Stamp printed in USA to commemorate the Boston Tea Party as part of the Bicentennial celebration in the United States, circa 1976. Image by neftali/Shutterstock
30 July 2020 – Over the last few days, I’ve engaged in a social-media exchange about events in Portland, OR involving protest demonstrations there, and camo-clad so-called “Federal agents.” So, it seems timely to point out why we have a First Amendment to our Constitution, and remind readers that the American Revolution started with a protest demonstration—the Boston Tea Party. Lest we forget, the Portland demonstrations were organized (if that word applies) by the Black Lives Matter movement to protest police brutality, especially the alleged murder of George Floyd by Minneapolis, MN police officer Derek Chauvin.
The social-media exchange I mentioned above devolved into a dispute about where protest demonstrations fit into the workings of a democracy. My position, which I get to explain in this essay because I pay for this space in the World Wide Web to post whatever I darn well please, is that protest demonstrations are a necessary part of a properly functioning democratic society. My opponent (who will remain unnamed, as will the social-media platform that carried the exchange) took the position that such demonstrations were not. Effective or not, he (There, I’ve narrowed his identity down to 49.1% of the U.S. population!) claimed that protest demonstrations were not part of the formal functioning of government, and were, thus, illegitimate. In rebuttal, I pointed him to the First Amendment, which guarantees “the right of the people peaceably to assemble, and to petition the Government for a redress of grievances,” and to the history of the Boston Tea Party that effectively began the American Revolution.
In this essay, I’m not going to recite the history of the Boston Tea Party, which you can read for yourself by following the link above. It’s a pretty good account that agrees with the mass of American History texts I’ve read over the years. (It’s important to point that out these days, as an example of how we verify that something is not fake news.) Instead, I hope to point out parallels between Boston Tea Party events and public protest demonstrations in the 21st century.
The Revolutionary War in America is generally acknowledged to have started with what Ralph Waldo Emerson called “Shot Heard Round The World,” in Lexington, MA in 1775. The actual American Revolution, as an historical movement, began years earlier, however. A protest organization named “The Sons of Liberty,” which had by then been active for over a decade, was responsible for mounting a force of 100 protesters, who boarded the ships Dartmouth, Beaver, and Eleanor docked at Griffin’s Wharf in Boston, MA disguised as Native Americans. The Sons of Liberty, of course, are an exact parallel to today’s Black Lives Matter movement.
Once aboard the ships, the protesters dumped the ships’ cargoes of tea, belonging to the East India Trading Company and valued at $1 million today, into Boston Harbor. After dumping the tea, the protesters cleaned up the decks of the American-owned ships! This represents, of course, an ideal example of how a peaceful protest as envisioned by the First Amendment should be carried out
Protests this Summer in the streets of Portland, Minneapolis, and other cities have been far larger, involving hundreds of thousands of protesters. They have also sometimes devolved into violence. However, it should be noted that the 2020 demonstrations were in response to government actions (i.e., police brutality) that ended with loss of life, rather than just a tax on tea. It is reasonable to expect folks to get a bit more worked up after suffering homicidal attacks perpetrated by government agents (which policemen are)!
That said, the modern protest demonstrations have been predominantly peaceful. Most violence has occurred in situations where demonstrators have been met with armed resistance. The same thing happened in the American Revolution. Five years before the Boston Tea Party, British soldiers shot at demonstrators protesting the presence of armed troops in city streets, injuring six protesters and killing five. Called “The Boston Massacre, the moral of that story is that the surest way to make a demonstration turn violent is to send in armed troops.
To summarize my position on protest demonstrations’ place in a democracy, when government in a democratic society fails to function properly for any reason, the people have the duty to take to the streets in protest. It is every bit as important as having a free press, which is generally acknowledged as a requirement for proper functioning of a democracy. Far from being some kind of extra-legal activity, both are specifically written into the U.S. Constitution by the First Amendment. You can’t get more legal than that!
The government-funded project to develop Polaris, the first submarine-launched ICBM, transformed the way projects – and indeed most 21st-century businesses – are run. Image by Alexyz3d/Shutterstock
9 February 2020 – I’m about half way through a course on global economics at Keiser University, and one of this week’s assigned readings is a 2012 article by Argentine-American legal scholar Fernando R. Tesón discussing his views on the ethical basis of free trade. I was particularly struck by the wording of his conclusion section:
More often, trade barriers allow governments to transfer resources in favor of rent-seekers and other political parasites. … Developed countries deserve scorn for not opening their markets to products made by the world’s poor by protecting their inefficient industries, while ruling elites in developing nations deserve scorn for allowing bad institutions, including misguided protectionism. (p. 126)
This was unusually blunt in a scholarly article! Tesón, however, did a good job of making his case. Citing David Ricardo’s and Hecksher-Olin’s theories of comparative-advantage, He provided a well-thought-out, if impassioned, argument that trade barriers are misguided at best, and at worst unconscionable. Among the practices he heaped scorn upon are “tariffs, import licenses, export licenses, import quotas, subsidies [emphasis added], government procurement rules, sanitary rules, voluntary export restraints, local content requirements, national security requirements, and embargoes” (Tesón, 2012, p. 126).
Generally, that was a defensible list. All of those practices tend to slew market-based purchase decisions toward goods produced by firms lacking true competitive advantage. The case against subsidies, however, is not so simple. There are various reasons for creating subsidies and ways of applying them. Not all are counterproductive from an economic-development standpoint.
Stephen Redding, in a 1999 article entitled “Dynamic comparative advantage and the welfare effects of trade” pointed out that comparative advantage is actually a dynamic thing. That is, it varies with time, and producers can, through appropriate investments, artificially create comparative advantages that are every bit as real as the comparative-advantage endowments that the earlier theorists described.
The original Ricardian model envisioned countries endowed with innate comparative advantages for producing some good(s) relative to producing the same good(s) in another country (Kang, 2018). Redding pointed out that a country’s productivity for manufacturing some good increases with time (experience) spent producing it. He posited that if the country’s competitors’ comparative advantage for producing that good is not great, it may be possible for the country to, through investing in or subsidizing development of an improved production process, overtake its competitors. In this way, Redding asserted, the relative competitive advantage/disadvantage situation may be reversed.
The counterargument to subsidizing such a project is that the subsidy has an opportunity cost in that the subsidy uses funds exacted from the country’s taxpayers to benefit one or more selected firms. Tesón’s position is that this would be an inappropriate use of taxpayer funds to benefit only a small subset of the country’s citizens. This is ipso facto unfair, hence his stigmatizing such a decision. The reductio ad absurdum rejoinder to this argument is that it leaves government powerless to effect economic development.
In a democracy, government decisions are assumed to have tacit acceptance by the whole population. Thus, an action by the government to support a small group developing a comparative advantage through a subsidy must be assumed to have a positive externality for the whole population.
If the government is an autocracy or oligarchy, there is no legitimate claim to fairness for any of its decisions, anyway, so the unfairness argument is moot.
