Creative Modeling for
Technology Visionaries
Qualitative & Simplified Quantitative Modeling for Product Creation
Module 11: Little Models
David E. Goldberg
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
deg@uiuc.edu

Want Little Quantitative Models
Going quantitative, need to walk
before run.
Existing categories often have many
analyses & models.
New categories often have little
understanding.
Build quantitative understanding as
needed.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 2

This Module
The approach of little models.
Dimensional analysis.
Lift coefficients & innovation numbers revisited.
Turning points.
Little models and data.
Organizational example: deciding-doing model.
Little models from elementary optimization.
Will Rogers theory of models.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 3

What is a “Model?”
Low Cost/ High Cost/
High Error Low Error
Unarticulated Articulated Dimensional Facetwise Equations
Wisdom Qualitative Models Models of Motion
Model
The Modeling Spectrum
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Little Models Defined
Our interest is in models that are
Principled
Quantitative
Not equations of motion
Call them little models, where “little” is a
term of approbation.
Little models simplified, not universal.
Where do little models come from?
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 5

Sources of Little Models
Dimensional analysis (more in moment)
Construction of model for single facet.
Reduction of equation of motion for one
or small number of facets.
Incorporation of qualitative reasoning.
Extremum principle.
Data usage (data-influenced), but
empirical fit alone not enough.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 6

Aside on Dimensional Analysis
Common in physics and engineering, but not CS.
Buckingham PI theorem: n dimensional parameters, m
dimensions  n – m independent dimensionless
parameters.
[V ] = L/T, [D ] = L, [ν ] = L2/T
n = 3, m = 2, n – m = 1
R = VD/ν, the Reynolds number
One difference: many CS parameters are pure
numbers. Must derive time, spatial, or other scale, then
renormalize.
Can play the same game for GAs, AI, & AL.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 7

Lift Coefficient Revisited
λ
CL =
ρV A
2
2
Ratio of two forces.
Lift to inertial force.
Angle of attack is
dimensionless.
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The Race Deconstructed
Have two facetwise models, but want
integrated understanding.
Putting models in t terms gives us an
idea.
Consider relative magnitudes of the two
times: a dimensional argument.
Consider which is favorable to innovation:
a qualitative argument.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 9

Schematic of the Race
Schem atic of "The Race"
t*
ti
1
0.8
Market Share
0.6
0.4
0.2
0
0 5 10 15 20 25
Generations
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Consider Ratio of Two Times
Define innovation number G = t*/ti
G = pc pi n lnn/ lns.
Want takeover time greater than
innovation time or G > 1.
Quantity like Reynolds number in fluids.
Argument was a dimensional argument.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 11

Another View: Turning Point
t* = ln n/ ln s
ti = (pc pi n)-1
Consider intersection of the two
curves as function of s.
Sketch.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 12

Standing Back
Key element was the juxtaposition of two
functional dimensions.
Lift coefficients: Lift vs. inertial forces.
Race: selection vs. innovation.
Simplified style of model works pair by
pair.
m 
Theoretically, m functional dimensions   
2
pairings
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3 Roles of Data for LMs
 Verify model & determine range of
applicability (LMs not valid throughout
domain).
 Determine parameters.
 Derive model (functional curve fit on
dimensionless parameters).
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Interaction of Little Models & Data
Relationship of data and LMs 2-way
street.
Little models can give idea of what data
to collect.
Dimensional analysis and LMs suggest
appropriate or better visualization.
Not purely empirical.
Not purely theoretical.
Back and forth.
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Another Domain: Organizations
Much organizational theory is qualitative and
remains qualitative.
Computational organizational theory dominated
by busy complexity of detailed simulations.
Would like simplified theories.
Analogy: Current situation in orgs would be like
doing finite elements or elasticity in structures
before understanding beam bending.
δ = PL3/3EI
Small number of terms, relevant variables,
qualitatively and quantitatively relevant
predictions.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 16

Simon’s Administrative Behavior
Primary dichotomy is
between deciding and
doing.
Can we use this dichotomy
as first focal point for entry
into organizations?
Need to assume topology
of decision and doing and
make up little models.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 17

How Do Teams Decide?
Have a discussion amongst n
participants.
Present to the boss, take a vote, come to
consensus.
Details important, perhaps, but let’s start
by assuming that time to decision goes
up as size of the team n.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 18

How Do Teams Do?
n participants divide the workload
amongst themselves somehow.
Perhaps one workhorse does and others
stand around.
Perhaps they all work well and divide
work equally.
Perhaps there is some slacking, or
perhaps there is some synergy.
Start by assuming time going down
inversely with n.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 19

Deciding and Doing Model
Team size: n
Discussing what is to be done: T1
Total time to do the task alone: T2
Total time required for task completion:
Model integration via summation.
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Do the Math
Take derivative of T(n) with respect to n.
Set to zero.
Do it.
Efficient team size
Optimal time:
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A Specific Case
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Dimensionless Form
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Dimensional Analysis Tames Viz
Note how form simplifies under
dimensional analysis.
All cases collapse to a single curve.
Don’t need infinite family of curves.
Log transform asymptotically gives
straight lines up and down.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 24

Speedup
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Consider Turning Point Derivation
Tdecide = T1n
Tdo = T2/n
Set equal to each other.
T1n* = T2/n*
Same as before:
Not generally the case, but not bad
approximation.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 26

Elementary Optimization Problem
EOPs involve a function of one variable,
sum of increasing & decreasing function:
Multiplicative form:
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Double Power-law Model
Double power-law particularly useful.
Arises in cases with  n 
 
topology.
 
k
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 28

Lessons of LMing
Facetwise approach is fast.
Requires some skill in identifying correct facets
and in integrating them.
Payoff in understanding is out of proportion to
complexity of the effort.
Do not waste time on needless parametric
study.
Verify expected behavior and move on.
Facetwise understanding improves pedagogy
and ability to explain things simply.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 29

Will Rogers Theory of Modeling
I never met a model I didn’t
like.
Need to relax notion of
“theory” to achieve
objectives.
Theory is not the end goal.
Theory is a means to better
products, better
organizations, better
processes..
Want principled approach,
but rigor can safely be Will Rogers (1879-1935)
relaxed.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 30

Bottom Line
Deconstruct the race.
Consider dimensional analysis and turning
point approaches to derivation. The approach
of little models.
Lift coefficients & innovation numbers
revisited.
Little models and data.
Organizational example: deciding-doing
model.
Little models from elementary optimization.
Little models give great insight for the effort.
Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 31