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

[gabrielh]

I consider this a very weak argument against he existence of a god. There are many ways of viewing this that make logical sense, both in favor of and against. For instance, a less common interpretation:

Knowledge is power. Therefore ultimate knowledge is ultimate power, ergo, omniscience = omnipotence = god. By this interpretation, when you ask the question related to the 'Big Rock' you are essentially asking, 'Can a being which can do anything do that which it cannot do?' which is a self canceling statement.

Not to mention omnipotence and omniscience are very loosely defined in these types of arguments, just take a look at this thread. It also raises the question as to whether logical rules apply to the omnipotent. If the omnipotent being created these sets of laws, the omnipotent being could easily bend and break them as it saw fit.

It may be all we have at present, but to me it's nothing beyond throwing words out and tripping up people in their subjective meaning.

 

[JoeDawg]

I consider this a very weak argument against he existence of a god.

I think you're missing the point of the 'argument'. Its supposed to make you think about the ill-defined and often contradictory notion of 'omnipotence'. Its basically a nonsense word. Also, this is really more a theological discussion, as opposed to philosophy, as it depends largely on the nature of said hypothetical monotheistic god.

Another problem with omnipotence is that if you have a creator god which is omnipotent and omniscient, then everything that happens is a direct result of this gods action or inaction, which negates human freewill, and reaffirms the problem of evil.

Ultimately the monotheistic god is either logically non-existent, or evil, by most human standards. Gnosticism has an interesting take on this.

 

[Hurkyl]

Hurrah, you can prove anything if you first assume a contradiction!

 

[WaveJumper]

Another problem with omnipotence is that if you have a creator god which is omnipotent and omniscient, then everything that happens is a direct result of this gods action or inaction, which negates human freewill, and reaffirms the problem of evil.

Ultimately the monotheistic god is either logically non-existent, or evil, by most human standards. Gnosticism has an interesting take on this.

Well said. However i wonder if the hypothetical creature God is supposed to have emotions at all. IMO, emotions are very misleading and would weaken such an entity/force. There is no room(currently) for emotions in mathematics and we know this presumed being is a very strong mathematician.

 

[JoeDawg]

Well said. However i wonder if the hypothetical creature God is supposed to have emotions at all. IMO, emotions are very misleading and would weaken such an entity/force.

Emotions are essentially just evolved instincts.
A deist god might have nothing resembling human intelligence.

There is no room(currently) for emotions in mathematics and we know this presumed being is a very strong mathematician.

I'm not sure what you mean by this. There is no taste or smell to mathematics either... so what? And I'm not sure attributing mathematics to a god makes much sense. Mathematics is a human invention used to abstractly describe the universe via logical relations. One could just as easily say god is a very strong linguist, since english and russian both can be used to describe the world.

 

[WaveJumper]

And I'm not sure attributing mathematics to a god makes much sense.

It makes, if said deity(s) is a software engineer/programmer that uses F=M.a, E=m.c^2,
p=m.v, etc. to "build" a self-functioning mathematical/informational universe. This pre-supposes that mathematics can describe all of reality, which is not yet a fact, just a logical assumption that stems from the observed extraordinary power of mathematics' so far.

Mathematics is a human invention used to abstractly describe the universe via logical relations.

The argument - is mathematics invented or discovered cannot be resolved. My firm opinion however is that mathematics is discovered, not invented(otherwise the opposite would imply that we create a large portion of the perceived reality)..

One could just as easily say god is a very strong linguist, since english and russian both can be used to describe the world.

No, no. Very few physicists will agree with this. Very very few. Languages are a very poor tool to describe the true nature of reality, there is no question about that, at all.

Answer this- "What is an electron?". Answer in a non-mathematical way with dictionary definitions. It's definitely not a "particle" as per dictionary definitions.

I contend that this is the only unambiguous way to describe it:

ψ in (mathematical)Hilbert space.

 

[Moridin]

It makes, if said deity(s) is a software engineer/programmer that uses F=M.a, E=m.c^2,
p=m.v, etc. to "build" a self-functioning mathematical/informational universe. This pre-supposes that mathematics can describe all of reality, which is not yet a fact, just a logical assumption that stems from the observed extraordinary power of mathematics' so far.

This of course ignores the fact that F = ma, E = mc² and so on are quite precise approximations to reality, rather than an all powerful law controlling the universe. Instead of thinking of scientific laws as controlling reality, you should think of them as precise and general descriptions of reality. The universe does not mind wonky circles.

The argument - is mathematics invented or discovered cannot be resolved. My firm opinion however is that mathematics is discovered, not invented(otherwise the opposite would imply that we create a large portion of the perceived reality).. [...] No, no. Very few physicists will agree with this. Very very few. Languages are a very poor tool to describe the true nature of reality, there is no question about that, at all.

The philosophical Platonism versus social constructivism is clearly a false dichotomy. It is entirely reasonable to hold that mathematics is a language for describing relations, quantities, structure, space, change, patters and so on, but is special compared to most or all other language because of its non ambiguity and component simplicity. This means that the specific symbols of mathematics is an arbitrary social convention (since we can change them if we want without altering the claims) but that which mathematics refers to is not a social construction, but actually existing relations, quantities, changes, patters and so on.