There are thus conditions under which subsidizing firms or industries to develop enhanced productive capacity for some good make economic sense. Those conditions are as follows:
Competitors’ comparative advantage is small enough that it can be overcome with a reasonable subsidy over a reasonable length of time;
There is reason to expect the country will be able to maintain its improved comparative advantage situation after subsidies have been removed;
Achieving a comparative advantage for production of that good will have ripple effects that will generate comparative advantage throughout the economy.
If and only if all of these conditions obtain is it reasonable to create a temporary subsidy.
An example of an inappropriate subsidy is that by the European Union for Airbus, which began with the company’s launch in 1970 to create an EU-based large civil aircraft (LCA) industry to compete with the U.S.-based Boeing Aircraft Company and continues today (European Commission, 6 October 2004). While this history indicates that item 1 on the list above was fulfilled (Airbus became an effective competitor for Boeing in the 1980s), and item 3 certainly was fulfilled, the fact that the subsidies continue today, half a century later, indicates that item 2 was not fulfilled.
On the other hand, the myriad salutary effects that came out of the Polaris missile program of the mid-20th Century shows that all three conditions were valid for that government-subsidized project (Engwall, 2012).
References
Engwall, M. (2012). PERT, Polaris, and the Realities of Project Execution. International Journal of Managing Projects in Business,.5(4), 595-616.
European Commission. (6 October 2004). EU – US Agreement on Large Civil Aircraft 1992: key facts and figures. (MEMO/04/232). Retrieved from https://ec.europa.eu/commission/presscorner/detail/en/MEMO_04_232
Kang, M. (2018). Comparative advantage and strategic specialization. Review of International Economics, 26(1), 1–19.
Redding, S. (1999). Dynamic comparative advantage and the welfare effects of trade. Oxford Economic Papers, 51, 15-39.
Tesón, F.,R. (2012). Why free trade is required by justice. Social Philosophy & Policy, 29(1), 126-153.
Motivational theorists are figuring out how to use applied math to quantify motivation. Image by JK Jeffrey/Shutterstock
18 September 2019 – The following essay is taken verbatim from a posting I made to the discussion forum for a class in my Doctor of Business Administration program at Keiser University.
For those who were disappointed by my not posting to this blog last week, I apologize. Doctoral programs are very intensive and I’ve found myself overloaded with work. I’ve had to prioritize, and regular postings to this blog are one of the things I’ve had to cut back. When something crosses my desk that I think readers of this blog might find particularly interesting, I’ll try to take time to post it here and let folks know about it through my Linkedin and Facebook accounts.
In the essay below I suggest an extension to a method for understanding human motivation using applied mathematics techniques. What, you didn’t think that was possible? Read on!
Almost at random, I happened to pick up Chung’s (1969) paper from this week’s reading list first. Since it discussed an approach to questions of motivation that I find particularly interesting, I was inspired to jump in and discuss my reaction to it immediately.
The approach Chung took was to use applied mathematics (AM) techniques for analyzing motivation. Anyone not steeped in AM methods could be excused for being surprised that the field could have anything to say about motivation. On the surface, motivation might seem completely qualitative, so how could mathematical techniques be at all useful for analyzing it?
In fact, quantification of anything that you can rank is possible. For example, Zheng & Jiang, (2017) discussed methods of quantifying species diversity in ecosystems. The fact that you can say this ecosystem is more diverse than that ecosystem means that ecosystem diversity is quantifiable.
Similarly, the fact that you can say that such-and-such a person is more motivated to do something than some other person indicates that motivation is quantifiable as well. Before proposing his Markov-chain model, Chung (1969) discussed five other analytical methods for studying motivation based on Maslow’s hierarchy, all of which descriptions he started by describing some method of quantifying motivation.
It happens that I am quite familiar with the mathematics Chung (1969) used. It is called linear algebra, and is a staple technique for analyzing theoretical physics problems. I started my career as an astrophysicist, so Chung’s paper is right in my intellectual wheelhouse. Reading it stimulated me to think: “Yeah, but what about …?”
What Chung’s analysis left out was how human motivation is subject to chaotic exogenous forces. I’ve more than once used the following thought experiment to illustrate this phenomenon. Imagine Albert Einstein scratching away at General Relativity Theory on the blackboard in his office. I mention Einstein particularly because he was known to be fond of thought experiments, so including him in this one seems appropriate. So, Einstein is totally absorbed in his work puzzling out GRT. Maslow would say that he is motivated at the “self-actualization” level. Suddenly, our hero realizes that it’s lunch time because his body signals a physiological need for a ham sandwich. An exogenous event (lunchtime) has modified Einstein’s needs state.
In Chung’s (1969) analysis, Einstein’s transition matrix P has suddenly switched from having element values that cause Einstein’s needs vector N to remain stable at Maslow’s level five to values that cause his needs to switch to level one at the next transition. At that point, Einstein puts down his chalk and roots around in his briefcase for the ham sandwich he knows his wife put in there this morning.
So, how would we handle this situation from a linear algebra standpoint? Using Chung’s (1969) notation, the transition from the ith state to the (i+1)th state is given by Equation 1:
Ni+1 = Ni P (1)
I’ve modified the notation slightly by writing vectors in regular italic typeface and matrices in bold italic typeface. That satisfies my need to have vectors and matrices sybolized in different typefaces. It’s a stability thing for me, so it’s down at Maslow’s level two (Chung, 1969) in my personal hierarchy of needs.
What we need now is to modify the transition matrix by applying another matrix that isolates the effect of the exogenous event. If we add a subscript 0 to specify the original transition matrix, and multiply it by a new matrix X that accounts specifically for the exogenous event, we get a new transition matrix given by Equation 2:
P = P0 X (2)
Finally, Equation 1 becomes Equation 3.
Ni+1 = Ni P0 X (3)
What is left to do is to develop methods of determining numerical values for the elements of these vectors and matrices in specific situations. This addition shows how to extend Chung’s (1969) Markov-chain model to situations where life events modify an individual’s motivational outlook. Such events can be anything from time reaching the lunch hour to the individual becoming a parent.
References
Chung, K. H. (1969). A Markov Chain Model of Human Needs: An Extension of Maslow’s Need Theory. Academy of Management Journal, 12(2), 223–234.
Zheng, L. & Jiang, J. (2017) A New Diversity Estimator. Journal of Statistical Distributions and Applications, 4(1), 1-13.
External information about team attributes, group dynamics and organizational goals ultimately determine project success.
4 September 2019 – I’m in the early stages of a long-term research project for my Doctor of Business Administration (DBA) degree. Hopefully, this research will provide me with a dissertation project, but I don’t have to decide that for about a year. And, in the chaotic Universe in which we live a lot can, and will, happen in a year.
I might even learn something!
And, after learning something, I might end up changing the direction of my research. Then again, I might not. To again (as I did last week ) quote Winnie the Pooh: “You never can tell with bees!”
