Paradox: The incoherence of common sense

My musings on mathematicians and engineers were provoked by my Love’s reaction to something I saw in a quotes file:

There’s no way to develop an ambitious, broad-ranging, self-consistent metaphysical system without doing serious violence to common sense somewhere.
Eric Schwitzgebel

When I saw that, I laughed. It sums up what I’ve always thought about metaphysics. It sums up what almost everyone thinks about analytic philosophy.

I quoted it to my Love, who was trained as a pure mathematician. (For those of you who have never spent time with a pure mathematician: They make Mr Spock seem illogical.) She smiled and said,

Of course, sweetheart. Everything in mathematics, everything in science, did serious violence to the common sense of its time. That’s why we remember Galileo and Newton and Euler and Einstein. They defied common sense. Common sense is always wrong, unless it’s based on science that did violence to the common sense of its time.


The perils of quotes files: They lack context.

After that conversation with my Love, I read the whole interview with Professor Schwitzgebel. He said essentially the same thing as my Love said. He’s not criticizing metaphysics. He’s criticizing common sense. I still think metaphysics (other than Kant) is mostly silly, but he’s devastatingly right about common sense.

In context, Professor Schwitzgebel says,

Common sense is incoherent in matters of metaphysics. There’s no way to develop an ambitious, broad-ranging, self-consistent metaphysical system without doing serious violence to common sense somewhere. It’s just impossible. Since common sense is an inconsistent system, you can’t respect it all. Every metaphysician will have to violate it somewhere.

Common sense is an acceptable guide to everyday practical interactions with the world. But there’s no reason to think it would be a good guide to the fundamental structure of the universe. Think about all the weirdness of quantum mechanics, all the weirdness of relativity theory. The more we learn about such things, the more it seems we’re forced to leave common sense behind. The same is probably true about metaphysics.

You don’t even need to get into the weirdness of quantum mechanics. The Sun orbits the Earth? Common sense. A heavier stone falls faster than a lighter stone? Common sense. Species were as God created them in the Garden of Eden? Common sense. Newtonian mechanics? Crazy. Invisible animals cause disease? Insane! Send pictures through the air? Get this guy a straitjacket.


Even in the most abstract pursuits, there’s a place for common sense. Professor Schwitzgebel again:

But here’s the catch: Without common sense as a guide, metaphysics is hobbled as an enterprise. You can’t do an empirical study, for example, to determine whether there really is a material world out there or whether everything is instead just ideas in our minds coordinated by god. You can’t do an empirical study to determine whether there really exist an infinite number of universes with different laws of physics, entirely out of causal contact with our own. We’re stuck with common sense, plausibility arguments, and theoretical elegance – and none of these should rightly be regarded as decisive on such matters, whenever there are several very different and yet attractive contender positions, as there always are.

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Mathematician and engineer

My fiancée is trained as a pure mathematician. If you’ve ever spent time with a mathematician, you understand why Pythagoras and his gang were considered a strange, unworldly religious cult. Mathematicians aren’t like you and me.

When my fiancée was eight or nine, her mother bought her a boxed set of books called, The World of Mathematics. The description in the catalog made it sound like a book of puzzles and games. Instead, it’s a collection of essays and papers, some historical, some philosophical, some theoretical, some practical. Some are out-and-out funny – Bishop Berkeley’s The Analyst: A DISCOURSE Addressed to an Infidel MATHEMATICIAN. WHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith.

All are far over the head of an eight- or nine-year-old; most are aimed at a mathematically literate college graduate. Many assume an understanding of calculus. And yet, she read it over and over until she understood it.

Her favorite essay? G H Hardy’s A Mathematician’s Apology. (You can read it here.) It’s what inspired her to become a mathematician. Hardy says that the joy of mathematics isn’t that it’s useful. It’s that it’s beautiful. The beauty isn’t in the usefulness of the thing proved, it’s in the elegance of proof itself.

