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You may be able to get by without math, but you won’t be able to get by without integrity.

Everybody lies.  This is a pretty well established fact.    The bad news is that we don’t realize most of the times we lie.   We constantly edit the narrative of our lives to better fit… ourselves.   Whether we know it or not, a great deal of our own memories and sense of self is constructed in order to make ourselves feel better.   People justify their own actions and emotions at any given time, and as time goes on we also revise our own memories (or even just the stories we tell) to paint ourselves in a better light.

As far as I can tell, this is just a natural part of the human psyche.   If you think about it, you’ve probably witnessed others doing it.   If you think about it hard, you can spot where you’ve done it yourself.  Humans are social animals, and this isn’t just an individualized phenomenon.   From groups as small as a junior high school clique, to bigger places like megachurches, and even nations do these things.   They filter information and color experiences through their own collective bias, sometimes with horrible results.   (On a global scale I can think of AIDS denialism, as one example)

This is why it is so important to be able to have the cognitive and intellectual tools to evaluate new claims.   Or old ones.

There are countless tools to this:  you can use a therapist to help you through patches of cognitive dissonance, and this can be good.   Or you can educate yourself, and use some of your own tools.   The point is that you can’t always trust everything you think.    I like to think that as a teacher I can help to give my students some of these tools.   Critical thinking is hard skill to master, and not one that is always comfortable to use.   How often do you honestly think about the quality of your own thought?

There are some pretty good signs that you may be deceiving yourself:   absolutes concerning people are a good one. Reliance on one viewpoint without examining counterarguments is another.   And of course, if you honestly feel that your sense of identity or way of life is threatened by more information, then something is wrong. It isn’t easy changing your view of things, but it does mean that you have a clearer picture of the world.

One thing that I admire about the sciences, is that when they are wrong, they revise their worldview to incorporate better information. They aren’t always quick, but they are good about self-examination.

So… I’ve been wrong about stuff before.   I will again.

… just not today.


Well, it is final’s week for summer quarter at last.   I have loved my class this quarter, they have done fantastic work and made some pretty remarkable breakthroughs.

So here is what I’m going to be doing my grading to this quarter:


And now I go apply for unemployment.   Woo*fucking*hoo.   Summer vacation (hopefully without starvation).

“Foolish consistency is the hobgoblin of little minds…” Ralph Waldo Emerson

How often have you wanted to learn something, and just didn’t know how to proceed?   Or desire to get fit, but no real plan to do so.   I’ve heard people say they want to “learn naturally” and not want to have any barriers to their education.   And then they may complain as to not having appropriate material to suit their incredibly vague needs.

One of the barriers that a lot of students face is the necessity of structure.   From setting aside set times to meet and study, to a (hopefully organized) calendar of topics to cover.   Sprinkle in to that regular practice and some benchmarks and you can actually make progress towards learning something!

It goes way beyond classrooms though.   What do you do without a plan?   How well does that work out?   Even if you don’t stick to your plans, at least they give you a jumping off point. Once you have a pattern that you can learn from, you can then adapt it for other things!

Let me be absolutely clear: there is a world of difference between the regimented world that Emerson talked about, and the necessary structure of our daily lives.   Structure isn’t a straightjacket holding you back, but climbing harness… not comfortable but necessary.

(wow… I suck at analogy…)

I understand that freeform classrooms can be interesting.   I can see how a lot of emergent things can be created in a classroom, and some very interesting creative projects can happen as well. (But also notice: there is still an underlying classroom structure!   Muahahahaha!)

So with all due respect to Emerson, bite me.   Even creative people keep a schedule, and even consistent people can be misunderstood.

There is a lot to be said for being detail oriented.   Big things are made up of little things, and little mistakes can bloom in to full blown disasters if you aren’t careful.    Details matter.     Sometimes though, focus on details can eclipse the creative flow of a process and make it joyless.

Have you ever played an instrument, and just thought exclusively of the notes you were playing?    My guess is that it didn’t sound very good.

