Can we determine if we are in a simluation using different variable precision

Question

I'm posing it as more of a philosophical question.

Assume our Universe is a simulated one.

What features would I put in a Universe simulation (e.g. to reduce computational requirements) and how could we people living in the simulation detect these computational artifacts?

To keep this from being a duplicate of other similar questions I wanted to drill down and see if I could get some specific questions answered.

Assume we find discrepancies between observed and calculated values for things like the Pioneer anomaly (I am aware that current thinking attributes this to thermal effects of the RTG but thought something like this would be a great example).

If we made the discrepancy (between calculated and observed behavior) disappear by increasing our variable precision to some level but increasing our precision beyond that level reintroduces a discrepancy, would we consider this evidence that we're in simulated reality or am I barking up the wrong tree?

If this would not indicate we live in a simulation (even weakly), then what other evidence might we find that we could use to figure this out?

Answer 1

No.

How would this appear any different from any other scientific discovery that we needed to model, such as relativity or quantum physics. We'd simply develop a new model that matches the observations, and move on. As a software developer, I can tell you no simulation artifact is stranger than those two laws of nature!

If anything we would find it to be some rather interesting natural law. There is also no guarantee that they use IEE-754 floating point numbers in the simulation of the world. We may not even recognize the round off when it occurs.

As for what we could use? The truth is that there's not very much and there's everything. From one perspective, the problem you're trying to resolve is the "brain in a jar" thought experiment, which still has no "solution." On the other hand, you don't need to know you are in a simulation, you just need to believe it. That turns out to be a very different bar. Absolutely anything unique in the world could make you believe it is a simulation. A quirk in pi, or the fibonacci sequence appearing a little more often than you are comfortable with. Perhaps it's deja vu that tips you off.

Answer 2

No.

If we found increasing precision up to a point, but not beyond, yielded the most accurate calculations to match observation it would not be evidence that we're in a simulation. Presumably you're asking based on this kind of news.

It would be evidence that our universe is quantized or evidence that our universe is a hologram. Being a hologram is not the same as being simulated.

Unless you're on the holodeck.

Answer 3

Almost certainly no, as Samuel says. However... Yes if, and only if, the precision obeys artificial rounding rules.

For example, we might expect the following to be potentially natural rounding in a quantizied universe:

1. Always round down (if you can't make it to the next quanta step, you don't go anywhere).
2. Always round up (any distance is at least one quanta).
3. Round always at some step (.5, .4, etc) - we're not sure why, but this might be explainable. It's weird, but it's not evidence.

On the other hand, I can hypothetically imagine aliens implementing something like the following:

Always round down, but store the remainder. When the remainder reaches 1 base unit, add it back in.

That would be pretty good evidence for an artificial implementation of physics.

Answer 4

You mentioned finding "discrepancies between observed and calculated values"; I would argue that this is impossible.

For instance, say the value for pi in the simulated universe is rounded to 3.14. In order for us to find the value for pi, it needs to be used in the universe. Thus, there is a circle that uses this value of pi to calculate its diameter and circumference relation. Any object that does not use this value of pi is not a circle, as it does not fit the mathematical definition of a circle.

Say someone imagines a circle. As explained above, this circle uses 3.14 as its value of pi. Say someone measures a circle. As explained above, the circle will use 3.14 as its value of pi. Any considerations of an object that uses the real value of pi will be strictly hypothetical, as there is no object in the universe that follows those properties.

This is all based on the idea that circles would be simulated based on the number pi. In reality, I assume they would be simulated without pi, then the number pi will be inferred from these simulations. In fact, all you really need to know about a circle is its diameter, from which you can derive both its circumference and the value of pi (maybe not with pure math, but with a stick and some measuring tape I could definitely do it). In a similar way, I'd think that most things end up getting all their values from one single value, or a single set of axioms. As these are axioms, they must be agreed upon before making any measurements or calculations, and thus everyone in the simulated universe would have to accept them as just the way things are.

The short answer is that the simulation is using math to simulate the universe, and we're using math to describe the universe. The idea that we'd use a different or more precise math than the math we are being simulated on seems impossible to me; and even if we did, the math itself would violate the very laws of the universe, and thus be purely theoretical.