TPF : Information and Randomness

A place for discussion of ideas presented in the BothAndBlog, or relevant to the Enformationism thesis.
User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

TPF : Information and Randomness

Post by Gnomon » Sun Apr 07, 2024 4:20 pm

The greatest degree of information is found in the most random or irrational sequences.
I find this strange and counter intuitive.
— Benj96

That common mis-understanding of Information theory is indeed counterintuitive, because we know from experience that randomness is the antithesis of meaning-bearing Information. But Shannon was not claiming that random sequences are inherently meaningful. Instead, he compared mental Information to physical Entropy. And noted that it is "surprising" to find meaningful information in random patterns*1. That eye-opening distinction of meaning from background noise is what semiotician & cyberneticist Bateson called "the difference that makes a difference"*2. . The first "difference" is the Surprise, and the second is the Meaning.

According to the second law of thermodynamics, all order ultimately decays into disorder. And yet, here we stand on a tiny exception to that rule in the vast universe : the pocket of organization we call home. As far as we know, this is the only instance of Life & Mind in the universe. Ironically, some thinkers miss the exceptional nature of Information, and are still looking for communications from little green men, or the advanced race of San-Ti, out there in the near infinite crucible of random accidents. Information is not accidental.

*1. Information is the surprising exception to common randomness :
The core idea of information theory is that the "informational value" of a communicated message depends on the degree to which the content of the message is surprising.
https://en.wikipedia.org/wiki/Entropy_( ... on_theory)

*2. Information as a difference :
We propose a difference theory of information that extends Gregory Bateson’s definition that information is any difference that makes a difference.
https://www.tandfonline.com/doi/full/10 ... 19.1581441

CAN YOU SEE THE DIFFERENCE ?
Surprising Signal within Meaningless Noise
static.png

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Sun Apr 07, 2024 4:24 pm

Did Shannon ever write or say anything about 'mental information'? And have you read the origin of how Shannon came to start using the term 'entropy' in relation to information, on the prompting of Von Neumann, who was a peer, and who said one of the advantages of using the term is because he would always win in arguments if he used it, because 'nobody knows what it means'? — Wayfarer

No, Shannon was not concerned with the metaphysical aspects of Information. He was focused on physically communicated Data, not metaphysically (semiotics, metaphors, analogies) communicated Meaning. In my post I used the "mental" term to distinguish Metaphysical from Physical forms of information. In my Enformationism thesis, I refer to Generic Information (universal power to transform) as a "Shapeshifter", taking-on many physical and metaphysical forms in the world. That notion is based, in part, on Einstein's E=MC^2 formula. In my view, Causal Energy is merely one of many forms of Generic Information (EnFormAction).

Yes, I'm aware of the "entropy" backstory. That abstruse term may be responsible for the common mis-understanding that Information is essentially random. It is instead, the Order within Chaos ; the Surprise within Randomness ; the Relevant bits within the mass of Irrelevant bytes.


von Neumann Versus Shannon Entropy :What is the difference between entropy and Shannon entropy? :
The intuition for entropy is that it is the average number of bits required to represent or transmit an event drawn from the probability distribution for the random variable. … the Shannon entropy of a distribution is the expected amount of information in an event drawn from that distribution.
https://machinelearningmastery.com/what ... n-entropy/

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Tue Apr 09, 2024 3:21 pm

I'm reading his Demon in the Machine at the moment, and I've been reading Deacon. But I'm still dubious that 'information' has fundamental explanatory power - because it's not a metaphysical simple. The term 'information' is polysemic - it has many meanings, depending on its context. — Wayfarer

Your ambiguity (uncertainty) about Deacon's novel notion of Information as Absence is understandable, because Shannon defined his kind of Information*1 as the presence of detectable data. The essence of his statistical definition is the Probability ratio of 0% (nothing) to 100% (everything) : 0/1 or 1/0, and everything in between. So, information is like a quantum particle in that a Bit exists only as a Possibility until measured (understood). Moreover, several quantum theorists concluded that Probability (not yet real) was converted into Certainty by the evaluation of an inquiring mind. That sounds magical & mystical, but the scientists' intentions were pragmatic*2.

