LHC - the last chance for all theories of everything?

[Vanadium 50]

I think Auger even pinpointed some nearby AGN sources of cosmic rays (though not of this ultra high energy.)

That correlation has either weakened or disappeared, depending on who you talk to.

 

[marcus]

That correlation has either weakened or disappeared, depending on who you talk to.

I'm glad to learn of this! Do you have any paper or news item that tells about it?

 

[tom.stoer]

Yes, this is what he says: mathematics does not DESCRIBE the reality, it IS reality.
But if you do this step, then the next step you unavoidable. If some mathemetical system describes OUR Universe, then why it is special?

This question stillmakes sense.

You should take into consideration that for many known mathematical frameworks you can construct a meta-framework from which the individual frameworks can be derived. In that case the meta-framework can provide a selection rule.

 

[Dmitry67]

Could you explain your motivation, why do you want to find some "selection rule"?

Selection rule adds complexity. Number 456 contains more information then ALL integers, because you can ask "why 456? what is selection rule?" For ALL integers you don't need a selection rule.

 

[Vanadium 50]

I'm glad to learn of this! Do you have any paper or news item that tells about it?

Glad? Indeed. Why?

The most positive interpretation comes from Auger themselves: see their presentation at ICRC 2009 in Lodz. They say that the correlations have "not strengthened" or "weakened", despite having added more data to the analysis.

Others did the natural thing and subtracted the new numbers from the old numbers to look at the correlation in just the events they added. Nothing much there.

 

[marcus]

Glad to get new information about an interesting question like the origin of UHECR.

The most recent thing I've seen about this is April 2009
http://arxiv.org/abs/0904.4277
Correlations between Ultrahigh Energy Cosmic Rays and AGNs
Glennys R. Farrar, Ingyin Zaw, Andreas A. Berlind
(Submitted on 27 Apr 2009)
"We investigate several aspects of the correlations reported by the Pierre Auger Observatory between the highest energy cosmic rays (UHECRs) and galaxies in the Veron-Cetty Veron (VCV) catalog of AGNs. First, we quantify the extent of the inhomogeneity and impurity of the VCV catalog. Second, we determine how the correlation between the highest energy Auger UHECRs and VCV galaxies is modified when only optically-identified AGNs are used. Finally, we measure the correlation between the published Auger UHECRs and the distribution of matter. Our most important finding is that the correlation between UHECRs and AGNs is too strong to be explained purely by AGNs tracing the large scale distribution of matter, indicating that (barring the correlation being a statistical fluke) some substantial fraction of UHECRs are produced by AGNs. We also find that once we take into account the heavy oversampling of the VCV catalog in the Virgo region, the lack of UHECR events from that region is not incompatible with UHECR having AGN sources."

If you have a link handy to some particular abstract from the conference you were talking about, I'd be glad to give a look.

 

[moniker2]

Maybe it's time to redefine temperature.

 

[tom.stoer]

Could you explain your motivation, why do you want to find some "selection rule"?

Selection rule adds complexity. Number 456 contains more information then ALL integers, because you can ask "why 456? what is selection rule?" For ALL integers you don't need a selection rule.

The explanation is as follows:

I believe that we are living on one of many possible worlds. Possible means logically or mathematically possible = (at least) consistent.

As I said I think that a universe with (e.g.) a fourth heavy fermion generation would be "possible" and would not differ so much from ours. So we must take this into account when we study candidates for a ToE.

Then I believe that (even if you insist on some kind of a multiverse) not ALL but only a certain SUBSET of all possible worlds exist "somewhere". Of course I do not know what this subset is but I strongly believe in this subset.