No, this is not an appropriate forum for publishing academic research results. For that we need peer-reviewed scholarly journals. There are lots of them out there, and I plan on using them. Actually, if I’m gonna get the degree, I’m gonna have to use them!
This is, however, an appropriate forum for summarizing some of my research results for a wider audience, who might just have some passing interest in them. The questions I’m asking affect a whole lot of people. In fact, I dare say that they affect almost everyone. They certainly can affect everyone’s thinking as they approach teamwork at home and at work, as well as how they consider political candidates asking for their votes.
For example, a little over a year from now, you’re going to have the opportunity to vote for who you want running the United States Government’s Executive Branch as well as a few of the people you’ll hire (or re-hire) to run the Legislative Branch. Altogether, those guys form a fairly important decision-making team. A lot of folks have voiced disapprobation with how the people we’ve hired in the past have been doing those jobs. My research has implications for what questions you ask of the bozos who are going to be asking for your votes in the 2020 elections.
One of the likely candidates for President has shown in words and deeds over the past two years (actually over the past few decades, if you care to look that far into his past) that he likes to make decisions all by his lonesome. In other words, he likes to have a decision team numbering exactly one member: himself.
Those who have paid attention to this column (specifically the posting of 17 July) can easily compute the diversity score for a team like that. It’s exactly zero.
When looking at candidates for the Legislative Branch, you’ll likely encounter candidates who’re excessively proud to promise that they’ll consult that Presidential candidate’s whims regarding anything, and support whatever he tells them he wants. Folks who paid attention to that 17 July posting will recognize that attitude as one of the toxic group-dynamics phenomena that destroy a decision team’s diversity score. If we elect too many of them to Congress and we vote Bozo #1 back into the Presidency, we’ll end up with another four years of the effective diversity of the U.S. Government decision team being close to or exactly equal to zero.
Preliminary results from my research – looking at results published by other folks asking what diversity or lack thereof does to the results of projects they make decisions for – indicates that decision teams with zero effective diversity are dumber than a box of rocks. Nobody’s done the research needed to make that statement look anything like Universal Truth, but several researchers have looked at outcomes of a lot of projects. They’ve all found that more diverse teams do better.
Anyway, what this research project is all about is studying the effect of team-member diversity on decision-team success. For that to make sense, it’s important to define two things: diversity and success. Even more important is to make them measurable.
I’ve already posted about how to make both diversity and success measurable. On 17 July I posted a summary of how to quantify diversity. On 7 August I posted a summary of my research (so far) into quantifying project success as well. This week I’m posting a summary of how I plan to put it all together and finally get some answers about how diversity really affects project-development teams.
Methodology
What I’m hoping to do with this research is to validate three hypotheses. The main hypothesis is that diversity (as measured by the Gini-Simpson index outlined in the 17 July posting) correlates positively with project success (as measured by the critical success index outlined in the 7 August posting). A secondary hypothesis is that four toxic group-dynamic phenomena reduce a team’s ability to maximize project success. A third hypothesis is that there are additional unknown or unknowable factors that affect project success. The ultimate goal of this research is to estimate the relative importance of these factors as determinants of project success.
Understanding the methodology I plan to use begins with a description of the information flows within an archetypal development project. I then plan on conducting an online survey to gather data on real world projects in order to test the hypothesis that it is possible to determine a mathematical function that describes the relationship between diversity and project success, and to elucidate the shape of such a function if it exists. Finally, the data can help gauge the importance of group dynamics to team-decision quality.
The figure above schematically shows the information flows through a development project. External factors determine project attributes. Personal attributes, such as race, gender, and age combine with professional attributes, such as technical discipline (e.g., electronics or mechanical engineering) and work experience to determine raw team diversity. Those attributes combine with group dynamics to produce an effective team diversity. Effective diversity affects both project planning and project execution. Additional inputs from stakeholder goals and goals of the sponsoring enterprise also affect the project plans. Those plans, executed by the team, determine the results of project execution.
The proposed research will gather empirical data through an online survey of experienced project managers. Following the example of researchers van Riel, Semeijn, Hammedi, & Henseler (2011), I plan to invite members of the Project Management Institute (PMI) to complete an online survey form. Participants will be asked to provide information about two projects that they have been involved with in the past – one they consider to be successful and one that they consider less successful. This is to ensure that data collected includes a range of project outcomes.
There will be four parts to the survey. The first part will ask about the respondent and the organization sponsoring the project. The second will ask about the project team and especially probe the various dimensions of team diversity. The third will ask about goals expressed for the project both by stakeholders and the organization, and how well those goals were met. Finally, respondents will provide information about group dynamics that played out during project team meetings. Questions will be asked in a form similar to that used by van Riel, Semeijn, Hammedi, & Henseler (2011): Respondents will rate their agreement with statements on a five- or seven-step Likert scale.
The portions of the survey that will be of most importance will be the second and third parts. Those will provide data that can be aggregated into diversity and success indices. While privacy concerns will make masking identities of individuals, companies and projects important, it will be critical to preserve links between individual projects and data describing those project results.
This will allow creating a two-dimensional scatter plot with indices of team diversity and project success as independent and dependent variables respectively. Regression analysis of the scatter plot will reveal to what extent the data bear out the hypothesis that team diversity positively correlates with project success. Assuming this hypothesis is correct, analysis of deviations from the regression curve (n-way ANOVA) will reveal the importance of different group dynamics effects in reducing the quality of team decision making. Finally, I’ll need to do a residual analysis to gauge the importance of unknown factors and stochastic noise in the data.
Altogether this research will validate the three hypotheses listed above. It will also provide a standard methodology for researchers who wish to replicate the work in order to verify or extend it. Of course, validating the link between team diversity and decision-making success has broad implications for designing organizations for best performance in all arenas of human endeavor.
References
de Rond, M., & Miller, A. N. (2005). Publish or perish: Bane or boon of academic life? Journal of Management Inquiry, 14(4), 321-329.
van Riel, A., Semeijn, J., Hammedi, W., & Henseler, J. (2011). Technology-based service proposal screening and decision-making effectiveness. Management Decision, 49(5), 762-783.
What counts as success depends on what your goals are. By Andrey Armyagov/Shutterstock
7 August 2019 – As part of my research into diversity in project teams, I’ve spent about a week digging into how it’s possible to quantify success. Most people equate personal success with income or wealth, and business success with profitability or market capitalization, but none of that really does it. Veteran project managers (like yours truly) recognize that it’s almost never about money. If you do everything else right, money just shows up − sometimes. What it’s really all about is all those other things that go into making a success of some project.
So, measuring success is all about quantifying all those other things. Those other things are whatever is important to all the folks that your project affects. We call them stakeholders because they have a stake in the project’s outcome.
For example, some years ago it started becoming obvious to me that the boat tied up to the dock out back was doing me no good because I hardly ever took it out. I knew that I’d get to use a motorcycle every day if I had one, but I had that stupid boat instead. So, I conceived of a project to replace the boat with a motorcycle.