Deacon saw what others missed in the statistical nature of Information : Probability is nothing until Actualized somehow. But that nothingness (absence) is the metaphysical power behind all Change (causation) in the world. He referred to that invisible power as "Constitutive Absence"*3, which is the capability (force + control) to construct something from scratch. The most familiar causal power in science is labeled "Energy", and defined as the ability to do useful work. Yet the substance of that power is left undefined, because it is not a material object, but more like a metaphysical force, which is knowable only after it has done its work and moved on.

In my personal information-based thesis, I merged several of those polysemantic applications of "Information" into a single "metaphysical simple"*4 : the power to transform. Which I labeled EnFormAction to make it signify Energy + Form + Action. I'm sure that Deacon has never heard of that term, and he may not think of his Constitutive Absence as a metaphysical concept. But I think it can be used to narrow down the various meanings of Information to something like a philosophical Atom, brimming with potential causal power.


*1. What is Shannon information? :
Although the use of the word ‘information’, with different meanings, can be traced back to
antique and medieval texts (see Adriaans 2013), it is only in the 20th century that the term begins
to acquire the present-day sense. Nevertheless, the pervasiveness of the notion of information
both in our everyday life and in our scientific practice does not imply the agreement about the
content of the concept. As Luciano Floridi (2010, 2011) stresses, it is a polysemantic concept associated with different phenomena, such as communication, knowledge, reference, meaning,
truth, etc.

https://philsci-archive.pitt.edu/10911/ ... mation.pdf

*2. Information, What is It? :
Deacon addresses many of those self-referencing feedback-loop mind-bogglers in his book. But perhaps the most fundamental enigma is the ultimate “nature” of Information itself. The original usage of the term was primarily Functional, as the content of memory & meaning. Then Shannon turned his attention to the Physical aspects of data transmission. Now, Deacon has returned to the most puzzling aspect of mental function : Intentions & Actions. For example : a> how one person’s mind can convey meaning & intentions to another mind; b> how a subjective intention (Will) can result in physical changes to the objective world? How can invisible intangible immaterial (absent) ideas cause physical things to move & transform. Occultists have imagined Mind as a kind of mystical energy or life-force (Chi; psychokinesis) that can be directed outward into the world, like a laser beam, to affect people and objects. But Deacon is not interested in such fictional fantasies. Instead, he tries to walk a fine line between pragmatics & magic, or physics & metaphysics.
http://bothandblog4.enformationism.info/page26.html {click here}
Note --- Jesus told his disciples that Faith can move mountains. But his brother James explained "“Show me your faith without the works, and I will show you my faith by my works.” Today, if you want to move a mountain, it helps to make use of dynamite and earth-moving equipment : pragmatic faith.


*3. Constitutive : having the power to establish or give organized existence to something.
___Oxford Languages

*4. Metaphysical Simple : an immaterial atom ; a non-physical element ; the fundamental constituent of a complex structure
22 hours ago

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Tue Apr 09, 2024 3:26 pm

The relationship of logical necessity and physical causation is a deep topic and one of interest to me. . . . .
I think where it shows up is in Wigner's unreasonable effectiveness of mathematics in the natural sciences.
— Wayfarer

I have come to think of human-constructed Mathematics as our synthetic imitation of the natural Logic of the universe. By that I mean, chemistry/physics is an expression of fundamental Logic in the substance of Matter (functional organization) and the action of Energy ("physical causation"). Another way to put it is that "all Math is Geometry", where we can extend the geo-centric label to include all causal & formal inter-relationships in the entire Cosmos.

If so, then the "effectiveness" of Math, in scientific endeavors, is an indication that we humans have correctly interpreted the Logic of the universe --- "constraining affordances" --- as natural laws and mathematical ratios. Hence, our artificial "designs" (e.g. computers) are workable as information processors, even though they may not yet be literally "semantic engines" (apologies to ChatGPT).


