Редактирование: Are We Living In Nick Bostrom’s Speculation

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<div style="text-align:center;">'''Are We Living In Nick Bostrom’s Speculation?'''</div>

<div style="text-align:center;">Danila Medvedev</div>

<div style="text-align:center;">''danila.medvedev@mail.ru''</div>

<div style="text-align:center;">Lappeenranta</div>

<div style="text-align:center;">2003</div>


&nbsp;

''The rapid development of computing technologies can make possible realistic computer simulations inhabited with intelligent humans. The Simulation Argument, proposed by Nick Bostrom[[#ftn1|[1]]] ''in the article Are You Living In a Computer Simulation, states that if such simulations will be created by us or our descendants, then we almost certainly live in a computer simulation. This paper analyses serious mathematical and logical errors in the Simulation Argument. It follows that the Simulation Argument is incorrect and the reality of our world remains a question of individual beliefs.''

&nbsp;

Keywords: reality, simulation, posthuman civilisations, ancestor simulations, simulation argument, consciousness, human.

= I.         Introduction =

The idea that our world might be a computer simulation is a relatively recent one. The first ideas of full reality simulation appeared only about 20 years ago. In 1989 Jaron Lanier coined the term «virtual reality», but only since 1990s it became conceivable that a whole world could be simulated. Computer games, especially 3D ones, such as Doom, Quake and many more recent titles, showed how the world (or at least a large part of it) could be recreated on the computer monitor. Several science fiction movies made in the end of 1990s and in the beginning of the 21st century elaborated on these ideas, developing some of the philosophical consequences of simulations and, more importantly, communicating them to the wide audience for the first time.* Abre los ojos (Open Your Eyes), 1997 [2] — The main character in this movie signed a contract with a cryonics company. After his death his body was frozen and his mind placed into a computer simulation. In this story, the personalities of all humans are simulated only to the extent necessary for their interactions with the main character. For example, one of the secondary characters, a psychiatrist, has two daughters, but does not know their names. 
* Dark City, 1998 [13] — This movie was also a mystery thriller, hence it showed a more mystical picture of the world and never explained the mechanism of the simulation. However, it led to the Matrix and The Thirteenth Floor films, which developed the idea of world simulation more rigorously and in more details. 
* The Matrix, 1999[[#ftn2|[2]]] [8] — In this film most of the humans are connected to the large computer simulation (the Matrix) from birth, but they do not know about it, unless someone from outside the simulation can tell them the truth. The machines that run the simulation can make arbitrary changes to the simulation in real-time. Humans from the real world can be inserted into the simulation as new people. The Matrix became the first widely known film about simulation and it introduced many people to the ideas of simulated realities for the first time. 
* The Thirteenth Floor, 1999 [13] — This movie introduced the idea of nested simulations and travel from one level to another. A simulation of the early 20th century city is developed in a computer company (in the end of 20th century). It turns out later that the real world is in fact also a simulation, run from what appears to be 21st or 22nd century. Characters can enter the simulation (or exit it) only by being inserted into the body of existing human. 
* Vanilla Sky, 2001 [15] — This is an American remake of Abre lost ojos. The story has not changed much and basic scientific and philosophical premises behind the story are also the same. 



An interesting theme that is present in The Thirteenth Floor, The Matrix and Dark City is the idea of limited size of the simulated world and of people coming to the literal end of the world (also happens in The Truman Show, 1998) and perceiving the limits.

In addition to being presented in popular culture, these ideas are being pursued by professional philosophers now. The philosophical ideas behind The Matrix are further developed in the “Philosophy of the Matrix” section of the film website [12]. But the most profound development related to these ideas was the controversial theory, known as the Simulation Argument.

The main idea of the Simulation Argument, as proposed by Nick Bostrom [1] is that “if we don’t think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears.”

This idea was further developed in the works of Robin Hanson and Barry Dainton. In his paper How to Live in a Simulation [7] Hanson gives some recommendations on optimal behaviour for people who believe that they might be living in a simulation. Unfortunately, his ideas are based on the wrong premises (as will be shown in this paper) and his suggestions are far from rational and effective. For example, at one place Hanson speculates that “simulations [might] tend to be ended when enough people in them become confident enough that they live in a simulation” and therefore “you might want to prevent too many others learning that they live in a simulation” [7]. This is nothing more than a random speculation, demonstrating disregard for likelihood, internal consistency and rationality of the hypotheses. It could very well be possible that when enough people realise that they live in a simulation, they will be taken to the real world and simulation will be stopped. Later Hanson suggests that seeking people who might be visitors from the outside and making them interested in you can be beneficial. He completely ignores a just as likely possibility that our world is a GTA[[#ftn3|[3]]]-like game. Such speculations clearly have no use except to satisfy people’s curiosity and entertain them.

In Innocence Lost: Simulation Scenarios: Prospects and Consequences [2] Barry Dainton introduces several new concepts, such as different modes of virtual life. Then he makes the simulation argument in a way similar to Are You Living In a Computer Simulation?, making the same mistakes. In the end of the article he discusses several possible ethical arguments against our simulation:# The Objection from Lesser Value — simulations should not be created because life in a simulation is inherently worse than life in reality. 
# The Deception Objection — simulations should not be created because it involves mass deception. 
# The Self-Interest Consideration — simulations should be prohibited to be sure that you are not in a simulation yourself. 