Reason 1: I don't like the multiverse idea, because it has too much metaphysical ballast and does not satisfy Ockham's razor criterion; I don't believe in an entity that is in principle invisible, not measurable and therefore unphysical. Compared to the multiverse one selection rule seems to be much simpler and much easier to believe in (at least for me).
Reason 2: All discussions regarding the multiverse idea (many-worlds interpretation, landscape) I ever participated in came sooner or later to a point which I would describe like "I cannot explain why it's this way or that way - and therefore it's both ways!" That's not a sientific argument but an excuse only.
Reason 3 - and this is the most important one: even if you insist on the multiverse idea, it is by no means clear why ALL logically consistent ToEs should be physically real - why not only a certain subset? Compare it to evolution: not ALL possible species are alive, but only a certain subset. Why is this? Simply because there are selection rules (not hand made, but external to the species' ToE framework = the DNA, namely the environment) which suppress or constrain the evolution. In our case this could be some meta-theory, but nevertheless it must not be excluded.

So this selection rule could restrict the number of real worlds to just ONE, or it could drive an evolution of universes such that we are living in a TYPICAL one.

(Smolin's idea was that a universe spawns children from black holes, so a selection rule is that a typical universe is one in which the numer or density of black holes is maximized such that as many baby universes as possible are spawned - I don't think he was able to define this mathematically and prove why our universe nearly maximizes the number of black holes).

Finally I would like to explain reason 4 - even if I did not study the paper in question in all details: From a philosophical point of view I still do not see how the concept of a DESCRIPTION of a world is converted into the WORLD itself. I still believe in a kind of dualism, namely that the world and its description are two different "entities". Therefore the mathematical frameworks do not exist on the same level as the worlds.
Of course there is a sketch of a proof: The mathematical framework is eternal and exists "forever". It does neither exist "in time" nor "in space". But a universe can be created out of "something" and eventually it can fade away. Therefore the lifetime of a universe could be finite, whereas the lifetime of the corresponding mathematical framework is certainly not (homework: when will the prime numbers die?)
If you believe that the prime numbers will never die, then
a) either the universe (by similar reasons: all universes!) is (are) eternal, which means that only eternal universes are allowed, which is a selection rule!
b) or the prime numbers exist in some "outer space" = some meta-theory in which the "universes" = ToEs are embedded. In that case the eternal framework turns again into an eternal description of a mortal world, which proves that the two entities in question do not exist on the same level.


(Logical positivists grounded some of their disproofs in a mismatch of categories. E.g. they claimed that the color red is not identical with a certain wavelength, but is its representation. I have the feeling that this concept for a ToE is vulnerable due to similar reasons).

My conclusion is that I am still not convinced that the entity "description of the world" is identical with the "world" it describes.

Last but not least I would like add an idea how ToEs could be categorized:
- first requirement is that the ToE incorporates all known interactions in some way, e.g. as low-energy effective theories
- second requirement is that the ToE is a consistent mathematical framework, i.e. it must be mathematically well-defined
- third requirement is that the theory must post-dict at least some known facts like the standard model gauge symmetries, number of generations, number of space-time dimensions etc.
- forth requirement is that the theory must predict new phenomena which should be (at least in principle) falsifiable by experiment
A (meta) requirement) for a (meta) ToE is that the theory in question can at least support why she is the ToE. That means if the ToE contains a certain mathematical structure, there should be an explanation in terms of deeper structures or insights why this structure MUST be contained. This is subtle, of course. EXample: if the ToE is grounded on local gauge symmetries, I would like to know WHY.

 

[moniker2]

Maybe you can use Knot theory to satisfy Ockham's razor criterion in the multiverse idea.

 

[Dmitry67]

Tom,

Regarding 1,2,3 and Occams razor. In informational sense, “information should not be multiplied unnecessarily”. When we build something, we add building blocks, adding new information an every step. That is why every new stone you put in the building must be well justified. However, using this method you can add only finite number of stones/entities. You can’t define integers by providing a complete list, right?

When we manipulate with infinite numbers of entities we go in the opposite direction: we start from the Universum, and then remove something. Each removal adds new information (and list {12438, 59859599, 858585, 77} contains MORE information than a list of ALL integers), so each removal must be justified.

It seems you understand it and for that reason you call a “selection” rule (selection – taking one from many = removing others). Again, you are not asking how to justify the creation of OUR universe( that would be natural for one going from nothing to the Universum), you seek the justification of removal for the others. So we are on the same page.

