Strenner: Pseudo-Anosov mapping classes not arising from Penner’s construction

Balazs Strenner, a Ph.D. student of Richard Kent graduating this year, gave a beautiful talk yesterday in our geometry/topology seminar about his recent paper with Hyunshik Shin.  (He’s at the Institute next year but if you’re looking for a postdoc after that…!)

A long time ago, Robert Penner showed how to produce a whole semigroup M in the mapping class group with the property that all but a specified finite list of elements of M were pseudo-Anosov.  So that’s a good cheap way to generate lots of certified pseudo-Anosovs in the mapping class group.  But of course one asks:  do you get all pA’s as part of some Penner semigroup?  This can’t quite be true, because it turns out that the Penner elements can’t permute singularities of the invariant folation, while arbitrary pA’s can.  But there are only finitely many singularities, so some power of a given pA clearly fixes the singularities.

So does every pA have a power that arises from Penner’s construction?  This is what’s known as Penner’s conjecture.  Or was, because Balazs and Hyunshik have shown that it is falsitty false false false.

When I heard the statement I assumed this was going to be some kind of nonconstructive counting argument — but no, they actually give a way of proving explicitly that a given pA is not in a Penner semigroup.  Here’s how.  Penner’s semigroup M is generated by Dehn twists Q_1, … Q_m, which all happen to preserve a common traintrack, so that there’s actually a representation

\rho: M \rightarrow GL_n(\mathbf{R})

such that the dilatation of g is the Perron-Frobenius eigenvalue \lambda of \rho(g).

Now here’s the key observation; there is a quadratic form F on R^n such that F(Q_i x) >= F(x) for all x, with equality only when x is a fixed point of Q_i.  In particular, this shows that if g is an element of M not of the form Q_i^a, and x is an arbitrary vector, then the sequence

x, g x, g^2 x, \ldots

can’t have a subsequence converging to x, since

F(x), F(gx), F(g^2 x), \ldots

is monotone increasing and thus can’t have a subsequence converging to F(x).

This implies in particular:

g cannot have any eigenvalues on the unit circle.

But now we win!  Because \rho(g) is an integral matrix, so all the Galois conjugates of \lambda must be among its eigenvalues.  In other words, \lambda is an algebraic number none of whose Galois conjugates lie on the unit circle.  But there are lots of pseudo-Anosovs whose dilatations \lambda do have Galois conjugates on the unit circle.  In fact, experiments by Dunfield and Tiozzo seem to show that in a random walk on the braid group, the vast majority of pAs have this property!  And these pAs, which Shin and Strenner call coronal, cannot appear in any Penner semigroup.

Cool!

Anyway, I found the underlying real linear algebra question very appealing.  Two idle questions:

  • If M is a submonoid of GL_n(R) we may say a continuous real-valued function F on R^n is M-monotone if F(mx) >= F(x) for all m in M, x in R^n.  The existence of a monotone function for the Penner monoid is the key to Strenner and Shin’s theorem.  But I have little feeling for how it works in general.  Given a finite set of matrices, what are explicit conditions that guarantee the existence of an M-monotone function?  Nonexistence?  (I have a feeling it is roughly equivalent to M containing no element with an eigenvalue on the unit circle, but I’m not sure, and anyway, this is not a checkable condition on the generating matrices…)
  • What can we say about the eigenvalues of matrices appearing in the Penner subgroup?  Balazs says he’ll show in a later paper that they can actually get arbitrarily close to the unit circle, which is actually not what I had expected.  He asks:  are those eigenvalues actually dense in the complex plane?

 

 


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ageofdestruction: solar corona, photographed by stereo a, 8th…



ageofdestruction:

solar corona, photographed by stereo a, 8th september 2012.

20 images over 10 hours, inverted. the dots moving in the background are stars.

image credit: nasa/stereo. animation: ageofdestruction.

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myjetpack: My book of cartoons ‘You’re All Just Jealous of my…



myjetpack:

My book of cartoons ‘You’re All Just Jealous of my Jetpack’ is available now:US: http://www.amazon.com/dp/1770461043
UK: http://www.amazon.co.uk/dp/1770461043
Other stockists, info and prints for sale at www.tomgauld.com

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Code-X (49)

nesteaExplosive Potential
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uneven-growth: A promise is a cloud (2014) appropriates…



uneven-growth:

A promise is a cloud (2014) appropriates artisanal techniques used to harvest water from fog. The nets provide daily up to 1,000 litres of water for a community of 500 families in the outskirts of Lima, who like millions of Limeños live without access to clean water.

