The Fourth Star

“Even those who learn from history are surrounded by those who are doomed to repeat it.” – Chuck B. on Twitter, April 12, 2016.

The Iraq War tested four four-star generals: John Abizaid, George Casey, Jr., Peter Chiarelli, and David Petraeus. This is their story. (The Fourth Star: Four Generals and the Epic Struggle for the Future of the United States Army by David Cloud and Greg Jaffe, Random House, 2009.) Each of them had a correct view of the challenges and answers. However, without being able to work together, their efforts could not support and reinforce each other. They were not in conflict against each other. Rather, their assignments – and their acceptances of those roles – left them distanced in space and time from each other. Beyond the specifics of the Second Gulf War, this is a book about leadership, leadership styles, and the natural limits to the complete fulfillment of our goals. The narratives here are richly detailed. The writing is tight and active. The authors were the Pentagon correspondents for the Wall Street Journal, the New York Times, and the  Washington Post.

Each of these four generals is an outside-the-box creative thinker. Each is competitive, driven, focused and intelligent. All hold advanced university degrees. Though Petraeus and Casey are connected by family ties within the military general staff, Abizaid and Chiarelli came from blue collar homes. Whereas Casey and Abazaid graduated from West Point, Chiarelli and Petraeus earned their commissions through ROTC. On their way to the top, each took detours within the military. Chiarelli and Petraeus taught in the social science department at West Point. “Sosh” is a fraternity of strategic planners and political thinkers whose connections in the Pentagon allow them to help younger peers get their careers back on track with assignments to combat brigades. Interestingly, Lt. George W. Casey, Jr. first met Lt. David Petraeus through their mothers. Casey’s father was a two-star general. That put Elaine Casey in the same social set as Peggy Knowlton, also the wife of a general, and George Petraeus’s mother-in-law. When Casey was finishing Ranger School, his mother called him and told him to introduce himself to Petraeus who was headed to the 509^th Parachute Infantry, the unit Casey had just left. (page 21) 

USA Today

Ethnically Syrian, Gen. John Abizaid is a second-generation American whose foreign language in school was French. He learned Arabic later, completing his MA from Harvard in Middle Eastern Studies with a year at the University of Jordan in 1979-80. In 1985, Major Abizaid was assigned to a UN mission during the Israeli occupation of Lebanon. His experiences gave him an understanding of the problems that the US would face in Iraq. He believed that sectarian divisions, discord, and violence are endemic to the Middle East: no military solution is possible. He accepted the Powell Doctrine: crush the conventional forces of a conventional opponent and get out before you get bogged down in another Vietnam. As the commander of CENTCOM, Abizaid was responsible for the work of the other generals who were charged with delivering a successful conclusion to the invasion of Iraq.

Gen. George W. Casey, Jr. earned his BS in International Relations at Georgetown in 1970. An ROTC student, he expected to repay the army with four years and then go to law school.  Instead, he followed his father, Brig. Gen. George W. Casey, Sr., who was the commander of the 1^st Air Cavalry Division when he was killed in Vietnam. (His father also attended Georgetown, earning an MA in international relations in 1958 before completing an MBA at George Washington in 1965. Much more in Wikipedia, of course.) Casey, Jr., went on to complete his MA in international relations at the University of Denver in 1980.  “George had become an expert in navigating the middle ground between his Georgetown friends and his family. He generally supported the war [in Vietnam], but wasn’t the kind of person to get in arguments or begrudge his friends their opinions. Neither was his dad.” (pp. 6-7)

NBC News

Serving in Kosovo in 2000 was Casey’s experience in peacekeeping and counterinsurgency. Having labored to broker a ceasefire for one village, he saw the truce shattered when rifles and hand grenades were found in the home of the village mayor who had been on the negotiating committee. It taught Casey that the US military cannot keep the peace in a country that does not want the peace. But, like all soldiers, he served those who called.  “Just three months before the invasion [of Iraq] he assembled a small group of active and retired officers that was rushed to the Middle East to deal with electricity generation, clean water, and other expected postwar problems.” (p. 162)

Tasked with restoring the nation while fighting the insurgency, Casey’s plan was to draw the resistance into the government to defuse them, to make them part of the solution, and let them hassle out their problems within the structure of the government. That, too, failed.

