Statistics is an instrument of truth.

You can make truer statements with statistics than without. Statements that apply to some fraction of people for some fraction of the time can be stated as such, instead of as absolutes.

No one ‘always’ does anything. If you said to someone “You always do this!” the statement can only be false.

‘All’ people of a certain demographic don’t do any one thing. “All women (or all men) behave a certain way”, is less true than a statement that specifies what fraction of men or women you mean, and how you estimated this fraction.

Degree of knowledge and applicability can only be expressed with completeness using statistical tools like sample size, probabilities, and likelihoods. Without them, you are stuck with either the wishy-washy ‘sometimes’ or the overconfident ‘always’.

The phrase ‘lies, damn lies, and statistics’ was created in response to bad practitioners of statistics — people waving their hands and deflecting from the truth with jargon they know their audience doesn’t understand, trying to give an impression they know is incorrect.

Horrible as this is, statistics is not inherently prone to promoting falsehoods. With greater literacy, statistics can be an instrument of truth with nuance and accuracy.

Originally appeared on Medium.

Sustainability Research: Where to Start?

There’s a big world of change needed for a sustainable future. There are millions of people looking for a way to help. It’s going to take a variety of skills and talents to devise solutions, implement them, make new and better products, market them, and create and enforce policies and regulations. It’s a vast array of possibilities and opportunities to get involved.

How to wrap our heads around it all, and join in to contribute?

I’m starting by informing myself and sharing what I learn. I’ve got the UN Biodiversity report from 2019 and a sustainability textbook downloaded and skimmed. To prioritize finding the answers I need in a sea of research, I’m starting with questions to answer (or QTAs, explained in this blog post by Jessica Abel).

The first two questions I’ve set for myself are:

  1. What is the current status of environmental policy in the US?
  2. What framework shall I use to organize and communicate what I learn?

I hope that focusing down on these two questions will make my next step easier.

Your Sustainability Efforts Will Pay Off, Suddenly

Even if it seems like nothing is happening for now

Photo by Thomas Kinto on Unsplash

A message for people who care about sustainability and the environment: you might be discouraged by the slow progress of countries and people toward sustainable development. Over recent decades, the problems have been clear and yet the solutions have stalled.

We recycle and buy package-free. We carry our own reusable bags and mugs to the store. We scour the internet for the most sustainably produced couch or dental floss, knowing that we are only one customer and the ‘other’ couches and dental flosses are doing a roaring trade without us. We sign petitions and advocate for new processes in the face of inertia and resistance. Is any of this even working?

It is. But we can’t see it yet.

Widespread change tends to be sudden

The change we are trying to make is widespread and distributed. In the future, stores in every town across the world, factories in every country, people sitting at their kitchen counters in their homes will need to behave a little differently in the future. The whole economy needs to change.

That makes it sound difficult, but changes of this scale have happened over and over in the past, and they tend to be sudden.

The sudden going in and then out of favor of — smoking, packaged food, social media — nothing was changing, and then it did, all at once.

In our lifetimes, we have seen social media touted as the thing that would connect us, free lonely teens from their isolation in the remote parts of the world, and reaffirm our common humanity, to regarding it as monopolistic, surveilling, democracy-destroying, and mental health-addling.

We have gone from low-fat, high sugar, ‘labor-saving’ packaged food and white bread to sprouted grains, avocado, paleo, keto, single-ingredient organic.

The public perception has changed beyond recognition. Plastic could be next.

There’s a tipping point in sustainable options

Right now, the easiest, cheapest, most convenient option is the most plastic-wrapped and factory-farmed product available. There are, and will be for the foreseeable future, vast swathes of every population who can or will only use the easiest, cheapest, most convenient option. Some, because that’s all they can afford. Some, because they have other concerns on their mind that leave no room for environmental considerations. Understandably.

Every day, sustainable solutions inch closer to being the easiest option. As they get slightly easier, a small segment of the population adopts them. People who had a little money, effort, and consideration to spare, for whom the new option brings sustainability within reach.

But these rates of adoption are small. There are only so many climate-conscious, affluent people you can add to your customer base.

But as the space of options shifts, as the easiest option becomes the sustainable one, the adoption rate explodes. In what seems like an instant. Like a powder keg.

Don’t be discouraged by the pace of change

We feel like we’re falling behind, and nothing is happening. But change won’t be linear.