The first two arguments are worth considering, but the last one is clearly invalid, as it also suffers from the causation error and circular reasoning fallacy.

The simulation argument is closely related to one of the fundamental questions of philosophy — the choice between two alternative world views, materialism and idealism. The distinctive feature of the simulation argument is that some of its aspects are materialistic and some agree with objective idealism. In particular, the idealistic concept of the first cause reflects the start of the simulation by its creators and the concepts of “ideas” or “ideal numbers” corresponds with the simulation as a computer program. The materialistic beliefs that the world is understandable and that our senses reflect the reality accurately are wrong. Simulation “is the world that has been pulled over… [man’s] eyes to blind… [him] from the truth” [8].

It can be said that overall the metaphysical nature of the simulation, as observed by its inhabitants is mostly idealistic. At the same time, from the point of view of the creators of the simulation, its nature is materialistic. The consciousness (and intelligence) of a simulated human is the emerging property of computer components, highly organised by means of complex software programs. The base reality itself (and therefore the metaverse) can be materialistic in nature.

Unfortunately, all papers on the topic of simulation argument listed above contain a number of similar errors, namely circular reasoning, auto-reference, ignoring observational bias, causality errors and disregard for the control of the simulation by its creators. The existing critique of the simulation argument usually ignores the most serious errors and concentrates on particularities. The level of logical argumentation is usually low. I was not able to find any articles with a comprehensive analysis of the simulation argument.

In this paper I provided a detailed analysis of the simulation argument, demonstrated the logical errors in the original reasoning, suggested several alternatives to the simulation ideas. I also examined the ethical principles of posthuman civilisations in regards to running simulations and formulated several hypotheses about these principles that are not dependent on qualities of our own civilisation.

Based on the conducted analysis it can be concluded that the simulation argument is wrong. It seems to be impossible to avoid logical mistakes made by Bostrom. It has to be admitted that the reality of our world is still the matter of individual belief. At the same time, the reality of our world does not impose any limitations on the prospects of technological development, the possibility of reaching the posthuman stage and creating ancestor simulations.

In the first part of this paper I provide a summary of the original paper by Nick Bostrom and list the tacit assumptions of the simulation argument.

In the second part I examine the main formula for calculating the probability of living a simulation is and demonstrate calculation errors made by Bostrom.

In the third part I discuss the logical mistakes in the simulation argument. In this part I also demonstrate the inconsistency between Bostrom’s arguments and the scientific approach.

In the fourth part I give independent arguments against us living in a simulation that are not related to the errors in the original paper.

In the last part I comment on Bostrom’s original interpretation of the simulation argument. I propose the idea that simulations are fully controlled by the creators.

== Definitions ==

In this paper a number of special terms related to the problem of world simulations are used. Terms suggested by other authors are used in their original meanings.

Posthuman civilisation — a civilisation of human descendants, who were changed to the degree when they no longer can be considered humans. A posthuman civilisation would probably possess advanced computational technologies, nanotechnology, strong AI technologies and many others.

Simulation — a computer program modelling in some form the intelligence and/or consciousness of one or several people, as well as a physical environment that they can interact with. Realistic simulations model the environment similar to the real world.

Ancestor simulation — a simulation of a part of past human history.

Base civilisation — a civilisation that exists in the real world and not in the simulation.

First-level simulation — a simulation run by the base civilisation.

Parent civilisation (with respect to some simulation) — the civilisation that runs this simulation.

Metaverse — a hypothetical set of all existing universes. This set includes all basic realities, as well as all simulations run from any of the universes (both real and simulated) in this set.

= II.      Overview of the original article =

In the first part of the paper (The Assumption of Substrate-Independence), Bostrom describes the prerequisites for the simulation argument. He first outlines the assumption of substrate-independence, the idea that “it is not an essential property of consciousness that it is implemented on carbon-based biological neural networks inside a cranium” and “that mental states can supervene on any of a broad class of physical substrates” [1]. Although no references are provided and the issue is not discussed at length, it appears consistent with current scientific paradigms in the computer science and biological sciences. There have been some opposition to this idea from Roger Penrose [7] and a few other authors, who suggested that consciousness is possible because of specific quantum mechanisms in the human brain that cannot be reproduced on other substrates, but these ideas are not accepted by most of the scientists in these fields.

In the next section (The Technological Limits of Computation), Bostrom gives a detailed analysis of the computational requirements for the simulation of human mind and entire civilisations. The most important indicators are the following:* Computational complexity of the human brain: ~1016—1017 operations per second. 
* Maximum human sensory input: ~108 bits per second. 
* Computational cost of the realistic simulation of human history: ~1033—1036 operations. 
* Computational power of a nanotech-based computer: 1021 operations per second per cm3. 
* Maximum computational power per 1 kg of mass: 5*1050 operations per second. 



The estimates he provides appear sound and well-grounded.

It must be noted, however, that this analysis is irrelevant to the simulation argument. As will be explained later, only capacities of the base civilisation are significant. If we assume that we might live in a computer simulation, only the capacities of the parent civilisations are important, but there is no way to determine them.