But: if we go in the opposite direction, from the Universum, then any REMOVAL adds new information and hence is a subject of Occams razor. Going from nothing to the Universum we must justify any addition, going back we must justify any removal. You mentioned Occams razor and on the very next step started inventing NEW entity which you call a “selection rule”. Do you agree with my logic?

So Occams razor is the very reason I believe other Universes exist.

I still do not see how the concept of a DESCRIPTION of a world is converted into the WORLD itself.

It is not CONVERTED. It IS WORLD.

You know, there are some naïve questions like “what is space?”. People tend to ask such questions because of the intuitive conception that if something is not made of something then it is void and collapses. So the most satisfactory answer would be “space is made of spacions”. “Ah, yes, it makes sense”. Of course, after a while they would start wondering what spacions are made of.

We always had a situation that something was made of something: molecules of atoms, atoms of elementary particles, then came quarks, now we expect them to be made of strings. We so got used to it that we are not psychologically ready to the fact that in TOE that infinite reduction MUST END.

Say, you are looking at the page with few beautiful equations. These TOE equations describe, say, some function Q in some quaternion-valued space and some equations that function Q obeys. All other entities: time, space, gravity, particles, emerge from these equations.

But you start to worry. this is just an equation What makes it real, you ask yourself. You are desperately trying to find a magic wand which would touch the paper with formulas and the formulas will start to “live”. You are not satisfied with the fact that this IS TOE. If I would say that the reality is made of “realityons”, obeying these formulas, you will be satisfied, right? If I would say that there are JUST formulas, you will be not. You will be even satisfied if I would say that these formulas are emulated on some supercomputer. Because again it shows that there is smoothing behind the curtain – realityons, computers, or something.

Max Tegmark article is so shocking because he insists that there is nothing behind the curtain – no spoons, no realityons, no supercomputers. Fundamental notions are fundamental only if they do not consist of anything. Fundamental notions do not need any agents to be “incarnated”. Otherwise they are not fundamental and the theory is not a TOE.

The mathematical framework is eternal(B) and exists "forever"(Dmitry67 - wrong, because forever is (A) category). It does neither exist "in time(B)" nor "in space". But a universe can be created out of "something" and eventually it can fade away(A). Therefore the lifetime(A) of a universe could be finite(A), whereas the lifetime of the corresponding mathematical framework is certainly not(B) (homework: when will the prime numbers die?)

That logic is wrong. Time is a notion INSIDE our Universe. Other universes can have no time (euclidean space) or might have multidimensional time, or something else. Abstract world of Universes does not have time defines.

You are mixing 2 things:
(A)“eternal” as “lasting for eternity of time” = “being infinite in time”
(B) “eternal” as “existing independently of time” = “something to which a concept of time is not applicable”
In your quote I put marks (A) and (B) showing how you mix these notions. In the highlighted part you compare (A) and (B) which is incorrect.

 

[RUTA]

You know, there are some naïve questions like “what is space?”. People tend to ask such questions because of the intuitive conception that if something is not made of something then it is void and collapses. So the most satisfactory answer would be “space is made of spacions”. “Ah, yes, it makes sense”. Of course, after a while they would start wondering what spacions are made of.

We always had a situation that something was made of something: molecules of atoms, atoms of elementary particles, then came quarks, now we expect them to be made of strings. We so got used to it that we are not psychologically ready to the fact that in TOE that infinite reduction MUST END.

We make exactly this point in the Conclusion of arXiv 0908.4348. Our answer is to put a self-consistency criterion at bottom, i.e., a mathematical co-definition of space, time and divergence-free sources (QFT parlance), that underwrites a discrete action for the path integral in the transition amplitude.

 

[tom.stoer]

First of all I don't think that you responded to reason 2 and 3. Regarding Ockham's razor and reason 1 we should not waste too much time.

Some clarifications and remarks:

Each removal adds new information... contains MORE information than a list of ALL integers), so each removal must be justified.

I do not want to create selection rules by hand - I expect them to arise automatically. The idea regarding lifetime (see below) is one example.

It is not CONVERTED. It IS WORLD.

I do not mean "converted during a process", but "converted during our philosophical discourse". It's not the description that's converted into something but our understanding about the mathematical framework. So forget about this.