I wasn’t alone, however. Whether we had a boat or a motorcycle would make a difference to my wife, as well. She had a stake in whether we had a boat or a motorcycle, so she was also a stakeholder. It turned out that she would also prefer to have a motorcycle than a boat, so we started working on a project to replace the boat with a motorcycle.
So, the first thing to consider when planning a project is who the stakeholders are. The next thing to consider is what each stakeholder wants to get out of the project. In the case of the motorcycle project, what my wife wanted to get out of it was the fun of riding around southwest Florida visiting this, that and the other place. It turned out that the places she wanted to go were mostly easier to get to by motorcycle than by boat. So, her goal wasn’t just to have the motorcycle, it was to visit places she could get to by motorcycle. For her, getting to visit those places would fulfill her goal for the project.
See? There was no money involved. Only an intangible thing of being able to visit someplace.
The “intangible” part is what hangs people up when they want to quantify the value of something. It’s why people get hung up on money-related goals. Money is something everyone knows how to quantify. How do you quantify the value of “getting to go somewhere?”
A lot of people have tried a lot of schemes for “measuring” the “value” of some intangible thing, like getting where you want to go. It turns out, however, that it’s easy if you change your point of view just a little bit. Instead of asking how valuable it is to get there, you can ask something like: “What are the odds that I can get there?” Getting to some place five miles from the sea by boat likely isn’t going to happen, but getting there by motorcycle might be easy.
The way we quantify this is through what’s called a Likert scale. You make a statement, like “I can get there” and pick a number from, say, zero to five with zero being “It ain’t gonna happen” and five being “Easy k’neezie.”
You do that for all the places you’re likely to want to go and calculate an average score. If you really want to complete the job, you normalize your score by weighting the scores for each destination with how often you’re likely to want to go there, then divide by five times the sum of the weights. That leaves you with an index ranging from zero to one.
You go through this process for all of the goals of all your stakeholders and average the indices to get a composite index. This is an example of how one uses fuzzy logic, which takes into account that most of the time you can’t really be sure of anything. The fuzzy part is using the Likert scale to estimate how likely it is that your fuzzy statement (in this case, “I can get there”) will be true.
When using fuzzy logic to quantify project success, the fuzzy statements are of the form: “Stakeholder X’s goal Y is met.” The value assigned to that statement is the degree to which it is true, or, said another way, the degree to which the goal has been met. That allows for the prospect that not all stakeholder goals will be fully met.
For example, how well my wife’s goal of “Getting to Miromar Outlets in Estero, FL from our place in Naples” would be met depended a whole lot on the characteristics of the motorcycle. If the motorcycle is like the 1988 FLST light-touring bike I used to have, the value would be five. We used to ride that thing all day for weeks at a time! If, on the other hand, it’s like that ol’ 1986 XLH chopper, she might make it, but she wouldn’t be happy at the end (literally ’cause the seat was uncomfortable)! The value in that condition would be one or two. Of course, since Miromar is land locked, the value of keeping the boat would be zero.
So, the steps to quantifying project success are:
Determine all goals of all stakeholders;
Assign a relative importance (weight) to each stakeholder goal;
Use a Likert scale to quantify the degree to which each stakeholder goal has been met;
Normalize the scores to work out an index for each stakeholder goal;
Form a critical success index (CSI) for the project as an average of the indices for the stakeholder goals.
Before you complain about that being an awful lot of math to go through just to figure out how well your project succeeded, recognize that you go through it in a haphazard way every time you do anything. Even if it’s just going to the bathroom, you start out with a goal and finish deciding how well you succeeded. Thinking about these steps just gives you half a chance to reach the correct conclusion.
Throughout history, applied mathematics has been the key to human development. By Elnur/Shutterstock
31 July 2019 – Over the millennia that philosophers have been doing their philosophizing, a recurring theme has been the quest to come up with some simple definition of what sets humans apart from so-called “lower” animals. This is not just idle curiosity. From Aristotle on, folks have realized that understanding what makes us human is key to making the most of our humanity. If we don’t know who we are, how can we figure out how to be better?
In recent decades, however, it’s become clear that this is a fool’s errand. Such a definition of humanity doesn’t exist. Instead, what sets humans apart is a suite of characteristics, such as two eyes in the front of a head that’s set up on a stalk over a main torso, with two legs down below and a couple of arms on each side ending with wiggly fingers and opposable thumbs; a brain able to use sophisticated language; and so forth. Not every human has all of them (for example, I had a friend in Arizona who’d managed to lose his right arm and shoulder without losing his humanity) and a lot of non-humans have some of them (for example, chimpanzees use tools a lot). What marks humans as humans is having most of these characteristics, and what marks non-humans as not human is lacking a lot of them.
On the other hand, there is one thing that most humans are capable of that most non-humans aren’t: humans are capable of doing the math.
Yeah, crows can count past two. I hear that pigeons are good at pattern recognition. But, I’m talking about mathematical reasoning more sophisticated than counting past seven. That’s something most humans can do, and most other animals can’t.
Everybody has their mathematical limitations.Experience indicates that one’s mathematical limitations are mostly an issue of motivation. At some point, just about everybody decides that it’s just not worth putting in the effort needed to learn any more math than they already know.
That’s because learning math is hard. It’s the biggest learning challenge most of us ever face. Most of us give up long before reaching the limits of our innate ability to puzzle it out.
Luckily, there are some who are willing to push the limits, and master mathematical puzzles that no human has solved before. That’s lucky because without people like them, human progress would quickly stop.
Even better, those people are often willing – even anxious – to explain what they’ve puzzled out to the rest of us. For example, we have geometry because a bunch of Egyptians puzzled out how to design pyramids, stone temples and other stuff they wanted to build, then proudly explained to their peers exactly how to do it. We have double-entry accounting because folks in the Near East wanted to keep track of what they had, figured out how to do it, and taught others to help. We’ve got calculus because Sir Isaac Newton and a bunch of his buddies figured out how to predict what the visible planets would do next, then taught it to a bunch of physics students.
It’s what we like to call “Applied Mathematics,” and it’s responsible for most of the progress people have made since the days of stone knives and bear skins. Throughout history, we’ve all stood around scratching our heads about things we couldn’t make sense of until some bright guy (or gal) worked out the right mathematics and applied it to the problem. Then, suddenly what had been unintelligible became understandable.
These days, what I think is the bleeding edge of applied mathematics is nonlinear dynamics and chaos. Maybe there’s some fuzzy logic thrown into the mix, too. Most of the math tools needed to understand (as in “make mathematical models using”) these things is pretty well in hand. What we need to do is apply such tools to the problems that today vex us.
A case in point is the Gini-Simpson Diversity Index I described in this blog two weeks ago. That is a small brick in the wall of a structure that I hope will someday help us avoid making so many dumb choices. Last week I ran across another brick in a paper written by a couple of computer science professors at my old alma materRensselaer Polytechnic Institute (aka RPI, or as we used to call it when I was there as a graduate student, “the Tute”). This bit of intellectual flotsam describes a mathematical model the authors use to predict how political polarization evolves in the U.S. Congress.
