Infinitely powerful entities

[Astner]

One of the supplements to my work in process is a cosmology and it deals with the structures that overarches the universe—alternate realities, and so on—but also infinitely powerful entities, some more powerful than others.

Now my question to you, fellow Chroniclers, what is your initial reaction to this?

 

[TheDustyZebra]

infinitely powerful entities, some more powerful than others.

Well, my brain just imploded at that.

All animals are equal, but some are more equal than others?

 

[Astner]

Mathematically you can make a sensible quantification infinite numbers. The quantification of infinite numbers comes down to either cardinal numbers—which centers around one-to-one pairings—or ordinal numbers—which centers around the well-ordering property.

Without going into too much detail, just as there can be finite numbers of different sizes, there can also be infinite numbers of different sizes.

 

[TheDustyZebra]

Even though math is power, I'm not completely convinced that power is math, necessarily. Of course, if that's how it works in your worlds, then that's how it is.

Are your infinitely powerful entities only infinitely powerful in their own realities? I can see how a being could be capable of doing anything in its own universe, but not as powerful as another being who was capable of doing anything in another universe. "Anything" being relative to what's available, as it were.

But if they are all working in the same space, "anything" is, well, "anything". All anythings are the same, if they all have the same stuff to work with.

For some reason I'm reminded of Piers Anthony's Fractal Mode, though it's been many years since I read it. Over-arching structures of the universe, and alternate realities, and infinity. Probably not at all in the way you mean it, though.

 

[sknox]

@Astner: insufficient data for meaningful answer (to quote Asimov)

Did you really mean "infinite" power, or did you merely mean extremely powerful? How do their powers vary? Since it is supplemental information, do you really expect your reader to read this, or is this really just world-building background?

 

[Astner]

Even though math is power, I'm not completely convinced that power is math, necessarily. Of course, if that's how it works in your worlds, then that's how it is.

You wouldn't be able to make a sense of their power unless you took the theory of transfinite numbers into account.

Are your infinitely powerful entities only infinitely powerful in their own realities?

No their powers aren't localized.

Did you really mean "infinite" power, or did you merely mean extremely powerful?

Infinite power.

How do their powers vary?

In nature the powers do not vary, because it more or less reflects a level of omnipotence. And the only reason an entity of less infinite power would be unable to do something would be if someone of greater infinite power prevented him from doing it.

Since it is supplemental information, do you really expect your reader to read this, or is this really just world-building background?

The latter.

 

[Mirannan]

Hmmm... To be honest, a story that needs the reader to have at least a grounding in Cantor's transfinite set theories would be of (IMO) limited appeal?

The only distinction that I can think of to make sense is one between universal omnipotents and multiversal omnipotents. It's worth, IMHO, digressing into the different classes of universe that have been portrayed in various places. One scheme that has been used in scientific works is a hierarchy; first level is the observable universe. Second tier is our universe but including the bits that are unobservable for reasons of light travel time. Third tier is the multiverse of quantum observables; to explain this very briefly, one theory is that every time any observation is made the universe splits into at least two separate timelines.

The fourth tier is that which uses different sets of laws as a base. Not just the same laws with different numbers, BTW. And the fifth is of universes that use completely different subsets of mathematics as the basis for laws. I think that's as far as it goes; it's been a while since I've read anything on this subject.

Useful references for this might be Cantor; Olaf Stapledon's "Star Maker" (prepare to have your mind expanded!); and oddly enough an under-appreciated classic IMHO, Heinlein's "Job". In the last of these he explores the subject of a hierarchy of omnipotents.

It's worth mentioning, perhaps, that it is pretty well impossible to conceive of the possibilities that a second-tier omnipotent might have for action.

 

[thaddeus6th]

The infinite argument reminds me hearing that black holes all have infinite mass, but that some are larger than others. I think the analogy used was an ant crawling on the surface of a tennis ball. It's effectively an infinite journey because the ant will never reach the end, but a beach ball would also be infinite and larger too.

As for the initial question, I'd probably want more detail.

 

[Boneman]

You could always read 'Anton York Immortal'... but you'd hate me afterwards.

 

[chrispenycate]

I don't think the principle of multiple infinitely powerful beings is mathematically viable. An infinitely powerful being would be able to entirely destroy anything, includding any other infinitely powerful being. If you give the others the power to prevent their destruction, the first being is being limited, and is thus non-infinite. If you don't give them this power, then they are limited, and non-infinite. Take away the possibility of wanting to destroy, and that's a limitation. Infinities are only really capable of coexisting if they are orthogonal, like the set of all real numbers, and the set of all solid angles, so they don't interact. But limiting interactions between entities renders them finite, too; infinity can only have one boundary. I suppose you could have one entity 'the set of all positive real numbers', and another the negatives, so they could never detect each other, and each was omnipotent within its personal domain, but that doesn't really sound like infinite power to me, just a large block of ignorance (omnipotence does not assume omniscience).

