Futures in the Math Class

Dr. Peter Bishop, Futures Studies, University of Houston

Futures in the Math Class

Dr. Peter Bishop

Futures Studies

University of Houston


The Study of the Future


Questions

What is the purpose of education? How many of us were specifically prepared for

a different (or changed) future? How many of us were specifically prepared to

influence (or change) the future? Should we specifically prepare (teach) students

to anticipate and/or influence the future? If so, are we doing it? If not, why not? ??

???? ????


Thinking about the Future

Foresight is a natural human ability -- the human

ability to create (or re-create) sensations and images

that are not immediately present

– Some of those lie in the past – memory

– Some lie in the present -- imagination

– Some lie in the future – foresight

– Some are fanciful – fiction

In lieu of formal training in foresight, we learn to

think about the future in three different ways from

three different sources, but not where you would

expect to.


Sociology and Social Change

Tables of contents from the 10 highest ranked sociology textbooks on Amazon.com– Average of 15 sections in each book (15 weeks in a

semester)

– Three did not have a chapter on social change

– Seven did…» 7% of the chapters

» 3% of the pages

No social change textbook in print for a years


The Scientific Future

Predictability, according to natural law, was one of the

most powerful cornerstones of the scientific revolution

-- Newton, Leibniz, Enlightenment So much so that it became the default assumption

about the future for physical science,

social science, and the professions Based on the belief of order,

causality, connectedness, and flow The future as a river, following

one path and leading to a specific point


The Contingent Future

We learn history as a series of events and actions usually with clear causal connections.

But, in last century, the contingencies and uncertainties inherent even in natural phenomena have become apparent – Stochastic processes -- Galton

– Quantum mechanics -- Bohr, Heisenberg

– Biological evolution -- Gould

– Chaos theory -- Lorenz

– Complexity science -- von Neuman, Wolfram, Kauffman

Based on the dominance of chance and uncertainty over determinism and predictability

The future as a dice game


The Chosen Future

The religious, economic and political traditions of Western society place primary responsibility for the future on individuals—on their intentions and their actions.

Examples –– Religion claims that we will be rewarded and

punished according to our actions; the law also holds individuals responsible for their actions.

– Individuals in a market economy must provide for themselves and their families.

– When something goes wrong, we look for someone to blame; when something goes well, we hand out awards.

Based on the dominance of human agency and free will over the forces of determinism and chance

The future as a blueprint


The Actual Future

Which one is correct? If we teach about the future, which one should we use?

Why not use all three as the best way to think about the future?– The Expected Future

» Where we are headed

» The future if everything continues as it has

» The result of conditions and trends (momentum)

– The Alternative Futures» What might happen instead

» The set of plausible futures if something less likely or unexpected happens

» The result of events and issues (contingencies)

– The Preferred Future(s)» What we want to happen

» Either the expected or any of the alternative futures that is preferable

» The result of our vision, goals, plans and actions (agency)


Foresight in the Classroom

Three simple questionsWhat is going to happen? – Expected future

What might happen instead? – Alternative futures

What do you want to happen? – Preferred future(s)

Limit o

f Plausib

ility

AlternativeFutures

Limit of Plausibility

Past

Expected

Present

VisionVision


Strategic Foresight


Strategic Foresight

Forecasting

Describing the future

With maps, vistas, landscapes

Planning

Influencing the future

With compasses, headings, navigation

Captain LeaderFirst Mate ManagerNavigator PlannerLookout Scanner


Foresight Techniques

Framing Purpose, scope Research Information, Scanning

Intelligence Forecasting Baseline, Scenarios Visioning Vision, Goals Planning Mission, Strategy Acting Initiatives,

ResultsThinking about the Future: Guidelines for Strategic Foresight, Andy Hines & Peter Bishop, 2007


Futures MethodsFutures Methods


Quantitative Futures Methods


Current ConditionsHow big?


How Big is What?

People Nature

Technology

Government

Economy

People Number, place, sex, age, ethnic

use technology Farming, energy, construction,manufacturing, transportation,information, military, biology

to transform resources Water, food, materials, energy

into economic goods Global, national, industrial, occupational, organizational

(and waste products) Air, water, solid, hazardous

under government International, financial,regulation social, infrastructure

in a cultural context Traditions, beliefs, valuesLanguageLanguage

BeliefsBeliefs ValuesValues

NormsNorms


Top 15 Most Important Quantitiesfor U.S. and World

Population – number Environment – amount of food produced, energy

produced/imported, carbon released, temperature increased

Technology – number of autos, phones, computers, Internet nodes

Economy – size of workforce, GDP Government – size of budget, proportion by

major category Culture – number of books, movies produced


But they are all big (or small) numbers

Orders of magnitude, powers of ten, zeros

(thousand, million, billion, etc.), prefixes

(micro, nano, pico, etc.)

