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jlhredshift
2010-Jun-30, 10:50 PM
This is interesting on many levels, in the most recent edition of GSA Today is an article by Peter Kosso, Department of Philosophy, at Northern Arizona University:

Super-rotation of Earth’s inner core and the structure of scientific reasoning (http://www.geosociety.org/gsatoday/archive/20/7/pdf/i1052-5173-20-7-52.pdf)

He discusses the "inverse problem".


The defining characteristic of an inverse problem is the challenge of determining properties of an unobserved cause based on observed properties of the effect. This provides an opportunity to raise some worthwhile methodological questions.

Also, I find acceptance of the inner core rotating faster than the mantle very "cool".

Ken G
2010-Jul-02, 11:34 PM
Yes, the inverse problem is what Einstein used his watch metaphor for-- we are trying to figure out the workings of a watch without opening it. An insightful metaphor, but it shouldn't be taken too literally-- Einstein tended to be something of a naive realist (which is why he never liked quantum mechanics). It is safer to say that our goal is to devise models that allow us to predict and understand at a simple level some kind of mental simulacrum we create to represent a watch. There's really no need, and no call, to claim that science is like trying to understand how a watch actually works without opening it, because that pushes the watch analogy too far: it is we who created the watch, after all.

jlhredshift
2010-Jul-03, 01:36 AM
Yes, the inverse problem is what Einstein used his watch metaphor for-- we are trying to figure out the workings of a watch without opening it. An insightful metaphor, but it shouldn't be taken too literally-- Einstein tended to be something of a naive realist (which is why he never liked quantum mechanics). It is safer to say that our goal is to devise models that allow us to predict and understand at a simple level some kind of mental simulacrum we create to represent a watch. There's really no need, and no call, to claim that science is like trying to understand how a watch actually works without opening it, because that pushes the watch analogy too far: it is we who created the watch, after all.

Could give some examples of problems in physics, astrophysics, or GR that we are trying to solve via the "inverse" methodology?

Ken G
2010-Jul-03, 03:25 AM
Could give some examples of problems in physics, astrophysics, or GR that we are trying to solve via the "inverse" methodology?At some level, all of them. But some have a more "forward" character, before we get to the "inverse" aspects. Let's say you see a rainbow and you want to understand it. That's an inverse problem-- nature has handed you a rainbow, and you essentially wish to reverse-engineer it, either conceptually or quite literally. The forward aspects appear when you start doing things in the lab that simulate a rainbow, like doing refraction and internal reflection experiments on light. You might even create water droplets, bounce light off it, and get a rainbow in the lab. That has a forward flavor, because you created the phenomenon yourself, but you will still encounter reverse elements when you try to say what happened in the lab. You can say "what happens in a rainbow I made happen in my lab", but someone else can still ask "OK, but what happened in your lab?" And so you will still be handed an inverse problem, because at some point, you always have to turn the situation over to nature, and get what you get. Then you will have to conceptually reverse-engineer whatever you got at that point, it's unavoidable. Indeed, this inverse character is not a bug in physics, it is rather the point of physics.

grapes
2010-Jul-03, 06:33 AM
There's really no need, and no call, to claim that science is like trying to understand how a watch actually works without opening it, because that pushes the watch analogy too far: it is we who created the watch, after all.I think that's assuming a little too much of the mantle :)


Could give some examples of problems in physics, astrophysics, or GR that we are trying to solve via the "inverse" methodology?If you take a given model of the earth with various properties, you can use physics to predict the effect of an earthquake at a particular location, the magnitude of the effect on a detector or many detectors. Inversely, use the detector records to infer the structure and properties of the earth.

jlhredshift
2010-Jul-03, 12:55 PM
Thank you Ken and Grapes, then, the gist of it is when we take readings from our instruments of an "event", whatever it might be, that is the beginning of the inverse process. The next step would be to form a hypotheseis as to how the "event" was created and then on from there would be the "forward" part of the process. So for example, when it was first realised that the spectra lines of hydrogen were shifted from distant stars, that was the "inverse" problem?

Ken G
2010-Jul-03, 03:40 PM
Thank you Ken and Grapes, then, the gist of it is when we take readings from our instruments of an "event", whatever it might be, that is the beginning of the inverse process. The next step would be to form a hypotheseis as to how the "event" was created and then on from there would be the "forward" part of the process. So for example, when it was first realised that the spectra lines of hydrogen were shifted from distant stars, that was the "inverse" problem?Right, there's a kind of "meeting in the middle" that happens in astronomy, even moreso than physics. The forward process looks like asking "what would be the ramifications if such-and-such happened", and in laboratory experiments, you can make such-and-such happen and find out. But when "such-and-such" is an astronomical event of some kind, you can't make it happen in the laboratory, you can only make some tiny part of it happen, or something analogous on a different scale. Then you extrapolate to the astronomical event, which has an inverse flavor because all you know about the astronomical event is what it looks like.

The major difference between forward and inverse problems (in addition to issues like the philosophy of what you are doing, and the reliability of the laws you are invoking) has to do with uniqueness. Forward problems are unique in deterministic settings that are not chaotic-- you set up the phenomenon you wish to understand (either in the lab or on your computer), and the ramifications just play out. But inverse problems are often not unique, even in non-chaotic deterministic settings. You see something, and you infer that a particular event could look like that, but you don't know that other events might not also look just like that too. It's a bit like the problem a detective faces-- you can say "if Colonel Mustard was the murderer then the victim's blood would be on his hands", and then note that the victim's blood was indeed on his hands, but you cannot then say "since the victim's blood was on his hands, he must be the murderer." There are other ways the blood could have gotten there, so proving a fact from an inverse standpoint is much more tenuous, and that's largely the reason why "prove" is used in science more like it appears in a courtroom than in a mathematics textbook.

mugaliens
2010-Jul-06, 07:44 AM
Hmm... I always assumed it would, due to tidal friction slowing down the Earth's crust and mantle.

jlhredshift
2010-Jul-06, 01:14 PM
Hmm... I always assumed it would, due to tidal friction slowing down the Earth's crust and mantle.

I had always assumed the opposite because I felt that there had been enough time for things to reach equilibrium. But, I think what you propose as a mechanism, which may be true, is going to be very difficult to quantify.