... there are some naïve questions like “what is space?”

That's not naive, that's a question which drives the whole scientific progress! w/o the question "what are atoms" we would not know anything about quantum mechanics.

... if something is not made of something ...

That's not my intention. I do not want to reduce the entities of the ToE to some more fundamental entity. This can happen, of course, but it's not required. In philosophy you can ask "what is goodness?" or "why does something exist instead of nothing?" or "what is time?" These questions do not automatically imply reductionism.

... he insists that there is nothing behind the curtain – no spoons, no realityons, no supercomputers. Fundamental notions are fundamental only if they do not consist of anything. Fundamental notions do not need any agents to be “incarnated”. Otherwise they are not fundamental and the theory is not a TOE.

But a mathematical framework consists of "something"; it consists of fundamental entities like an alphabet, definitions, rules and axioms. How do you "create" a mathematical framework out of nothing? You can only "create" it out of these constituents. But as I said above, that's not my basic concern here.

You are mixing 2 things:
(A)“eternal” as “lasting for eternity of time” = “being infinite in time”
(B) “eternal” as “existing independently of time” = “something to which a concept of time is not applicable”

Maybe I was not so accurate here, so I try again.

My basic intention is INDEED to mix these two "categories of existence", simple because the theory you are describing FORCES me to do this.

I start with my statement that each mathematical framework is eternal; there seems to be no meta-mathematics which "creates" or "kills" mathematics. So as mathematics has not been "created" at some "time", all mathematical frameworks are eternal, too.

The mathematical frameworks in question do not exist "in physical time" because time (and space) are entities "emerging" from these framework (not necessarily from all frameworks, as the ToE may allow for universes where physical time does not exist.

Up to now I do not mix these to "categories of existence". No my reasoning is as follows:

If some specific mathematical framework DESCRIBES a universe, the existence of the framework and the existence of the universe are two different "categories of existence"; therefore their "lifetimes" are independent. Whereas the description of the universe exists "before" the universe is "created" and after it "dies", the universe itself has a finite (physical) lifetime.

If a universe with finite "physical existence" IS IDENTICAL WITH the corresponding mathematical framework, you are in trouble. Either you have to forbid by some selection rule universes=frameworks with finite lifetime, or you have to lift the framework to some meta-level where its existence and "lifetimes" is again independent.

You are telling me that the universe and the framework are identical. So there must be a one-to-one correspondence of all entities, structures and aspects including EXISTENCE; especially you have to specify, what it means on the level of the framework that "the univeses dies" = "its existence comes to an end" = "the mathematical framework dies".
Either the existence of the framework comes to an end, too, then you have to explain what that means in pure mathematics, or the theory rules out universes with finite lifetime, or the framework does not die, but then its not identical to the universe in all aspects which contradicts your theory.
You have to explain how these sentences correspond to each other and how they can be formulated in a mathematically well-defined way.

Assume you are right and we are living in a universe=framework created by a big bang from nothing. What was the mode of existence of the framework before the big bang and how has it been created?

 

[tom.stoer]

Not to forget - what do you think about my ideas:

... I would like add an idea how ToEs could be categorized:
- first requirement is that the ToE incorporates all known interactions in some way, e.g. as low-energy effective theories
- second requirement is that the ToE is a consistent mathematical framework, i.e. it must be mathematically well-defined
- third requirement is that the theory must post-dict at least some known facts like the standard model gauge symmetries, number of generations, number of space-time dimensions etc.
- forth requirement is that the theory must predict new phenomena which should be (at least in principle) falsifiable by experiment
A (meta) requirement) for a (meta) ToE is that the theory in question can at least support why she is the ToE. That means if the ToE contains a certain mathematical structure, there should be an explanation in terms of deeper structures or insights why this structure MUST be contained. This is subtle, of course. Example: if the ToE is grounded on local gauge symmetries, I would like to know WHY.

 

[Dmitry67]

First of all I don't think that you responded to reason 2 and 3. Regarding Ockham's razor and reason 1 we should not waste too much time.

