Why Would Reality Be a Simulation?

In 2003 philosopher Nick Bostrom advanced a provocative trilemma known as the Simulation Argument. It does not assert that we are definitely living inside a computer simulation. Instead, it presents three mutually exclusive propositions, at least one of which must be true. Either civilizations like ours invariably go extinct before achieving technological maturity, or mature civilizations choose not to run vast numbers of ancestor simulations, or we are almost certainly living within such a simulation. The core insight is probabilistic: if technologically advanced beings create enormous numbers of simulated minds, then simulated observers will vastly outnumber biological ones. Absent evidence to the contrary, any randomly sampled observer should expect to be simulated. The argument sidesteps details about hardware or the intentions of hypothetical simulators and instead focuses on counting.

Translating Philosophy into Numbers

This calculator invites you to quantify the Simulation Argument. Bostrom expresses his reasoning using three variables, often denoted $\mathrm{f\_1}$ for the fraction of civilizations that reach a posthuman stage, $\mathrm{f\_2}$ for the fraction of those that run ancestor simulations, and $\mathrm{f\_3}$ for the average number of simulated minds produced by each civilization. Rather than separating $\mathrm{f\_1}$ and $\mathrm{f\_2}$, this tool assumes you already have an overall fraction of civilizations that actually carry out ancestor simulations, labelled $f$. If we denote the average number of simulations per civilization by $n$ and the number of conscious minds per simulation by $m$, then the total simulated population becomes $\mathrm{N\_\{sim\}\; =\; f\; \times \; n\; \times \; m}$. Meanwhile the number of real historical humans is $\mathrm{N\_\{real\}}$. The probability that you are simulated is given by

$$\mathrm{P\_\{sim\}}=\frac{\mathrm{N\_\{sim\}}}{\mathrm{N\_\{sim\}}+\mathrm{N\_\{real\}}}$$

This expression simply compares the number of simulated minds to the total population of minds.

Entering Your Assumptions

The input fields correspond to the variables described above. The first field accepts a fraction between 0 and 1 representing the proportion of posthuman civilizations that decide to run ancestor simulations. The next field asks how many separate simulations each such civilization runs on average. The third field captures the typical number of conscious entities within each simulated world. Finally, the last field records the number of actual biological humans that have ever lived. The default values treat simulations and real history as roughly comparable in population, but you can explore extreme scenarios: perhaps civilizations run billions of simulations, each containing trillions of minds, or perhaps almost none do.

What the Results Mean

After clicking the compute button, the calculator displays three quantities. First, it shows the total number of simulated minds implied by your assumptions. Second, it reports the probability that a randomly selected mind is simulated, which is also the subjective credence that we ourselves are simulated if we treat ourselves as randomly selected. Third, it provides the complementary probability that we inhabit base reality. Even tiny changes in the inputs can swing the result dramatically because the numbers involved are astronomical. If the universe hosts 10^11 real humans but just one posthuman civilization runs 10^5 simulations of comparable size, then simulated minds outnumber real ones a hundred thousand to one, pushing the simulation credence to 99.999%.

Beyond Binary Outcomes

The Simulation Argument is often misunderstood as a proof that we live in a simulation. It is instead a conditional statement about ratios. If $f$ or $n$ is near zero, then simulated minds are rare and we are probably real. If they are large, we are almost certainly simulated. The argument remains agnostic about how simulations operate, whether they include quantum effects, or how consciousness arises. This calculator embodies that agnosticism by treating simulations purely as counting exercises. It does not attempt to address philosophical issues such as the reference class problem, the nature of personal identity, or whether simulated minds are morally equivalent to biological ones.

Sample Scenarios

The table below illustrates several hypothetical combinations of inputs and the resulting simulation credence. These are not predictions but explorations of the parameter space.

Fraction f	Simulations n	Minds per Sim m	Simulated Minds	P(sim)
0.1	100	1e11	1e12	0.91
0.01	1000	1e12	1e13	0.99
0.5	1	1e10	5e9	0.05
0.9	10000	1e12	9e15	~1.0

The first row suggests that even if only ten percent of civilizations run a hundred simulations each, simulated minds still outnumber real ones by an order of magnitude. The fourth row underscores how quickly the probability saturates near unity when simulations are abundant. Readers can use the calculator to test more nuanced assumptions, perhaps considering different population sizes, varying civilization behaviors, or limits imposed by computational resources.

Interpreting the Credence

What should one do with a high simulation credence? Bostrom himself cautions that the argument does not necessarily entail radical behavioral changes. If we are simulated, the simulators might have moral standards, might be indifferent, or might terminate the simulation if we act suspiciously. Alternatively, the simulation could be a faithful recreation of base reality with no special intervention. Some thinkers speculate that finding bugs or low-resolution artifacts could provide evidence of simulation, yet this assumes the simulators cut corners. Others propose that advanced beings might run simulations precisely to study authentic behaviors, implying we should act as we would if real.

Critiques and Counterarguments

Several objections challenge the Simulation Argument. One criticism points to the self-sampling assumption, the idea that we should treat ourselves as randomly selected from all observers. Critics argue that observer selection effects might be more complex, especially if simulations differ qualitatively from base reality. Another objection questions whether consciousness can be simulated at all. If sentient experience requires non-computable phenomena, then no amount of computation would produce genuine minds. Skeptics also highlight resource constraints: perhaps no civilization can muster enough energy to run many detailed simulations. These debates highlight the speculative nature of the argument and underscore why this calculator is more of a philosophical toy than a scientific instrument.

Experiment Freely

The Simulation Argument invites us to reflect on the nature of reality, the trajectory of technological progress, and the responsibilities of potential simulators. By playing with the inputs, you can explore how optimistic or pessimistic assumptions about future civilizations translate into probabilistic conclusions. Whether you treat the result as a serious posterior probability or as fodder for science fiction, the exercise provides insight into how simple numerical reasoning can inform profound metaphysical questions. Ultimately, the calculator is a reminder that even abstract philosophy can be quantified, offering a bridge between speculative thought and concrete numbers.