In the main section (The Core of the Simulation Argument), Bostrom suggests a formula for calculating the probability for a random person to live in a simulation. He concludes that at least one of the following propositions must be true[[#ftn4|[4]]]:* Share of civilisations that reach posthuman stage is close to zero. 
* Share of posthuman civilisations that are interested in running ancestor-simulations is close to zero. 
* The majority of people live in one of the simulations. 



There are a number of serious mathematical errors in this section. In addition, Bostrom makes several unwarranted assumptions about variables used in these formulas. A detailed explanation of these errors will be provided in part 3 of this paper.

In the next section (A Bland Indifference Principle), Bostrom explains and justifies the logic behind his calculations and attempts to show that selecting a human from our world can be considered random for the purposes of the simulation argument. It is in this section that the major errors are made, including using a false analogy in the example about DNA. Part 4 of this paper deals with the reasoning errors in the simulation argument, uncovering a fallacy of circular reasoning and other mistakes. Additionally, in part 5 several reasons are given against simulating a world similar to our own.

Finally in the last section (Interpretation), Bostrom gives various explanations for the formulas derived in the main section. The main mistake done there is ignoring the fundamental difference of the simulations — that they are primarily governed by the simulators and only secondary by various laws designed for the simulation. In part 6, the errors in the interpretation are explained.

== Necessary assumptions ==

The original paper introduced certain basic ideas about substrate-independence and computation possibilities, but failed to mention necessary philosophical and world view assumptions necessary for the simulation argument. Below, I try to provide the most important hypotheses that should be true in order for the simulation argument to be valid and logical.

1) '''There is a basic reality.''' Without it, the whole discussion about realities and simulations would be pointless. We must also note that assumption about reality existence is on a level similar to the question of whether our universe is real or just a simulation.

2) '''It is possible to run a world simulation inside a reality.''' In the original article this hypothesis was just taken for granted by the author without even mentioning it. However we do not have sufficient experience with simulations to be able to prove that a simulation indistinguishable from the reality can be created at all. The best simulations to date are modern computer games and movies, but even the most advanced of them are only partially realistic. Bostrom refers to the works of Drexler and Kurzweil, but these authors mostly discuss the technical aspects of reality simulations and not philosophical aspects of such possibility.

3) '''There are no simulation cycles, where some sequence of nested simulations ends up with the original reality or part of it.''' If cycles were possible we would be left without real criteria for defining the world a simulation. Moreover, in such a case our conception of reality would be shattered strongly enough to make the simulation argument irrelevant.

4) '''The complexity of the simulation is less than the complexity of the parent universe.''' This follows from the mathematical principles of information encoding. The importance of this assumption is that it leads to objective differences between simulation on different nesting levels and between simulations and reality.

5) '''The laws of logic and mathematics are absolute.''' If it is not so, than it might be possible that the law of excluded third and other laws of logic are false in our universe and simulation argument (just like any other argument) is inherently invalid. It must be noted that it is entirely possible to run a simulation where logic does not work from a logical world.

6) '''There are a finite number of simulations.''' The simulation argument relies heavily on calculations of probabilities and average values for all universes. If there are an infinite number of simulations (or an infinite number of universes), such calculations are no longer valid.

Additionally, the simulation argument implies several less general assumptions about the metaverse.# The base reality contains at least one human civilisation. 
# A human civilisation has non-zero probability of becoming a posthuman civilisation. (No distinction is made in simulation argument between those civilisations that can become posthuman and those that cannot.) 
# A posthuman civilisation has non-zero chances to launch at least one simulation. 



= III.    Calculation errors in the original paper =

In addition to the logical weaknesses, the formulas that are used to calculate probability of living in a simulation have various errors and shortcomings. Some of them are not very important and do not affect the reasoning, while others are more serious.

== Infinite universes ==

One minor error in the formulas concerns a possibility of infinite number of civilisations. Frank Tipler [10] have shown how infinite computational capacity can be possible near the Omega Point, a hypothetical point prior to the Big Crunch (collapse of the Universe). Other scientists [16] extended this theory to the possibility of thermal death of the Universe (another possible outcome — the infinite expansion). If infinite computational capacity is possible, all variables used in the main formula (&nbsp;''fP'', [[Image:image004.gifImage6.png|top]]&nbsp;and [[Image:image006.gifImage7.png|top]]) are invalid. This does not invalidate the simulation argument, as the formula can easily be expanded to cover the case of infinite number of simulations, but it might affect some of the corollary arguments. A stronger objection is the possibility of multiple universes in reality (not being simulations) or multiple human civilisations in the base physical universe. This leads to a wide range of possibilities, such as:* The posthuman stage will only start after most of the human civilisations on different planets meet together (see below the arguments about posthuman stage being in the far future). This allows a larger number of real humans than in the case of one real civilisation and the same number of simulated realities. 
* Depending on the nature of the multiple universes, the difference between civilisations simulated in different universes might be negligible (see below arguments about identical people in simulations), while the difference between real civilisations in different universes is large enough. By considering several simulations to be just instances of the same one we reduce the number of simulated humans. Real humans, on the other hand, are still different in different universes. 



