Simulated realities and why this calculator exists

This page treats the idea that our universe could be a computer simulation as a playful, quantitative thought experiment. It does not claim that we are in a simulation or that the outputs are empirical predictions. Instead, it gives you a simple probability model for one specific question:

If we live in a simulation that can be reset after anomalies, how likely is at least one reset over a chosen time horizon?

To answer that, the calculator combines four ingredients:

How often anomalies happen (events per year).
How likely each anomaly is to be noticed or flagged (detection probability).
How likely a detected anomaly is to trigger a full reset (reset probability).
How long you are “watching” the simulation (observation horizon in years).

Mathematically, the model uses a standard rare-event tool: the Poisson process. Poisson processes are widely used in reliability engineering, queuing theory, and risk analysis to model counts of random, independent events in time. Here we simply apply that same structure to a speculative scenario.

From anomaly rate to reset probability

The core idea is to move step by step:

Start with an anomaly rate, the average number of anomalies per year.
Thin that down to the rate of detected anomalies, using the detection probability.
Thin it again to get the rate of resets, using the reset probability given detection.
Use Poisson math to convert that reset rate into the probability of at least one reset over the time horizon.

Step 1: Poisson model for anomalies

Suppose anomalies occur at an average rate of $λ$ events per year. If you watch the simulation for $T$ years, the expected number of anomalies is $λ T$ . In a Poisson process, the probability of seeing exactly $k$ anomalies in that window is:

P (K = k) = \frac{{(\lambda T)}^{k}}{k} e^{- \lambda T}

You do not need this full formula to use the calculator, but it is the standard Poisson probability mass function. Two properties matter most here:

The mean number of anomalies is $λ T$ .
Events are assumed independent and occur at a constant average rate.

Step 2: Detection probability per anomaly

Not every anomaly has to be noticed. Let $p_{d}$ be the probability that a given anomaly is detected or flagged as important by the simulators (or by monitoring systems in the simulation). Under the Poisson framework, “keeping” each event with probability $p_{d}$ just scales the rate:

Anomaly rate: $λ$ (per year)
Detected anomaly rate: $λ p_{d}$ (per year)

This is sometimes called “thinning” a Poisson process: each anomaly independently passes a detection filter with probability $p_{d}$ .

Step 3: Reset probability given detection

Even a detected anomaly does not have to trigger a reset. Let $p_{r}$ be the conditional probability that a detected anomaly causes the simulators to reset the entire simulation. Treat each detected anomaly as a potential reset trigger with probability $p_{r}$ .

Applying the same thinning idea one more time gives a reset event rate:

Reset rate: $λ * = λ p_{d} p_{r}$ resets per year.

This $λ_{*}$ is sometimes described as a hazard rate: the average rate at which full reset events occur in continuous time, under the model’s assumptions.

Step 4: Probability of at least one reset

If resets themselves follow a Poisson process with rate $λ_{*}$ , then over a horizon of $T$ years:

The expected number of resets is $λ_* T = λ p_d p_r T$ .
The probability of seeing no resets is $\exp (- λ p_{d} p_{r} T)$ .

Therefore, the probability of at least one reset in that period is:

P (at least one reset in T years) = 1 - e^{- \lambda p_d p_r T}

This is the main quantity the calculator reports: the chance that, somewhere in the chosen time horizon, at least one reset occurs.

How to use the calculator

The input fields correspond directly to the symbols in the formula:

Anomaly Rate (events per year) – $λ$
Average number of “weird” or anomalous events per year that might matter to the simulators.
Detection Probability per Anomaly – $p_{d}$
For each anomaly, the chance that it is noticed and flagged as significant.
Reset Probability if Detected – $p_{r}$
Given that an anomaly is detected, the chance it triggers a full simulation reset.
Observation Horizon (years) – $T$
The length of time over which you want to evaluate the risk of at least one reset.

After entering values, the calculator applies the formula:

reset_probability = 1 - exp(-anomaly_rate * detection_probability * reset_probability_if_detected * horizon)

The output is a single probability between 0 and 1 (or 0% to 100%), representing the model’s estimate of at least one reset occurring over the chosen horizon.

Worked example

Imagine the following toy scenario:

Anomaly rate $λ = 0.1$ events per year (about one anomaly every 10 years).
Detection probability $p_d = 0.5$ (half of anomalies are noticed).
Reset probability if detected $p_{r} = 0.2$ (one in five detected anomalies trigger a reset).
Observation horizon $T = 100$ years.

First compute the reset rate:

$λ_= λ p_d p_r = 0.1 \times 0.5 \times 0.2 = 0.01$ resets per year.

Over 100 years, the expected number of resets is:

$λ_* T = 0.01 \times 100 = 1.0$ .