Polarization is one of four (at my last count) toxic group-dynamics phenomena that make collaborative decision making fail. Basically, the best decisions are made by groups that work together to reach a consensus. We get crappy decisions when the group’s dynamics break down.
The RPI model is a nonlinear differential equation describing an aspect of the dynamics of decision-making teams. Specifically, it quantifies conditions that determine whether decision teams evolve toward consensus or polarization. We see today what happens when Congress evolves toward polarization. The authors’ research shows that prior to about 1980 Congress evolved toward consensus. Seeing this dynamic at work mathematically gives us a leg up on figuring out why, and maybe doing something about it.
I’m not going to go into the mathematical model the RPI paper presents. The study of nonlinear dynamical systems is far outside the editorial focus of this column. At this point, I’m not going to talk about solutions the paper might suggest for toxic U.S. Government polarization, either. The theory is not well enough developed yet to provide meaningful suggestions.
The purpose of this posting is to point out that application of sophisticated mathematics is necessary for solving society’s most intractable problems. As I said above, not everybody is ready and willing to become expert in using such tools. That’s not necessary. What I hope you’ll walk away with today is an appreciation of applied mathematics’ importance for societal development, and a willingness to support STEM (science, technology, engineering and mathematics) education throughout our school system. Finally, I hope you’ll encourage students who show an interest to learn the techniques and follow STEM careers.
Maslow’s pyramid of needs analyzes human needs and arranges them in a hierarchy. By Shutter_M/Shutterstock
24 July 2019 – Abraham Harold Maslow (1908-1970) was a 20th century psychologist famous for describing human motivation as an hierarchy of needs in a 1943 paper entitled “A Theory of Human Motivation” published in Psychological Review. He was a central figure in the founding of Humanistic Psychology, which concentrates on studying mentally healthy humans.
You have to remember that Maslow did his most important work in the middle of the 20th century. At that time there was great popular interest in the works of Sigmund Freud, who worked with the mentally ill, and B.F. Skinner who mainly studied lower animals. Indeed, the entire arts-and-letters school of Surrealism explicitly drew inspiration from Andre Breton’s interpretation of Freud’s work. Despite (or perhaps because of) this interest in Freud and Skinner’s work, there had been little, if any, study of mentally healthy people.
Humanistic Psychologists felt these earlier studies were of limited value to understanding the healthy human mind. Maslow chose to study the workings of healthy human minds from all social strata, but he was especially interested in studying high achievers. For this reason those of us interested in organizational behavior find his humanists of particular interest. We kinda hope our organizations are populated with, and run by, mentally healthy humans, rather than Freud’s neurotics or Skinner’s lab rats!
Maslow’s emphasis on studying high achievers likely gave rise to the first misconception I want to talk about today: the idea that his work gives cover to elitist views. This elitist theory assumes that everyone strives to reach the self-actualization level at the top of the so-called “Pyramid of Needs” used to illustrate Maslow’s hierarchy, but that only an elite fraction of individuals reach it. Lesser individuals are doomed to wallowing in more squalid existences at lower levels.
The second misconception I want to treat today is a similar notion that people start out at the lower levels and climb slowly up to the top as their incomes rise. This theory substitutes a ladder for the pyramid image to visualize Maslow’s hierarchy. People are imagined to climb slowly up this ladder as both their income and social status increase. This, again, gives cover for elitist views as well as laissez-faire economics.
Maslow’s Conception
What Maslow’s Hierarchy really describes is a priority system that determines what people are motivated to do next. It has little to do with their talents, income or social status. To illustrate what I mean, I like to use the following thought experiment. This thought experiment involves Albert Einstein and it’s particularly appropriate because the Grizzled Genius loved thought experiments.
Albert Einstein’s greatest joy was becoming immersed in translating his imaginings about the physical universe into mathematical equations. This is an example of what Maslow called “peak experiences.” Maslow believed these were periods when self-actualized people (those engaged in satisfying their self-actualization need) are happiest and most productive.
Once in a while, however, Einstein would become hungry. Hunger is, however, one of those pesky physiological needs down at the bottom of Maslow’s Hierarchy. There’s nothing aspirational about hunger. It’s what Fredrick Herzberg called a “hygiene factor” or “demotivator.” Such needs are the opposite of aspirational.
If you’ve got an unsatisfied demotivator need, you become unhappy until you can satisfy it. If, for example, you’re hungry, or have a toothache, or need to pee, it becomes hard to concentrate on anything else. Your only thought is (depending on the nature of the unmet physiological need) to go to the bathroom, or the dentist, or, as in Einstein’s case, go find lunch.
The moral of this story is that people don’t sit somewhere for extended periods of time on a shelf labeled with one of Maslow’s categories. Rich people don’t float in a blissful self-actualizing state. Poor people don’t wallow in a miasma of permanently unmet physiological needs. People constantly move up and down the pyramid depending on what the most pressing unmet need of the moment is.
The hierarchy is therefore actually an inverted priority list. Physiological needs are more important than safety needs. When something frightens you – a safety need – the first thing that happens is you feel an urge to pee to take care of a physiological need to prepare your body for running like a scared rabbit. When you see a fast-moving Chevy bearing down on you, you immediately forget pride in that (esteem level) achievement award you just got.
Elitist Fallacy
A combination of confusion about how Maslow’s heirarchy works and his preference for studying high achievers has led many people to imagine his work gives cover for elitist views. If you’re predisposed to imagine that rich people, smart people, or those of high social status are somehow innately “better” than denizens of what 19th century novelist Edward Bulwer-Lytton called “the great unwashed,” then you’re an elitist. An elitist can derive great comfort by misinterpreting Maslow’s work. You can imagine there being a cadre of elite people destined to spend their lives in some ethereal existence where all lower needs are completely satisfied and life’s only pursuit is self actualization.
The poster child for elitism is 16th century theologian John Calvin. In Calvin’s version of Protestant theology everyone was tainted with original sin and doomed to an eternity in Hell. That was a pretty common view at the time of the Protestant Reformation. Calvin added an elitist element by hypothesizing that there was a limited number of individuals (the elect) whom God had chosen for salvation.
It’s called predestination and those folks got tickets into the elite ranks through no merit of their own. There was nothing anybody could do to beg, borrow, or steal their way in. God decided, while making the Universe in the first place, who was in and who was out based on nothing but His whimsey. (Sexist pronoun used specifically to make a point about Calvinism.)
Of course, the requirements of natural selection logically lead to everyone having a desire to be part of an elite. We all want to be different, like the Dada-esque avant garde group King Missile. That’s how DNA measures its success. Only elite DNA gets to have long-term survival.
So, elitism has a lot of natural appeal. This natural appeal accounts for all kinds of rampant racism and xenophobia. Misunderstanding Maslow’s heirarchy provides a pseudoscientific rationale for elitism. To the elitist, the fact that this view is completely mistaken makes no nevermind.
