality cannot reach.

Objectivity is an ideal.

If you like, we are talking about the ontology of the epistemology!

Clever, but I think that's still pretty clearly under the umbrella of epistemology.

This is why when I hear "paradox" its like three fruit coming up on a slot machine. Jackpot. You have refined your concepts to the point they are successfully unreal. Your work is done. You are no longer standing subjectively inside the system you are trying to describe but standing "objectively" outside it. You have to move beyond the real to stand on the unreal and look back across all the reality you just departed.

The problem I see is balancing that, the further into the unreal you get, the less correspondence it will have with the real. Objectivity, in this sense, doesn't guarrantee correspondence. Fantasy can be objective the way you use the word.

 

[apeiron]

A model does not necessarily represent reality. Those that do are useful.

A model should not even purport to "represent" reality. Models normally exist to control reality. And they prove themselves useful, or "real", to the degree they serve that purpose.

This goes back to faulty understandings of consciousness as veridical re-presentations of reality, when consciousness too is "just modelling".

If we want to talk carefully about epistemology, as we do here, these finer distinctions matter.

But they don't actually place us outside anything.
I have no real problem with what you are saying here.. You can place limits anywhere you like... for instance if you want to narrow your focus, by accepting premises. But the model only relates to the thing being modeled in the way we define it. Whether the model accurately, for our purposes, represents the thing being modeled is a different question.

I agree models don't have to be ultimate theories. They can be partial stories. But here we were talking about taking things to their limits. And the tricky relationship with ontology that ensues.

The problem I see is balancing that, the further into the unreal you get, the less correspondence it will have with the real. Objectivity, in this sense, doesn't guarrantee correspondence. Fantasy can be objective the way you use the word.

I don't really see how you can get further into the unreal. For instance, I said omni-potence would be the outer limit extreme to potence - as far as you could go in that real direction before you make the sudden transition to the impossible. But once you are (in the imaginary sense) into the omni-state, you can't keep getting more omni-. That would be illogical.

You could think of omni as an event horizon or some other kind of singularity shielding device. Or what the speed of light is to a massive object. Approach is possible. Arriving is impossible.

Anyway, the key point I wanted to make in this discussion was the way that all concept development is based on dichotomisation - thesis and antithesis. And then that the development of a concept must become unreal in the extreme - precisely because it is a bounding constraint to reality.

These standard epistemological features of our ontic concepts are crucial to understand to avoid getting mired in the kind of beginner paradox debates we see time and again,