u/Unique-Rice9999

Thermodynamics can tell us, for example, what happened to the entropy along the path, but ΔS is not the path itself. Two different chains of transitions may well have the same initial and final states and the same change in a certain measure, but different internal structures.

So the “entropy table” may well turn out to be one column in a much larger table.

And we started with heat, because it is one of the phenomena that we have known since the very beginning of our existence. Then we found ways to obtain and control it, and after some time eventually formalized the second law, for example as dS_total ≥ 0 for an isolated system. But this is only one aspect for describing the transition, not the transition itself.

ΔS may characterize one aspect of a transition, while a more detailed description could characterize the realized structure of the process itself: the sequence and organization of interactions along the path.

even if we accept the working axiom:

∃L - existence of life.

and assume that life arises in many variations and projections, this is still far from enough for contact. two living structures must simultaneously occupy a shared domain of accessibility.

we can define civilization L_i not just by a coordinate, but by the area of ​​its existence and possibilities:

A_i=A_i(x,t,P,C)

where
x - is the spatial position,
t - is the time of existence,
P - represents the available projections or observation methods,
C - represents the accessible transitions or technological capabilities.

consequently, two civilizations can literally belong to the exact same Universe, both be highly developed, and yet practically not exist for one another.

this happens because mutual detection requires, at the very least, that their regions of accessibility overlap:

A_1 ∩ A_2 ≠ ∅

P.S. in some cases, looking along the time axis (t), we could hypothesize that a civilization exists somewhere asynchronously. for instance, these could be precursor species who ventured into deep space long ago, or conversely, a past civilization whose DNA we might have inherited or received.
while we are likely radically different, we may still share a common foundation — for example, the fundamental way we study and model the Universe

this is a speculative thought experiment, not a proposed replacement for established black-hole physics. I’m starting from Bekenstein–Hawking entropy and asking an information-theoretic question about whether loss of locally accessible structure necessarily implies loss of the underlying information.

black-hole thermodynamics associates an event horizon with the Bekenstein-Hawking entropy, which is proportional to its area:

S_BH = (k_B · c³ · A) / (4 · G · ℏ)

expressed in bits, this entropy corresponds to:

N_bits = S_BH / (k_B · ln 2)

consider an information-theoretic description in which crossing an event horizon does not destroy information, but changes how the structure of an infalling system is encoded.

as an extreme limiting case, suppose that the locally accessible distinction approaches a binary one:

*C*(S) ∈ {0,1}

This would obviously not be enough to reconstruct the original structure by itself, since many different states S could map to the same local code.

but what if the missing structural information is not lost? Instead, it could become distributed through correlations in the black hole and, eventually, Hawking radiation:

S_object -> S_B*H* -> S_Hawking

then the interesting distinction would be between three different things:

information preservation is not the same as structural preservation, and neither is the same as reconstructibility.

could an event horizon therefore be treated as a boundary where the locally distinguishable structure becomes drastically compressed, while the full information remains encoded nonlocally in correlations?

and if so, would the relevant quantity be the information contained in the system itself, or the number of structural distinctions still accessible from a given perspective?

P.S. by preservation, I do not necessarily mean local reconstructibility: information could remain encoded in the global state even if it is no longer reconstructible from the locally accessible description alone.

this is a speculative thought experiment, not a proposed replacement for established black-hole physics. I’m starting from Bekenstein–Hawking entropy and asking an information-theoretic question about whether loss of locally accessible structure necessarily implies loss of the underlying information.

black-hole thermodynamics associates an event horizon with the Bekenstein-Hawking entropy, which is proportional to its area:

S_BH = (k_B · c³ · A) / (4 · G · ℏ)

expressed in bits, this entropy corresponds to:

N_bits = S_BH / (k_B · ln 2)

here, by structure I mean the distinguishable relations among the degrees of freedom of a system, rather than simply its total information content.

consider an information-theoretic description in which we assume that crossing an event horizon does not destroy information, but changes how the structure of an infalling system is encoded.

Let C_P(S) denote the locally accessible code of state S from a given perspective P. As an extreme limiting case, suppose this code approaches a binary distinction:

C_P(S) ∈ {0,1}

this would obviously not be enough to reconstruct the original structure by itself, since many different states S could map to the same local code. Thus, two distinct underlying states could become indistinguishable under the same locally accessible code:

S_i ≠ S_j, C_P(S_i)=C_P(S_j)

but what if the missing structural information is not lost, but instead remains encoded in correlations associated with the black hole and, eventually, its Hawking radiation?

S_object -> S_black-hole
-> S_Hawking-radiation

then the interesting distinction would be between three different things:

information preservation is not the same as structural preservation, and neither is the same as reconstructibility.

could an event horizon therefore be treated as a boundary where the locally distinguishable structure becomes drastically compressed, while the full information remains encoded nonlocally in correlations?

and if so, would the relevant quantity be the information contained in the system itself, or the number of structural distinctions still accessible from a given perspective?

Consider an information-theoretic description in which crossing an event horizon does not destroy information, but changes how the structure of an infalling system is encoded.

At the extreme limit, the locally accessible distinction at the boundary could approach a binary one:

C(S) ∈ {0,1}.

This would obviously not be enough to reconstruct the original structure by itself, since many different states S could map to the same local code.

But what if the missing structural information is not lost? Instead, it could become distributed through correlations in the black hole and, eventually, Hawking radiation:

S_object -> S_BH -> S_Hawking.