I hope that by now I have disposed of the elitist fallacy.
Economic Ladder Fallacy
Hoping that I’ve disposed of the idea that Maslow’s work gives cover to elitism, I’ll turn to the fallacy of imagining his hierarchy as an economic ladder. This puppy is a natural outgrowth of the Pyramid of Needs image. The top (self actualization) level of the pyramid is imagined as “higher” than the bottom (physiological) level.
This image actually works from the viewpoint that “lower” needs take precedence over “higher” needs in the same way that a building’s supporting foundation takes precedence over the walls and roof. Without a foundation, there’s nothing to support walls or a roof in the same way that without fulfilling physiological needs, there’s no motivation for, say, self actualization.
Think of it this way: dead people, whose physiological needs are all unmet, hardly ever want to run for President.
So, how do you reach something high? You use a ladder!
That’s the thinking that transforms the Pyramid of Needs into some kind of ladder.
If you’re a strict materialist (and way too many Americans are strict materialists) the “high” you care about reaching is wealth. Folks who haven’t understood last month’s posting entitled “The Fluidity of Money” often confuse income with wealth, so there’s some appeal to thinking about Maslow’s Hierarchy of Needs as a metaphor for income levels. That completes the economic-ladder fallacy.
With this fallacy, folks imagine that everyone starts out at the bottom of the ladder and, with time, hard work and luck, climbs their way to the top. There are obvious problems matching income levels with needs levels, but if you’re sufficiently intellectually lazy, you can unfocus your mind’s eye enough to render these problems invisible.
I especially get a kick out of efforts to use the idea of Engel curves (from economics) to make this ladder fallacy work. Engel curves map the desireability (measured as the demand side of the economics law of supply and demand) of a given good or product against a given consumer’s income level. If the good in question is, for example, a used Mazda Miata, the desirability may be high when the consumer has a low-to-moderate income, but low if that particular consumer has enough income to pay for a new Ferrari SF90 Stradale. If you want to, it is obvious you can somehow conflate Engel curves with the ladder idea of Maslow’s Heirarchy of Needs.
The problem with this thinking is, first, that the Ladder doesn’t make a lot of sense as a visualization for Maslow’s Heirarchy, since the latter is formost a priority-setting scheme; second, that Maslow’s Hierarchy has little connection to income; and, third, that Engel curves present an incomplete view of what makes a product desirable.
The elitist fallacy and the economic-ladder fallacy are not the only fallacies people, with their infinite capacity to generate cockamamie theories, can concoct in connection to Maslow’s work. They are just two that have come up recently in articles I’ve had occasion to read. I think analyzing them can also help clarify how the Hierarchy of Needs applies to understanding human behavior.
Besides, I’ve had a bit of fun knocking them around, and I hope you have, too.
Diversity of membership in decision-making teams leads to better outcomes. By Rawpixel.com/Shutterstock
17 July 2019 – It’s come to my attention that a whole lot of people don’t know how to calculate a diversity score, or even that such a thing exists! How can there be so much discussion of diversity and so little understanding of what the word means? In this post I hope to give you a peek behind the curtain, and maybe shed some light on what diversity actually is and how it is measured.
This topic is of particular interest to me at present because momentum is building to make a study of diversity in business-decision making the subject of my doctoral dissertation in Business Administration. Specifically, I’m looking at how decision-making teams (such as boards of directors) can benefit from membership diversity, and what can go wrong.
Estimating Diversity
The dictionary definition of diversity is: “the condition of having or being composed of differing elements.”
So, before we can quantify the diversity of any group, we’ve got to identify what makes different elements different. This, by the way, is all basic set theory. In different contexts what we mean by “different” may vary. When we’re talking about group decision making in a business context, it gets pretty complicated.
A group may be subdivided, or “stratified” along various dimensions. For example, a team of ten people sitting around a table trying to figure out what to do next about, say, a new product could be subdivided in various ways. One way to stratify such a group is by age. You’d have so many individuals in their 20’s, so many might be in their 30’s, and so forth up to the oldest group being aged 50 or more. Another (perhaps more useful) way to subdivide them is by specialty. There may be so many software engineers, so many hardware engineers, so many marketers, and so forth. These days stratifying teams by gender, ethnicity, educational level or political persuasion could be important. What counts as diversity depends on what the team is trying to decide.
The moral of this story is that a team might score high in diversity along one dimension and very poorly along another. I’m not going to say any more about diversity’s multidimensional nature in this essay, however. We have other fish to fry today.
For now, let’s assume a one-dimensional diversity index. What we pick for a dimension makes little difference to the mathematics we use. Let’s just imagine a medium-sized group of, say, ten individuals and stratify them according to the color of tee-shirts they happen to be wearing at the moment.
What the color of their tee-shirts could possibly mean for the group’s decisions about new-product development I can’t imagine, and probably wouldn’t care anyway. It does, however, give us a way to stratify the sample. Let’s say their shirt colors fall out as in Table 1. So, we’ve got five categories of team members stratified by tee-shirt color.
NOTE: The next bit is mathematically rigorous enough to give most people nosebleeds. You can skip over it if you want to, as I’m going to follow it with a more useful quick-and-dirty estimation method.
The Gini–Simpson diversity index, which I consider to be the most appropriate for evaluating diversity of decision-making teams, has a range of zero to one, with zero being “everybody’s the same” and one being “everybody’s different.” We start by asking: “What is the probability that two members picked at random have the same color tee shirt?”
If you’ve taken my statistical analysis course, you’ll likely loathe remembering that the probability of picking two things from a stratified data set, and having them both fall into the same category is:
Where λ is the probability we want, N is the number of categories (in this case 5), and P is the probability that, given the first pick falling into a certain category (i) the second pick will be in the same category. The superscript 2 just indicates that we’re taking members two at a time. Basically P is the number of members in category i divided by the total number of members in all categories. Thus, if the first pick has a blue tee-shirt, then P is 3/10 = 0.3.
This probability is high when diversity is low, and low when diversity is high. The Gini-Simpson index makes more intuitive sense by simply subtracting that probability from unity (1.0) to get something that is low when diversity is low, and high when diversity is high.
NOTE: Here’s where we stop with the fancy math.
Guesstimating Diversity
Veteran business managers (at least those not suffering from pathological levels of OCD) realize that the vast majority of business decisions – in fact most decisions in general – are not made after extensive detailed mathematical analysis like what I presented in the previous section. In fact, humans have an amazing capacity for making rapid decisions based on what’s called “fuzzy logic.”
Fuzzy logic recognizes that in many situations, precise details may be difficult or impossible to obtain, and may not make a significant difference to the decision outcome, anyway. For example, deciding whether to step out to cross a street could be based on calculations using precise measurements of an oncoming car’s speed, distance, braking capacity, and the probability that the driver will detect your presence in time to apply the brakes to avoid hitting you.