Or have you run, and tried to focus on your form and gait?   Awkward, awkward, awkward!

Let alone talking to people.   Say you’re at a party and you see someone intriguing… and you go up and are focused so much on what you are going to say, that you end up  feeling like a total fool?

How does this relate to teaching?     As teachers, we often teach certain skills.   Whether it is constructing a sentence,  multiplying numbers, or deconstructing literature, the details of the process are often foremost in our minds.   There does come a point where we need to switch gears from the detail oriented to the overarching process.    Teaching confidence in newfound skills and just… going with the flow.

Letting goA couple of things need to happen before this transition from focus on details to overall process.   The first step is building trust in their abilities, followed by trust in the process.   Once a student sees that they are working from a solid foundation along workable lines, then it becomes much easier for them to relax into a greater process.   From the specifics to the general, students will learn to do big things made up of the little skills they have learned.  And it is so rewarding as you see those details click into place, transforming from mere knowledge and information into genuine understanding.

This is one of the things that I think we should keep in mind as teaching migrates toward recorded lectures and computerized drills.   Various media can demonstrate individual skills fairly well, but people will always need an overview for how those skills fit together.   Teachers are need to show how to see beyond the details and make the process flow into something that feels natural.   Or how to go from playing notes, to playing a song.

Only then do people find genuine joy.   When it moves away from laboring over details, and more about play.

As I write this, I’m also reminded to “let the details go” in my teaching from time to time, and just go with the flow.


I asked a friend yesterday what I should write about, and she said “paranoid schizophrenia”.     I think she had some suspicion what I would do with this sort of instruction, so if you take offense… blame J–.   I know the strangest people.     It’s quite awesome, really.

Paranoid Schizophrenia vs. Study of Mathematics

The study of mathematics is a mental process that is marked by visualization of unreal systems, feelings of of persecution from instructors and textbook writers,  spending obsessive amounts of time analyzing bizarre systems, and anxiety.   Schizophrenia is a mental illness that can cause auditory or visual hallucinations, delusions, paranoia,  bizarre thought patterns, and disorganized speech and anxiety.

Trying to understand either what a math textbook or a schizophrenic may be telling you is frequently an exercise in futility, unless you have some greater context with which to try to make sense of it.   Even so, the internal logic of a mathematician may break down and you may find them staring blindly into space for a long time.    Bouts of depression are common.

The treatment of schizophrenia is often at institutions which are in danger of defunding.

Ahem… (do I even need to say it?)

Fortunately, the outlook and prognosis for both mathematicians and schizophrenics is depends largely on their social support  network.   With adequate socialization (and sometimes medication), mathematicians can be integrated into the workplace and will lead healthy, productive lives.    Schizophrenic also enjoy this outlook, although the role of medication is somewhat more important.

While schizophrenia and the study of mathematics are often misunderstood, feared and frequently avoided, both will benefit from greater social acceptance and support.



 This is satire.   In reality schizophrenia is a disorder that affects about 1% of the population.   People with schizophrenia can live active and healthy lives with treatment, and treatment for this illness has come a long way in the last few decades.   Untreated, this is a scary disease… both to its sufferers and to their loved ones.   Mental illness is stigmatized to a terrible degree.   Having a mental illness is no more shameful than having blue eyes or red hair… it is the result of biological processes.  But like many uncontrolled biological processes, many people seem to have an unreasoning fear, and discomfort around the subject.


My opinion, as with a lot of social issues, is to educate yourself.   Schizophrenic people are people, deserving of dignity and respect.   Whereas the study of mathematics is more of a choice, and for many folks just as scary and offputting.

One of the things that I have to deal with is students who have a hard time taking tests.   Now I know that there is a lot of hullabaloo about “teaching to the test”, but there is also a clear need to teach people how to take tests.

I teach future doctors, nurses, and law enforcement people.   Do you want these people to fall apart during pressure?