Cosmic Voyage, positive only, Morgan

Freeman (4:51) – Copy 1, Copy 2

Power of 10, French translated to English,

both positive and negative (10:17) Population clocks


#1a – Cutting numbers down to size -- Best between .01 and 100

Ratios – similar units– Proportions, percents of same quantities

– Compare one time with another

– Compare one location with another or a part to whole – city, county, Michigan, US, North America, Western Hemisphere, World

Examples– Population – age, ethnic distribution

– Energy – source, use

– Economy – industry, occupation, income (median, mean, percentiles)

– Government – govt budget compared to GDP, employment compared to total

– Maps – World Mapper


U.S. Energy Flow, 2009

http://www.eia.gov/emeu/aer/pdf/pages/sec1_3.pdf


#1b – Cutting numbers down to size -- Best between .01 and 100

Rates – different units– Same quantities but per something else

– Rate of change (per unit of time) covered in the next section

Examples– Population – per capita, per household

– Environment – parts per million, per billion

– Technology – processor speed, number of devices per capita

– Economy – , per worker, per $ GDP

– Government – per Congressional district, per candidate


Benefits

Individual numbers are meaningless!– European population = 831 million

– CO2 emitted per year = 29.3 billion tons

– # transistors on a chip = 2 billion

– Size of Michigan economy = $382 billion

– # Federal employees = 2.1 million

Knowledge comes from comparisons– U.S. population = 331 million

– China emissions = 6.5 billion tons

– # neurons in human brain = 100 billion

– Size of Taiwan economy = $379 billion

– # transportation employees = 4.2 million

So what do you know now?

So what do you know now?

What can you conclude?

What can you conclude?

What can say that’s interesting?

What can say that’s interesting?


TrendsHow fast?

World Population in 2:45 minWorld Population in 2:45 min


Data Sources

The Statistical Abstract of the U.S.

The Statistical Abstract of the U.S.: Historical Statistics

U.S. Energy Information Agency

International Energy Agency

The Economic Report of the President

What’s your favorite?


U.S. Energy Overview

http://www.eia.gov/emeu/aer/pdf/pages/sec1.pdf


Total Energy Production

0

10

20

30

40

50

60

70

80

1949 1959 1969 1979 1989 1999 2009

Qu

ads

A picture is a worth a thousand numbers!

What do you see?


Impressions make a big difference

U.S. Government Receipts

$-

$0.5

$1.0

$1.5

$2.0

$2.5

1930 1940 1950 1960 1970 1980 1990 2000

Billion $

Federal Receipts

U.S. Government Receipts

$-

$0.5

$1.0

$1.5

$2.0

$2.5

1930 1940 1950 1960 1970 1980 1990 2000

Billion $

0%

5%

10%

15%

20%

25%

Federal ReceiptsAs % of GDP


Rates of Change

Continuous change• gradual improvement over long periods

• usually preserves the framework/context

Discontinuous change• sudden change to new levels

• usually destroys the framework/context

• always involves short-term loss


The Shapes of Incremental Change

Linear

CyclicAsymptotic

Exponential


S-Curve

The Real Shape of Change

1

No problem.

2

What is going on here?

3 Whew!

LogisticGompertzPearlFisher-Pry

LogisticGompertzPearlFisher-Pry


Eras in Information Technology


Other disruptions

Source:http://www.bsos.umd.edu/socy/vanneman/socy441/trends/divorce.jpg


Speed

Transportation Eras

Running

Riding

Motoring

Flying

Inherent capacity

for perfo

rmance

Law of dim

inishing

returns


Measurements of Change

Absolute = X2 – X1Absolute = X2 – X1

Numerator of x2

Numerator of difference

Base of x1

Ratio change x2 / x1

Proportional change (x2 - x1 ) / x1

Base of 100Index numbers

x2 / x1 * 100

Percent change (x2 - x1 ) / x1 * 100


U.S. Energy Production, 1949-2009

Absolute = 41.2 QuadsAbsolute = 41.2 Quads

Numerator of x2


Base of x1

Ratio change 2.30

Proportional change 1.30


230Percent change

130%




Numerator of x2


Base of x1Ratio change Proportional change

Base of 100 Index numbers Percent change

111%




Numerator of x2


Base of x1

Ratio change 2.11

Proportional change 1.11


211Percent change

111%


Measures per Unit of Time

1949 - 2009

1949 -1970

1970 -2009

Average change per unit (year)

(x2 - x1 ) / # yrsabsolute change / # yrs 68.7 Q 1.5 Q 0.2 Q

Annual average growth rate (AAGR)

(x2 - x1 ) / x1 * 100) / # yrs percent change / # yrs 2.2% 5.3% 0.8%

Compound average growth rate (CAGR)

(x2 / x1) ^ (1 / # yrs) – 1

[ Solving x2 = x1 * ( 1 + r ) ^ # yrs for r ]

1.4% 3.6% 0.7%


ForecastsHow far?