Another aspect of using average values that Bostrom ignores is that different civilisations are in different positions. If additional assumptions listed above are valid (especially the one about decreasing complexity of nested simulations), then those civilisations that are “deeply” simulated (simulated in a simulation in a simulation etc.) are less likely to reach a posthuman stage (and therefore run simulations themselves). In this case, using an average value of ''fP'' is misleading, because there can be observable signs in the world indicating that the civilisation is likely to be deeply simulated. We can speculate that our ability to think about creating simulations is an indicator that we are closer to reality (how close and whether we actually are in reality is, of course, uncertain). Thisisanargument (althoughnotadecidingone) againstindifferenceprinciple.

== Number of individuals ==

Special attention must be paid to calculating the number of individuals with human experiences ([[Image:image007.gifImage8.png|top]]). It is possible that even though the raw number of simulated people is large, the number of unique simulated people will be much smaller. There is also a possibility that a significant fraction of simulated people is fundamentally different from us by lacking self-consciousness.

== Identical people ==

In his paper, Bostrom does not mention any reasons for running an ancestor simulation, taking the desire to do it for granted. This lack of specific reasons given for running a simulation means that currently no specific requirements for the simulations are known. Thus it is entirely possible a posthuman civilisation that will run many simulations will use identical people for these simulations.

The possibility of having identical people in different simulations raises a lot of questions. This is a serious complication, because the issue of identity is far from simple even in more basic cases. There can be strong arguments both for regarding them as a single person and against it.

These people can have similar, indiscernible or even completely identical personalities. The same can be said about their experiences. The simulation rules, governing accumulation and propagation of changes in time can be designed for the convenience of the people running the simulation. There is no reason why in a simulation dedicated to the medieval Japan people in the rest of the world and in other epochs must be different from people in other simulations.

The consequences of this possibility for the simulation argument are not obvious. It is not clear whether these people should be regarded as individuals or simply as instances of one individual. In the latter case the total number of simulated individuals ever can be comparable with the number of real individuals in the base reality. This in turn means that ''fsim'' can attain a large value, such as 0.5.

== Non-conscious people ==

Another possibility that affects the simulation argument is simulating non-conscious people. This can be done for ethical reasons, because simulating a real world (supposedly similar to our human history) necessarily causes harm and suffering for simulated people. It can be argued that posthuman civilisations will have a deep respect for conscious entities in any form and are unlikely to cause suffering to them unless absolutely necessary.

These non-conscious people may nevertheless be intelligent. Or they may be controlled by the central simulation program and have no individual intelligence whatsoever. Bostrom discusses this possibility, saying “The rest of humanity would then be zombies or ‘shadow-people’ — humans simulated only at a level sufficient for the fully simulated people not to notice anything suspicious.” He talks about this only in relation to the “me-simulations”, where a small number of people are fully simulated and the rest are “shadow-people”. He then goes on to say that this option can be safely ignored because the number of people in full ancestor-simulation is necessarily much bigger, as each one probably includes billions of people.

Bostrom mentions only one possible reason for creation of “shadow-people” — that they might be “…cheaper… to simulate than real people”. He completely ignores the ethical aspect, which will undoubtedly be more important for the posthuman civilisation than the material aspects. There exists a real possibility that simulations with “shadow-people” may be sufficient for all practical purposes and that posthuman civilisation will not want to fully simulate real conscious people. The main criteria for allowing the simulation will be the ability of the simulated entity to have subjective experiences, including ability to feel pain and suffering. If that is the case, then the fact that we have conscious experiences proves that we most likely do not live in a simulation.

== Errors in the formula ==

First, it should be noted that most of the adjustments to the formulas used in the original argument do not help to avoid circular reasoning and other logical errors. Therefore, only most important comments are given about the formulas in this paper.

Bostrom provides the following formula for calculating the share of people living in a simulation:

[[Image:image009.gifImage9.png|top]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)

where ''fP'' — is the fraction of all human-level technological civilisations that survive to reach a posthuman stage, [[Image:image010.gifImage10.png|top]]&nbsp;— is the average number of ancestor-simulations run by a posthuman civilisation and [[Image:image011.gifImage11.png|top]]&nbsp;— is the average number of individuals that have lived in a civilisation before it reaches a posthuman stage.

Bostrom claims that ''fsim'' — is “the actual fraction of all observers with human-type experiences that live in simulations” [1], but he is obviously mistaken. The formula, as it is written, makes practically no sense. The numerator is equal to the average number of people simulated by one civilisation and not to the total number of simulated people (by all civilisations in the metaverse). The denominator makes no mathematical sense but it is similar to the average number of people living in a civilisation and one level below (in simulations run in this civilisation). Evidently, the value of ''fP''[[Image:image012.gifImage12.png|top]] will usually be very close to 1, because

[[Image:image014.gifImage13.png|top]]&nbsp;and [[Image:image016.gifImage14.png|top]]

CPH — number of posthuman civilisations, Csim — number of simulations.

Therefore the value of ''fsim'', calculated using the formula (1), will be in most cases extremely close to 0.5, which obviously contradicts Bostrom’s conclusions.

