This document discusses concepts from physics, chemistry, economics, and statistics as they relate to inertia and disruptive change. It covers topics like Lorentz force, Le Chatelier's principle, Samuelson's Correspondence Principle, the universe of clocks, statistical implications of change, and Benford's law. The overall theme appears to be examining how systems resist change through the lens of different disciplines and considering when resistance may be artificial.

1. Empirical Observations Inertia Disruptive World of Clouds
§ 1.4 Inertial Frame of Reference
Salon: Cloud vis-`a-vis Clock
Preston S. Fan
School of Management, New York Institute of Technology
April, 2014
Preston S. Fan § 1.4 Inertial Frame of Reference

2. Empirical Observations Inertia Disruptive World of Clouds
Table of Contents
1 Empirical Observations
Lorentz Force
Le Chˆatelier’s principle
Samuelson’s Correspondence Principle
2 Inertia
The Universe of Clocks
3 Disruptive World of Clouds
Statistical Implication
Preston S. Fan § 1.4 Inertial Frame of Reference

3. Empirical Observations Inertia Disruptive World of Clouds
Lorentz Force
Observed in electromagnetism, Lorentz force acts as a
resistance to any wire loop moving through a magnetic field.
Crucial difference:
Ampere force does work on moving charges, but Lorentz
force never does work.
Preston S. Fan § 1.4 Inertial Frame of Reference

4. Empirical Observations Inertia Disruptive World of Clouds
Lorentz Force
Much ado with nothing,
but its result is similar to optimal control in economic science.
F = q − φ −
∂A
∂t
+ (v · A) − (v · ) A
which can take the convenient Euler’s equation:
F = q − X (φ − x · A) +
d
dt ˙X
(φ − x · A)
as a necessary F.O.C. to economic optimization problem.
Preston S. Fan § 1.4 Inertial Frame of Reference

5. Empirical Observations Inertia Disruptive World of Clouds
Le Chˆatelier’s principle
Le Chˆatelier’s principle could be be used to predict the
effect of a change in conditions on a chemical equilibrium
qualitatively.
Under certain conditions, a balanced system struggles to
keep the initial balance (equilibrium).
The (discrete) movement of equilibrium is predictable.
Preston S. Fan § 1.4 Inertial Frame of Reference

6. Empirical Observations Inertia Disruptive World of Clouds
Le Chˆatelier’s principle
Comparative static version of pV = nRT
”Any change in status quo prompts an opposing reaction in
the responding system.”
ex: buffer solution (such as the blood), buffer pairs such as
H2CO3 − NaHCO3, NaH2PO4 − Na2HPO4;
H2CO3 − KHCO3, KH2PO4 − K2HPO4
Preston S. Fan § 1.4 Inertial Frame of Reference

7. Empirical Observations Inertia Disruptive World of Clouds
Samuelson’s Correspondence Principle
Samuelson’s Correspondence Principle secures asymptotic
stability of an economic system, which has been a foundation of
comparative statics in general equilibrium analysis.
General Correspondence Principle
(Locally) Any Robustly Stable equilibrium exhibits the
Robust Law of Demand.
(Globally) If a system is globally Robustly Stable then it
has at most one equilibrium point and this is Robustly
Stable.
Preston S. Fan § 1.4 Inertial Frame of Reference

8. Empirical Observations Inertia Disruptive World of Clouds
The Universe of Clocks
Inertia
Resistance to new changes
Adaptive (disruptive?)
Preston S. Fan § 1.4 Inertial Frame of Reference

9. Empirical Observations Inertia Disruptive World of Clouds
The Universe of Clocks
Discussion on organizational changes or dynamics
The universe of clouds
Every clock becomes the cloud
Unpredictable: the loss of security
Unpredictable in direction
Unpredictable in speed
Preston S. Fan § 1.4 Inertial Frame of Reference

10. Empirical Observations Inertia Disruptive World of Clouds
Statistical Implication
In Frequentist statistics, we face a trade-off between Power
and Type I error.
Questions:
Is it for safe to be conservative against the changes?
Resistance to new change is artificial?
Preston S. Fan § 1.4 Inertial Frame of Reference

11. Empirical Observations Inertia Disruptive World of Clouds
Statistical Implication
A trial:
Open any Form-10 of any firm, extract the numbers from
its B/S or P/L in Excel.
Compare among these numbers:



= sumproduct(− − (left(”your dataset”, 1) = ”1”))
= sumproduct(− − (left(”your dataset”, 1) = ”2”))
...
= sumproduct(− − (left(”your dataset”, 1) = ”9”))
What do you discover?
Preston S. Fan § 1.4 Inertial Frame of Reference

12. Empirical Observations Inertia Disruptive World of Clouds
Statistical Implication
Newcomb (1881) noted the probability of a single number
N being the first digit of a number was equal to
log10(N + 1) − log10(N), rediscovered by Benford (1938).
Questions:
Resistance to new change is a behavioral pattern of the
data per se?
Herding effects?
Preston S. Fan § 1.4 Inertial Frame of Reference

13. Relevant Readings
John Stachurski
Economic Dynamics: Theory and Computation
MIT Press. 2009.
Gandolfo, Giancarlo
Economic Dynamics
Springer-Verlag Berlin Heidelberg. 2009.
Preston S. Fan § 1.4 Inertial Frame of Reference