Reason 2: All discussions regarding the multiverse idea (many-worlds interpretation, landscape) I ever participated in came sooner or later to a point which I would describe like "I cannot explain why it's this way or that way - and therefore it's both ways!" That's not a sientific argument but an excuse only.

Reason 3 - and this is the most important one: even if you insist on the multiverse idea, it is by no means clear why ALL logically consistent ToEs should be physically real - why not only a certain subset? Compare it to evolution: not ALL possible species are alive, but only a certain subset. Why is this? Simply because there are selection rules (not hand made, but external to the species' ToE framework = the DNA, namely the environment) which suppress or constrain the evolution. In our case this could be some meta-theory, but nevertheless it must not be excluded.

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours. Not I should explain why other universes exist, but you must proof that they don’t. See may explanation about justification of addition and removal. You can not agree with my reasoning, then let's discuss it. But your ‘Reason 2’ is just variation of Reason 1. The same for Reason 3 – again, it is variation of the same question, don’t you see? Yes, I insist that ALL Toes are physically real and there is no selection rule.

 

[Dmitry67]

If a universe with finite "physical existence" IS IDENTICAL WITH the corresponding mathematical framework, you are in trouble. Either you have to forbid by some selection rule universes=frameworks with finite lifetime, or you have to lift the framework to some meta-level where its existence and "lifetimes" is again independent.

You are telling me that the universe and the framework are identical. So there must be a one-to-one correspondence of all entities, structures and aspects including EXISTENCE

I recommend you checking the concept of Block Time:
http://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time )

Time does not "move". Universe is not a "movie". It does not "dies". "NOW" is just an illusion. Past is as real as future.

You are claiming that video tape turns to dust as soon as observers see "THE END" title, or Videogame self-destroys on your computer as soon as you go thru it to the very end.

Mathematical frameworkd is an analog of a program or a videotape.

If you have a universe which exists limited time (say from Big Bang to Big Rip) then the mathematical system describes it completely, from the very beginning, to the very end. it is a tape. You can look at it over and over. You can move at any direction.

As you know from SR, time is dimension (slightly special). Now replace time with space and repeat your reasoning. So, if universe is finite (limited volume) and say is only 100 meters long, the you say, I am in trouble, because my formulas disappear to the left or to the right from the universe :)

 

[Dmitry67]

Not to forget - what do you think about my ideas:

- first requirement is that the ToE incorporates all known interactions in some way, e.g. as low-energy effective theories
Agreed

- second requirement is that the ToE is a consistent mathematical framework, i.e. it must be mathematically well-defined
Definitely

- third requirement is that the theory must post-dict at least some known facts like the standard model gauge symmetries, number of generations, number of space-time dimensions etc.
Yes

- forth requirement is that the theory must predict new phenomena which should be (at least in principle) falsifiable by experiment
It would be good, but I am not sure.

A (meta) requirement) for a (meta) ToE is that the theory in question can at least support why she is the ToE. That means if the ToE contains a certain mathematical structure, there should be an explanation in terms of deeper structures or insights why this structure MUST be contained. This is subtle, of course. Example: if the ToE is grounded on local gauge symmetries, I would like to know WHY.
- Ha Ha.
I can not help you with it.
At first you violate occamz Razor and invent an unneeded notion - "selection rule"
They you ask: what properties does that rule have?
I don't have a selection rule, then I don't need to answer that question

 

[tom.stoer]

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours ...

Sorry, but that's demonstrably false!

We see, observe and live in exactly one universe. All other universes (frameworks, ToEs, ...) are speculations and not accessible experimentally. Therefore they are metaphysical ballast - as long as you cannot show that they MUST exist.

 

[RUTA]

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours. Not I should explain why other universes exist, but you must proof that they don’t. See may explanation about justification of addition and removal.

In general, the burden of proof is always on the positive claim. For example, if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't. If you claim QM entails multiple worlds, then that's something you must prove and in this case, since there are interpretations of QM without MW, the proof/evidence would have to be experimental.

 

[tom.stoer]

Mathematical framework is an analog of a program or a videotape.

If you have a universe which exists limited time ..then the mathematical system describes it completely ... it is a tape.