Inspired by an Arab saying, the project presents a critical reflection of Lima based on its meteorological conditions: a city spread throughout the desert, whose main source of water comes from melting glaciers and is permanently covered by a gloomy cloud that rarely produces any rain.

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“On Tuesday, I attended court for the Silk Road trial closing arguments and watched the defense…”

“On Tuesday, I attended court for the Silk Road trial closing arguments and watched the defense struggle to carve out a plausible defense of their client. All of the blended fiction and real elements of life on the internet were yanked from the dark mirror and presented as evidence to a courtroom full of people who left their digital devices with security at check through. It is entirely reasonable to believe Ross Ulbricht was a pretty nice, normal seeming guy and also Dread Pirate Roberts, the Silk Road kingpin. That’s not to say he got carried away either. Silk Road was an ideological anarcho-capitalist enterprise. (One of the exhibits, notes on daily operation of the deep web black market included this handshake: “read any good books lately?” “anything by rothbard.”)”

-

The Internet is Real — The Message — Medium

I wrote this ;)

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groundhog bites mayor



groundhog bites mayor

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Bob Marley

bob-marley-live-8“Babylon system is the vampire”
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noseracontacto: O



noseracontacto:

O

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noseracontacto: o



noseracontacto:

o

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noseracontacto: A girl smeared with colors reacts as another…



noseracontacto:

A girl smeared with colors reacts as another girl throws powder at her during Holi celebrations in Chennai on March 16, 2014.(Reuters/Babu)

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noseracontacto:clown



noseracontacto:

clown

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“Within the next generation I believe that the world’s rulers will discover that infant…”

“Within the next generation I believe that the world’s rulers will discover that infant conditioning and narco-hypnosis are more efficient, as instruments of government, than clubs and prisons, and that the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging and kicking them into obedience. In other words, I feel that the nightmare of Nineteen Eighty-Four is destined to modulate into the nightmare of a world having more resemblance to that which I imagined in Brave New World. The change will be brought about as a result of a felt need for increased efficiency. Meanwhile, of course, there may be a large scale biological and atomic war — in which case we shall have nightmares of other and scarcely imaginable kinds.”

- Letters of Note: 1984 v. Brave New World
Aldous Huxley in a letter to George Orwell
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thingsmagazine: Cardboard City: Brutal London



thingsmagazine:

Cardboard City: Brutal London

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brownshoesonly: standard patching #CRTpic



brownshoesonly:

standard patching #CRTpic

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The Unconquerable (32)

macinnesThe Decision
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kiameku: Magnus Thierfelder Fountain 2004 Coleman Project,…



kiameku:

Magnus Thierfelder
Fountain
2004
Coleman Project, London

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coitusandcarnage: publicity photo by Helmut Newton for Bram…



coitusandcarnage:

publicity photo by Helmut Newton for Bram Stoker’s Dracula

Vanity Fair, 1992

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Air Bridge (1)

innes thumbI pushed the paper away and said, "Why didn’t you hand me over?"
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How to hold a blood drive in the spirit of intellectual freedom

StateLibQld_1_131955_Book_Depot_float,_Red_Cross_Procession,_Brisbane,_1944

It’s been fun being able to follow along with the ALA Midwinter conference on a bunch of different social media fronts. I was just reading the Stonewall Book Awards press release (congrats everyone) and noticed the GLBT Round Table page where I read the press release about the blood drive that happened during ALA. And it made me happy. Both because there was a blood drive but also because there was the recognition of the discriminatory nature of the decisions regarding the eligible donor pool–nearly all gay and bisexual men can’t donate blood at all–and they not only mention this in the press release but there is a panel discussing this and related issues. Nice work.

ALA and LBC (Librarians Build Communities) recognize there are many restrictions regarding blood donations. Among those is the ban on accepting blood donations from men who have had sex with another man since 1977. This effectively removes all gay and bisexual men from being eligible blood donors. However, the FDA has recently announced plans to relax the ban to allow donations by gay and bisexual men if they have not had sex with another man in the past year.


From the onset, this ban has been controversial. While the government has imposed exclusions that limit or restrict the donor pool, the ban on accepting blood donations from gay and bisexual men is deemed by many as unjustified and discriminatory, unfairly prohibiting healthy men from donating much needed, life-saving blood.


In an effort to educate the library community about the issues regarding blood donations, the ALA Gay, Lesbian, Bisexual, and Transgender Round Table (GLBTRT) is sponsoring the discussion panel “Blood Donation: Facts, Fear, and Discrimination,” on Sunday, Feb. 1, 2015, from 8:30 a.m. to 10 a.m. LBC supports the GLBTRT’s panel discussion and encourages ALA members to both donate blood and attend the panel discussion to be informed and have their voices heard.