Similarity, "chair" is a social construction (since we can call it "stol" or "stuhl" and so on), but it is obvious that chairs themselves are not social constructions.

Furthermore, you can translate the concept of mathematics into English.

$$\lim_{x\to 0}f(x)=2$$

"The limit of f for x as x approaches 0 is 2"

The English statement captures the essence of the math above reasonably well. It is not at all clear that this translation would be possible if mathematics was not a language. When it comes to translating more complex mathematical statements, natural languages fall behind because of their ambiguity and component complexity.

I would like to argue that this view of mathematics both avoids the real threat of social constructivism, but also avoids the unexplainable metaphysical baggage of Platonism, yet still retains the power and usefulness of mathematics. I can of course be wrong, but I like this solution.

I contend that this is the only unambiguous way to describe it:

This is the smoking gun. You are describing an electron. How can you describe something without using a language?

 

[DaveC426913]

This is the smoking gun. You are describing an electron. How can you describe something without using a language?

Ok, let's make a distinction between a verbal language and a mathematical language.

Verbal languages are not very good at describing nature. Mathematical language(s) are.

 

[JoeDawg]

Ok, let's make a distinction between a verbal language and a mathematical language.

Verbal languages are not very good at describing nature. Mathematical language(s) are.

I just ate an apple. That's a pretty natural event.

Feel free to describe that with mathematical language.
While I'm sure it will be a good description...
Personally, I think most english speakers would say the english description is more useful than the mathematical.

 

[JoeDawg]

It makes, if said deity(s) is a software engineer/programmer that uses F=M.a, E=m.c^2,
p=m.v, etc. to "build" a self-functioning mathematical/informational universe.

The universe is not made of equations, equations describe the universe.

The argument - is mathematics invented or discovered cannot be resolved. My firm opinion however is that mathematics is discovered, not invented(otherwise the opposite would imply that we create a large portion of the perceived reality)..

And that is bad, why?

Answer this- "What is an electron?". Answer in a non-mathematical way with dictionary definitions. It's definitely not a "particle" as per dictionary definitions.

It's a subatomic structure with a negative electric charge.
Do I get a gold star or something?

I contend that this is the only unambiguous way to describe it:

ψ in (mathematical)Hilbert space.

Its only unambiguous if you understand to a level that you are satisfied with. Which is completely subjective.

 

[DaveC426913]

I just ate an apple. That's a pretty natural event.

Feel free to describe that with mathematical language.
While I'm sure it will be a good description...
Personally, I think most english speakers would say the english description is more useful than the mathematical.

I'm sure non-physicists - those who are not in the business of describing nature down to its fundamentals - will be quite satisfiied with descriptions such as sweet and tart. Alas, your sweet and my sweet aren't the same thing, so you tell me how useful it is as a description.

 

[JoeDawg]

I'm sure non-physicists - those who are not in the business of describing nature down to its fundamentals - will be quite satisfiied with descriptions such as sweet and tart. Alas, your sweet and my sweet aren't the same thing, so you tell me how useful it is as a description.

Being satisfied with a description is usually about how useful it is to you. If I tell you something is sweet, your experience may be different from mine, but assuming you don't have some illness that affects your taste buds, I'm sure we would both be satisfied with my description of something as such, whether we are physicists or acrobats.

Calling a sugar molecule sweet is simply less useful, because when a person is talking about sugar molecules, taste is not generally what they are interested in, nor would they taste much of anything if they only had one molecule of any substance. Similarly talking about spin or electric charge with regards to apple pie isn't very useful.

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.

 

[apeiron]

I just ate an apple. That's a pretty natural event.

Feel free to describe that with mathematical language.
While I'm sure it will be a good description...
Personally, I think most english speakers would say the english description is more useful than the mathematical.

That brings up the fact that modelling can lie on a continuum of "languages". What is the deeper principle at work?

It is all about the epistemological dichotomy - generals vs particulars, universals vs instances, models vs measurements.

Modelling depends on abstracting - shedding unnecessary detail to create the general principle. Then having created a model, it can be used to re-generate a world of particulars.

So a law like F = MA. As general a statement as can be imagined. Applies anywhere and anywhen. And we can plug in any local particulars to get a local prediction. From the single universal can be generated an infinity of possible instances.

More everyday languages are tailored to making more everyday models and predictions. So "ate" is a model of an action. A fairly generalised concept. Then this general is constrained by modifiers that increasingly particularise the statement being made. We generate a detailed local instance of eating - such as that it was I who ate, and what I ate was an apple.

We could of course then treat I and apple as too general, and add constraints. So it was I as a three year old sitting on the lawn. The apple was a braeburn that fell of my tree.

So there is no essential difference that puts maths in some special place. It is just the most formal and generalised tool of modelling which we have managed to develop.