Smilodon TestsRealistically, everyone faces situations when they get flustered and can’t cope from time to time.    There can be many reasons why a person has a stressful reaction, but it all comes down to brain chemistry.    We all have an amygdala, that little piece of our brain that we evolved to survive living alongside Smilodon… and our amygdala are responsible for governing our stress response.   Fight, flight, freeze and appease:  our innate defenses in times of life-threatening stress.

Unfortunately, the amygdala cannot differentiate between saber-toothed-tigers and math tests.

So here is what you can do before a (known) stressful event (e.g. your math test):

  • Overprepare.    While reviewing material is a good idea, if you are anxious about a test it can be useful to give yourself extra time to polish your skills (and build your confidence).
  • Give yourself triggers.  Memory is a funny thing.  Often we will unintentionally link stimulus with certain skills or memories.   You can do this with a scent, or a physical trigger like tapping your hand.  I had one student who literally had a thinking… thong.   He told us about it.   It was endearing, and a little awkward.
  • Reframe the event.  If you are the kind of person to work yourself up before a test, then see if you can change the context for yourself.   If the word “test” freaks you out, see if “quiz”, “assessment”, or “exercise” is better.
  • Take care of your body.    Mind and body are not separate, and abusing your body will play out in poorer brain function and more dramatic stress reactions.   Which means you should eat healthy, and sleep regularly.


Here is what you can do during your test:

  • Feel it, then act (not react).   There is nothing you can do to prevent a stress reaction once it has started.   But if you can recognize the fact and have a plan in place, you can think rather than just flail destructively.
  • BREATHE.   One thing that happens in all stress reactions is people will hold their breath, or breathe very shallowly.   So take a few deep, regular breaths.   It allows your body to relax and get past its stress reaction.
  • Affirm yourself.    Remind yourself there are no saber-tooth-tigers in the room.   Also tell yourself that you are going to ace the hell out of this test.   Tell yourself you are both too stubborn and sexy to fail.
  • Use your memory triggers.   Now is the time to chew that special gum, tap your hand, or remind yourself that you are wearing your thinking thong.


Whether we always recognize it or not, our brains are just like the rest of our bodies.   Tools that we can use to do what we want them to do.   But you will need to train them.    Just like it takes practice to learn how to run a marathon, it also takes practice to put ourselves in stressful (but necessary) situations.

And for my students who just survived your first test:   smile.   You were not killed by a mathematical Smilodon.

Live to study another day.

“I just happen to like apples, and I’m not afraid of snakes.”  – Ani DiFranco

One thing that I’ve never understood is the desire to remain ignorant.

The notion of information or knowledge being dangerous just seems laughable to me.    You are not actually hurt by an idea.   You may have to wrap your head around new thoughts, you may need to revise your viewpoint of the world.   But the ultimate notion of learning things that are “forbidden” is foreign to me.   All you are doing is giving yourself a broader, more nuanced view of the world.

The worst thing that knowledge can do to you is make you uncomfortable.

Some ideas are at odds with each other.   This is the source of discomfort for many people.   This is because some ideas inherently have more merit than others… and of course some ideas may seem at odds with each other but may be unrelated and exclusive.     People also live with differing levels of cognitive dissonance every day:  if you ask a parent who doesn’t vaccinate their children why not, they will likely tell you that they don’t want their children to get sick.   (Irony, anyone?)

It is also okay if people know more than you.   Trying to convince someone that you know about something you don’t isn’t going to make you look better in the long run.   All it will do is make you seem insecure.    I love finding people who know more than I do.   It is so much fun to explore new ideas and to learn something outside my experience.

Here is the kicker for me:   some people do not want you to seek out other ideas.   The reason for this is that they may not feel secure in their own ideas, and need to try to foster their own faulty (although often comforting) ideas in an atmosphere of ignorance.   ANYONE who tries to control who you talk to, what you read, or what to think is trying to control you for their own sakes.   Any person or organization who cuts off discussion like this is controlling at best, and maliciously abusive at worst.     I have literally lost family members because of this kind of abuse, and I find it abhorrent.