Multiple infinities are something to juggle with great care, and that's without starting on transfinites.

 

[Astner]

Hmmm... To be honest, a story that needs the reader to have at least a grounding in Cantor's transfinite set theories would be of (IMO) limited appeal?

I've actually created an article constructing the cardinals, ordinals, and surreal numbers from scratch. This to help the reader better understand the concepts as they're applied.

 

[Brian G Turner]

This to help the reader better understand the concepts as they're applied.

If you're writing for advanced mathematicians it might work.

I think I've seen it mentioned elsewhere that world building is like an iceberg - only the top is visible to the reader - only the author knows the rest.

In the meantime, "infinitely powerful entities"? I would think most people would class those in the realms of Gods, angels, and demons, etc.

 

[paranoid marvin]

Infinite means beyond measure; if you can't quantify one thing then you can't say another thing has more.

Maybe just say that they have tremendous power rather than infinite? That way one can be more powerful than another.

 

[paranoid marvin]

Or say that some have greater powers in certain realities.

 

[chrispenycate]

Ooh, it's a long time since I did this stuff

.ii. Symmetry: If A = B then B = C should be 'then B = A'

It is not clear which letters represent sets, and which natural numbers.

If one entity can be mapped to the infinite set of integers (or it's power can, and the entity can be mapped to its power) then any other entity which can be mapped onto the same set has identically equal powers and is indistinguishable.

PM, infinity is not 'beyond measure' it is 'without limit'. The universe is unmeasurably large; if the big bang theory is correct, it is not infinite. Sure, it requires a pedantic unfrocked mathematician to recognise the difference, but infinity is a very clear (and not intuititive at all) mathematical concept, that doesn't work very easily with 'powers' at all.

 

[ralphkern]

Hi Astner, an interesting concept. My initial reaction, along with trying to muddle my way through your thesis is: what is your objective here?

I would suggest that if you are intending a story most readers would, in the politest possible way, not be interested in having to keep referring to your 133 page paper on Omnipotence: The Cosmology, especially as it's fairly heavy math. Also the Abstract doesn't indicate a clear cut question for the paper, instead you have, as you have indicated got it as what appears to be a living document about enhancing understanding.

Your comment on this thread:

In nature the powers do not vary, because it more or less reflects a level of omnipotence. And the only reason an entity of less infinite power would be unable to do something would be if someone of greater infinite power prevented him from doing it.

This implies to me that there is either competition or heirachy between your entities? If competition then surely by some kind of 'godly' darwinism then there would only be one entity of infinite power as they would likely simply eliminate the competiton? If Heirachical then surely you would have your top dog, then infinite - 1 would be the next down, followed by infinite - 2 the next and so on and so forth.

Additionally this appears on the surface to be a look at something akin to a Greek style of infinitly powerful set of 'dudes' but there is a pecking order?

 

[paranoid marvin]

Ooh, it's a long time since I did this stuff

.ii. Symmetry: If A = B then B = C should be 'then B = A'

It is not clear which letters represent sets, and which natural numbers.

If one entity can be mapped to the infinite set of integers (or it's power can, and the entity can be mapped to its power) then any other entity which can be mapped onto the same set has identically equal powers and is indistinguishable.

PM, infinity is not 'beyond measure' it is 'without limit'. The universe is unmeasurably large; if the big bang theory is correct, it is not infinite. Sure, it requires a pedantic unfrocked mathematician to recognise the difference, but infinity is a very clear (and not intuititive at all) mathematical concept, that doesn't work very easily with 'powers' at all.

It all depends! By it's very nature one can never truly say that something is without limit. If it is impossible to meaure , then it is impossible to say that it is without end.

 

[chrispenycate]

Ah, but for a mathematician – and only mathematicians have any interest in infinity, even theologians blanching at the concept – practical measurements are irrelevant. Practical anything is considered questionable to a determined maths specialist.

 

[paranoid marvin]

Ah, but for a mathematician – and only mathematicians have any interest in infinity, even theologians blanching at the concept – practical measurements are irrelevant. Practical anything is considered questionable to a determined maths specialist.

I would have thought that mathematicians would have hated anything that wasn't quantifiable!

I will bow to your better judgement on this one.

 

[Glitch]

I don't have a problem with powerful entities. In fact I've used such characters myself.

The question is how these characters use, or don't use their powers. If you have a collective of entities with such powers, do they have rules on how they may be used? My stories on the subject tend to deal with characters who bend or break such rules and the ensuing consequences; either for them or those they use the powers on.