The Logic of Information : A Theory of Philosophy as Conceptual Design
by Luciano Floridi
This is a book on the logic of design and hence on how we make, transform, refine, and improve the objects of our knowledge. The starting point is that reality provides the data, to be understood as constraining affordances, and we transform them into information, like semantic engines.
https://academic.oup.com/book/27824

Randomness & Information : inverse logical/mathematical relationship
In a statistical mechanics book, it is stated that "randomness and information are essentially the same thing," which results from the fact that a random process requires high information. . . . .
But, later it says that entropy and information are inversely related since disorder decreases with knowledge. But, this does not make sense to me. I always thought that entropy and randomness in a system were the same thing.

https://physics.stackexchange.com/quest ... randomness
Entropy & randomness are directly related; but randomness & semantics (meaning ; useful information) are inversely related.

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Tue Apr 30, 2024 4:49 pm

I don't believe all information in the universe is predictable because of heisenbergs uncertainty principle. Sure 99% of things can be non random but even if the fundamental 1% is that throws a huge spanner in the works — Benj96
I don't agree with the use of random here. Stochastic phenomena are just simply not precise (this is the word I was looking for) as an analysis. Commonly, (and I say erroneously) it is the precision upon which we judge whether something is random, or in the case of Heisenberg, uncertain. But to further judge a phenomena as undetermined is really troubling. — L'éléphant

Both of you may be correct. You're just focusing on different aspects of the Uncertainty problem. ↪Benj96 seems to be assuming that the world itself is fundamentally stochastic, while ↪L'éléphant seems to be saying that the uncertainty is an observer problem. In truth, the answer to the "troubling" emotion caused by the random appearance of quantum phenomena may be to do as the quantum pioneers did : accept the inherent limitations of both observer and object.

As long as scientists were observing macro scale objects, their assumption of predictable mechanical determinism was pragmatic. But now, as we delve into levels of reality that the human mind and eye were not adapted to, for all practical scientific applications, non-classical sub-atomic physics is indeterminate & uncertain. Hence, for theoretical philosophical purposes we must accept the ambiguity of our knowledge (measurements) of reality at the fringes of technological precision and human decision.



Is reality fundamentally random? :
The answer is that yes, as far as we can test, all quantum interactions that rely on a statistical or stochastic effect are random, as far as we can measure. The less helpful answer is that we don't know, because there is fundamentally no way to know if something is truly random just by its output.
https://arstechnica.com/civis/threads/d ... n.1497773/

Is anything in nature truly random? :
This is a problem about the philosophy of physics; it's sometimes known as Laplace's demon. Our current best theories of the fundamental laws of nature are quantum mechanical in nature. In this theory, the outcome of measurements is truly random; however, whether this implies that nature contains fundamental randomness depends on how you think the measurement problem should be solved.
https://www.reddit.com/r/AskPhysics/com ... ly_random/

Laplace's Demon :
The future is determined. This is known as scientific determinism. Laplace expanded this idea to the entire universe – if some {omniscient} creature knew everything's position and motion at one moment, then the {mathematical} laws of physics would give it complete knowledge of the future. That creature is Laplace's demon. {my brackets}
https://elements.lbl.gov/news/spooky-sc ... ces-demon/
Note --- From the perspective of the all-knowing demon, the physical world is precisely determinate and predictable, but in the view of a mortal scientist, using imperfect machinery, the quantum realm is indeterminate & unpredictable, and perplexing. Which may be "troubling" for those who can't deal with ambiguity.

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Fri May 03, 2024 11:16 am

More broadly speaking, Einstein always stood for a realist attitude: that everything is determined by or subject to general laws. That's why he couldn't abide the implications of quantum physics - entanglement ('spooky action at a distance') and uncertainty being prime examples. — Wayfarer

Yes, it was that "Realist Attitude" that I was referring to in my post above : "Yet, the general scientific attitude toward Nature is that nothing is left to Chance". I suppose the necessity for mixing subjective Metaphysics*1 with objective Quantum Physics is what Realists and Materialists most strenuously object to. By "chance" I refer, not to Luck or Fate, but to the free-wheeling randomness underlying the apparent mechanical determinism of macro reality.