Then the interesting distinction would be between three different things:

information preservation is not the same as structural preservation, and neither is the same as reconstructibility.

could an event horizon therefore be treated as a boundary where the locally distinguishable structure becomes drastically compressed, while the full information remains encoded nonlocally in correlations?

and if so, would the relevant quantity be the information contained in the system itself, or the number of structural distinctions still accessible from a given perspective?

by “flat world” I mean a hypothetical two-dimensional world, not necessarily a geometrically flat one, and definitely not a flat Earth.

by the flat world problem, I mean a difference between an internal and an external description of reality.

an observer confined to the flat world experiences only its realized structure and its changes. An external observer, however, can describe the world as one structure selected from a space of possible structures.

if we then introduce allowed transitions between these structures, the object of description seems to change: instead of considering only possible states, we can consider possible histories through the state space.

this makes me wonder whether time should be understood here as an additional dimension of the world, or as an ordering/structure of transitions between possible states.

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then adding time doesn't just add another coordinate to the plane. It turns the question from "how many possible structures are there?" into "how many possible sequences of structures are there?":

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures?

this is an experiment in examining intersections between possible structures, carried out in a world one dimension below our own so that different possible projections can be compared relative to an additional dimension. In this sense, the two-dimensional model does not contradict a three-dimensional description; it provides a simpler case in which their structural relations can be examined.

by “flat world” I mean a hypothetical two-dimensional world, not necessarily a geometrically flat one, and definitely not a flat Earth.

by the flat world problem, I mean a difference between an internal and an external description of reality.

an observer confined to the flat world experiences only its realized structure and its changes. An external observer, however, can describe the world as one structure selected from a space of possible structures.

if we then introduce allowed transitions between these structures, the object of description seems to change: instead of considering only possible states, we can consider possible histories through the state space.

this makes me wonder whether time should be understood here as an additional dimension of the world, or as an ordering/structure of transitions between possible states.

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then adding time doesn't just add another coordinate to the plane. It turns the question from "how many possible structures are there?" into "how many possible sequences of structures are there?":

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures?

in the previous Flat World thought experiment, adding time turned a set of possible states into possible histories through those states.

this raises another question: what can an internal observer actually learn from such a history?

imagine a civilization confined to a two-dimensional world.

its observers can move only within their plane and cannot directly perceive anything outside it. however, this does not necessarily mean that information about structures beyond their directly accessible geometry is unavailable to them.

through instruments and interactions, they may observe projections, cross-sections, or other effects produced within their world. a single observation may reveal only a limited part of such a structure. but as the observer moves, or as the system changes over time, different moments may provide different projections.

by accumulating and comparing information from multiple moments, the observer may reconstruct properties of a structure that cannot be directly perceived in any single moment.

this leads to a slightly amusing question.

if a higher-dimensional structure interacted with our own world, what would its projection look like to us?

there is no reason to assume that it would look unusual, complex, or even alive. a projection does not have to resemble the structure that produces it. perhaps, from the perspective of an internal observer, it could look like something completely ordinary.

a stone, for example.

this is not a suggestion that stones are higher-dimensional organisms. It simply illustrates the problem: the appearance of a single projection tells us very little about the complete structure that produced it.

modern chips provide a less speculative example of a related distinction. Viewed at one moment, a chip is a physical arrangement of matter. but across many moments, its states, memory, computation, adaptation, and even forms of reconfiguration reveal a much larger functional structure. that structure cannot be understood from one static observation alone.

the important object of observation may therefore be not only the form present in a particular moment, but the relations between forms across many moments.

In this sense, an internal observer is not necessarily limited by what can be perceived directly. the observer is limited by the information that accessible interactions can carry into the observable world.

what is inaccessible in a single moment may become accessible through the structure of multiple moments.

by the flat world problem, I mean a difference between an internal and an external description of reality.

an observer confined to the flat world experiences only its realized structure and its changes. An external observer, however, can describe the world as one structure selected from a space of possible structures.

if we then introduce allowed transitions between these structures, the object of description seems to change: instead of considering only possible states, we can consider possible histories through the state space.

this makes me wonder whether time should be understood here as an additional dimension of the world, or as an ordering/structure of transitions between possible states.

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then adding time doesn't just add another coordinate to the plane. It turns the question from "how many possible structures are there?" into "how many possible sequences of structures are there?":

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures?

the flat world problem

the flat world problem is that we can see their reality as a whole, while they cannot. for them, reality is confined to a plane, and anything beyond it can only be conceived mathematically. we, on the other hand, can use this picture directly because we can conceive of their plane as a whole

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then adding time doesn’t just add another coordinate to the plane. It turns the question from “how many possible structures are there?” into “how many possible sequences of structures are there?”:

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures?

I am treating the state of the flat world as a single realized spatial structure selected from a set of possible structures

once time is introduced, however, the object we are considering changes. We are no longer describing only a space of possible states, but possible paths through that space

would this be better understood as simply adding a temporal dimension, or as moving from a state space to a space of possible histories?

P.S. Definitions
Structure: A complete configuration of the degrees of freedom of the flat world at a single moment.
State space: S = { all possible structures }
Allowed transitions: R ⊆ S × S

by the flat world problem, I mean the difference between an internal and an external description of reality in a hypothetical two-dimensional world.

an observer confined to the flat world experiences only its realized structure and its changes. An external observer, however, can describe the world as one structure selected from a space of possible structures.

if we then introduce allowed transitions between these structures, the object of description seems to change: instead of considering only possible states, we can consider possible histories through the state space.

this makes me wonder whether time should be understood here as an additional dimension of the world, or as an ordering/structure of transitions between possible states.

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then introducing time does not necessarily mean simply adding another coordinate to the plane. It turns the question from "how many possible structures are there?" into "how many possible sequences of structures are there?":

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures? 🤣

this is an experiment in examining intersections between possible structures, carried out in a world one dimension below our own so that different possible projections can be compared relative to an additional dimension. In this sense, the two-dimensional model does not contradict a three-dimensional description; it provides a simpler case in which their structural relations can be examined.

#theflatworldproblem
#ПНПІ #CIFR