What’s a Mathematician To Do?

Great answer on Math Overflow by mathematician Bill Thurston (1946-2012) to the question, “What’s a mathematician to do?”:
Bill Thurston

It’s not mathematics that you need to contribute to. It’s deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually.

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat’s Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

The world does not suffer from an oversupply of clarity and understanding (to put it mildly). How and whether specific mathematics might lead to improving the world (whatever that means) is usually impossible to tease out, but mathematics collectively is extremely important…

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians.

(via Hacker News)

Recipe For a Good Human Society

My friend JoAnn gave me this recipe card today:

Recipe For a Good Human Society

  1. Start with one View of basic self-worth — apply liberally and marinate continuously.
  2. Add high quality principles. Cook’s note: I suggest generosity, patience, compassion, kindness, and intelligence. Be careful not to cross-contaminate ingredients with doubt.
  3. Stir well, then let rest — this allows confidence to arise.
  4. Infuse essence of mixture into daily conduct, particularly situations that break the heart.
  5. Yields one good human society.

Serves: Limitless numbers of beings
Level of difficulty: Simple, but not easy

Running Through the Grief

Even though I know things must be as they are, I am still struggling. The grief is coming in waves now, occasionally incapacitating me. That’s better than before, when I was overwhelmed for weeks on end. It’s still hard to surrender and accept that sometimes I am helpless because of it.

Yesterday was a hard day, and I was still feeling the effects this afternoon at work. I felt my creativity waning. When that happens to my team members I say, go take a nap or a walk, do something that helps get you back into a creative place.

I am not a napper – that’s a super-power I would love to have but don’t (yet). What to do instead? My intuition said, “The blessing is outside your comfort zone. Go for a run.” Fortune shone on me— this time I listened.

That was a victory. An hour later I found myself in Lincoln Park, running along the shore, silver light shining off dark blue water. I climbed the cliff trail and ran through the forest. I felt a lot better after the run and sat by the water a long time, watching the golden sun set over the Olympic mountains. As the light faded so did my struggle.

Maybe it will be back tomorrow. But right now I am at peace.

The Wisdom in Dark Emotions

Great article in The Lion’s Roar on the Wisdom of Dark Emotions:

Knowing how our grief, fear and despair may be connected to larger emotional currents and social conditions de-pathologizes these emotions, allowing us to accept and tolerate them more fruitfully, and with more compassion for ourselves and others. We begin to see the dark emotions as messengers, information-bearers and teachers, rather than “negative” energies we must subdue, tame or deny. We tend to think of our “negative” emotions as signs that there’s something wrong with us. But the deepest significance of the feelings is simply our shared human vulnerability. When we know this deeply, we begin to heal in a way that connects rather than separates us from the world.

Learned Optimism

In a previous post I mentioned that science didn’t know much about how to teach or grow optimism. I was wrong about that – quite a bit is known, actually. After I wrote that post I became more interested in how to learn optimism, and came across Martin Seligman’s great book on the subject, Learned Optimism.

This book is the product of Seligman’s many years of scientific research on optimism – what it is and how to learn it. There are scientifically studied ways to learn optimism. In the book Seligman is critical of therapy (one of my recommendations in the last blog post). He’s not critical of therapy because it is ineffective – indeed, he says it is quite effective in helping people be optimistic. But it can never be available to millions of people just because there just aren’t enough therapists to go around. That is a compelling argument.

So if therapy is out for most people, then what’s in? Techniques that you can learn and practice on your own. So meditation counts (although he doesn’t talk about it in the book). The main technique Seligman focuses on in this book is called “ABCDE”:

  • Adversity – being aware of the situation or event which triggers your pessimism.
  • Belief – noticing how you interpret the adversity
  • Consequences – being aware of what you did, how you acted or behaved, and how you felt
  • Disputation – making an effort to argue with yourself and dispute your beliefs – redeploying your attention
  • Energization – noticing the outcome or effect of redirecting one’s thoughts and attention

The idea behind this technique is to notice when you are experiencing adversity, what your beliefs about it are, and how you feel and act because of that. That’s the noticing part. Then you can take some distance from those beliefs and stories about the adversity, and argue with yourself about them – in other words, deploy some rationality and tear down the negative judgements, thoughts, and beliefs. The thoughts often lose a lot of their power when we see that they may not be rational or valid. Once they have lost some power, we aren’t so paralyzed by them, we often feel better, and can frequently begin to take positive action.

It sounds almost too simple to work, but it has been extensively taught and studied, and it is effective. It can be learned quickly, and practiced in daily life when those critical voices come up.

I’d also add, meditation enhances its effectiveness, because meditation helps one develop the “watcher” part of our mind that has a little bit of distance from our thoughts, and can see what’s happening without getting caught up in it so much. One way to look at meditation is that it is made up of awareness and mindfulness. Knowing what’s happening is awareness, key to the first three steps. Mindfulness is coming back to the breath or the present moment, being able to return and place our mind on what we want. In this technique, that’s the disputation, and the practice of being able to see and feel the results. Meditation also helps in developing self-compassion which can help add warmth, connection, and a larger perspective to the noticing and disputation.

