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Comment by ses1984 | Hacker News Reader

ses1984

I think our ability to look backwards is limited by the precision of our instruments and the precision of floating point computation.

Any error in our measurements would be magnified as we look backwards to the point that the simulation would at some point significantly diverge from reality, I wonder how many years back you can look before that happens?

Also floating point error would compound on top of that.

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Typically the error due to your numerical integrator that runs Newtons law backward in time (or forward for predictions) is larger than the floating point error after a few time steps and it is not uncommon to run for millions of time steps. This is not just true for the trivial but terrible Euler integrator, but also for high-order symplectic integrators. I know that my office mate has run simulations of planet systems with different codes and they tend to diverge at around 100 million years. They still look like the same system, but orbital phases disagree.

The uncertainty in the orbital elements (current orbital position and velocities) from which you start is not a major problem as long as all bodies are well separated. But our model would for example completely miss the body that crashed into the young Earth and left us with a moon.

Floating point error is far far smaller than measurement error and missing data.

Is there a reason you couldn't use whole numbers in place of decimals?

The problem still exists. It's less so specific to floating point numbers and more so a product of the limited number of states any data type can hold. Integers and floating point numbers are both still 64 bit on most modern computers, unless you are using big-int structures which are much more computationally intensive.

Granted, I'm no mathematician, but...

If we have a limit of 2^64 for $x, can't we set $y = representive of multiples of $x's upper limit?

$y = 5 = 5x2^64

What's the reason for not being able to sub-divide numbers and operations into smaller, more manageable forms?

Eh, was that rule not circumvented with conway? You can compress more data into a given numeric format, by moving the complexity into rule systems- aka determinstic games? Like a big number of chess games, or a group of possible games growing from just a sequence of letters and numbers.

The tradeoff for this limited space is though a complex ruleset and to recreate the data, lots of computation.

I'm no physicist, but isn't the 3-body problem relevant here too?

Only in the sense that you couldn’t directly compute the locations at arbitrary points in time given current positions and velocities.

The three body problem doesn’t stop you from running a simulation and getting the correct answer.

I think the point was that n-body systems with n>2 are chaotic, such that very small differences in starting position lead to massive differences as time unfolds.

Wouldn't this make it very difficult to do the highly precise detective work needed to find alleged former solar system bodies? Or are simulations accurate enough these days?

Not an expert, but I think n>2 means that chaotic behavior is possible, but not inevitable. Consider an isolated sun-earth-moon system, that doesn't appear to be chaotic. Simulating a "3-earth" system would, AFAIK, usually be chaotic.

I'd be happy to be corrected, of course.

That sounds correct. I would guess that systems like that can be approximated fairly accurately as nested 2-body problems.

Couldnt you make a backwards scenario filter, that kills simulations that run against evidence? Like - if this planet ceases to be, or that condition is not fullfilled, you are history.

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