Hardy was a number theorist. To Hardy, much of the charm of Number Theory was that it had no immediate use. It was pure elegance. Mathematics purely for the joy of Mathematics.

Hardy was a pacifist; he wrote the Apology in 1940, as the Second World War was raging and the Great War still fresh in his mind. He was pleased that Number Theory couldn’t be used to make bombs or poison gas. The joke (if there is one) was on Hardy: Number Theory is the basis for modern cryptography and code-breaking. Polish mathematicians had already used it to crack the Nazi Enigma code machine. Alan Turing and his gang would build on that to crack more sophisticated code machines. General Eisenhower said the Enigma intelligence was “decisive” in defeating the Nazis.

Hardy not only inspired my Love to be a mathematician, he inspired her to become a number theorist. This summer, she gave me a copy of a textbook Hardy wrote with E M Wright, Introduction to the Theory of Numbers. It’s an incredibly elegant book, accessible to anyone who passed ninth grade algebra. Even an engineer can see why it enthralled her.

You might think that Number Theory means proving things about numbers. If so, you’d be wrong. She proved things about constructs that have some attributes of numbers, but have strange and interesting pathologies. As she describes it, it’s taking something familiar (the integers) and then removing the elements that make it familiar.

I don’t pretend to understand any of it. One afternoon, I picked up one of her books, entitled A Course in Arithmetic. “Aha,” I thought, “Arithmetic. I can understand that!”

I was wrong. There’s nothing in there that you or I would recognize as arithmetic. The only numbers are page numbers. Should you so desire, you can read the original French or an English translation on the internet.


Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
— Edna St Vincent Millay, Euclid alone has looked on Beauty bare


She insists that she’s not a mathematician now: Mathematicians prove things; she hasn’t proved anything since she was in graduate school. Her partners tell me that’s false: She has proved dozens of theorems fundamental to her business. They insist that she could write as many as 20 ground-breaking, publishable papers over a weekend.


Engineering is as ruthlessly pragmatic as Mathematics is ruthlessly unworldly. Mathematics is logical. Engineering is empirical.

Engineers delight in teasing mathematicians.

Who cares if you can prove it? The only thing that matters is, does it work?

Thanks for the rules of thumb!

Mathematicians are horrified at what engineers do with Mathematics. They are particularly horrified at engineers’ use of dot notation for derivative. (You are not expected to understand this.)

Still, the joy of engineering is also in creating something elegant – and tangible and useful.

I started my career as a design engineer. There’s a purity to design engineering, which one doesn’t really understand until one visits a jobsite where one’s design is being executed. (Or, as any design engineer will tell you, being butchered.) Then you realize that,

The map is not the territory.
— Alfred Korzybski

I worked while I pursued my graduate degrees. My interesting papers are on integration of complex subsystems. They are abstract, theoretic and analytic.

My work career quickly took a different direction. I left the desk for the field. I loved taking on difficult practical problems. The more bizarre and difficult the problem, the better I liked it. I wasn’t married, I had no social life, I didn’t have any ties or distractions. I could throw myself into problems, working on them every waking hour. Even while sleeping: I got some of my best ideas while asleep.

The problems that seemed most intractable – and interesting – involved integration of complex subsystems. My academic career was heavy on abstraction, but the abstractions helped me think clearly about solving concrete problems.


My fiancée and I work in overwhelmingly male-dominated fields.

Mathematics is not so male-dominated as it once was. But in the uses to which my fiancée puts Mathematics, the decisions are made by men: CEOs, CFOs and heads of corporate strategy for major multinationals; managers of high-risk international ventures; senior bankers and investment bankers. She’s usually the only girl in the room, and she has to prove that she’s smarter than all the boys.

Engineering and construction are overwhelmingly masculine and testosterone-laden. A girl engineer is a rare thing, especially a girl engineer in charge. I’m usually the only girl in the room, and I have to prove that I’m smarter than all the boys.

At that level respect is critical. Man or woman,

Respect isn’t given. It must be earned.