Western political theory accepts majority rule that is always limited by constitutional law and tradition. That did not apply in Iraq. The authors do not mention that Saddam Hussein ruled like other strongmen by balancing his opponents against each other, while also favoring his power base. That meant oppressing the majority Shiites and minority Kurds, and giving power to the Sunnis. The fall of Saddam Hussein left the Sunnis at the mercy of the merciless Shiites who now controlled the government of Iraq.

Also here, the reader today can see the roots of the ISIS Caliphate. Back then, moderate Sunnis united with the Shiite authorities to fight radical Sunni Islamists from Al Qaeda who were making life hell for everyone. But it was too little, too late.

Conservative Treehouse

Peter Chiarelli earned his BS in political science at Seattle University where he did his ROTC. (He later completed a master’s in public administration at the University of Washington in 1980. He was granted an MA in national security strategy from Salve Regina University. Wikipedia.) Rejected three times for law school - poor at standardized tests, apparently - he entered the army. Sent on orders first to earn the master’s, Chiarelli was tapped for the social science department at West Point. He loved the challenge of teaching. He did not have to take a position personally in order to advocate it. In one class, he said that the US invited the attack at Pearl Harbor by encircling the Japanese and threatening them. Disagree as they did, the cadets were only allowed to argue back with facts. It was good training, both for them, and for him. 

Chiarelli’s goal in Iraq was to win the war by rebuilding the economy. Instead of big-ticket projects to highly-placed defense contractors like Bechtel, Chiarelli wanted many small projects paid for immediately to clean the streets of garbage, to restore electricity to neighborhoods, and to distribute clean water.  He was successful. Sunni fighters left their guns behind to do the simple and dirty work of civil engineering in their neighborhoods. When the money stopped, they went back to being insurgents, and life got worse for everyone. The Sunni grievances were real. Shiite death squads under the cover of government legitimacy as police and security forces pushed the Sunnis out of mixed neighborhoods. The government closed the only bank in Sadr City, forcing Sunnis to travel through deadly Shia territory. Gen. Chiarelli’s rebuilding faltered.

The Telegraph (UK)

General Petraeus was the most conventional of them though his winning strategy was contrary to the wisdom of the time. (Petraeus completed his doctorate from Princeton while he was teaching in the social science department at West Point.) Petraeus pushed for the deployment of 21,000 additional troops – called “The Surge” – to bolster the failing occupation. However, rather than stationing them in huge bases with swimming pools, and a BX the size of a Walmart, he placed them in 120 small detachments close to the civilians. They also worked as advisors and supporters to the Iraqi police and army who were tasked with keeping the peace. The first advantage was that the Iraqi people, civilians and military both, would stop seeing the occupying force as distant and aloof, but in and of them as collaborators. Moreover, the soldiers would come to know the people, not only gaining valuable intelligence, but also becoming less likely to stereotype the locals. More to the point, the strategy came with an exit policy: eventually, the US forces would minimize, and the Iraqi role would strengthen. The first happened. The second did not.

In the Middle Ages, military authority and civil authority were identical. As Europe reawakened, the military was subordinated to civilian control. Ever less often did dukes, kings, and emperors lead their troops into battle.The capture of Napoleon III at Sedan in 1871 was the dunce’s after school lesson. And military dictatorships are notoriously unsuccessful. So, the modern army carries out the orders it is given. The Second Gulf War was not just winnable: it was won. The fifth largest army in the world melted and evaporated. We then met them again in a new fog of war, a war that could not be won. Sometimes, being brilliantly intelligent is just not enough.

PREVIOUSLY ON NECESSARY FACTS

Leadership

Primary Leadership Training

Texas State Guard Basic Non-Commissioned Officer Course

Independence Day 2012

BNOC: Texas State Guard Basic Non-Commissioned Officer Course

BNOC is required of all non-commissioned officers seeking promotion from E-5 (“buck” sergeant) to E-6 (staff sergeant), in my case from Petty Officer 2^nd Class to Petty Officer 1^st Class.  The training is offered online, but I elected to take the live classroom presentation specifically because it is delivered by the US Air Force Joint Base San Antonio Leadership School at Lackland AFB.  That course was recommended to me by one of the Master Gunnery Sergeants in TMAR, the Texas Maritime Regiment of the Texas State Guard. The class exceeded my expectations.