The first necessary change is adding the total number of civilisations ''C'' to the formula:

[[Image:image018.gifImage15.png|top]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)

The next problem is that the [[Image:image019.gifImage16.png|top]]&nbsp;in the denominator of the formula (1) is a wrong value for the number of individuals that have lived in a ''base civilisation ''before it reaches a posthuman stage. This is a specific number that has nothing whatsoever in common with the average value for all civilisations in the metaverse. Therefore the next change is a replacement of [[Image:image020.gifImage17.png|top]]&nbsp;with the new variable ''Hbase'', the number of people that lived in the base civilisation before it reached the posthuman stage:

[[Image:image022.gifImage18.png|top]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)

A similar problem is that the number of simulations that the base civilisation runs is probably different from the average as well. An additional variable ''Nbase'' should be added. Assuming that the number of individuals in the first-level simulations is similar to the average for the simulations, the following change should be made:

[[Image:image024.gifImage19.png|top]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (4)

This formula is more correct than the one suggested by Bostrom.However, even with all these changes there is still one fundamental problem with the formula. The ''fP'' variable is completely irrelevant for the base civilisation. As will be shown later, the base civilisation is governed by different laws than the simulated civilisations. Since the transition to the posthuman stage by the base civilisation is a non-repeating event, whose outcome is already determined (although it usually cannot be obtained from within a simulation) and which directly corresponds with the nature of the reality (existence of the metaverse). With regards to the base civilisation, instead of ''fP''probability a different variable have to be used that takes on the values of 0 (base civilisation reaches the posthuman stage and, if ''Nbase''>0, the metaverse exists) and 1 (base civilisation does not reach the posthuman stage, there is no metaverse and we live in the real world).

== Usingthe “probability” term ==

In most of the paper, Bostrom uses the term probability, which can be misleading for the reader. In my opinion, a better term would be “degree of certainty”. It is more correct, because Bostrom speaks not about repeating random events and finding the outcome of the future test, but about deducing whether a certain statement about already occurred event is true or not. The degrees of certainty can also be calculated using probability theory (if they conform to the Kolmogorov axioms), but the transition from probabilities to degrees of certainty that Bostrom makes when switching from calculating the probabilities in the metaverse to applying the found values to our existence is, in my opinion, not entirely correct.

It is also questionable to what extent the probabilities can be calculated for the ''completely deterministic ''world, such as a computer simulation that does not use any input from the real world after it is launched.

Another problem with the use of the “probability” term is that it implies that if the mathematical calculations are correct, then the outcome is governed by these probabilities. “Degree of certainty” term, on the other hand, better shows that the final answer is very much dependent on the additional information that might be missing (as is the case with other philosophical speculations about the nature of our world). By using probability theory, it is not possible to get any fundamentally new information that was not available before (one can only modify the form in which this information is presented), therefore the answer depends very much on the assumptions about the nature of the metaverse that we make (as will be shown in the next section).

== Possibility of nested simulations ==

Bostrom says: “It may be possible for simulated civilisations to become posthuman. They may then run their own ancestor-simulations on powerful computers they build in their simulated universe.” [1, p. 9]. Bostrom does not speak about this before, but his earlier calculations actually directly depend on this assumption.

Bostrom claims: “Therefore, if we don’t think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears.” [1]. But if there are no nested simulations than it is only possible to have simulations in the base reality and we arrive at completely opposite conclusion. In this case if we believe that our descendants (or ourselves) will run simulations, we live in the real world.

It therefore makes sense to examine the probable reasons that may cause simulated civilisations to be unable to run their own simulations or become posthuman. There are several such reasons possible.# It might be too expensive to run a nested simulation (running nested simulations can increase the computational cost of the first-level simulation very quickly). 
# It might be technically impossible due to the laws of nature in the simulation. 
# The parent civilisation may unobtrusively prohibit running the nested simulation or even thinking about doing that. Since the base reality civilisation will have complete control over the simulation, it can easily do that. The base reality civilisation may have no interest in having nested simulations. Since the purposes of creating simulations are to a large extent selfish, if creation of nested simulations does not serve these purposes, the base civilisation will have an option to prohibit that. 



In addition to the reasons against allowing nested simulations, there are reasons against running simulations of the posthuman civilisations in general. They will be examined later.

= IV.   Reasoning errors in the original paper =

The main mistakes in the Bostrom article are related to circular reasoning, auto-reference, observational bias and causation errors. To sum it in a few words, it is not correct to derive anything from our experience if we live in a simulation.

== Circular reasoning ==

If we do not live in a simulation, the whole logic of using ''fI'' or ''fP'' is invalid, because ''fsim'' is precisely zero. We know that we do not run any simulations and therefore whole argument is flawed. This is a common logical fallacy, known as a circular reasoning[[#ftn5|[5]]]. It was used, for example, by Rene Descartes to construct an argument that God exists, known as the Cartesian Circle [3].

One may object to this by saying that even if we do not run any simulations today, there might be simulations run in the future and they must be accounted for. Clearly such argument is without merit. Taking into account future simulation not only makes no sense (if we assume that we live in a real world, the simulation argument is useless), but also violates several important philosophical and physical principles. First, it violates the causality rules by allowing future events to affect our present world. Second, it ignores the fact that uncertainty principle in the quantum mechanics makes future effectively non-deterministic and it is impossible, neither practically, nor in theory to predict what simulations will be run by us in the future.

