Archive for September, 2011

Flavor: Preparing a (research) talk.

September 28, 2011

1. What’s going on mathematically?

Often I have to give a talk about my research, or a survey talk about relatively advanced mathematics. This post is not about giving the talk, but preparing it.

2. What is the emotional and logistical context?

Before starting to prep, there’s always some degree of nervousness and anticipation, depending on how important the talk is and how comfortable I am with the material.

I’ve experimented with a wide range of logistical contexts for prepping talks. This is one experience for which the math culture permits a significant amount of flexibility and alchemy. Among mathematicians, “He/She has to prepare for a conference talk next week” translates to “he/she is going to be acting a little strange; give him/her some extra space.” I’ve tried locking myself away until it’s done, or prepping during a long hike without writing anything down, or sitting in front of a waterfall and practicing my words for hours. There isn’t much common context.

3. What thoughts are there?

The goal is to develop a human connection to the content of the talk, in order to figure out how to communicate the content so it can be best understood by the range of people in the audience. There is usually some learning and relearning of material, piece by piece. But the biggest challenge is in reorganizing the ideas into a story that is linear enough to flow as a narrative, but nonlinear enough to convey the robust intuitive interconnections. The second-biggest challenge is aiming for your audience – including the right balance of detail and metaphor, rigor and exposition.

A good starting point is immersion in the subject – getting comfortable with all the important ideas, the different perspectives on those ideas, the history of the ideas. I recently spent 15 hours preparing for a one-hour talk. Then it’s necessary to zoom out, try to see the big picture, and from a good vantage point to construct your story. Towards the end of the preparation, the talk becomes more gestural in my mind – it has organized itself into parts, with transitions, and an engaging structure and flow. The talk is ready when I can see it all in my head – all the information batched into articulate clumps, which are batched into sections, each section occupying a place in a conceptual outline whose shape I see clearly in my head.

4. What quality of awareness?

The hardest, but perhaps most important, task is to constantly and consciously shift between the different levels of detail. Zooming in, zooming out – the talk needs to work on multiple levels, so that the audience can comfortably engage the talk and follow it, from a range of backgrounds and focus. It’s easy to passively let the math lead you, while prepping a talk, but the result usually lacks perspective and is boring.

I try to see the content for the first time, to be my own audience. I try to forget that I already know how the story ends, so I can perfect the story-telling. It feels like trying to hear your own voice, from outside your head.

Each expository challenge starts with a tension, which is broken by a moment of freshness and newness, which then rearranges itself into an enjoyable obviousness.

When the talk is ready, I feel like I’ve transcended the math/non-math boundary. I’m holding, in my mind, an object (the talk) that is mathematically rigorous and true, but crafted to interface with the multi-dimensional, non-rational, colorful and robust real world.

5. What emotions?

There are the emotions associated with the impending performace – fear, adrenaline, excitement, nausea. The preparation itself is, while usually an anxious experience, also very pleasant. It is a gradual shift from confusion to certainty, confidence, familiarity, and friendship. They say that you don’t really understand something until you’ve tried to explain it to someone else.

6. What does it resolve to, after how much time?

It might take 30 minutes or 15 hours to prep the talk, but it’s clear to me when it’s done. I stop thinking about it, move on to something else.

7. How frequent is this flavor?

About four times a year. There are lots of lectures to prepare when I’m teaching a course; the experience is similar to prepping a research talk but much more mellow, since I’ve only taught 300-level courses.

8. What are good/bad ways to change or follow it up?

I have a strict post-talk-prep routine, which consists of actively doing nothing. I’ve found it’s important to rest, not worry, get sleep, do enjoyable things like listen to music or eat, maybe meditate or get some exercise. The talk is prepped; there’s nothing to worry about. It’s out of my hands, and now my job is to be the best performer I can be. If the talk was prepared well, the performance of the talk is really fun. The worst thing to do is to indulge in nervousness and anxiety.

Flavor: Mathache.

September 20, 2011

1. What’s going on mathematically?

I’ve been doing lots of math, maybe too much: research, writing up a paper, teaching, applying for jobs, other projects. There’s a lot more to do. I stop to self-reflect.

2. What is the emotional and logistical context?

Maybe after a long day of conference talks; or a frustrating afternoon of getting nowhere with research; or late at night when my brain has stopped working and I should be done by now, but I have more to do.

3. What thoughts are there?

My head feels saturated with information, strained from too many self-imposed cognitive tasks. I keep thinking of how many more things I have to do. Often there’s a frustrating problem that I’m stuck on but can’t seem to give up. Usually my body is struggling as well as my mind, and I start to think about my physical aches and discomforts.

4. What quality of awareness?

I’m existing very shallowly. Even if I do non-math things, there’s such a loud noise in my head, of math ideas chasing each other, that I can’t focus on or process life much. The noise has a wide spectrum of frequencies – some of it conscious math thoughts, some of it low-frequency “percolation” (my word for when a math idea hijacks mental bandwidth for an indeterminate amount of time, for mostly-subconscious learning and processing). I’m very aware of physical discomfort and fatigue.

It reminds me of the drained and saturated feeling after a long day of socializing and talking to people, when you want to lock yourself away and listen to silence. But it’s hard to lock the math out of your head.

5. What emotions?

I feel pain, tightness in between my shoulders, often a headache or stinging eyes. Tired, drained. Disconnected from real life emotions and experiences. I feel behind, and sometimes like I’m drowning. It is a particularly physical math experience, and an unpleasant one.

6. What does it resolve to, after how much time?

Eventually things get done, or I sleep, or take a break. somehow my cup gets emptied a little. But it might take a while, and it might get worse first. There have been points of graduate school that really tested me, with burnout or breakdown a nebulous possibility.