In all, we had seven different presenters. Each was an expert in one or more fields, but all were instructors at the school and each had volunteered to work with us, in addition to their regular duties.

One of the Many Sights to See at Lackland AFB

The lectures were generally interactive. Questions were always encouraged. On the second day, we had more live exercises.  In many ways, these were similar to other management classes, a comment made, also, by one of my classmates who is working on another master’s degree, this one in administration. The focus, however, was on the military. Some of it was a bit foreign to the TXSG. Although about half of us are prior federal service, what we do seems to draw little from the Warrior Ethos. We take care of people.  However, in our battle books, taken from standard military reporting forms, we do list an enemy: the hurricane, flood, or wildfire. The introductory lecture pointed out that depression is an intangible enemy.

• Are leaders born or made?
• What are the characteristics of a good leader?
• What are the characteristics of a good follower?

Another Sight to See at Lackland AFB, 
Gateway to the Air Force

We explored the interactions between leaders and followers as we learned about contingency theory, skills theory, and transformation theory. We inventoried intrinsic and extrinsic values.

• What is personal power?
• What is positional power?
• What a referential leader? 
• How can you increase or decrease power? 
• If all else fails, can you play Rock, Scissors, Stripes?

We learned about Vision Statements and Mission Statements and were encouraged to look up the ones written by and for our own commands.

Team dynamics is an ongoing process involving interaction of individuals (within a team) to achieve a desired result.

Straight out of management theory we were presented with the six stages of a project: Forming, Storming, Norming, Performing, (Adjourning), and Transforming.  That transformation occurs to the team, its wider organization, and to the individual members of the team.

Everyone else in the class seemed pretty sure that we were a team because we had the same goal, passing the class.  I was not so sure.  For one thing, if that sergeant over there did not take good notes, if she let it go in one ear and out the other, I could still pass the class. More to the point, the set and setting did not provide either a motive or an opportunity to help that other noncom to be successful in this class.  It was a problem that I slept on.

Of course, we explored out own personality types. This class used the “True Colors” or “Four Lenses” temperament theory proposed by Don Lowry, which is apparently based on the Myer-Briggs.  I came out Green: independent, non-conforming, head over heart, data-driven, non-decisive, curious, complex, abstract, and logical. When we Greens created a poster to show our type, we started with an ice cube at the lower left taken by an arrow to a lightbulb at the upper right. Between them were the Starship Enterprise and CDR Spock, a broken heart, and a computer. “Ah!” the instructor said, “you Greens do not have feelings.” Oh, we have feelings, our leader replied. “We just don’t care about yours.”

Making Friends: Two of us were from TMAR

Then we had to devise a no-smoking campaign targeted at our opposites, the feely-squishy Blues.  “No one else is smoking,” we said. “And when you die, you will make everyone else sad.”

Coming back to Earth, we discussed the Oath of Enlistment and the Non-Commissioned Officer’s Creed, and how they define the core values of the profession of arms.

Finally, we debated several either-or propositions, such as “What happens TDY [temporary duty] stays TDY.”  At first we thought of the analogy to Las Vegas, but do we keep commendations secret? We also examined ethical traps such as relativism and the loyalty syndrome.

This was the most professional set of presentations that I have had in the Texas State Guard. My wife thought that I was there to teach. Explaining to her that I was there as a student, referring to the instructors, I called them professors.

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Grammar is Important

"The Quadrilateral Coordination Group, made up of officials from Afghanistan, Pakistan, the United States and China, have been engaged in efforts to facilitate direct talks between the Afghan government and the Taliban.

The Taliban, who now control or contest more territory than at any time since they was ousted by a U.S.-led intervention in 2001, have attended none of the group's meetings."
Reuters, 18 May 2016 05:48 EDT
http://www.reuters.com/article/us-pakistan-afghanistan-taliban-idUSKCN0Y9133

It was a minor problem, I admit. From my experience, I guess that the author wrote "... it was... " referring to the Taliban as a collective entity, and an editor changed "it" to "they" without following through.  That error was noticeable.  