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Ordinary business expense

From today’s NYT:

But even if Hyundai is eventually forced to pay the full amount of the damages, the punishment could be substantially reduced through a tax loophole that permits the company to save millions of dollars by deducting any court-ordered punitive damages as an ordinary business expense. The result, critics say, is that taxpayers are in effect subsidizing corporate misconduct.

What’s terrible about this isn’t that companies are allowed to claim the fines they pay for malfeasance are an ordinary business expense.  What’s terrible is that it’s true.

 


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icancauseaconstellation: Michel Rougier… Saul Steinberg at work…



icancauseaconstellation:

Michel Rougier… Saul Steinberg at work on humorous cutouts depicting “People of America” at Brussels World’s Fair 1958 @ life

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narcissistic—panda:don’t mind the dancing groot. :)



narcissistic—panda:

don’t mind the dancing groot. :)

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rebel6: by Danilo Kato



rebel6:

by Danilo Kato

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aprilkrause:

aprilkrause:

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Code-X (48)

chinetIronic Biker
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fabriciusitalicus:Alois Kolb (1875-1942), ex-libris













fabriciusitalicus:

Alois Kolb (1875-1942), ex-libris

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postgraduategoth:vintagebrides:1935, Cleveland, Ohio – Minnie…



postgraduategoth:

vintagebrides:

1935, Cleveland, Ohio - Minnie Ruth Solomon waiting at the train station for her fiance, Olympic champion Jesse Owens on the eve of their wedding.  

Gorgeous.

I’d totally wear that!

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One of the best-loved places to eat is Watts Coffee House, the…



One of the best-loved places to eat is Watts Coffee House, the roots of which lie in the Watts Happening Coffee House, which opened shortly after the rebellion. Bruce and I first walked right past the restaurant because it’s practically hidden inside a building shared with a school. We did notice the mural, which is a holdover from the building’s past as the home of the Mafundi Institute in the early 1970s.

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“Cyberspies used social engineering trickery to steal Syrian opposition’s strategies and battle…”

“Cyberspies used social engineering trickery to steal Syrian opposition’s strategies and battle plans, according to security researchers. Hackers employed a familiar tactic: ensnaring victims through conversations with seemingly sympathetic and attractive women. As the conversations progressed onto Skype chats, the “women” would offer up a personal photo that was laden with malware and designed to compromise the target’s computer or Android phone.”

-

Fake hottie hackers flung info-slurping malware at Syrian opposition – FireEye • The Register

via melissa

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evergod:The Flight of Moloch, 1809 William Blake



evergod:

The Flight of Moloch, 1809

William Blake

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polychroniadis: Andrei Tarkovsky, ‘The Sacrifice’, 1986.



polychroniadis:

Andrei Tarkovsky, ‘The Sacrifice’, 1986.

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gifopera: temple of the running man(a slight variation of this…



gifopera:

temple of the running man

(a slight variation of this gif)

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The High Wire (14)

the-high-wire‘I’m a man without honour but I’m not a dishonoured man.’
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nitratediva: Harold Lloyd in The Freshman (1925).





nitratediva:

Harold Lloyd in The Freshman (1925).

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“What started with dozens of re-purposed boy scouts grew to hundreds, but there it hit a ceiling….”

What started with dozens of re-purposed boy scouts grew to hundreds, but there it hit a ceiling. When that happened, Putin’s team approached Russian advertisers. According to my sources, there are currently 10 different advertising agencies working for the Kremlin. These contracts are secret, and the firms are careful to maintain other, non-political clients.

The agencies compete fiercely with one another for contract extensions and bigger deals, making Russia’s online propaganda industry quite lucrative and surprisingly effective. It’s like Adam Smith’s “invisible hand,” except the opposite.

Combined, these efforts field a troll army of thousands. In some areas, like on the outskirts of St. Petersburg, the enterprise is so big that there are whole office buildings for these people.

It seems like a joke, but thousands of hired bloggers “go to work” every day, writing online about Vladimir Putin’s greatness and the decay of the West. They’re on Facebook, Twitter, news sites, and anywhere else the Kremlin feels threatened and outnumbered. Fresh instructions arrive every day in emails, specifying what to say and where to post it, all with the aim of bolstering Putin’s presidency amidst war and economic crisis.