This is part of why I teach.

I want people to be able to explore ideas freely.

I want people to be able to think for themselves, and make up their minds independently.

I want people to value knowledge over ignorance.



Okay, just to warn you, I’m going to get a little rant out of my system:


</begin RANT>

Stupid should hurtOne thing that really pisses me off is when people deliberately cloak themselves in ignorance.    The notion of “what I don’t know won’t hurt me” is probably something that was popular on Easter Island.    Denying information doesn’t change it.   All it does is move you from the category of naive to stupid.   At best it is intellectually dishonest.

Now I don’t have anything against faith.   We all have unjustified beliefs about one thing or another.   But here are my criteria:   belief in something without proof is faith, belief in something with proof is knowledge, and belief in something in contradiction to proof is stupidity.

I got MAJORLY pissed off at the supreme court Hobby Lobby decision last week.   They elevated one groups religious opinions over scientific facts, and let the religious  belief trump the rights of others.   I feel like we have our Plessy vs Ferguson court decision for our generation.

Know any nice, liberal countries in need of a kick-ass math professor?   I’m starting to shop.

</end RANT>


Be well, everyone.

And remember to use your powers for whatever you want to.   They’re your powers!

There is something funny about a “Summer Break”.   Often times, I find myself just as solidly booked as during the school term  as I try to catch up with friends and family.   And there is also the added fun of unpaid overtime as we get to prep our courses for the next quarter.   In any case, we’re back.

Now, for a completely random segment let us have your teaching horoscope!

 Aries (March 21 – April 20)

You are plagued by a feeling that you are missing something, like you were supposed to be in class for the entire term, but somehow you didn’t put it on your schedule.      I’m not saying that feeling is true or not, but I think you will want to check.   Check again, you may have missed something.

After that, check to see if you are wearing pants.

Taurus  (April 21 – May 21)

A student is going to approach you in absolute despair about their grade.   They will be young, cute and they think that because of this they deserve a better grade.   While this desperate flirting may help boost your ego in the short-term, you will be racked with guilt later.   Instead it is better to look deep into their eyes and ask, “you’ll do anything to get a better grade?”  When they agree, tell them to study more.   Laughing hysterically is optional, but also fun.

Gemini (May 22 – June 21)

I know you’ve heard a lot of creative excuses, but brace yourself for a wave of really bizarre reasons for not attending.    You can expect stories of alien abduction, burrowing botfly larvae, or stalking by a murderous ex.

Interestingly enough, one of these stories will be true.

Cancer (June 22 – July 22)

Well I’ve got good news and bad news, Cancer.    The good news is that you classes are going to go fairly smoothly.    Your student drama will be on the low side, and the administrative drama seems to be subsiding from the last few quarters.     The downside is that the rest of your life may decide to melt down.   Family matters will leave you squirming uncomfortably, and you may want to check and see if your supplemental insurance premiums are paid up.

Leo (July 23- August 22)

This is a good time to plan, not for action.   So procrastinate a bit, and start fleshing out your plans for world domination.   Or at least plan on taking over the school.    Figure out your game plan to bribe or blackmail the board of regents, simultaneous with a takeover of the teacher’s union.     Then repeat at the state, federal, and global levels.   Now is also a good time for romance.  Consider dating a Virgo:  they have a lot of passion pent-up, so it will be a little like seducing a suitcase bomb.

Virgo (August 23 – September 23)

You will start out the term filled with a sense of invincibility, which will be crushed mid-term by banal stupidity.    You have several different sources of solace.   The easiest route is simply breaking down publicly, so consider bursting into tears at random intervals.   Locking yourself in the bathroom will also garner you some extra attention.

If this strikes you as too passive, then set out a plan for vengeance instead.     Hostages may be necessary.