Less obvious is the disagreement in the first paragraph. "The Quadrilateral group... have been engaged in efforts..." The noun group is singular. Admittedly, it sounds funny to us to say " a group of people who play softball is meeting at the park." So, we excuse the subject-verb disagreement. Perhaps English is changing to allow the creation of plural collectives nouns. Alternately, the problem also stems from using the objective noun in the prepositional case as if it were nominative.  Prepositions make nouns into objects. "I give him the ball." is the same as "I give the ball to him." (not "I give he the ball." or "I give it to he."). Men are, but a group of men is.  Other languages, such as German and Latin, have stronger, more formal, and older rules for cases: nominative, genitive, accusative, dative, vocative, ablative, locative.  (Hungarian has about a dozen: progressive, regressive, inessive, adessive ...)

Simple as English is - and simplicity is a hallmark of civilized languages: so-called "primitive" people tend to have more complicated grammars - you can still open a can of worms.

"The plank that was approved by delegates at the party's convention this month reads: "Homosexuality is a chosen behavior that is contrary to the fundamental unchanging truths that has been ordained by God in the Bible, recognized by our nations founders, and shared by the majority of Texans."
Lone Star Q, which describes itself as the state's No. 1 source for LGBT news, asked on Twitter on Wednesday to have a "grammar debate" over the wording.

"In response, grammarians pointed out that placement of the final comma in the plank could lead to understanding it to mean that homosexuality is a chosen behavior shared by the majority of Texans. They also noted that "nations" should have an apostrophe and that by using "has been," the plank gives the impression that homosexuality has been ordained by God.

"Party officials did not respond to requests to comment."
 http://www.reuters.com/article/us-texas-lgbt-idUSKCN0YA2RQ

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Why Democracy is Difficult
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Indian English: Totally Legend Like Anything

Song: "Texans Serving Texans"

Texans Serving Texans
Lyrics by PO3 Michael Marotta
Music by PO3 Rodney Buckwalter

We are Texans serving Texans.

We are volunteers for you.

We are the Texas State Guard.

We’re the red, white and blue.

The Lone Star shines within us.

We are equal to the task; yes, it’s true.

Your community is in our care.

To republic and union we are true.

Second verse: 

We are Texans serving Texans.

We are volunteers for you:

Aiding civil authorities,

The defense force of our state.

We work to achieve; we are prepared.

We transport, shelter, and protect.

On water or land, search and rescue,

Hosting Web, and radio too.

 This past May 21-24, I attended the annual training exercise of the Maritime Regiment as an instructor for WebEOC. In addition to my primary duty, I was able to meet with Petty Officer Buckwalter and the band. The band worked on the music and we refined the lyrics. The band played the melody for the Awards ceremony on Saturday the 23rd.  Gen. Brian Smallwood asked to hear it again. He liked it. The lyrics here have not yet been approved by the Judge Advocate General. 

I also sent these cadence calls to my instructors from last year's Regional Basic Orientation Training. These calls are also not yet approved by the JAG.

CADENCE CALLS

We are Texans serving you.

State Guard is Red, White, and Blue.

 

Faithful, constant, strong as steel.

Train and drill and gain in skill.

Union and Republic true.

Equal to the task we do.

Transport, shelter, food, and care.

We achieve. We are prepared.

PREVIOUSLY ON NECESSARY FACTS
Primary Leadership Training
Community Emergency Response Team
Evaluating a Dive Team
Texans Serving Texans 

George P. Mitchell and the Idea of Sustainability

Everyone knows Bill Gates and Mark Zuckerberg. Few recognize the name of George P. Mitchell (1919-2013).  However, in a tribute after his death, The Economist said, “few businesspeople have done as much to change the world as George P. Mitchell.” The easiest label is that he was “the father of fracking.” Fracking is news. In fact, Mitchell worked for over 20 years to bring the idea to fruition. Working in the oil and gas industry, he earned billions of dollars building a Fortune 500 company. He also funded research into sustainablility.