The probability of at least one reset is:

$P (reset in 100 years) = 1 - e^{- 1.0} \approx 1 - 0.3679 = 0.6321$ .

In percentage terms, this model suggests about a 63% chance of at least one reset over 100 years in this speculative setup.

If you shorten the horizon to 10 years with the same parameters:

Expected resets: $0.01 \times 10 = 0.1$ .
Reset probability: $1 - e^{- 0.1} \approx 1 - 0.9048 = 0.0952$ , or about 9.5%.

The calculator automates these computations so you can explore how changes in each input affect the overall risk.

Interpreting the results

The output probability should be read as:

“Under the model’s assumptions and your chosen parameters, this is the chance that at least one reset happens during the specified time window.”

Some qualitative interpretations:

A higher anomaly rate (more weird events per year) increases reset risk.
A higher detection probability means more anomalies reach the simulators’ attention, raising risk.
A higher reset probability if detected makes each noticed anomaly more dangerous in terms of triggering a reset.
A longer time horizon always increases the chance that at least one reset occurs, because there is more time for rare events to happen.

For very small values of $λ p d p r T$ , the probability can be approximated by:

$P (reset) \approx λ p d_{} p r_{} T$ .

This linear approximation can make it easier to see proportional effects. For example, if you double $T$ , you roughly double the small probability, and similarly for small changes in the other factors.

Parameter comparison table

The table below illustrates how changing different parameters affects the reset probability over a 100-year horizon. These are not real-world estimates; they are illustrative scenarios.

Anomaly rate ( $λ$ )	Detection probability ( $p_{d}$ )	Reset probability if detected ( $p_{r}$ )	Horizon (T, years)	Reset probability $P (reset)$
0.01	0.2	0.1	100	$1 - e^{- 0.01 \times 0.2 \times 0.1 \times 100} \approx 0.0199$
0.1	0.5	0.2	100	$1 - e^{- 1.0} \approx 0.6321$
0.5	0.7	0.5	100	$1 - e^{- 17.5} \approx 0.99999997$
0.1	0.5	0.2	10	$1 - e^{- 0.1} \approx 0.0952$

Notice how large products of $λ p d p r T$ quickly push the probability close to 1, while small products keep the probability near 0. The calculator lets you explore this whole spectrum.

Assumptions and limitations

This model is deliberately simple and highly idealized. Keep these assumptions and limitations in mind:

Poisson anomalies: Anomalies are assumed to arrive as a Poisson process with a constant average rate $λ$ . Real-world anomalies (if they exist) could be clustered or time-varying.
Independence: Each anomaly, detection decision, and reset outcome is treated as independent of the others. Feedback effects or learning by the simulators are ignored.
Constant probabilities: The detection probability $p_{d}$ and reset probability $p_{r}$ are assumed constant over time and across anomalies. In reality, these could depend on context or on previous events.
Binary outcomes: The model only distinguishes between “no reset” and “at least one reset” over the horizon. It does not track multiple resets, partial rollbacks, or more complex interventions.
Speculative inputs: There is no empirical way to measure $λ$ , $p_{d}$ , or $p_{r}$ for an imagined simulation. The parameters are best treated as dials for exploring what-if scenarios, not as claims about reality.
Not a scientific prediction: Results are for entertainment and conceptual exploration only. They should not be interpreted as evidence for or against any simulation hypothesis.

If you want to dig deeper into the mathematics, you can look up introductory resources on Poisson processes and exponential distributions, which provide the underlying theory for this kind of constant-rate event modeling.

Summary

This calculator wraps a standard Poisson-style risk model around a speculative question about simulated universes. By specifying how often anomalies occur, how likely they are to be noticed, how dangerous each detected anomaly is in terms of triggering a reset, and how long you care about, you get a single probability for at least one reset within that window.

The math is straightforward, but the interpretation is intentionally playful: it is a way to quantify stories about glitches in the Matrix, not a way to forecast the actual fate of the cosmos. Used with that mindset, it can help build intuition about how rare events, detection, and intervention interact in any system that might be monitored and occasionally rebooted.

Simulation Reset Detection Probability Calculator

Simulated realities and why this calculator exists

From anomaly rate to reset probability

Step 1: Poisson model for anomalies

Step 2: Detection probability per anomaly

Step 3: Reset probability given detection

Step 4: Probability of at least one reset

How to use the calculator

Worked example

Interpreting the results

Parameter comparison table

Assumptions and limitations

Summary

Embed this calculator

Simulation Reset Detection Probability Calculator

Simulated realities and why this calculator exists

From anomaly rate to reset probability

Step 1: Poisson model for anomalies

Step 2: Detection probability per anomaly

Step 3: Reset probability given detection

Step 4: Probability of at least one reset

How to use the calculator

Worked example

Interpreting the results

Parameter comparison table

Assumptions and limitations

Summary

Embed this calculator

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