But, it’s usually not.
If we had to make the decision by the detailed mathematical analysis of physical measurements, we’d hardly ever get across the street. We can’t judge speed or distance accurately enough, and have no idea whether the driver is paying attention. We don’t, in general, make these measurements, then apply detailed calculations using Gallilean Transformations to decide if now is a safe time to cross.
No, we have, with experience over time, developed a “gut feel” for whether it’s safe. We use fuzzy categories of “far” and “near,” and “slow” or “fast.” Even the terms “safe” and “unsafe” have imprecise meanings, gradually shifting from one to the other as conditions change. For example “safe to cross” means something quite different on a dry, sunny day in summertime, than when the pavement has a slippery sheen of ice.
Group decision making has a similar fuzzy component. We know that the decision team we’ve got is the decision team we’re going to use. It makes no difference whether it’s diversity score is 4.9 or 5.2, what we’ve got is what we’re going to use. Maybe we could make a half-percent improvement in the odds of making the optimal decision by spending six months recruiting and training a blind Hispanic woman with an MBA to join the team, but are we going to do it? Nope!
We’ll take our chances with the possibly sub-optimal decision made by the team we already have in place.
Hopefully we’re not trying to work out laws affecting 175 million American women with a team consisting of 500 old white guys, but, historically, that’s the team we’ve had. No wonder we’ve got so many sub-optimal laws!
Anyway, we don’t usually need to do the detailed Gini-Simpson Diversity Index calculation to guesstimate how diverse our decision committee is. Let’s look at some examples whose diversity indexes are easy to calculate. That will help us develop a “gut feel” for diversity that’ll be useful in most situations.
So, let’s assume we look around our conference room and see six identical white guys and six identical white women. It’s pretty easy to work out that the team’s diversity index is 0.5. The only way to stratify that group is by gender, and the two strata are the same size. If our first pick happens to be a woman, then there’s a 50:50 chance that the second pick will be a woman, too. One minus that probability (0.5) equals 0.5.
Now, let’s assume we still have twelve team members, but eleven of them are men and there’s only one token woman. If your first pick is thewoman, the probability of picking a woman again is 1/12 = 0.8. (The Gini-Simpson formula lets you pick the same member twice.) If, on the other hand, your first pick is a man, the probability that the second pick will also be a man is 11/12 = 0.92. I plugged all this into an online Gini-Simpson-Index calculator (‘cause I’m lazy) and it returned a value of 26%. That’s a whole lot worse.
Let’s see what happens when we maximize diversity by making everyone different. That means we end up stratifying the members into twelve segments. After picking one member, the odds of the second pick being identical are 1/12 = 0.8 for every segment. The online calculator now gives us a diversity index of 91.7%. That’s a whole lot better!
What Could Possibly Go Wrong?
There are two main ways to screw up group diversity: group-think and group-toxicity. These are actually closely related group-dynamic phenomena. Both lower the effective diversity.
Group-think occurs when members are too accommodating. That is, when members strive too hard to reach consensus. They look around to see what other members want to do, and agree to it without trying to come up with their own alternatives. This produces sub-optimal decisions because the group fails to consider all possible alternatives.
Toxic group dynamics occurs when one or more members dominate the conversation either by being more vocal or more numerous. Members with more reticent personalities fail to speak up, thus denying the group their input. Whenever a member fails to speak up, they lower the group’s effective diversity.
A third phenomenon that messes up decision making for high-diversity teams is that when individual members are too insistent that their ideas are the best, groups often fail to reach consensus at all. At that point more diversity makes reaching consensus harder. That’s the problem facing both houses of the U.S. Congress at the time of this writing.
These phenomena are present to some extent in every group discussion. It’s up to group leadership to suppress them. In the end, creating an effective decision-making team requires two elements: diversity in team membership, and effective team leadership. Membership diversity provides the raw material for effective team decision making. Effective leadership mediates group dynamics to make it possible to maximize the team’s effective diversity.
The right to sit in a cafe, drinking coffee and reading newspapers is wasted unless that press is free! By Impact Photography/Shutterstock
10 July 2019 – ‘Way back in the late 1960s I spent an entire day as a news hawker. That is, I stood on street corners shouting things at passersby intended to induce them to by copies of a newspaper I was selling. The newspaper was something called The L.A. Free Press. It was produced and sold in Los Angeles, and the street corners I stood on had names like “West Hollywood Boulevard and Sunset.”
I’d recently transplanted from Boston, Massachusetts to the Los Angeles, California area and had never heard of The L.A. Free Press before. A small gang I’d been hanging out with that morning heard that I had a driver’s license on me, and knew that we could use it as collateral to get a great whacking stack of those newspapers to sell at a profit.
Seemed like a good idea at the time.
I initially thought the newspaper copies were somehow free for the taking (as so many local papers are today). I was quickly disabused of that idea because I got pretty decent money for buying copies of it at a low price, then selling them on street corners for a higher price. It clearly wasn’t that kind of free!
Then, I imagined that was (like so many thin publications of the time) some hippy-dippy propaganda rag full of free-love manifestos and ads for beatnik-poetry venues. Being a veteran hippy-beatnik-biker, that was okay with me. I didn’t care as long as there was coin to be had. I wasn’t one of Donovan Leitch’s “beatniks out to make it rich,” but I was interested in coming up with lunch money!
The main headline on the first page of the copies we got in exchange for a mortgage on my driver’s license sounded like a local-interest story that I was not embarrased to wave at potential newsprint buyers, so it didn’t seem to be some hippy-dippy propaganda rag, either. The papers actually sold pretty well!
I needed the money (being dead broke at the time), so I swallowed my pride and did the job. I kept the last copy from my stack, however, to read when I got back to wherever I was sleeping that night.
By the time I’d finished reading the thing I’d realized why the publication was called The L.A. Free Press. It was an independent newspaper founded by a small group dedicated to investigative journalism with nobody to answer to but their readers. I became proud to be working with them.
If I’d been smart and ambitious I would have tried to get a job with them writing copy. After all, part of my reason for relocating was to find some kind of writing gig. But, as is typical with homeless eighteen-year-olds living on the streets, I was more frightened and depressed than smart and ambitious. The next day I moved on to doing something that turned out to be another stupid career move.
Sometimes depression is not a sign of mental illness, but a rational response to the way your life is going.
What I learned from that episode of my misspent youth (What’s the point of misspending your youth if you’re not going to learn something from it?) was what intellectuals mean when they talk about “the Free Press.” It’s not just some empty slogan you hear once in a while on CNN. It’s how we, as citizens of a free country, keep track of what’s going on outside of our individual hovels.
The difference between we citizens of a free country and downtrodden medieval serfs slaving to feed their “betters,” is that we have some say in what goes on outside our hovels. We can’t affect things in a way that’s good for us and the people we care about unless we find out what’s actually going on out there. For that we hire independent journalists who have at least half a brain and make it their business to find out for us.