I, too, was ignorant of Mitchell’s works until I was given this book by the author. Jurgen Schmandt worked for Mitchell’s Houston Advanced Research Center. Schmandt also served as the director of the Mitchell Center for Sustainable development. This book delivers an insider’s view of the creation and development of an idea both more powerful and having more potential than the oil industry.

The concept of sustainability is not deeply rooted. Like science and constitutional government, hints of sustainability can be found in ancient texts, but the seed really was planted in 1713, as the Age of Reason blossomed into the Enlightenment.  Schmandt credits Hans Carl von Carlowitz with the invention of the word “nachhaltende” in German, i.e., sustainable in English.  He coined the phrases “nachhaltende Nutzung gebe” (sustainable yield) and “nachhaltende Entwicklung” (sustainable development).  Carlowitz was a mining administrator. Mines are shored with timbers. No hardwood, no mines. And hardwood grows slowly. Carlowitz wrote a book, Sylvicultura Oeconomica.

For 150 years, although forestry and fisheries knew the terms, most of the world was not awakened to the concepts until the late 1960s and early 1970s. 

Schmandt nicely segues from two chapters on the history of sustainability into a third on the Club of Rome. Mitchell supported the Club of Rome and its Limits to Growth thesis with his checkbook.  At the same time, as this book lays out in careful detail, Mitchell sought a business model that would make sustainability profitable. He was partially successful.

 

Report by the  US Energy Information Agency

George Mitchell, who died on July 26th, was a one-man refutation of the declinist hypothesis. From the 1970s America’s energy industry reconciled itself to apparently inevitable decline. Analysts produced charts to show that its oil and gas were running out. The big oil firms globalised in order to survive. But Mr Mitchell was convinced that immense reserves trapped in shale rock deep beneath the surface could be freed. He spent decades perfecting techniques for unlocking them: injecting high-pressure fluids into the ground to fracture the rock and create pathways for the trapped oil and gas (fracking) and drilling down and then sideways to increase each well’s yield (horizontal drilling).   The result was a revolution.-- The Economist, August 3, 2013 here.

The Woodlands community outside Houston did not mature according to the plans Mitchell envisioned, but it is nonetheless an island of sustainable calm in the permanent sea squall that is Houston.  That perpetual storm is a consequence of two colliding economic fronts: the success of the urban metroplex and the need for developers to offload their true costs as externalities for other people to bear.  Schmandt’s presentation is dispassionate and analytical, an engineer’s report, not a jeremiad.

 And, just as scientific literacy and liberal democracy are far from ubiquitous, so, too has sustainability proved to be a difficult problem. Despite his obvious efficacy with oil and gas, George P. Mitchell never created a business model for sustainability. We have no sustainability industry, but, rather, a myriad of local and personal efforts, most of them  marginally successful.

Mitchell himself was a man of two passions. One of his children called this “the Mitchell paradox” and that is title of Chapter 10.  It was the author’s choice: Chapter 10 could have been Chapter 1. Define the man, then show him to us.  Rather, Schmandt first introduces us to his employer, friend, and mentor. Then he provides the conceptual wrapper. 

Mitchell was not a Luddite. He parted from his ecologist colleagues when he insisted that economic growth and even expansive development may well be appropriate, especially if the billions of people in the less developed regions are to enjoy the prosperity of the Western democracies.  That does not change the fact that Earth is an island. 

Today’s news is dominated by the US Presidential election campaigns and the military campaigns in Syria and Iraq. But underneath them, continuing, and consistent, never to be completely forgotten and often to be a burr in our running shoes, are the problems of sustainable growth.

And, it is one thing to have some few privileged people working in science (as in 1713), but another that (in 2013) millions of people on every continent can recognize the periodic table. Similarly, the quest for sustainability crosses geographical, political, and economic boundaries, encompassing millions of people who can recognize the word, and have both an interest and (most important) an investment in its meaning.

This book is about the man who made that happen.