We can conclude that all probabilities used (explicitly or implicitly) in the simulation argument, including the probability of our own particular experiences being “implemented ''in vivo'' rather than ''in machina''” [1], depend on the qualities of the base civilisation and thus on whether we are the base civilisation or not.

== Observational bias ==

In trying to guess the nature of the metaverse there is significant inherent observational bias that must be accounted for. The problem of the simulation argument is that many assumptions are made about the metaverse and all simulations based on our present experience and the qualities of our civilisation.

There is no way to predict with confidence what kind of ancestor simulations we will create in our posthuman future. It might be possible that the transition to posthumanity will only happen in hundreds of thousands of years and most of the simulations will cover 1000th century and beyond. It is entirely possible that if extraterrestrials land on Earth and give us everything necessary to become a posthuman civilisation, we will all change ourselves to become alien posthumans (because the knowledge and technologies are alien, not human). We will then have no reason to create ancestor simulations that look like our 20th or 21st century, instead we will create simulations of alien ancestors. There are countless other possibilities.

It is even less possible to predict the nature of the base civilisation if we are not it. We have as much chances doing it correctly as a monster from Quake correctly guessing what kind of world Quake was programmed in.

Bostrom indirectly assumes the existence of the metaverse and then draws his conclusions about the probabilities, but the main premise of metaverse existence is not proven. The main problem of the simulation argument is that to know whether we live in a simulation or not is important in order to define the rules of the metaverse. This in turn is used to calculate the probabilities of living in a simulation. But if the argument bases the conditions of the experiment on its outcome, it cannot be valid.

If we live in a simulation, then we do not define the rules of the metaverse. Then any arguments such as “there are certainly many humans who would like to run ancestor-simulations if they could afford to do so” [1] are flawed. The moral, the laws of nature, the concepts of consciousness, everything is defined by the original civilisation. And if we are not it, there is no way we can be sure about anything in the metaverse.

The effects of observational bias are not discussed in the original paper. Bostrom completely ignores the impossibility of deducing the nature of the metaverse from within a simulation.

== Unscientific approach ==

In addition to the logical mistakes described above, there can be some confusion about what the simulation argument actually proves. As was shown above, it necessarily makes the assumption of metaverse existence. Therefore we can say that the simulation argument helps to determine where (in a simulation or in a real world) a random person is, ''given that his world is a part of the metaverse''. The simulation argument cannot be used to tell whether the metaverse exists and therefore does not provide even the slightest hint as to whether we live in a simulation or not.

Even if our civilisation is likely to get capacity and desire to run simulations in the future, it says absolutely nothing about our own origin. To put this into perspective, there are many alternative hypotheses about the origins of our world: creation by one of many gods, the Big Bang, living in a simulation, etc., and simulation argument does not help to make a choice between them. 

While there is evidence to support some of these hypotheses (most notably, the Big Bang), there is no evidence to support or refute the simulation hypothesis. The only evidence available to us at this time — the subjective experience of our existence in this world — is predicted equally well by the hypothesis that we live in a simulation, as it is by the hypothesis that we live in a real world. Philosophy or science in general do not allow unwarranted assumptions about the nature of the world. We can only judge the validity of these hypotheses by accumulating additional evidence, not by using preconceived ideas about the world.

There may be some possible ways to determine the nature of the metaverse or to test whether we are in a simulation or not from within a simulation. But it is also possible that such information can only be introduced to our world externally (or cannot at all if we are living in a real world). This is closely related to the idea of auto-reference or the ability to independently and clearly perceive yourself. A detailed explanation of the issues related to auto-reference can be found in Gödel, Escher, Bach. The Eternal Golden Braid by Douglas Hofstadter [5].

Another important implication of the scientific approach is that untestable hypotheses should be ignored. S. Novella [13] asks “What can a scientific sceptic say about such claims? Only that they are outside the realm of science, and that science can have only an agnostic view towards untestable hypotheses.” For this reason whether we live in a simulation or not should be a matter of personal belief, not scientific enquiry, unless additional evidence is uncovered.

= V.      Arguments against the simulation hypothesis =

In addition to uncovering logical errors with the simulation argument, it makes sense to point out several factors that can affect whether we live in a simulation or not. They all have in common an assumption that our civilisation might have some special qualities that are unlikely to be present in a simulated civilisation.

There are no reasons to be sure that the suggestions listed below are correct. Still, they are interesting, because they do not depend on the characteristics of our reality and are determined purely by universal qualities of a posthuman civilisation capable of running simulations.

It is possible that our time is usually not particularly interesting to simulate. There can be various reasons:* globalised world is less interesting than national and local societies 

* the 20th-21st century technological society is still too primitive to be worth simulating 
* simulating large populations have no real benefits as opposed to smaller ones 
* multi-cultural civilisations are too random and simulating them has no practical purpose. 



If any one of these reasons is valid, the fact that we live in early 21st century means that our world most likely is a real one.

Another very likely possibility is that posthumans do not run simulations with conscious individuals for moral reasons (as discussed earlier), instead replacing them with intelligent, but non-conscious entities. In this case the fact that we are conscious (apparently we do have subjective experiences) proves that we are not in a simulation. As was said earlier, Bostrom only discusses the possibility of “shadow-people” being used in “me-simulations”, but he ignores that they may be most practical for the “ancestor-simulations” as well.

