Hacker News Reader

Comment by tansey | Hacker News Reader

Actual paper: http://www.pnas.org/content/112/13/E1569.full

The idea (from 5 minutes of skimming plus watching the little 3min tutorial) seems to be that any multi-dimensional time series implicitly contains all the information necessary to reconstruct it entirely within a single dimension. The authors show an example of a 3-dimensional time series with a butterfly-type pattern that you can reconstruct just by looking at the values of X(t) and then using X(t-a) and X(t-2a) as the other dimensions. Not sure how that leads to prediction-- can someone explain that part?

View on HN

In complex analysis, this is generally true; in particular for any function on the real numbers, there is exactly one differentiable function on the entire complex plane that has the same value. https://en.wikipedia.org/wiki/Holomorphic_function . You can also go forward/backward in time with the functions, and knowing the value ahead of time is predicting it.

On the other hand, there are non-differentiable events all the time in nature. It's madness to claim that salmon populations contain enough information to predict earthquakes (that could dam a river and cause a massive population change).

It's probably more accurate to say that predicting earthquakes from salmon populations is far outside our current modeling capabilities. Undoubtedly the seismic stresses and crustal movements leading up to earthquakes have numerous weak causal links to the salmon population: most obviously, they alter the slopes and flow rates of streams leading into the ocean, altering the nutrient balance available to the algae there, but also they alter the distances flown by migratory birds by centimeters per year, and those birds will consequently eat very slightly different fish, etc. There might not even be a way to analyze the salmon population in such a way as to tell you how far the continents have drifted — but declaring that postulating the existence of such a thing is "madness" seems like being far too sure of yourself.

There's a science-fiction story that may be useful in gaining perspective on the limits of prediction at http://lesswrong.com/lw/qk/that_alien_message/.

The problem with earthquakes, as I see it, is not so much that they are non-differentiable as that they (like a bird eating or not eating a particular fish) have very large local derivatives with respect to their precipitating conditions.

If you have a theory that invalidates the Heisenberg Uncertainty Principle, go for it. Otherwise, I'm going to consider all of that pure science fiction.

Maybe you're not very familiar with the uncertainty principle, but continental plates and even individual birds have enough mass that the uncertainty in their position, for any reasonably large uncertainty in their momentum, is insignificant.

I'm claiming that to measure the salmon population well enough to predict earthquakes, you would have to violate the uncertainty principle.

Now that sounds like pure science fiction — specifically, the kind of technobabble that serves as filler in Star Trek scripts and New Age scam artist patter. "Captain! We can't measure the salmon population because the Heisenberg Uncertainty Principle is overwhelming the medium-range laser scanner array!"

... are you seriously claiming that you theoretically could predict earthquakes based solely on the salmon population?

I'm not sure it's worth arguing with you either way.

No, I'm seriously claiming that you have no idea whether you theoretically could predict earthquakes based solely on the salmon population. We don't have a good theory that bears on the question. We know we can't imagine how you could practically make such a prediction, but the only relevant theory that we have is the theory of inductive inference founded by Solomonoff in the 1960s, which is very far indeed from ruling out such predictions. And you making up bullshit about Heisenberg doesn't get us any closer.

I'm claiming I do have an idea.

Let's say you have a model that will predict earthquakes based on the number of salmon. I take that model, I see what will happen if I kill or don't kill a salmon, and how that impacts the earthquake. Then I kill or don't kill a salmon. Am I now causing an earthquake? If I am, am I changing the time of the earthquake by an amount that we can actually measure?

You're saying the salmon population isn't in a single eigenspace of it's number operator?!

A good explanation can be found in the video mockery linked below.[1]

Short summary: There's a theorem that says that (under certain conditions) if you have some model that evolves over time, then you can reconstruct the geometric properties of this model by only looking at how a single 'observable' (e.g. the number of salmon) evolves over time. Of course if you have multiple observables then you get multiple reconstructions and with enough data you can figure out how to go from one to the other.

Now how this leads to prediction is that you can use any one of the observables you can figure out the current state of the model, which tells you both the value of the observables you didn't know and how it's going to evolve. Of course the accuracy depends on the accuracy of the reconstruction.

[1]:https://news.ycombinator.com/item?id=10405320

It's worth noting that this doesn't work for any multi-dimensional time series, but only some. For example, the lat-long-elevation plot of an airplane's flight path could not be recovered from just the latitude plot, or one channel could simply be noise. Although, it's incredibly interesting to find cases where this does work, as it indicates there's some special underlying manifold structure.

Reply on news.ycombinator.com