- How Putin Secretly Conquered Russia’s Social Media Over the Past 3 Years · Global Voices
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Robert Greene discusses his and Catherine Texier’s translation of Jacques Mesrine’s “The Death Instinct” at Skylight Books

ROBERT GREENE discusses his and Catherine Texier's translation of JACQUES MESRINE'S THE DEATH INSTINCT

The Death Instinct (Tam Tam Books)
France's Public Enemy Number One from the late 1960s to the end of the 1970s--when he was killed by police in a sensational traffic shootout--Jacques Mesrine (1936-1979) is the best-known criminal in French history. Mesrine was notorious both for his violent exploits and for the media attention he attracted, and he remains very much a public media figure in France and Europe. In 2008 there were two feature-length films based on his life, one of them starring Vincent Cassel in the lead role. Mesrine wrote The Death Instinct while serving time in the high-security prison La Sante; the manuscript was smuggled out of the prison and was later published by Guy Debord's publisher Gerard Lebovici (who briefly adopted Mesrine's daughter, Sabrina, before being assassinated, a few years after Mesrine). The Death Instinct deals with the early years of Mesrine's criminal life, including a horrifically graphic description of a murder he committed early on in his career and a highly detailed account of the workings of the French criminal underworld--making this book perhaps one of the most intriguing and detailed anthropological studies of a criminal culture ever written.
Praise for The Death Instinct:
"Jacques Mesrine was a modern Robin Hood. Modern in the sense that his story includes violence, spectacle, and that he is not just a figure of legend. He did not let the tabloids write the only version of the story. He wrote this remarkable book. About the only thing Guy Debord and Michel Foucault ever agreed on is that this book is a top read." --McKenzie Wark, author of The Beach Beneath the Street
"Unputdownable, incendiary real-life noir. With a touch of Belle-Epoque anarchist criminal Bonnot, nurtured by disposition, pathology and war. No wonder Situationists admired this escape-artist-sociopath, whose sense of honor and justice was matched only by his contempt for society. In literate and lucid contraband prison prose which, as Mesrine says, mixes all the genres: “burlesque, gore, violence, friendship, and fugitives on the lam.” Too bad this "man of a thousand faces" isn't around to help deal with present-day bank corruption, or, for that matter, the prison-industrial complex."--Woody Haut, author of Heartbreak and Vine and Pulp Culture: Hardboiled Fiction and the Cold War
Robert Greene is the author of five books: The 48 Laws of Power (Penguin), The Art of Seduction (Penguin), The Strategies of War, (Penguin) The 50th Law (co-written with the rapper 50 cent, Harper Books), and Mastery (Penguin)He is currently at work on his next book, The Laws of Human Nature (Penguin). He has previously translated from the French, Considerations on the Assassination of Gérard Lebovici, Guy Debord (Tam Tam books). Robert Greene lives in Los Feliz.
Robert Greene photo by Susan Anderson
Event date: 
Thursday, February 12, 2015 - 7:30pm
Event address: 
1818 N Vermont Ave
Los AngelesCA 90027
By Jacques MesrineRobert Greene (Translator), Catherine Texier (Translator) 
$16.95 
ISBN: 9780966234688 
Availability: On Our Shelves Now 
Published: Tamtam Books - November 2014 
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love-of-words20: Did God promise you would go to heaven? You…





















love-of-words20:

Did God promise you would go to heaven?

You have burned a saint!

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The Sunday Series: Sunday No. 4 (February 1, 2015)



Sunday No. 4

It is not my natural mind-set to face an audience or a large group of people in a contained, maze-like space.  I’m doing a signing at the Los Angeles Art Book Fair that is located at the MOCA/Geffen museum.  On one level, it is an incredible fair, with tons of books and art related images from one booth to the next.  And then after being practically over-whelmed with the art books, one suddenly discovers that there is another large room just full of zines and its culture.  To really appreciate the art book world, one needs to spend the entire three days at this fair.  Nevertheless my purpose today is to sign my late dad’s album, which is called “Wallace Berman - In Conversation.” It’s a secret recording of my dad talking about art, curating exhibitions, and cultural life in Topanga canyon circa. 1968.  It’s an amazing document on many levels, but what is shocking to me is that I’m somewhere on that album, but more of a presence that was upstairs from the room where the conservation between my dad and guests took place.  I don’t think you can hear my voice, but I’m there.  And the sense of me being on the recording, in a very vague way, is a sharp contrast for me to be at this fair to sign copies of an album that exists in a world that is placed in my history, which at this point, is only  a memory.  