Since I'm an amateur philosopher, not a professional scientist, the "contamination" (impurity) of Reality with a bit of Ideality is a feature of sub-atomic science, not a fault. The 17th century Enlightenment revolution prided itself on empirical Objectivity (reality) & mathematical Precision (certainty), as opposed to the Subjectivity (private revelation) & Assurance (dogmatic faith) of Christian theology. So, it's understandable that the attribution of lawlessness on the frontiers of civilized Reality would be unbearable to those trained in the law & order certainties of Classical Physics.

Since modern Science was the legitimate offspring of secular Greek philosophy, I'm not offended by the family resemblance manifesting in the margins of observable reality. Besides, even the reality of Reality is not as unambiguous as philosophical Realism portrays it. Due to my BothAnd*2 attitude toward Science & Philosophy, I am able to accommodate the Yin and the Yang opposition in a single complementary worldview. ☯︎


*1. Metaphysical subjectivism is the theory that reality is what we perceive to be real, and that there is no underlying true reality that exists independently of perception. One can also hold that it is consciousness rather than perception that is reality (idealism).
https://en.wikipedia.org/wiki/Subjectivism

*2. Both/And Principle :
My coinage for the holistic principle of Complementarity, as illustrated in the Yin/Yang symbol. Opposing or contrasting concepts are always part of a greater whole. Conflicts between parts can be reconciled or harmonized by putting them into the context of a whole system.
https://blog-glossary.enformationism.info/page10.html

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Mon May 06, 2024 4:30 pm

↪Gnomon
I'll try and find time for that video, the first presenter, Beau Lotto, also figured in a video I attached to the Mind Created World OP. As for 'subjectivism', I almost accept that, with the crucial caveat that we are all subjects of similar kinds, and so the world occurs for each of us in similar ways. The subjective, so-called, is an ineliminable pole of reality, but there's no use looking for it, because it is what is doing the looking. — Wayfarer

I understand your qualification of acceptance regarding absolute Subjectivism*1, which would be essentially Solipsism. We moderns avoid the slippery slope of solipsism by comparing our private personal point-of-view with the publicized perspectives of others (e.g. TPF), in order to find commonalities between them. Modern Scientists tend to treat those common denominators*2 as-if they are Objective facts about True Reality*3.

As you suggested though, Subjectivism entails the Part looking at the Whole, from within the system being observed*4. That's why naive Solipsism must be viewed through a lens of reflective Skepticism*5. Those "Other Minds" may filter information about True Reality through their own private or communal prejudices. But that couldn't be true of Moi, could it?


*1. Subjectivism is the theory that perception (or consciousness) is reality, and that there is no underlying, true reality that exists independent of perception.
https://www.philosophybasics.com/branch ... ivism.html
Note --- Subjectivism = no absolute or objective Truth

*2. common denominator : a fact or quality that is shared by two or more people or groups.

*3. Empirical Science reveals the "Mind of God" without direct revelation :
Many early scientists were not only inspired to do science because they believed in God; they also thought that the natural world revealed the attributes and reality of God. . . . . Sir Isaac Newton argued that the delicate balance of forces at work in our solar system revealed “an intelligent and powerful Being.” . . . .
So how did we get from these great founders of modern science—with their conviction that science reveals the handiwork of God—to the modern New Atheists such as Richard Dawkins and Victor Stenger who think that science properly understood renders belief in God untenable?

https://stephencmeyer.org/2021/04/01/sc ... niverse-2/
Note --- The "handiwork" is self-existent? Hence no "hand" or "mind" needed?

*4. What is my invisible Milieu? :
Two young fish are asked by an older fish, “How's the water?” and one young fish turns to the other and says, “what the hell is water?”
https://humanitiesmoments.org/moment/th ... of-living/
Milieu : environment ; ambience ; surroundings ; context ; background
Caveat : a warning or proviso of specific stipulations, conditions, or limitations.