It is interesting to mention the Self-Interest Consideration, proposed by Barry Dainton. He makes a ridiculous suggestion that civilisation may decide not to create simulations as if this can have any effect on the nature of their own world, but he ignores a very real possibility of certain motivation that would prevent any posthuman civilisations from creating simulations with conscious people.

There is a possibility that simulations of posthuman civilisations (or posthuman individuals) are not interesting. The posthumans are unlikely to be significantly influenced by the society and may not have a society at all. That would remove one of the main points of simulating a civilisation — observation and analysis of group dynamics. Many posthumans in the real world might live in personal simulations and simulated posthumans are unlikely to be significantly different. Posthumans will also be capable of travelling between metaverse levels, moving from a simulation to a parent world and vice versa.

This possibility significantly reduces the total number of simulated people by eliminating nested simulations (as shown earlier). Additional ethical and other considerations can lead to a ban on simulating civilisations capable of reaching posthumanity (because those running a simulation would have to actively interfere or terminate such simulation). In this the case the fact that we can think about becoming posthumans and are certainly moving in this direction is an indicator that we do not live in a simulation.

== Posthuman stage in the far future ==

Bostrom says “[the] simulation argument works equally well for those who think that it will take hundreds of thousands of years to reach a “posthuman” stage of civilisation”. But this is not the case. The development of posthuman civilisation in the base reality may take much longer than in a simulation, for example because all simulations have accelerated scientific and technological development for convenience of the observers. If that is the case, the ''HBASE'' value (the number of people who lived in the base civilisation before it reached the posthuman stage) can be much greater than [[Image:image025.gifImage20.png|top]]. That would force ''fsim'', to be much lower, making the probability of living in a real world much higher.

= VI.   Errors in The Interpretation of the Simulation Argument =

== Laws governing the simulations ==

In his article Bostrom almost always ignores the distinctive feature of a simulation. It can be expected that in most cases those running the simulation will have a complete control over it. This means that any historical patterns, ethical considerations and even laws of nature in a simulation are of secondary importance. The events in the simulation will always primarily depend on the will of the observers, who are running the simulation.

However, Bostrom ignores this and often incorrectly states that the simulation will be governed by some specific laws. For example, he says that in order for ''fI'' (the share of posthuman civilisations interested in running simulations) to be very small “there must be a strong convergence among the courses of advanced civilisations” [1]. Then Bostrom describes two possibilities — that posthuman civilisations will not run simulations for ethical reasons or that they will simply lose the desire to do it — but he says nothing about the possibility of parent civilisation prohibiting its simulations from running nested simulations.

It will be very easy for a posthuman civilisation to control all first-level simulations and prohibit them from running any additional simulations. It might also be possible that all computers in simulations will not be simulated but (for efficiency, security or for some other reasons) the software will run directly on computers of the parent civilisation. This means that nested simulations can be run, but they will not contain any real (conscious or real by any other definition) people. At the same time, the individuals from a first-level simulation will have an impression of actually running a simulation.

== Extinction ==

Bostrom makes a similar mistake while speaking about extinction of a simulated civilisation as a natural event. If there are simulated civilisations then the majority of them will probably not go extinct in a natural way, but will be terminated by the simulators. The mechanisms for these two kinds of events are obviously different, since simulators are not limited to terminating civilisations in natural ways. There are many possible alternatives. For example, simulated civilisations can be slowed down (or even paused with saving the simulation state) by simulators when these civilisations approach the posthuman stage. It must be noted that being paused (with the possibility of being launched again) is probably better than going extinct.

The best alternative option is the one where upon the termination of the simulation all humans will be transferred from there to the parent universe. A less pleasant alternative is an artificial termination. The simulation can just be stopped and erased, regardless of the situation in the simulated world and without apparent reason (from the point of view of simulated humans, though they probably will not even notice the termination). The simulated world can also be destroyed in any way conceived by the simulators before the simulation itself will be stopped. This can be perceived by the simulated humans as apocalypse, Armageddon, Judgement Day or Ragnarok. But again, these events will be caused not by the processes in the simulation, but by outside forces.

== Rewards, Punishments and Afterlife ==

Inhisarticle, inanaïveattempt“to draw some loose analogies with religious conceptions of the world” [1, с. 10], Bostromsuggests possible mechanisms for several religious concepts.Based on the moral absolutism he proposes a metaverse where parent civilisations impose rewards and punishments on the simulated human beings and even provide afterlife to them based on their behaviour in the simulated world.

As was discussed earlier, we have no reasons to make any assumptions about the base civilisation if we are not one. Any ideas about morals of the parent civilisations are by their nature extremely speculative. In addition, the reasons for the existence of the simulation can vary greatly. A simple illustration is the difference between acceptable (as defined by simulators) behaviour for Quake monsters and ''sims'' in the Sims game.

But there are even stronger objections against these pseudo-religious ideas.# It is extremely irrational and plain silly to reward or punish your own creations (especially if they are essentially computer programs). The possible exception are experiments with artificial selection or training, but that has nothing to do with ethics and morals and criteria can be totally arbitrary. 
# The idea of afterlife is somewhat logical, as explained above in the, but there are no reasons to believe that there will be any sort of reward or punishment. The posthuman beings capable of running a simulation are very unlikely to have an irrational and barbarous mentality necessary for that. 



