Friday, February 11, 2011

How Much Should Scientists Extrapolate The Known To The Unknown?

We know an awful lot about the observable universe in the "low-energy" regime and a question that bugs my mind is: how much should we extrapolate what we know about the universe to regions we technically don't know much about? Three recent events have made me think about this:
  1. Dr. Kolb and Turner, who probably gave the most enjoyable talks at the AAS Meeting, bristled at the idea that many cosmologists are convinced we live in a multiverse from extrapolating what we know about the observable universe and went into outright mockery of string theorists who have dreamed up branes, landscapes, etc... by doing the same thing.
  2. Sean Carrol, who recently polled readers of how likely inflation was, suggested one of the reasons he only gives inflation a 75% chance of being real is that it involves energy scales that we know nothing about. (But in fairness to inflation, this leads to predictions that are verified so you can't put in in the same category as something like string theory. :))
  3. Jonathan recently asked if it was fair to say the universe is flat globally if we only have data showing flatness "locally".  
Now, first of all I think there is one very good reason to extrapolate: It's the best we can do given what we know now!

But I guess one question that bothers me is: How much confidence should we put in our extrapolation of known physics to the unknown?

I will give you an overly simplistic example just to make sure we are on the same page.  What if we were living in a one dimensional world and this was our observable universe:
Now, what would we, living at that red dot, conclude about the whole universe from extrapolation?  Probably that we live on a sine wave.  And from x between -6 and 6 that assumption would seem to work very well.

But what if it turns out this was our universe:
As we see here, our assumptions based on extrapolation would be wrong.

Now many of you will think this is childish, but is it?

For example: there was a day when humans had good reasons to believe the earth was flat.  They extrapolated... and they were wrong.  There were others who had good evidence that the sun and stars orbited around the earth.  They extrapolated... and they were wrong.  There were others who had experimental reasons to think gravity can effect all other matter instantaneously. (Action at a distance)  They extrapolated... and they were wrong. Etc...

And so I wonder how likely we are to be falling into the same trap as our ancestors?  On one hand extrapolation is all, and is the most honest thing, we can do.  But on the other, history has had a way of punishing the extrapolaters.  

One should be said though: once new data does come demonstrating our cherished "extrapolated" theories are wrong, eventually the mainstream science community drops them and moves on.  History has shown that eventually mainstream science will lead toward the right answer as more data comes in on the matter.

So what do you think?  How much confidence should we scientists put in our "theories from extrapolation"?


  1. I would expect our confidence to go down as we extrapolate farther outside the range of our observations. Think about prediction intervals on time series, for example. If you are predicting one or two steps ahead, then the interval is often pretty small, but if you want to predict 50 steps ahead, well, the interval gets to be enormous. As you go to infinity, so does the interval.

    Since you have represented your question with a curve on some data, I wonder to what extent scientific theorizing in general can be modeled as curve fitting. Is it fair to say that Newton was doing some curve-fitting and then extrapolated the curve beyond the observations?

  2. Jonathan,

    I would say my use of curve fitting is more metaphorical then physicists are literally fitting curves. (Just in case I gave that impression.)

    More realistically this is what is going on: scientists for centuries assumed that a "unification" of the machinery that goes into Newtonian physics would eventually explain all physics. However, that led them to make assumptions about the smallest and largest aspects of reality which tuned out to be wrong.

    Now we know new machinery (quantum mechanics and or general relativity) is needed to describe the very large and the very small.

    But now we are doing the same thing: trying to take the unification of the known modern machinery, quantum mechanics and general relativity, and assuming that unification will explain the whole universe.

    For example, string theory is the best attempt so far to unify quantum mechanics and general relativity. But the theory *only* unifies machinery that has been developed to describe the universe thus far observed.

    Is there any reason we should think this "extrapolation", or extrapolations like it, will be any more successful in describing the "full universe" then did the unification of all known physics in Newton's day?

  3. JS,

    Of course, and why not? Each extrapolation defines a physicality that may be realizable, or not, or may remain indeterminate, or may need a new set of building blocks for the Universe. It all adds to the knowledge. Knowledge that something is incorrect is much more important than what is correct. Jonathan might appreciate this.

  4. JS,

    This might be of interest to you, and may be to Jonathan.

  5. Ancient1,

    Thank you for the link. I am always interested in articles from the Stanford Encyclopedia of Philosophy.

  6. JS,

    I hope you enjoy it. My take on Causation, FWIW:

    If we recognize we exist, we accept causation. Replacement of cause by forces in PHILOSOPHICAL perspective - such a gravitational etc. - is sophistry at best. Force representation is a necessity for computability in sciences. I hope philosophers will catch on.

  7. Ancient1,

    Interesting perspective. Do you mind elaborating more on the idea that existence implies causation? I'm not trying to rebut that idea but just wondering if you have a good argument why existence implies causation.

  8. JS,

    I will try, but let me say that you have now learned the art to put others on thin ice too! Here it goes:

    All life is conceived (yes, including even a bacterial division) through an act that was initiated through a causal chain of events, many of these events we approve, many we abhor, and of many, we lack understanding. Much more to the point, each life thinks it is unique and even paramount over all other around it. Such thought is causal, and many faiths begin here, comprehended or not (this is also Philosopher's Achilles’ heel, they can not accept such subjectiveness as causal, tough!).

    If you care, take a look at PBS’ Nature program Moment of Impact: Hunter and Herds, and see if you come out convinced of causality, comprehended or not.


  9. Ancient1,

    Thank you for your thoughts and the link.

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