*5. Solipsism and Skepticism :
What is most distinctive about solipsism lies in what it calls for us to be skeptical of. Solipsism tends to involve skepticism about our knowledge of the world itself. It also involves a skepticism about the minds of others.
https://www.thecollector.com/what-is-solipsism/

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Mon May 06, 2024 4:32 pm

Those "Other Minds" may filter information about True Reality through their own private or communal prejudices. — Gnomon
Kastrup's 'dissociated alters'. — Wayfarer

Actually, the "other minds" I referred to are the perspectives of physically & mentally different people, who presumably have their own peculiar Solipsistic worldviews. Does Kastrup view his 'dissociated alters' as Other Minds in that sense?

My understanding of DID is more like demon possession. Jesus asked a demented man's possessors "what is your name?". The answer : “My name is Legion,” he replied, “for we are many.” {5 or 6 thousand soldiers}

Since I am an Introvert, a crowd of 100 alters, all babbling at the same time, would be confusing and unbearable. I would find single-self Solipsism more comfortable. In that case, other minds would be just a theory. But Wayfarer is a pretty good hypothesis.


Solipsism and the Problem of Other Minds :
Solipsism is sometimes expressed as the view that “I am the only mind which exists,” or “My mental states are the only mental states.”
https://iep.utm.edu/solipsis/

Dissociative Identity Disorder

“Alters” are your alternate personalities. Some people with DID have up to 100 alters. Alters tend to be very different from one another. The identities might have different genders, ethnicities, interests and ways of interacting with their environments.
https://my.clevelandclinic.org/health/d ... y-disorder

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Mon May 06, 2024 4:33 pm

It's not even predictable to the demon, if the demon is part of the world itself and has to interact with it. — ssu

By definition a metaphorical demon is not part of the real world, hence super-natural. It "interacts" only in hypothetical worlds. Hence, its predictions would be true only in the context of the metaphor.

User avatar
Gnomon
Site Admin
Posts: 3287
Joined: Thu Sep 14, 2017 7:07 pm

Re: TPF : Information and Randomness

Post by Gnomon » Mon May 06, 2024 4:47 pm

OFF-TOPIC : non-random evolution

↪Wayfarer

Orthogenesis, on the other hand, is an evolutionary hypothesis suggesting that life has an inherent tendency to evolve in a unilinear direction towards some kind of predetermined goal or ideal form. This concept implies that evolution is guided by an internal or directional force rather than by random mutations and environmental pressures.


As I was developing my own personal philosophical worldview, I was prejudiced against Intelligent Design arguments by the mainstream scientific accusations, that it required faith in the God of Genesis. But I had rejected that ancient hypothesis when I reached the age of Reason. Instead, I was impressed by emerging developments in various threads of scientific understanding in the 21st century, pointing toward Teleology or Teleonomy in evolution.

Surprisingly, even Darwin, in the primitive 19th century, postulated something like natural laws that regulated biological change in order to "select" fitter organisms for reproduction*1. Unfortunately, he lacked knowledge of chemical genes to serve as biological memory from one generation to another. In our own time though --- using randomly generated mutations and electronic memory and software selection (regulations, algorithms) --- computerized engineering*2 has learned to emulate Nature in its law-like limitations on replication to design improved or novel forms of technology.

Anyway, the term "orthogenesis" was "obsolete" long before my time. So, I had to rediscover the concept of directional evolution on my own. Several threads of empirical and theoretical science were attesting to the complementary roles of disorderly randomness and orderly Natural Laws. But they carefully avoided any words suggestive of Teleological progression. Consequently, I had to coin my own terms --- EnFormAction and Enformy --- to encapsulate the concept of a natural tendency toward increasing complexity & coordination in physical processes. Being inherent in nature, these "laws" required no occasional divine interventions.