Assumptions in Trend Extrapolation

Business School Enrollment, UH-Clear LakeDeseasonalized

80

85

90

95

100

105

110

115

120

80-1 81-1 82-1 83-1 84-1 85-1 86-1 87-1 88-1 89-1 90-1 91-1 92-1 93-1 94-1 95-1 96-1 97-1 98-1 99-1 00-1 01-1 02-1 03-1 04-1


Forecast to 2040

1949 - 2009 1970 -2009

Annual absolute change (AAC)

X3 = X2 + AAC * 30 93.6 Q 80.3 Q

Annual average growth rate (AAGR) X3 = x2 * ( 1 + AAGR * 30 ) 120.4 Q 91.5 Q

Compound average growth rate (CAGR)

X3 = x2 * ( 1 + CAGR) ^ 30 110.7 Q 90.8 Q


Three Different Measures

Growth Rate Comparison

-

50

100

150

200

250

2009 2019 2029 2039

Qu

ads

AAC

AAGR

CAGR


Forecasting from 1970


0

20

40

60

80

100

120

1949 1959 1969 1979 1989 1999 2009

Qu

ads


Still a Choice from 2009


0

10

20

30

40

50

60

70

80

90

1949 1959 1969 1979 1989 1999 2009

Qu

ads

Time series

1970-2009

1949-2009


Limit

of P

lausib

ility

AlternativeFutures

Limit of Plausibility

The Cone of Plausibility

Past

The Future is many,not one.

The Future is many,not one.

Source: Charles Taylor, Army War College

Implications

Baseline

Present


Take Aways

Things vary in size more than they appear to. It’s easy to underestimate orders of magnitude.

Graphs are better than tables for seeing patterns over time. And longer series show more patterns.

Impressions matter as much as actual numbers do, perhaps even more; different formulations give different impressions

Teach estimations on the fly. Close can be better than exact under the right circumstances.

Always compare! Single numbers are meaningless. Compare across similar objects (one country vs another), with larger

or smaller sets (proportion of the whole), or across time (difference or time series)

Make inferences based on the comparisons. What do you know that you didn’t know before? What is interesting, troubling, unbelievable?

All extrapolations are based on models, and all models have assumptions. Different assumptions give different result.


So What?


Foresight by Discipline

Mathematics – time series, extrapolation, probability, preference ranking, criteria weighting

History – flow, change over time, time series, patterns, uncertainties, contingencies, alternative histories, historical images of the future, historical analogy

Literature, language –future tense, subjunctive mood, science fiction, three questions for fictional conditions and characters

Physical science – time series, extrapolation, technological applications, social consequences, public issues

Social science – social change, time series, cultural concepts of time, national and global awareness


Benefits – the bottom line

The expected future– Causal reasoning – Mathematical extrapolation– Critical thinking, identifying assumptions– Implications analysis– Evaluation

The alternative futures– Challenging assumptions– Creativity, imagination– Causal reasoning from different premises– Estimation of plausibility– Implication analysis, evaluation

The preferred future– Values clarification– Preference ranking, criteria weighting– Communication, persuasion– Planning, organizing


The Language of Plausibility

Indicative

Will

Must

Should

Subjunctive

May

Might

Could

Past Present Future


Rules for Talking about the Future

1. The future is uncertain Admit uncertainty

2. The future is plural Talk possibilities

3. Different assumptions create Uncover and discuss different futures assumptions

4. The future is being created--

-- outside in the environment Tell stories

--- inside people’s aspirations Encourage visions


The Futures Education Project

Mission: help teachers include (more) material about the future in their existing courses and to offer (more) stand-alone courses in secondary schools, colleges and professional programs around the world

Target populations– Experienced futures educators – support and enhance their teaching– Aspiring futures educators – get them started on teaching about the future

Sponsored (at least initially) by the Futures Studies program at the University of Houston in collaboration with:– Learning Section, World Futures Society– Online Centre for Pedagogical Resarch, World Futures Studies Federation– Institute for the Future, Ann Arundel Community College– Futures Education and Research Network– Texas Future Problem Solving Program– Proteus, U.S Army War College– And the many universities and educators who already teach about the future

We teach as much about the future as we teach about the past!

We teach as much about the future as we teach about the past!


Appendix

1949-2009 1949-1970 1970-2009Absolute change 41.2 31.8 9.5

Percent change 130% 111% 33%

Ratio change 2.30 2.11 1.33

Years 60 21 39

AAC 0.69 1.5 0.2

AAGR 2.2% 5.3% 0.8%

CAGR 1.4% 3.6% 0.7%

Forecast to 2040

AAC 93.6 118.4 80.3

AAGR 120.4 188.2 91.5

CAGR 110.7 211.4 90.8

Futures in the Math Class

Education

future foresight

expected future

chosen future

actual future

contingent future

quantitative futures

foresight techniques

set of plausible futures