[Phys-l] season's greetings

[John Denker <jsd@av8n.com>]

    /It's that time of year again:  the start of school.   Chapter 1 of
    the textbook goes on and on about significant digits.  A few
    students sit there, fidgeting, wondering whether the teacher is
    really crazy enough to believe this stuff.  The more they think
    about it, the less sense it makes.  But// only a few of them bother
    to think about it at all; most of them learned long ago that
    thinking about classwork is a lose/lose proposition./


Maybe I'm overly optimistic, but I think we can do better than that.  We
can start by eradicating the sigfig nonsense.   I recently updated my
web page on the subject.


      How Many Digits Should Be Used?

Use many enough digits to avoid unintended loss of significance. Use few
enough digits to be reasonably convenient.


      How Should Uncertainty Be Expressed?

Express the uncertainty separately and explicitly. For example,
1.234(55) or equivalently 1.234±0.055.

State the form of the distribution, unless this is obvious from context.
Examples include Gaussian, square, triangular, et cetera.


      What About Significant Digits?

The whole notion of significant digits is heavily flawed; see section 8
<http://www.av8n.com/physics/uncertainty.htm#sec-abomination> for more
on this. Anything that can be done by means of significant digits can be
done much better by other means. People who care about their data don’t
use significant digits.


    Table of Contents

    * 1  Introduction <http://www.av8n.com/physics/uncertainty.htm#htoc1>
          o 1.1  How Many Digits Should Be Used?
            <http://www.av8n.com/physics/uncertainty.htm#htoc2>
          o 1.2  How Should Uncertainty Be Expressed?
            <http://www.av8n.com/physics/uncertainty.htm#htoc3>
          o 1.3  What About Significant Digits?
            <http://www.av8n.com/physics/uncertainty.htm#htoc4>
    * 2  Fundamental Notions of Uncertainty
      <http://www.av8n.com/physics/uncertainty.htm#htoc5>
    * 3  Propagation of Uncertainty
      <http://www.av8n.com/physics/uncertainty.htm#htoc6>
          o 3.1  Example: Extracting Signal from Noise
            <http://www.av8n.com/physics/uncertainty.htm#htoc7>
          o 3.2  Another Example: Magnesium Mass. Monte Carlo Solution
            <http://www.av8n.com/physics/uncertainty.htm#htoc8>
          o 3.3  Example: Interpolating Between Graduations
            <http://www.av8n.com/physics/uncertainty.htm#htoc9>
          o 3.4  Crank Three Times
            <http://www.av8n.com/physics/uncertainty.htm#htoc10>
          o 3.5  Manual Propagation of Uncertainty
            <http://www.av8n.com/physics/uncertainty.htm#htoc11>
          o 3.6  Example: Manual Propagation
            <http://www.av8n.com/physics/uncertainty.htm#htoc12>
          o 3.7  Amplification of Uncertainty
            <http://www.av8n.com/physics/uncertainty.htm#htoc13>
    * 4  How Much Accuracy Is Enough? How Much Data Is Enough?
      <http://www.av8n.com/physics/uncertainty.htm#htoc14>
          o 4.1  Why is this hard?
            <http://www.av8n.com/physics/uncertainty.htm#htoc15>
          o 4.2  Recommendations -- How To Do It Right
            <http://www.av8n.com/physics/uncertainty.htm#htoc16>
          o 4.3  Report the Form of the Distribution
            <http://www.av8n.com/physics/uncertainty.htm#htoc17>
          o 4.4  Too Many Digits, Oh My!
            <http://www.av8n.com/physics/uncertainty.htm#htoc18>
          o 4.5  How To Survive an Attack of Sig Figs
            <http://www.av8n.com/physics/uncertainty.htm#htoc19>
          o 4.6  Sensitivity Analysis, On-Line Analysis, and
            Cross-Checking
            <http://www.av8n.com/physics/uncertainty.htm#htoc20>
    * 5  “Correctness” versus Agreement
      <http://www.av8n.com/physics/uncertainty.htm#htoc21>
    * 6  Measurement Errors versus Modeling Errors
      <http://www.av8n.com/physics/uncertainty.htm#htoc22>
    * 7  Contributions to the Uncertainty -- and Related Notions
      <http://www.av8n.com/physics/uncertainty.htm#htoc23>
          o 7.1  Tolerance
            <http://www.av8n.com/physics/uncertainty.htm#htoc24>
          o 7.2  Significance
            <http://www.av8n.com/physics/uncertainty.htm#htoc25>
          o 7.3  Precision
            <http://www.av8n.com/physics/uncertainty.htm#htoc26>
          o 7.4  Accuracy
            <http://www.av8n.com/physics/uncertainty.htm#htoc27>
          o 7.5  Readability and Reproducibility
            <http://www.av8n.com/physics/uncertainty.htm#htoc28>
          o 7.6  Empirical Uncertainty
            <http://www.av8n.com/physics/uncertainty.htm#htoc29>
          o 7.7  Other Limits to the Notion of Uncertainty
            <http://www.av8n.com/physics/uncertainty.htm#htoc30>
    * 8  Significant Figures are an Abomination
      <http://www.av8n.com/physics/uncertainty.htm#htoc31>
          o 8.1  If You Mean Place Value, Say Place Value
            <http://www.av8n.com/physics/uncertainty.htm#htoc32>
          o 8.2  Uncertainty, Insignificance, and Guard Digits
            <http://www.av8n.com/physics/uncertainty.htm#htoc33>
          o 8.3  Rough -- Very Rough -- Uncertainties
            <http://www.av8n.com/physics/uncertainty.htm#htoc34>
          o 8.4  Sectarian Differences
            <http://www.av8n.com/physics/uncertainty.htm#htoc35>
          o 8.5  Some Answers Not Expressible Using Sig Digs
            <http://www.av8n.com/physics/uncertainty.htm#htoc36>
          o 8.6  Some Numbers are Exact
            <http://www.av8n.com/physics/uncertainty.htm#htoc37>
          o 8.7  Units Won’t Solve the Problem
            <http://www.av8n.com/physics/uncertainty.htm#htoc38>
          o 8.8  Relative versus Absolute Uncertainty
            <http://www.av8n.com/physics/uncertainty.htm#htoc39>
    * 9  Appendix: Mean, Standard Deviation, Gaussian, etc.
      <http://www.av8n.com/physics/uncertainty.htm#htoc40>
    * 10  References <http://www.av8n.com/physics/uncertainty.htm#htoc41>