Libra (September 24-October 23)

Due to a lack of interest,  Libra’s horoscopes have been cancelled.   You may want to consider moving your birthday to sometime more interesting.

Scorpio (October 23 – November 22)

We should have warned you earlier, Scorpio, that this was coming.   During a series of endless meetings you will snap.   After having lost your grasp of reality, your own personal demons will take control of your consciousness.   On the other hand, you can play this fairly close to the chest and no one will know the difference.

Now is the time to foster a new secret identity.

Sagittarius (November 23 – December 21)

The volume of events may get turned up to eleven during the next term, so now would be an excellent time to start writing a memoir.     Or you may want to contact Jerry Springer to try and score some extra cash off of the crazy quarter you have coming to you.

Heavy drinking may seem like a good option, but in the long run it will be more fun to get a substitute for a few days and take an impromptu vacation.

Capricorn (December 22 – January 20)

I love it when a plan comes together.

Your life during the next quarter will be a swarm of odd coincidences that all seem to work in your favor.   Scheduling conflicts work themselves out without effort, troublesome students decide to transfer to another class, and HR may discover that they “accidentally” forgot to pay you for something earlier last year.   I do want you to remember two important things:   (1)  happy stress is still stress, (2)  don’t question good luck.

Aquarius (January 21 – February 19)

This will prove to be an interesting quarter for you.   After an academic rejection, you may decide to seek refuge in sex work.  While it may seem like a desperate move at the beginning, it actually will feel very fulfilling after a short time.   Stock up on lube and condoms.

Craigslist will make you devalue your new career choices, and you may want to come back to teaching.

Pisces (February 20 – March 20)

There will be opportunities available to you sometime soon, Pisces.   Most likely a friend or colleague will burst into tears randomly.   First, you can step in and help.   And now that they have proven themselves vulnerable it is also a perfect time to exploit them for your own needs and desires,  you sick pervert.

And they will be appreciative.

If you are an evil teacher, have you considered blogging?   I am looking for a few dark hearted educators to join the evil league.   Post in the comment section, and I will be in touch!

Alphone Mucha - Zodiac 1896

Ah, Spring term is over and Summer is in the air… responsibilities seem so far away.   Now that those pesky final exams are out of the way.

Now, for a completely random segment let us have your student horoscope for next term.

Aries (March 21 – April 20) 

You are plagued by a feeling that you are missing something, like you were supposed to be in class for the entire term, but somehow you didn’t put it on your schedule.      I’m not saying that feeling is true or not, but I think you will want to check.     Check again, you may have missed something.

After that, you should read your syllabi to determine whether you missed a paper or a test.    Also check to see if you are wearing pants.

Taurus  (April 21 – May 21)

Crunch time is your time to shine.   You will find yourself reworking a project from start to finish after finding a minor error after finishing the FIRST time.   This means that you neglect your other classes for a few days, and the effect snowballs.    After working 90 hours per week for a few weeks in a row, you may start to consider a career as an exotic dancer.   Before you switch please remember that thongs can itch, especially if they are full of dollar bills.

Therefore, your mantra is:   done is better than perfect.

Gemini (May 22 – June 21)

You should help out a friend in need.   This help can come in many different forms.   It may be that they are in deep need of a homework intervention, so bring tequila and a study guide.   Or it may turn out that they are in desperate need for a rebound hookup, so bring condoms (avoid tequila, because that would be rape).   Or you may need to cheer up an instructor who is buried under a three foot tall stack of grading, in which case bring two bottles of tequila and an extra red pen.

For you, the worst thing about finals will be the hangover(s).

Cancer (June 22 – July 22)

After pulling several all-night study sessions this week, you are feeling out of touch with reality.   You will have a very important conversation regarding your academics, but later on in your imagination you will replace the people of this with tropical fish.   Afterwards, you will dream of turning your papers in to your instructor, who is now a giant squid.

Once you are caught up on sleep, you will find that you can only recall your course material while humming “Aqua” songs.    There is no logical explanation for this.