You do not understand my point.

In my opinion there are two "categories of existence", a) the video tape and b) the movie (I do not have a problem with this point you view)

In our opinion these two categories have to be identified, the video tape (framework) and the movie (universe) are identical. But then you have to identify all aspects, entities and structures of the tape and the movie as well. If you can't do that, you failed to identify these concepts.

My impression is that you (partially) still refer to the framewortk as something that is external to the universe, something that is "only" its description. If you idea is right, then it provides not only a MAPPING between structures of the tape and structures of the movie, it provides an IDENTIFICATION.

Let me ask one easy question: do you think that the word "apple", the meaning of "apple" in the english language, the representation of an apple as picture, as "entity" on your retina / in your brain and as wiki article are identical? You do you think they are different aspects of one ontological nucleus?

 

[tom.stoer]

Agreed ... Definitely ... Yes ... It would be good, but I am not sure.

Thanks!

Ha Ha.

Of course I expected this answer :-)
Are there other opninions as well?

 

[tom.stoer]

... if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't...

Thanks!

 

[Dmitry67]

In general, the burden of proof is always on the positive claim. For example, if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't. If you claim QM entails multiple worlds, then that's something you must prove and in this case, since there are interpretations of QM without MW, the proof/evidence would have to be experimental.

Yes, and the positive claim is in this case is "selection rule exists"
"Positive" is what is adding new information
Burden of proof is on the party which is adding new information

I copy what I said before, if you don't agree with the logic please tell me where:

Occams razor. In informational sense, “information should not be multiplied unnecessarily”. When we build something, we add building blocks, adding new information an every step. That is why every new stone you put in the building must be well justified. However, using this method you can add only finite number of stones/entities. You can’t define integers by providing a complete list, right?

When we manipulate with infinite numbers of entities we go in the opposite direction: we start from the Universum, and then remove something. Each removal adds new information (and list {12438, 59859599, 858585, 77} contains MORE information than a list of ALL integers), so each removal must be justified.

It seems you understand it and for that reason you call a “selection” rule (selection – taking one from many = removing others). Again, you are not asking how to justify the creation of OUR universe( that would be natural for one going from nothing to the Universum), you seek the justification of removal for the others. So we are on the same page.

But: if we go in the opposite direction, from the Universum, then any REMOVAL adds new information and hence is a subject of Occams razor. Going from nothing to the Universum we must justify any addition, going back we must justify any removal. You mentioned Occams razor and on the very next step started inventing NEW entity which you call a “selection rule”. Do you agree with my logic?

So Occams razor is the very reason I believe other Universes exist.

 

[Dmitry67]

Sorry, but that's demonstrably false!

We see, observe and live in exactly one universe. All other universes (frameworks, ToEs, ...) are speculations and not accessible experimentally. Therefore they are metaphysical ballast - as long as you cannot show that they MUST exist.

Please also tell me where exactly you don't agree with my logic about the Occams razor (above)

 

[tom.stoer]

I do not agree that the selection rule is the positive claim. My statement is that "other universes do exist" is the positive claim.

Maybe your proposal does not add information, but it adds an ONTOLOGICAL ENTITY for which you CLAIM existence w/o being able to PROVE existence. Either you can prove it experimentally or you have to demontrate it by other means. Otherwise these entities (universes) are metaphysical speculations.

 

[RUTA]

Yes, and the positive claim is in this case is "selection rule exists"
"Positive" is what is adding new information
Burden of proof is on the party which is adding new information

I copy what I said before, if you don't agree with the logic please tell me where:

I'm talking about ontology, you're talking about methodology. Ontologically speaking, you're claiming MW so you need an experimental result consistent with MW and inconsistent with a single universe.

For example, suppose you start methodologically with "Everything imaginable exists." According to you, qualifiers such as "A thing must have empirical consequences" would be a negative, so that it is incumbent upon your skeptics to prove unicorns don't exist.

 

[Dmitry67]

Lets talk about integer numbers.

Empty set, like a set of ALL integers is only one. It is, physically speaking, in the lowest entropy state.