We pay them a living wage and (if we’ve got at least half a brain ourselves) listen to what they tell us is happening. The Free Press is not, as some dishonest demagogues try to tell us, “the enemy of the people,” but a necessary part of a free democratic society.
For this reason, the journalistic profession has been called “The Fourth Estate” since the Enlightenment. Originally, the term was meant to indicate that a Free Press was available – in addition to the three original estates of clergy, aristocracy and commoners – whose writ was to frame the debate upon which society made common decisions. Later political systems still had (usually) three competing authorities explicitly charged with governing, along with a Free Press implicitly charged with framing the debate about what to do next.
In the United States, our Constitution explicitly delineates a government made up of three co-equal branches: Legislature, Court System, and Executive. The Founding Fathers (If that’s not a sexist term, I don’t know what is!) realized they’d forgotten the Free Press in the original document when they couldn’t get anybody to ratify (agree to) the thing without immediately amending it to include a Free Press (as well as the rest of the Bill of Rights).
The Free Press was considered so important that it was included in the first amendment.
Before anybody gets the idea that I’m criticizing the Founding Fathers as incompetent, I want to point out that this error just goes to prove that those guys were human, and humans make mistakes. Specifically, they were exceedingly bright guys to whom the need for a vibrant Free Press was so obvious that they forgot to mention it. The first ten Amendments – the Bill of Rights – should be seen as an “Oh, Shit!” moment.
“How could we have left that out?”
Having a Free Press, and making good use of it, is the first thing you have to have to set up a democracy. In a sense, it’s not the “fourth” estate, but the first. All the rest is afterthought. It’s bells and whistles designed to be the mechanical parts of a democracy. They’re of no value whatsoever without a Free Press.
On the other hand, once you have a functioning Free Press and a society that makes good use of it, the rest of the bells and whistles will inevitably follow. In that sense, the Free Press is not an afterthought or a result of democracy. Instead, it’s the essence of democracy. That’s why the first thing would-be authoritarians seek to eliminate is the Free Press.
Constructivist illustration with rooster’s head. By Leonid Zarubin/Shutterstock
3 July 2019 – Long time readers of my columns will know that one of my favorite philosophical questions is: “How do we know what we think we know?” Along the way, my thoughts have gravitated toward constructivism, which is a theory in the epistemology branch of philosophy.
Jean Piaget has been credited with initiating the constructivist theory of learning through his studies of childhood development. His methods were to ask probing questions of his children and others, in an attempt to understand how they viewed the world. He also devised and administered reading tests to schoolchildren and became interested in the types of errors they made, leading him to explore the reasoning process in these young children.
From his studies, he worked out a model of childhood development that mapped several stages of world-view paradigms they seemed to use as they matured. This forced him to postulate that children actively participate in constructing their own ideas – their knowledge base – based on experience and prior knowledge. Hence, the term “constructivism.”
Imagine a house that represents everything the child “knows.” Mentally, they live in that house all the time, view the world in relation to it, and make decisions based on what’s there.
As they experience everything, including the experience of having someone tell them something verbally or through written words, they actively remodel the place. The operant concept here is that they constantly do the remodeling themselves by trying to fit new information into the structure that’s already there.
My own journey toward constructivism was based on introspective phenomenological studies. That is, I paid attention to how I gained new knowledge and compared my experiences with experiences reported by others studying the same material.
A paradigm example is the study of quantum mechanics. This subject is difficult for students familiar with classical physics because the principles and the phenomena on which they are based seem counterintuitive. Especially, the range of time and distance scales on which quantum principles act is not directly accessible to humans. Quantum mechanics works at submicroscopic distances and on nanosecond time scales.
Successful students of quantum mechanics start by studying human-scale phenomena that betray the presence of quantum principles. For example, the old “planetary model” of atoms as miniature solar systems in which electrons revolve in stable orbits around the atomic nucleus like planets around the Sun is a physical impossibility. Students realize this after studying Maxwellian Electrodynamics.
In 1864, James Clerk Maxwell succeeded in summarizing everything physicists of the time knew about electricity and magnetism in four concise (though definitely not simple) equations. Taken together, they implied the feasibility of radio and not only how light traveled, but even predicted its precise speed. Maxwell’s Equations were enormously successful in guiding the development of electrical technology in the late nineteenth century.
The problem for physicists studying atomic-scale phenomena, however, was that Maxwell’s Equations implied that electrons whizzing around nuclei would rapidly convert all their energy of motion into light, which would radiate away. With no energy of motion left to keep electrons orbiting, the atoms would quickly collapse – then, no more atoms! The Universe as we know it would rapidly cease to exist.
When I say rapidly, I mean on the time scale of trillionths of a second!
Not good for the Universe! Luckily for the Universe, what this really means that there’s something wrong with classical-electrodynamic theory (i.e., Maxwell’s Equations).
The student finds out about dozens of such paradoxes that show that classical physics is just flat out wrong! The student is then ready to entertain some outlandish ideas that form the core of quantum theory. The student proceeds to piece these ideas together into their own mental version of quantum mechanics.
Every physics student I’ve discussed this with has had the same experience learning this quantum-electrodynamical theory (QED). Even more telling, they all report initially learning the ideas by rote without really understanding them, then applying them for considerable time (months or years) before piecing them together into a mental pattern that eventually feels intuitive. At that point, when presented with some phenomenon (such as the sky being blue) they immediately seize on a QED-based explanation as the most obvious. Even doubting QED has become absurd for them!
To a constructivist, this process for learning quantum mechanics makes perfect sense. The student is presented with numerous paradoxes, which causes cognitive dissonance. This state motivates the student to seek alternative concepts and fit them into his or her world view. In a sense, they construct an extension onto the framework of their world view. This will likely require them to make some modifications to the original structure to accommodate the new knowledge.
This method of developing new knowledge dovetails quite nicely with the scientific method that’s been under development since Aristotle and Plato started toying around with it in the fourth century BCE. The new development is that Piaget showed that it is the normal way humans develop new knowledge. Even children can’t fully comprehend a new idea until they fit it into a modified version of their knowledge base.
This model also explains why humans’ normal initial reaction to novel ideas is to forcefully reject them. Accepting new ideas requires them to do a lot of work on their mental scaffolding. It takes a powerful mental event causing severe cognitive dissonance to motivate them to remodel a mental construction they’ve been piecing together for years.
It also explains why younger humans are so much quicker to take up new ideas. Their mental frameworks are still small, and rebuilding them to fit in new concepts is relatively easy. The reward for building out their mental framework is great. They are also more used to tinkering with their mental models than older humans, who have mental frameworks that have served them well for decades without modification.
Of course, once they reach the point of intolerable cognitive dissonance, older humans have more experience to draw on to do the remodeling job. They will be even quicker than youngsters to make whatever adjustments are necessary.
Older humans who have a lifelong habit of challenging themselves with new ideas have the easiest time adapting to change. They are more used to realigning their thinking to incorporate new concepts and have more practice in constructing knowledge frameworks.