More than that, it has to be earned anew on every job.

“Those who can …”

orgtheory.net:

[T]he typical economics assistant professor makes 50% more than the typical sociologist

The author constructs an institutional model to explain the gap, but the reason is simple:

A quantitative economist can make more money outside the academy than can a sociologist. In Economics jargon, the opportunity cost of being an Economics professor is higher than the opportunity cost of being a Sociology professor. If the academy wants to keep an economist, it will have to pay more than for a sociologist.

It’s even worse for a humanities professor. What’s the alternative employment for a Gender Studies PhD?


I’m sure that pay gap generates rancor.

I’ve spent enough time in the academy to be acquainted with its utopian communitarian fancies. “It’s just as hard to get a Gender Studies PhD as an Economics PhD. It’s not fair!”

That doesn’t bother me. One doesn’t get paid for doing what one wants. One gets paid for doing what someone else wants. Ya pays yer money, ya takes yer choice.

In fact, I’m surprised that the premium to economists is only 50%.

There’s an old saw that a society that exalts philosophy and scorns plumbing will find that neither its pipes nor its logic hold water. A university that pays its professors the same will find that its Physics department can’t explain why pipes hold water and its Economics department can’t explain why California is running out of water.


My concern is different:

Can academia pay enough to retain first-rate economists? Mathematicians? Physicists? Engineers?

And if not, who will teach the next generation of economists, mathematicians, physicists and engineers?

My Love employs people with advanced degrees in quantitative disciplines: Mathematics, Statistics, Physics, Economics. She doesn’t compete with the academy for that talent. She competes with banks that need quants to analyze complex securities and strategies. The banks pay many times the salary of a tenured university position. My Love has to meet that salary expectation.

The gap in my profession (Engineering) is probably less stark. Professors can supplement their salaries with consulting fees and research grants. The range of incomes outside academia is much greater. Still, I make several times what my professors make.

There’s another, more brutal, old saw, “Those that can, do. Those that can’t, teach.” I have the utmost respect for my Engineering professors. My Love doesn’t just respect her professors, she reveres them.

But will the private sector’s premium to quantitative ability and training eventually undermine education in quantitative fields? Will those who can, quant?

Until this generation, the most brilliant mathematicians and physicists taught the next generation. In this generation and the next, will too many go to Goldman Sachs?

Then who will train the next generation?

Vulgar language

[This is not the password-protected post.
The password-protected post is here.
I apologize for the confusion.]


I don’t like vulgar language.

I’m not prissy. I’m no prig.

I’ve spent my working life on construction sites. Vulgar language is as common as dust, mud and pickup trucks. Put a woman in charge – a woman who’s proud to be a woman and leans toward the feminine – and it gets even louder and more common.

I’ve heard every vulgar word and phrase you have ever heard, and a lot more. I’ve heard them combined in ways you can’t imagine. I’ve had them used to belittle, describe or taunt me. I’m a big girl. I can deal with it. I get respect in the end.

Please pardon me if catcalling and wolf-whistling don’t give me the vapors. Yes, it’s immoral. No, it’s not rape.

I don’t even hear it any more. There’s a filter between my auditory nerves and my conscious brain.


I avoid using vulgar language. It doesn’t add anything, and a good engineer seeks economy.

Still, I would win any profanity-slinging contest.


My Love is even more fastidious than I am.

Her firm is the cleanest-mouthed organization I’ve ever been around.

She’s no prig, either.

She grew up on a cow-calf ranch. She’s castrated more bulls than you have seen, even in the movies. If she judges that a male is treating her with insufficient respect, she will describe the method for him. In detail.


Whenever she hears anything off-color, she has a Pavlovian reaction: “Do you eat with that mouth?”

The first time I heard her say that on the subway, I thought the punk would murder us, right there. Instead, he looked sheepish and apologized.

My Love is not a woman to be trifled with.

 

 

Dad

I should have posted this yesterday, of course. Dad will never see it (I hope!), so I’m not sure that matters.