Leo (July 23 – August 22)

Lets say that you are on a long vacation.   You have a plan for where you are going, and some ideas about what you would like to do.   When you get there, you make a random connection with someone which was entirely unexpected.  Nothing was according to plan, but it was perfect anyway.   You fall in love, then have your heart broken a week later when you have to leave.   Years later, you still pine for that lost person, even after you have a caring and stable relationship with another person.

This is a perfect analogy for school this term, Leo.

Virgo (August 23 – September 23)

Little changes will make big differences for you.   Even though you don’t need to do it to succeed, you decide to do your homework.   All of a sudden, it all makes sense!   You understand the deeper cosmological context of the knowledge, although you know that this feeling is fleeting and ephemeral.     You know the ultimate truth, we are like dust in the wind.

It is also a good time to make up an excuse for your extended absences to your instructor.   Be creative, they probably will forget something too pedestrian.

Libra (September 24-October 23)

Your natural leadership skills come to the fore this term.   It isn’t as though you asked for greatness, it seems to be thrust upon you.   So take it easy!  You are sure that you can get someone to do the work for you if necessary.  If the work didn’t get done, you can just as easily apportion blame.   Negotiate with your teachers, but be careful in case your instructor may also be a Libra.

Now is also a great time to work on your wider academic plan.   See if you can foster the image of a mastermind, and consider running for student government.

Scorpio (October 23 – November 22)

The winds of change are blowing.  You can feel them blowing you into a new academic direction soon.    If you were studying the arts, consider a change to the sciences.    Premed and engineering students may wish to pursue business.    Business students, you may find that art and history is calling your name.    Get inspired by something.

If you are daring, you could consider taking on a second major.   Or a third.   Student loans couldn’t really be that bad, could they?

Sagittarius (November 23 – December 21)

You may have found yourself in a slightly difficult situation, but you can overcome these setbacks.   It may be that you missed a few classes, and that put you in a slightly difficult situation.   You also may have accidentally slept through a test.   Be your smartest, most charming self, and go ask for some help to get through your term.

Seducing your instructor may seem like a good idea at the time, but be prepared to be laughed at.

Capricorn (December 22 – January 20)

How do I put this delicately Capricorn?   Uranus is in a sling, so watch where you point your moon.    You are going to feel cursed, but this isn’t really what the problem is.   The problem is you.   Now is the time to set aside your ego, and ask yourself who is actually calling the shots.

The difficulty here isn’t that the world is out to get you, it is just that the world doesn’t care about you.   Stop whining, and get to work.

Aquarius (January 21 – February 19)

 Years from now you are going to look back and realize that the most important events of your life happen this term.   You won’t notice them just yet, but make a note:   Thursday at 3:20 pm.   I’m not going to tell you which Thursday.

You may want to check and see if you have a valid passport, and know where your car keys are.   Buckle up and don’t speed, and for your sanity’s sake don’t look in the trunk.

Pisces (February 20 – March 20)

You know how to get out and party.     And by party, I mean you didn’t go over your notes in three different colors, and you only do 2 revisions of your latest paper.   You may get upset by missing a question on your final, leaving you with a 95% on the test, but this will be offset by Mercury in retrograde and the fact that you have turned in every single extra credit assignment.

Your quests for the week are to do 2 of the following:    read something fiction written within the last 20 years,  get laid (be safe), play Frisbee, learn how to say “ain’t”,  or talk to a stranger.

Coming soon:   teacher horoscopes!

The term is almost over for me.   This is always bittersweet… I look will miss my students (yes, even you  ____ ), but I also look forward to getting a break from things as well.    This term I don’t have as much grading to keep up with, but I do still need a playlist of slightly snarky songs.

It helps to keep me sane.   Or my facsimile of sane, anyway.

So without further ado, here is my finals week playlist.    It is also available here on YouTube, along with last quarter’s picks.


Wish me luck.   Finals are coming.