Another such orthogenetic thread is the surprising effectiveness of Artificial Selection in designing complex products for specific functions*3. Also, to the chagrin of most scientists, Secular Cosmology arrived at the Big Bang model of our universe, ironically reminiscent of a creation event. From that First Event, the physical world began to expand & evolve, from near nothing to almost everything*4, along a "unilinear" Arrow of Time, as portrayed in the image below. Note the progressive Phases*5 that emerge along the way, despite the random fluctuations within the quantum foundation of physical reality. Another thread was the developments in Information Theory, which portray mathematical information as both a causal and organizing force in the physical universe*6.

I could present lots of circumstantial scientific evidence in this post, but none of it would carry the weight of scientific orthodoxy that Modern Physics has constructed as a wall of separation between Religious Dogma and Empirical "Truth". FWIW : my personal name for that "internal or directional force", powering & guiding evolution, is EnFormAction (causation + information), of which physical energy is the best known form.

*1. Laws of Evolution :
Correlation of Growth, as Darwin called it. This law states that the specialised forms of separate parts of an organic being are always bound up with certain forms of other parts that apparently have no connection with them. . . . .
"The gradually increasing perfection of the human hand, and the commensurate adaptation of the feet for erect gait, have undoubtedly, by virtue of such correlation, reacted on other parts of the organism."

https://www.researchgate.net/publicatio ... _Evolution

*2. Evolutionary Programming :
Special computer algorithms inspired by biological Natural Selection. It is similar to Genetic Programming in that it relies on internal competition between random alternative solutions to weed-out inferior results, and to pass-on superior answers to the next generation of algorithms. By means of such optimizing feedback loops, evolution is able to make progress toward the best possible solution – limited only by local restraints – to the original programmer’s goal or purpose. In Enformationism theory the Prime Programmer is portrayed as a creative principle (e.g. Logos), who uses bottom-up mechanisms, rather than top-down miracles, to produce a world with both freedom & determinism, order & meaning
https://blog-glossary.enformationism.info/page13.html

*3. Evolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve.
It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence.

https://en.wikipedia.org/wiki/Evolutionary_programming
Note --- The software is structured by specific limitations (laws) on selection, while the intermediate forms produced are free to explore many unspecified niches (random). Note the irony of using ChatGPT to research the roots of its own evolution.

*4. Orthogenesis and Evolution :
Misinterpretations of orthogenesis describing it as mystical, teleological and linear are invalid. The orthogenetic aspect of evolution was recognized by Darwin as "laws of growth", but was neglected in favor of natural selection. Although an internal component to evolution is recognized by contemporary biologists, it is often considered to be secondary to natural selection. Where recognition is given to an internal tendency for evolution to proceed without requiring the action of natural selection, terms such as "constraints," "bias," and "potential" may imply orthogenesis.
https://www.researchgate.net/publicatio ... _Evolution

*5. Teleological Emergence :
Expand that notion to a Cosmological perspective, and we can identify a more general classification of stratified phase-like emergences : from Physics (energy), to Chemistry (atoms), to Biology (life), to Psychology (minds), to Sociology (global minds). Current theories attribute this undeniable stairstep progession to random accidents, sorted by “natural selection” (a code word for “evaluations” of fitness for the next phase) that in retrospect appear to be teleological, tending toward more cooperation of inter-relationships and entanglements between parts on the same level of emergence. Some AI enthusiasts even envision the ultimate evolution of a Cosmic Mind, informed by all lower level phases.
https://bothandblog3.enformationism.info/page23.html

*6. The Guiding Force of Evolution :
Glattfelder reaches the same conclusion that other Information theorists have inferred : that we live in “a universe built of Information”. Again, that insight is in agreement with the Enformationism thesis. Likewise, he concludes that “overall, the universe appears to be guided by an invisible force driving it to ever higher levels of self-organized complexity”.
https://bothandblog7.enformationism.info/page19.html
Note --- Glattfelder is a "Theoretical physicist turned quant, turned complexity scientist, with a strong commitment to philosophy."


TELEOLOGICAL EVOLUTION :
wpac8fb2c8_05_06.jpg

Post Reply

Who is online

Users browsing this forum: No registered users and 1 guest