In my memory, Dad lives in my Mother’s shadow. Mother is a force of nature. Dad is quiet, quietly amused at the passing parade.

But the older I get, and the more I look back at my life, the more I see of Dad, the more he becomes a main character.


Dad’s response to almost everything my Mother says is a slightly ironic, slightly exasperated, “Yes, my dear.”


Dad started me in Engineering. When I was little, we built things with wood blocks. He got end scraps from the lumberyard, mostly 2x4s, but lots of oddities, too. We built bridges, railroads, skyscrapers. He taught me about thrusts and vectors, corbelling and arching, catenary and centering, friction and balance.

He’s not an engineer. He’s got a college degree, but not in a scientific or quantitative discipline. Our discovery of engineering was purely experimental and empirical.

He gave me my favorite toys – wooden Brio trains. The Brio box has been in every place I’ve ever lived. I currently have a track set up in my Love’s apartment. I learned lattices and graphs and curves and grades.


Dad taught me the most important thing about Engineering and life:

When I was very young – maybe 5 years old – I was upset about something that had gone wrong. (A common experience in my life. If I start to wonder about what would happen if I did X, I normally try to find out. Experimentally. One of the nice things about having learned Physics, Math and Engineering is that I can get a first approximation before risking life and limb.)

Dad showed me a video tape of Galloping Gertie: The Tacoma Narrows bridge shook itself apart under a wind load. It’s studied by every engineer and physicist in the world. (Really: Please watch the video: It’s amazing. Think of how that would impress a curious 5 year old.)

Dad explained to me that we all make mistakes. Not all of them have results as spectacular as Galloping Gertie. Blame and guilt and fault are irrelevant. They are about the past, and the past can’t be changed. The important thing is to learn from our mistakes and use them for a better future. And engineers and physicists have learned a lot from Galloping Gertie.

I learned the most important lesson in Engineering before I started kindergarten.


When I was in kindergarten, the principal called my parents. I was engaging in some experimental activity. (I may have conscripted some other children as experimental subjects. My memory is hazy on specifics.) The teacher told me to stop, I would get hurt. I told her that the best way to learn was from your mistakes and she was stupid if she didn’t let me make mistakes.

I had to sit in the principal’s office while he explained this to my parents. On the drive home, Mother told me off. Dad just grinned. Mother chewed him out for encouraging bad behavior.

Dad: “Yes, my dear.”


Lindsay at Solo Mama reminded me of another event with Dad.

In catechism and confirmation class, I was a trial to our priest. The priest told my parents that I was refractory and that he would tell that to the bishop.

I said (to my parents) that the priest was an ignorant fool and, if the bishop backed him, the bishop was a stupid jackass.

Mother called me “Young Lady” (the highest level of censorious address, worse than being called by my full name) for only the second time in my life, then sent me to my room to consider how I should confess and apologize.

The last thing I heard before I closed the door to my room:

Dad: Well, he is a stupid jackass.


Dad was raised Catholic. My Mother was raised Protestant, but converted to marry Dad. The old saying, “Converts tend to be zealots”? That’s my Mother.

Dad has always been an indifferent Catholic. Mass every Sunday. Kids through catechism, first communion, confirmation. But it has always been a bemused (and, I think, amused) detachment at my Mother’s heartfelt Catholicism.

I knew how my Mother would react if I came out of the closet. (In the event, I was wrong, thank goodness.)

I didn’t know about Dad. I assumed he would not be happy. I assumed that he would back Mother. And he did.


I didn’t come out to Dad. Mother outed me to him before I got the chance. After my Love outed us to Mother, Mother took me back in the living room.

Mother: Your daughter is a lesbian. That was her girlfriend.

Dad: Yes, my dear.

Mother: Don’t “Yes, my dear” me. Your daughter is a lesbian.

Dad: Yes, my dear. I knew it the minute they walked in the door. Anyone could tell those two girls are in love. I’ve spent the last six hours trying to guess what you were going to do when you figured it out. If you don’t give her your unconditional love, I’m filing for divorce.