7. How frequent is this flavor?

Sometimes for days or weeks on end. As a flavor, it usually comes in the late afternoon, maybe five times a month.

8. What are good/bad ways to change or follow it up?

One thing that helps is physical rest – laying down, consciously fixing my awareness on my breath and on relaxing my body. Meditation is one of the best things to do, although depending on the state of my practice and the degree of mathache, sometimes I fail at dissolving the anxiety. Sometimes a good cry seems necessary, and makes me feel better.

The worst thing is to let it take over, and to wallow in mathache. My cutoff point is societal: if I start to become a mean person, then it’s gone too far.

Flavor: Discussing with a colleague.

September 12, 2011

1. What’s going on mathematically?

A live conversation with a colleague, about research. For example, with my PhD advisor, or someone at a conference.

2. What is the emotional and logistical context?

The context is pleasant. We’re sitting together, with paper and pen or at a chalk/whiteboard. I’m mildly prepped, with comments or questions. There might be coffee. There is always time, and patience.

3. What thoughts are there?

A dynamic back and forth, sharing and building, going beyond either individual. We express old ideas, new ideas, shared ideas. Sometimes there is a bit of translation involved (e.g. topologists say “finite” and “smash”; algebraists say “compact” and “tensor”), or effort in communication. But overall the thoughts themselves seem to move unhindered in our shared collective mind, via common mental imagery. There is a lot of mathematical “body language” – conceptual shorthand, written scribbles and diagrams, and physical gestures that convey so much.

4. What quality of awareness?

My awareness is always sharp, like lightning. I feel like I’m reading someone else’s mind, seeing inside their head. Often I’m simply absorbed in the moment, without self-reflection; there’s nothing else around, no time, no bodies. When I talk with my advisor at our weekly meetings, I have enough perspective to reflect on the experience while it’s happening, to witness the mind-meld from outside as well as inside.

5. What emotions?

These discussions are usually exhilarating; I’m on the edge of my seat. There’s a deep, deep pleasure in connecting and speaking the same esoteric language, especially with someone who is a stranger in so many other ways. The math is a strong bond, of a common research philosophy (of how to think about things), common research modes (of how to go about doing research), and common upbringing (of learned content). The precision of our language allows us to go very deep very quickly, in spite of other cultural differences.

6. What does it resolve to, after how much time?

There are usually some of the following: new answers, new questions, new directions, and/or new perspectives.

7. How frequent is this flavor?

Usually once a week, with my advisor. Possibly twice a day, at a conference. During my recent Solo Math Intensive, I only video-chatted once a month.

8. What are good/bad ways to change or follow it up?

It’s helpful to quickly review any notes from the discussion, to document the new ideas, add things to a To Do list, or hunt down new references. Getting frustrated, intimidated, or discouraged is very unproductive.

Season: Crescendo.

September 12, 2011

1. What mathematical activities? What level of rigor?

Everything is building. I’m writing papers, the research is coming together. I’m seeing new vistas, with new leads to follow. And there are other projects – writing for blogs, applying for jobs, teaching, etc. There are moments of pure rigor and moments of rigor-less scheming.

2. What relevant interactions with other mathematicians?

As many as possible – with my advisor, with other grad students, with others in my field.

3. How does it feel, what is the mood?

I’m unnervingly busy. There’s too much to do. It’s exhilarating but tiring. I’m anxious, and slightly worried about where this is heading, worried that I’ll burn out. I want to be available to allow the math research to grow and spread as it wants to, but it’s growing faster and faster and demanding more and more.

4. What state of mind? stable vs. chaotic? focused vs. dispersed?

My mind is constantly on, and needs to be constantly on. There’s no chance to be dull or to drop the ball on anything; I feel like I’m performing 24/7. I’m asking for an on-demand delivery of focus or dispersion, stability or chaos, and my mind is indulging me. For now.

There’s a constant noise in the background, of unattended-to things, of lists.

Occasionally I find myself staring at stable geometry – staircases, buildings, trees – and finding comfort in the solidity of their existence.

5. What type of self-reflection during the experience, and did it help?

I notice a growing demand for personal time, to process my experiences. I need to find new time-management schemes. I need to consciously leave behind certain things – research directions or interesting projects. I’m aware of the threat of burnout, and am able to mindfully shift to new modes, to rest or actively refresh the different parts of my mind.

I’m amazed at just how much I can push my mind – how much new and old information I can juggle at once. It helps to appreciate this, to be grateful and positive.

6. An everyday metaphor for the experience?

It reminds me of building a sand castle. If you want to go higher and higher, your castle needs to get a bigger and bigger base. But the relationship is not linear; consecutive increases in height require larger investments in the growing base. I also have the image of pinching a sheet of fabric and pulling it up. As my research progresses, I need to call on a larger and larger circles of knowledge. As my various projects continue, their demand on resources seems to increase quadratically or exponentially.

In terms of state of mind, I think of a cup that is full of water, that threatens to overflow. I’m constantly intentionally emptying the cup, and more water is constantly pouring in. The situation can be sustainable and reach an equilibrium, as long as the emptying and filling rates are balanced.

7. An example of a good day and a bad day?

On a good day, I get a lot done and have the time to appreciate it. Sometimes the math itself fuels me and no effort is required.

On a bad day I push myself too hard, or feel like the math is in control of me and I can’t say no.

8. What did you do when you were stuck?

Rest is always good, or giving myself a pep talk, or positive affirmation and gentleness.

9. When and why did it end?

This season is going on currently. I hope that after I get these few papers out, write my thesis, and get a PhD and a job, then there might be a decrescendo season.