Now I add a number, say, 34553. I add new information. There are mnay different lists which contain only one n umber, right? Interestingly enough, the set of all integers minus one number has the same property.

Now I add a second number, second entity. Now I have a combination of 2 numbers, and I have even more information. Adding more and more numbers to my list I add more and more information.

But this is true only if I add a finite number of integers. I can add an infinite number of integers, filling all voids, thus making my list a full list of integers. So adding an infinite number of integers I had reduced information!

So give an example,

{} - empty set - 0 bits.
{n} - one number - info about 1 number
{n,m} - 2 numbers - info about 2 numbers
...
{all except n,m} - info about 2 numbers
{all except n} - info about 1 number
{all integers} - universum - no info

I attract your attention to the fact that information at first increases and then decreases.

Maybe your proposal does not add information, but it adds an ONTOLOGICAL ENTITY for which you CLAIM existence w/o being able to PROVE existence.

No. I don't add AN ENTITY. If I would be adding ONE entity you would be absolutely right.

I am adding an infinite number of entities to a list with one element (only our universe). The list I add in complementary to that list and union becomes a Universum - a list of all possible universes.

Hence I decrease an information, and occams razor is on MY side.

 

[RUTA]

Lets talk about integer numbers.

So give an example,

{} - empty set - 0 bits.
{n} - one number - info about 1 number
{n,m} - 2 numbers - info about 2 numbers
...
{all except n,m} - info about 2 numbers
{all except n} - info about 1 number
{all integers} - universum - no info

I attract your attention to the fact that information at first increases and then decreases.

This has nothing to do my claim about methodology and ontology, but I believe your claim is false. In fact, I would argue that the set of all integers contains an infinite amount of information. To make my point, produce the set -- not the words "all integers" but the elements themselves.

 

[Dmitry67]

"You are wrong"
These 13 characters gives you some information.
Now I provide you a list of all 26**13 combinations of characters. Beginning from AAAAAAAAAAAAA to ZZZZZZZZZZZZZ. Somewhere in the middle you will find "YOU ARE WRONG" and "YOU ARE RIGHT". What information you have now? Nothing!

And asking me to write all integers... Science would end if we stop at the level of "2 apples plus 3 apples makes 5 apples". How do we suppose to work with infinite sets if we need to write all the elements?

 

[RUTA]

And asking me to write all integers... Science would end if we stop at the level of "2 apples plus 3 apples makes 5 apples". How do we suppose to work with infinite sets if we need to write all the elements?

This has nothing to do with the progress of science, we're talking about how much information is contained in the set of all integers. I say it's infinite and you say it's zero. To argue my point, all I have to do is "play dumb" and require you to give me the information explicitly, i.e., list the elements of the set. If you're correct, you have nothing to send me. If I'm correct, you have an infinite number of numbers to send me. That's my argument.

How does this bear on the original post for this thread? I've lost track.

 

[tom.stoer]

... and occams razor is on MY side.

No it isn't.

From a ontological point of view we can be sure that one universe exists; everything else is speculation.

From a computational-complexity point of view there is no difference between the two statements
a) one universe exists
or
b) all possible universes exist - except one
Of course specifying the one in both cases should require the same amount of information.

Similarly computationally the statements
a') no universe exists
and
b') all possible universes exist
have the same complexity.

If you argue strictly based on computational complexity and with Ockams razor, then you cannot distinguish between a') and b') nor can you distinguish between a) or b). So in order to do that you have to refer to some experimental result, i.e you have to enlarge your reasoning beyond computational complexity.

You do that by taking into account "known facts" and by going from a mathematical to an ontological reasoning. Of course you can rule out a') immediately. You can trust in a least one universe which means that ontologically and based on Ockams razor you should not add more assumptions than strictly necessary. So you add the assumption that one universe exists and - wow - it agrees with the known facts. If you would instead add an uncountable set of universes it would still agree with the known facts, but you have to explain why "they are there but invisible". Therefore you add assumptions which you cannot prove.

And don't forget: you cannot use your "mathematical multiverse hypothesis" as starting point for your proof as your quest is just to prove exactly this "mathematical multiverse hypothesis".