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Tofurky: For Paleolithic Vegetarians

If our ancestors had not eaten animals, we would not be here.  On the other hand, not everything paleolithic is appropriate to the 21st century. Bashing each other is just one example. To satisfy that primal need for the genuine down-home taste of burned meat - without the cholesterol and carcinogens - there is Tofurky.  

"In 1980, after making from-scratch tempeh to share with friends and family, 30-year-old teacher/naturalist/hippie Seth Tibbott opens his own company in Forest Grove, Oregon. He expands operations to a vacant elementary school in 1983 -- and decades ahead of the tiny house trend, he builds a 300-square-foot treehouse to call home. Fast forward to 1995, Tofurky debuts the very first Holiday Roast. It strikes a cultural chord with a nation hungry for a tastier meat-free Thanksgiving. 2000 and beyond welcomes even more deliciousness, with the addition of deli slices and sausage and frozen items. Today our growth plans include new products, but also new countries. We're so inspired by a world that is waking up to the benefits of veg cuisine."  -- www.tofurky.com (of course).

 

Lauren of Horizon Marketing in Austin
visiting Wheatsville Co-op to bring us
the new flavors.

"The tale begins in 1980, when Seth Tibbott’s beard was still dark and Forest Grove was home to a few thousand fewer people.

"Tibbott longed for alternative environmentally friendly menu options for vegetarians like himself. His quest led him through two states and the founding of Turtle Island Foods, a company now based in Hood River, poised to sell its 3-millionth Tofurky this year.

"That was unimaginable when Tibbott ventured out to Oregon and found a job that “changed my life” — teaching at an outdoor school in Cherry Grove, where he made $25 per week in addition to a place to stay.

“ 'It opened my eyes to the natural world I had been missing all these years,' Tibbott said."  (Portland Tribune here: http://portlandtribune.com/fgnt/36-news/123488-turkey-or-tofurky--its-still-thanksgiving).

When our vegetarian friends get insufferable, my lawful wedded wife, Laurel, says, "Carrots have feelings, too."

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Epic Meat Bars

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Dishonest Scientists: Who is the Guardian?

The "Routine Activities" theory of crime developed by Marcus Felsen and Lawrence Cohen posited a crime triangle: a willing perpetrator, an available victim, and the lack of a capable guardian. That guardian could just be a neighbor, sitting on their porch, watching the street. In scientific research, it seems to be not clear to some that we all share the roles of capable guardians.

Elsevier's executive publisher, Dr. Jaap van Harten, offered a fallacious analogy when he likened the dishonest researcher to a thief in a shoe store and the reviewer to the shop owner. Dr. van Harten wrote:  

 “No. It is NOT the role of the reviewer to spot ethics issues in papers. It is the responsibility of the author to abide by the publishing ethics rules. Let’s look at it in a different way: If a person steals a pair of shoes from a shop, is this the fault of the shop for not protecting their goods or the shoplifter for stealing them? Of course the fault lies with the shoplifter who carried out the crime in the first place.”

The comment is in a sidebar to this article: “Why unethical research behavior could result in a revoked doctorate: An expert who investigates misconduct cases shares his thoughts and experiences” by Tony Mayer (Posted on 5 April 2016), here. I read it first on the Retraction Watch blog (here). I sent this comment, which was not approved by the moderator:

“The analogy is not parallel. The reviewer is not the shop owner, and neither is the publisher. The publisher is the purchasing department of a retailer. The reviewer is an auditor. If an auditor discovers that the purchasing department is acquiring goods that lack clear title, that fact must be reported. It must be reported, first, internally, but, also, quite likely, to law enforcement authorities with competent jurisdiction. Those people are analogous to the ethics committee or integrity office of the institution for which the authors work.
 Rather than a dodge, we deserve a higher standard of ethics from one of the world's leading publishers of scientific research. Instead of limiting the roles of publishers (and their reviewers), it would be more productive for a renowned expert like Dr. van Harten to suggest the standards and means for strengthening and extending them.”

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IMAGINARY NUMBERS ARE REAL. Pegasus is Not.