Mother: I gave her my blessing, and I don’t want anyone giving her any trouble about it.

Dad: Yes, my dear.

The jet-setting life

An obligatory
“Sorry for not posting”
post

For almost 35 years, my life was bounded

  • on the North by the Canadian border
  • on the East on a line through Rapid City, South Dakota
  • on the South by a line through Santa Fe, New Mexico
  • on the West by the Pacific Ocean.

Seattle and Denver were the largest cities I had ever been in.

Since March, I have been around the world. Twice.

“Oooh. Glamorous! Jet setter! Front of the plane! Grand hotels!”

No.


My latest trip:

Redeye to Frankfurt. Redeye to Singapore. 22 hours.

Clear Customs and Immigration. Disembarkation card:

WELCOME TO SINGAPORE

WARNING
DEATH FOR DRUG TRAFFICKERS
UNDER SINGAPORE LAW
.

You can’t say you weren’t warned.

Check into hotel. Shower and dress. Go to meeting.

Room full of sponsors, bankers, lawyers, investors and engineers. Half of them insulted that my firm would send a girl. The other half that we would send only one person, and she barely out of school.

8-hour grilling by sponsors, bankers, lawyers, investors and engineers. One of the senior engineers (whose work I am implicitly shredding) refers to me as, “Young Lady”. I smile.

Increasing signs of respect, beginning with the senior engineers.

Meeting breaks up. We got the job. General consensus that the Young Lady knows what she’s talking about.

Banker: Give you a lift?

Me: Sure. Thanks.

Banker: A drink and dinner?

Me (showing ring): I’m engaged.

Banker (laughing): I’m gay.

Me (laughing): I’m engaged to a girl.

Banker takes me to the Long Bar at the Raffles. I order a Singapore Sling, because: Raffles. Take one sip. Ewwww. Order a gin and tonic.

Banker takes me to the Seafood Centre. I order chili crab, because: Singapore. Holy cow! Amazing! They don’t serve chili crab at the diner in West Jerkwater. Sadly, the craft beer craze has not reached the Singapore Seafood Centre.

Catch midnight flight to Frankfurt.

24 hours later, back in New York.

That’s right folks:

A day trip to Singapore.

40 hours on planes.

Ugh.

The only girl in the room

In our previous episode, I extolled the virtues of a clawfoot tub and Jo Malone bath oil. Soft skin. Nice scent. A girly girl, no?

I like being a woman. No: I love being a woman.

I like men. I don’t want to sleep with one, but I like working with them.

Men dominate my profession and work environment to a greater degree than any other profession. At my level, I’m usually the only woman in the room. Usually, I’m the person with the ultimate responsibility to the owner or the bank.

I want my style to send three messages:

  • I am a woman.
  • I am selling competence.
  • Everything else is a distraction.

My style is quiet, conservative, traditionally feminine. A dress or a skirt, knee length. Not short. Not tight. Not peek-a-boo. Blue, gray or a neutral color. Flats or low pumps. Nude stockings. Light natural makeup. Natural hair color, medium length. A little gold or pearl necklace. Stud earrings.

I’m not Barbie. I’m not selling sex. I’m not making a political point. I’m not a canvas for tattoos or a pegboard for piercings.

Is that bending to heteronormativity? Advancing the patriarchy? I don’t care. I have a job to do: Build or fix something. Something useful. Something that makes people’s lives better. That job is far more important than smashing the patriarchy.

Besides, I like this style. It’s comfortable. It doesn’t distract from the message. Am I brainwashed? A cowardly conformist? So be it.


Of course, if I’m inspecting conduit or storm drains, I wear a Pendleton plaid shirt, Levi 5o5’s, Red Wing boots, a neckerchief, leather work gloves, a hardhat and Chapstick.

Just call me Butch.

As in, You just keep thinkin’, Butch. That’s what you’re good at.