We also know that maths suffers limits. Many working in systems science think in fact maths is only a job half done as it is only just beginning to find the universals that lie in holistic or complex systems.

Another story. But the message is that maths is only a tool of modelling. So don't worship it. It is only a further development of something we were already doing. Though it has become an impressively universal tool (bit like a swiss army knife? too many options and only one or two blades you will ever use much?)

 

[TheStatutoryApe]

I think you're missing the point of the 'argument'. Its supposed to make you think about the ill-defined and often contradictory notion of 'omnipotence'. Its basically a nonsense word. Also, this is really more a theological discussion, as opposed to philosophy, as it depends largely on the nature of said hypothetical monotheistic god.

The only problem arises when you take the definition to the furthest reaches of imagination. Omnipotence can easily be defined as the ability to do all things possible, there is no necessity that an omnipotent being be capable of doing the impossible.

 

[JoeDawg]

The only problem arises when you take the definition to the furthest reaches of imagination. Omnipotence can easily be defined as the ability to do all things possible, there is no necessity that an omnipotent being be capable of doing the impossible.

That's really just playing with definitions.

You've basically said, an omnipotent being can do 'anything', except for those things it can't, 'possibly', do.

Which doesn't really address the problem of a being that is 'all powerful'. Nothing should be impossible, for a being, that can do 'anything'.

I can do anything too, except for the things that are impossible for me to do.
We are all omnipotent, by your definition.

 

[Hurkyl]

Which doesn't really address the problem of a being that is 'all powerful'. Nothing should be impossible, for a being, that can do 'anything'.

Giving "thing" to wide of a scope is problematic. Not for this discussion, but for logic itself. e.g. you would run into the Liar's paradox in its full glory as an actual paradox rather than a subtle error in reasoning.

 

[TheStatutoryApe]

That's really just playing with definitions.

You've basically said, an omnipotent being can do 'anything', except for those things it can't, 'possibly', do.

Which doesn't really address the problem of a being that is 'all powerful'. Nothing should be impossible, for a being, that can do 'anything'.

I can do anything too, except for the things that are impossible for me to do.
We are all omnipotent, by your definition.

Funny, I thought that I was accusing you of playing with definitions. ;-p

And I meant anything that is at all possible. There are obviously things which are possible to accomplish which you can not.

Its easy to point out flaws in a concept when you create your own standard of its definition without regard for other possible and equally valid definitions. You can logically invalidate anything this way as I think we have seen in other threads. ;-)

 

[JoeDawg]

Funny, I thought that I was accusing you of playing with definitions. ;-p

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

And I meant anything that is at all possible. There are obviously things which are possible to accomplish which you can not.

So what you mean is 'logically possible'. But that is still an unfair limitation. When we talk about omnipotence, what we really are talking about is god, and specifically the creator god. So if that god created the universe, then it created its logical underpinnings. Which means concievably, it could create a universe with different logical constraints, or... none at all. What you might call chaos... Thus the problem rears its ugly head again. Is omnipotence constrained by consistency, and if so, why?

Its easy to point out flaws in a concept when you create your own standard of its definition without regard for other possible and equally valid definitions. You can logically invalidate anything this way as I think we have seen in other threads. ;-)

This is true, but my point is, there is no logically consistent way to construct omnipotence, it by definition, contradicts itself.

 

[TheStatutoryApe]

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

So what you mean is 'logically possible'. But that is still an unfair limitation. When we talk about omnipotence, what we really are talking about is god, and specifically the creator god. So if that god created the universe, then it created its logical underpinnings. Which means concievably, it could create a universe with different logical constraints, or... none at all. What you might call chaos... Thus the problem rears its ugly head again. Is omnipotence constrained by consistency, and if so, why?

This is true, but my point is, there is no logically consistent way to construct omnipotence, it by definition, contradicts itself.

Is omnipotence necessarily limited to creator gods? The paradox in general deals with the definition of omnipotence regardless of the particular religious context. Resorting to the definitions of certain religions does not necessarily address the idea in general. You can similarly attempt to invalidate the general theory of the propagation of light by spefically attacking the theory of aether instead of addressing all theories. The problem of one theory or definition does not necessarily contaminate all of them.

 

[JoeDawg]

Is omnipotence necessarily limited to creator gods?

If you would like to suggest another example, then I'd be happy to address it. Creator gods are, however, the common historical context for these sorts of discussions.

The paradox in general deals with the definition of omnipotence regardless of the particular religious context.

I only noted the context so as to be clear about how it is 'generally' applied, and where the most common definitions come from. Claiming that omnipotence can be discussed generally, without such a context, is taking it out of its 'generally' understood framework. If you wish to do so, fine, but you would have to define that context.

Resorting to the definitions of certain religions does not necessarily address the idea in general. You can similarly attempt to invalidate the general theory of the propagation of light by spefically attacking the theory of aether instead of addressing all theories. The problem of one theory or definition does not necessarily contaminate all of them.

Since the history of discussions of the word, and the concept, are very tightly woven into specific religious traditions, I think it would be erroneous to ignore where the word comes from in any discussion.

 

[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?