The serious problem I have of being in a crowd is I fear many things.  One, I’m quite shy, and I’m not really used to be in a position where people need my attention.  And due to the fear, I have a habit of forgetting people’s names - even friends who are very close to me.  There is a name for people who “fear” in forgetting - athazagoraphobia.  So I have that as well as agoraphobia, which is the fear of open spaces or of being in crowded public spaces like markets, or popular book fairs, like this one.   So the combination of my shyness, agoraphobia, as well as the killer blow, athazagoraphobia, makes this experience quite painful for me.  



I know the face, and I know it very well. The problem is when I try to place a name with that face.  Also most people are usually offended if you can’t remember their name at a specific time, and that can cause great anxiety on my part. I never want to offend someone, but at the same time, I am slightly turned-off by people who feel their title, their given name, is something that is more important than their being.   A name is just a title. It really doesn’t explain who or what you are.  I know who you are, just because of your personality, your looks, and so forth.  A name doesn’t convey the depth of the essence that is “you.” Yet, here I’m struggling at a signing, trying to remember the names of people who are in front of me.  The pure torture of it, causes an incredible anxiety within me.  

At the moment, there is this beautiful woman in front of me.  In fact, I have often had sexual fantasies of her - and for whatever reason, of course due to my combination of phobias, I can’t recall her name right away as I ‘m in the position to sign “For _ love, Tosh Berman."   I want to replace the dash so strongly, especially for her, but the name, the spelling, just doesn’t come to me at the moment.  She was polite enough to slip her name in the conversation during this transaction, but then there is this horrible awkward moment of her knowing that I totally forgot her name.  And I have known her for at least 20 years or so.  20 years of lusting for her, yet when the time of great importance comes upon me, I totally forgot her name. 




I feel a great sense of disgust with myself, and of course besides the hatred, the shame as well.   And now, she has a copy of the album, and when she sees it, she will think of the moment that I forgot her name.  I don’t think she will hate me for it, but for sure, there will be a tinge of disappointment for as long as she keeps that album.  Also, when I think of the album, I will go back to that moment as well.  So, the one thing we will share in the future is the failure of memory and communication.   As a writer, it's the finalized blow to the body. 
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Bad lesson

From the New York Times, “Why You Should Tell Your Children How Much You Make”:

When Scott Parker wanted his six offspring to know more about the value of money, he decided to do something that many parents would consider radical: show them exactly what he earned.

One day, he stopped by his local Wells Fargo branch in Encinitas, Calif., and asked to withdraw his entire monthly salary in cash. In singles. It took 24 hours for the tellers to round up that many bills, so he returned the next day and took away the $100 stacks in a canvas bag.

His oldest son, Daniel, who was 15 at the time, remembers the moment his father walked into the house and dumped the $10,000 or so on a table. “It looked like he had robbed a bank,” he said.

Parker was trying to teach his kids a lesson about the value of money.  But the lesson I would learn from this is “If somebody, like a bank teller, works in a service job, and makes a lot less money than I do, I can make them spend a full day of their life carrying out an incredibly tedious task without thinking about whether this is a reasonable way for them to spend their time.”

 

 

 

 


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John Ford

john fordEntertainment, grand landscapes, and dialectical troubles.
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S.J. Perelman

s_j_perelmanStrutting, superior but somehow also self- deprecating.
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Full professors make more money than bus drivers

Former Republican Congressional candidate and current UW-Madison history professor John Sharpless stands up for us against the Governor:

He said he arrives no later than 9 a.m. and leaves no earlier than 5 p.m. During that time, he said he’s either teaching, preparing lectures, doing research, attending required committee meetings, advising students and managing teaching assistants. Sharpless added that he often spends his evenings reading and grading papers.

“None of this seems like work to a guy like Walker because he lives a different life,” he said. “And I’m not going to make fun of what he does. I’m sure being a governor is a lot of work. He has to spend a lot of time in Iowa and South Carolina and North Carolina and courting other Republican big-wigs. That taxes the man horribly.”

But just to make it clear he’s still on board with GOP, he drops this in:

“I will retire with a salary that’s less than a Madison bus driver,” he said.

UW-Madison salaries are public records, so I can tell you that Sharpless’s is just under $80,000.  In 2012, only 9 employees of Metro made more than $70K.  And the ones who made that much, I’m pretty sure, are the ones who worked tons of overtime.

In other words, what Sharpless said is likely true in the strict sense of

“There exists a Madison bus driver whose salary this year exceeds mine”

but gives the wrong impression about typical full professors in the history department and typical bus drivers.


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