Technical language is derived from common language to allow more accurate and precise statements, and more penetrating and perceptive questions. Commonly, when we say “real” we mean “true”, independent of the observer, valid, or verifiable, actual; not imaginary or mythical. Pegasus was not a real animal.  Polyphemus the Cyclops was not real, though Odysseus may well have been. In mathematics, “real” numbers are the set that includes all integers, rational, and irrational numbers. “Imaginary” numbers are those whose square (or other “even” power) is a negative number; in other words, the square roots of negative numbers are imaginary. But imaginary numbers are real in the common sense.

Euler's Equation. As sin^2(x) + cos^2(x) = 1
this can be applied to the analysis of
alternating current electricity. 

Imaginary numbers are important to the design and analysis of alternating current circuits. (See, for instance, the Wikipedia article on Volt-ampere-reactive.)   Without imaginary numbers we could not have complicated electrical power systems, just as we could not have modern commerce without negative numbers.  Overcoming the confusion and ignorance about the reality of numbers has been a historical process.

The Golden Ratio seen in the Parthenon
has many applications.
Geometrically pleasing,
its algebraic expression
(1 + sqrt(5))/2 is irrational

It is said that the followers of Pythagoras killed one of their disciples for revealing that the square root of two is irrational. Apparently, until about 5^th century BCE, the Greeks accepted that every number must be rational, only that not all reductions were known. For example, the Egyptians chose to represent all fractions as sums of fractions with 1 in the numerator: ¾ = ½ + ¼ or 3/7 = 1/3 + 1/14 + 1/42.  

Diophantus of Alexandria (3^rd century CE) denied the reality of negative numbers.  The Nine Chapters on Mathematical Art (Jiu zhang suan-shu) of about the same time accepted their reality. Although early conceptions of zero as a placeholder are known from Babylonian and Egyptian texts, zero was not accepted as a number in the modern sense until about 500 CE.  What is nothing? And in the technical language of metaphysics, nothing is not a different kind of something. “Nothing exists beyond the universe” does not mean that “beyond the universe” is “something else.” The confusion over zero comes from the difference between “nothing” and “none.”  The number 207 has no tens; it does not have metaphysical “nothing” in the tens place. 

But we are not confused by that in daily life.  When Mom asked “What’s going on?” and you replied “Nothing!” she was not thrown into a metaphysical conundrum.

So, too, with imaginary numbers. They have an unfortunate etymology, but we use them every day. If the operators in control rooms of electrical power plants could not manipulate reactive power – expressed in imaginary numbers—with real controls, we would suffer blackouts. 

My motivation here is a post on the Galt’s Gulch Online discussion board.  On April 5, 2016, about 7:00 AM local time, frequent contributor ewv wrote: “Mathematics by itself doesn't describe reality. It is the means by which you relate in terms of concepts what can be measured. Mathematics is a science of method, not about things like physics does.” (Reply here in "What is Science?" here.)

Her keyboading error aside (“physics does” for “physics is”), she is usually a very adept student of Objectivism. As a quip, I once accused her of being Dr. Leonard Peikoff.  Her comment about mathematics was a direct derivation of statements by Ayn Rand in Introduction to the Objectivist Epistemology, as well as elucidations by David Harriman in The Logical Leap. However, mathematics does describe reality, as does any language. 

We can give expression to falsehoods using common language, as when we attempted to deflect Mom’s inquiry about our noisy play. Pegasus and Nike of Samothrace are other examples. They are mathematically impossible. Whatever the wings represent symbolically, they cannot function from the meager muscles on the back of the horse or the girl. Arguments about politics and religion, and Monday morning quarterbacking supply a surfeit of such falsehoods. That silliness is impossible in mathematics.

Patent for application
of the Moebius strip
to a power conveyor.

Can you have a sheet of paper with only one side? Can you have a container with only an inside? The Möbius Strip and the Klein Bottle were inventions of topology, a study in mathematics that contravenes common sense. But they do exist; and they do have practical applications. As an investigation of relationships, topology is based on qualities, not quantities. Topology is nonetheless a study within mathematics. Topology is rigorous and consistent. It does not allow for internal contradictions, just as integer arithmetic does not.  

Mathematics does have unsolved challenges. Science always has frontiers.  However, anything that is proved to be mathematically true must be realizable, even if we have not found one or built one yet.

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