The book goes into quite a bit of detail about how to effectively dispute one’s own inner voices. Good questions to ask are:

  • Evidence? – What is the evidence for this belief or story?
  • Alternatives? – Are there alternative explanations?
  • Implications? – Can I decatastrophize the story by seeing if the implications are exaggerated?
  • Usefulness? – Is it constructive to hold this belief or see the story as valid?

There’s quite a bit more I could say about this book – Seligman covers what optimism and pessimism are made of, optimism and children, optimism on teams and at work, and the relationship between optimism and depression. I’ll have to save those topics for other posts. I found this book interesting and I recommend it if you’re interested in optimism, how to become optimistic, or how to teach it as a skill.

(Available from Amazon)

I’m Hiring

I’m hiring for two software developer positions:

We’re a fast-growing, fun, high-performance team working on some interesting large-scale machine learning applications. We use Scrum and Extreme Programming methodologies, Linux and Open Source software (and we contribute back also), and know that it’s creativity that matters, not the number of lines of code, so we take a humanistic, positive psychology-based approach to work. If you’re interested in breaking the bounds of what’s possible in terms of creativity and personal growth, we want to know you!

Both these positions report to me. You’d be joining a team of 5 other developers, and an engineering organization of about 15 total. If you like what you see on these pages, or over on Live In Greatness, I would love to hear from you. We also have more positions open: MetaBrite Careers page, or if you don’t see one that fits, but you’re still interested, get in touch anyway! You can email me at adam@metabrite.com, or use my personal email found on the About page.

These jobs are located in downtown Seattle. Here’s the MetaBrite website.

You Are Living in a Poem

“You are living in a poem,” says poet Naomi Shihab Nye.

“What do you mean, we’re living in a poem?” Or, “When? All the time, or just when someone talks about poetry?” And I’d say, “No, when you think, when you’re in a very quiet place, when you’re remembering, when you’re savoring an image, when you’re allowing your mind calmly to leap from one thought to another, that’s a poem. That’s what a poem does.”

From the wonderful and optimistic interview Your Life Is a Poem with Naomi Shihab Nye at On Being.


Before you know what kindness really is
you must lose things,
feel the future dissolve in a moment
like salt in a weakened broth.
What you held in your hand,
what you counted and carefully saved,
all this must go so you know
how desolate the landscape can be
between the regions of kindness.
How you ride and ride
thinking the bus will never stop,
the passengers eating maize and chicken
will stare out the window forever.

Before you learn the tender gravity of kindness
you must travel where the Indian in a white poncho
lies dead by the side of the road.
You must see how this could be you,
how he too was someone
who journeyed through the night with plans
and the simple breath that kept him alive.

Before you know kindness as the deepest thing inside,
you must know sorrow as the other deepest thing.
You must wake up with sorrow.
You must speak to it till your voice
catches the thread of all sorrows
and you see the size of the cloth.

Then it is only kindness that makes sense anymore,
only kindness that ties your shoes
and sends you out into the day to gaze at bread,
only kindness that raises its head
from the crowd of the world to say
It is I you have been looking for,
and then goes with you everywhere
like a shadow or a friend.

Naomi Shihab Nye, available in the book Words Under the Words: Selected Poems. Or hear her read the poem: Kindness.

(via Stacy Lewis)

Change Backtick to Escape Key for MacBook Pro with Touchbar

MacBook Pro with Touchbar - ESC key closeupMy work computer is a new MacBook Pro. It’s great except one thing – it has a Touchbar, and that means there’s no physical Escape key. I’m a vim user and so have been feeling pain about that, since the Escape key is essential to using vim.

Then I discovered Karabiner Elements. It allows you to make physical keys emit whatever keycodes you want, so can change any key, even modifier keys like Escape, in all applications. So I could change Command to Escape. Now I could use vim. But I wanted something better – I wanted a physical Escape key in roughly the same position as older Macs. Could I change the Backtick key to Escape?

Yes. Here’s a Karabiner Elements complex modification file that will change Backtick (grave accent) to Escape; make Option-Backtick into Backtick; Shift-Backtick into Tilde (as usual); and make Command-Backtick work as normal. If you download Karabiner Elements, install, and run it, you can use the following button to install the modification. After installing, you will need to enable it.

Import “Change Backtick To Escape Complex Modification” Into Karabiner Elements

Now I’m totally happy with this laptop. I have a Touchbar and a physical Escape key.

(Update: this has been merged into KE-complex_modifications master branch, direct link to json file or source code on Github)

The First White President

Great article by Ta-Nehisi Coates in October’s Atlantic Monthly: The First White President. Brilliant and intelligent. It begins:

It is insufficient to state the obvious of Donald Trump: that he is a white man who would not be president were it not for this fact. With one immediate exception, Trump’s predecessors made their way to high office through the passive power of whiteness—that bloody heirloom which cannot ensure mastery of all events but can conjure a tailwind for most of them. Land theft and human plunder cleared the grounds for Trump’s forefathers and barred others from it. Once upon the field, these men became soldiers, statesmen, and scholars; held court in Paris; presided at Princeton; advanced into the Wilderness and then into the White House. Their individual triumphs made this exclusive party seem above America’s founding sins, and it was forgotten that the former was in fact bound to the latter, that all their victories had transpired on cleared grounds. No such elegant detachment can be attributed to Donald Trump—a president who, more than any other, has made the awful inheritance explicit.