= VII.Conclusion =

Bostrom’s formula for calculating the probability of living in a simulation contains serious mathematical errors. The probability theory is used in the original paper incorrectly and without taking the philosophical aspects of the problem into consideration. The arguments based on the mathematical calculations have additional logical errors, such as circular reasoning, and ignore the observational bias.

Based on the analysis done in this paper, we can infer that the simulation argument is incorrect. It seems to be impossible to avoid the logical errors made by Bostrom. In addition, there are some reasons to concede that certain qualities of our civilisations point to our existence in reality.

It can be concluded that the reality of our world remains the question of personal beliefs. At the same time, the reality of our world does not impose additional limitations on the prospects of the technological progress, the possibility of reaching the posthuman stage and running simulations.

= VIII.         References =

1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Are You Living In a Computer Simulation? Nick Bostrom. Philosophical Quarterly, 2003, Vol. 53, No. 211, pp. 243-255.http://www.simulation-argument.com/simulation.html

2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Abre los ojos (Open Your Eyes). Alejandro Amenábar, 1997http://www.imdb.com/Title?0125659

3.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Cartesian Circle. Philosophy Circlehttp://www.philosophycircle.com/features/features39.html

4.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Dark City. Alex Proyas, 1998http://www.imdb.com/Title?0118929

5.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Gödel, Escher, Bach: an Eternal Golden Braid. Douglas R. Hofstadter. BasicBooks, 1979

6.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Innocence Lost: Simulation Scenarios: Prospects and Consequences. Barry Dainton, 2002, Draft.http://www.simulation-argument.com/dainton.pdf

7.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; How to Live in a Simulation. Robin Hanson, 2001, Journal of Evolution and Technology, Vol. 7. http://www.transhumanist.com/volume7/simulation.html

8.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Matrix. Andy Wachowski, Larry Wachowski, 1999http://www.imdb.com/Title?0133093http://www.whatisthematrix.com

9.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Philosophy & The Matrix. John Partridge, Christopher Grau, Colin McGinn, Kevin Warwick et al.http://whatisthematrix.warnerbros.com/rl_cmp/phi.html

10.&nbsp; The Physics of Immortality. Frank Tipler. Doubleday, 1994Summary of the Omega Point theory: http://www.math.tulane.edu/~tipler/summary.html

11.&nbsp; Shadows of the Mind: A Search for the Missing Science of Consciousness. Roger Penrose, Oxford University Press, 1994.

12.&nbsp; The Simulation Argumenthttp://www.simulation-argument.com/

13.&nbsp; Skepticism and Religion Revisited. Steven Novella. The New England Journal of Skepticism Vol. 1 Issue 3 (Summer 98)http://www.theness.com/articles/skepticismreligionrevisited-nejs0103.html

14.&nbsp; The Thirteenth Floor. Josef Rusnak, Daniel F. Galouye (novel), 1999http://www.imdb.com/Title?0139809

15.&nbsp; Vanilla Sky, Cameron Crowe, Alejandro Amenábar, 2001http://www.imdb.com/Title?0259711

16.&nbsp; Source unknown. An announcement by a group of British scientists in 2001.

&nbsp;


<div style="margin-right:4.9043in;"></div><div style="margin-left:0in;margin-right:0in;">[[#ftnref1|[1]]] Nick Bostrom — a researcher in the field of philosophy of science, ethics of technology and science, transhumanism. From 2000 to 2002 a lecturer in the Department of Philosophy of Yale University (USA), from 2003 a Research Fellow in Oxford University (United Kingdom). Author of 16 articles on topics of anthropic principle, technological development, artificial intelligence and simulation argument. Author of the book Anthropic Bias: Observation Selection Effects. 2002. Routledge, New York.</div>

Personal site: www.nickbostrom.com<div style="margin-left:0in;margin-right:0in;">[[#ftnref2|[2]]] On 15 May 2003 Matrix: Reloaded, the second part of the trilogy, was released. Third part, Matrix: The Revolutions, is scheduled for November 2003. The actual simulation, the MMORPG (massively multiplayer online role-playing game) The Matrix Online, will be released in 2004.</div><div style="margin-left:0in;margin-right:0in;">[[#ftnref3|[3]]] Player in GTA (Grand Theft Auto) game series usually drives or runs around the city, causing mayhem and destruction to the inhabitants of the city, killing pedestrians and shooting policemen (www.grandtheftauto.com).</div><div style="margin-left:0in;margin-right:0in;">[[#ftnref4|[4]]] This is an approximate interpretation of mathematical formulas derived in this section of the original paper. Because of the logical and mathematical errors made in the derivation, the formulas are incorrect, thus making a strict interpretation impossible. Bostrom gives his detailed interpretation of these formulas in the corresponding section (Interpretation).</div><div style="margin-left:0in;margin-right:0in;">[[#ftnref5|[5]]] An argument that uses circular reasoning (also known as “begging the question”) makes a conclusion based on material that has already been assumed in the argument.</div>