The fraction of Americans who think protecting the environment should be a top priority of government has been growing since 2011, and was 64% in 2020. People care, but they don’t have a lot they can do. If we can make things easy enough for them to take action, we’ll catch up to where we want to be, because change tends to be sudden.

There’s hope, so don’t give up. Keep innovating. Keep incentivizing companies to innovate. Keep supporting the ones that do. Keep experimenting.

Originally appeared in Sustainability Experiments.
Also featured on CofoundersTown.

Write Ideas Down Before They’re Formed

What I learned at the intersection of math and fiction

Photo by Christian Wiediger on Unsplash

Sometimes I prove mathematical theorems in my work as an engineer. It’s one of the most intense types of brain work that I do. I also write fiction, and it taught me one of the most important lessons about all my creative work: to write down everything that I know.

Setting the scene

I’m hunched over my desk with grid paper in front of me and a PDF of a textbook with reference material on my computer. I glanced up at the PDF and back at the page full of symbols I’ve written. My brow is furrowed. I’m stuck.

Involuntarily, I stretch my neck a bit and let out the breath I didn’t know I was holding — oblivious to my need for a break — even though my head’s throbbing and my shoulders are stiff.

Almost there. Almost there!

I can’t stop even if I want to. The discomfort is mounting, and so is the promise of success.

This is how I usually feel when I am about to figure something out. I have all the different aspects of the problem stuck in my head and work them simultaneously. I’m switching and comparing approaches, thinking about which ones will probably work, and suddenly become aware of the existent disadvantages! Time to consider borrowing an element of one approach to offset a disadvantage of another.

Prelude to Success, turning Discomfort into Anticipation

Holding so many alternate and competing possibilities in my mind is exhausting. It is also exciting because I have learned to recognize these symptoms as being on the brink of a creative breakthrough.

In the past, sessions like this one, be it over a period of months or even years, usually add up to a proof of a theorem, where every step has been checked from every angle for holes. In one session I build a step, and in the next, I find a flaw in the step. In the next session, I try to fix it. Eventually, I look for flaws and don’t find any. The proof is as bulletproof as I can make it.

And that is the result I’m seeking — the mathematical result I can apply to my engineering problem. And achieving that means I can finally rest my straining, pulsing brain and bask in the glow of success.

Photo by Kyle Glenn on Unsplash


Recently, I learned a new method that I borrowed from one of my other areas of interest: fiction writing. An exercise commonly recommended to fiction writers is free-writing (also known as Morning Pages), that is, stream-of-consciousness writing where you put down on paper whatever is in your mind, without pause, for three pages. You write before you’ve had a chance to complete the train of thought; in fact, the train of thought is altered by the writing of it. The exercise forces your mind to work differently, slows down for your writing and helps increase your ease and fluency.

When I start writing fiction, I don’t have the whole story in my head — at least, not in a form that performs the function of a story. I may have the plot or a loose structure, but I don’t have the elements that make for a memorable reader experience or create an emotional impact.

The emotional complexity of characters and the journey that the reader goes through are too complicated to hold in my head, but I can divide the creative process over several sessions to make it manageable. Before this though, I have to write everything I know about the story at the time and let the story evolve on the page.

Photo by Blanca Paloma Sánchez on Unsplash

A Mathematical Theorem is Like a Fiction Piece

Mathematical theorems, like fiction pieces, are thought processes too complex to hold in my head. One day, more or less by accident, it occurred to me that I could apply my writing method to my mathematical proving process.

Instead of completing the thought in my mind and then writing it down, I wrote while I was thinking. I started getting my thoughts down while they were still half-formed. By downloading ideas onto the page, I was effectively freeing up my working memory and making space for my next thought. This allowed me to create more complex, layered, and multifaceted ideas because I was not limited by how much I could hold in my mind at a given moment.

For example, while still proving a theorem, I just wrote in my notebook all the half-formed thoughts and possibilities I knew.

Maybe, I can change notation?

Or change parameterizations and have simpler forces?

What about switching parameterizations in between?

I just wrote down my approaches as they appeared and went back to work each of them out in more detail.

Okay. So here’s the sticking point. I think we’re going to get to this result, but unfortunately, this term doesn’t cancel.

I wasn’t able to finish the theorem that day. Thanks to my notebook, though, I could bookmark a Lemma (an intermediate conclusion that will be used in the theorem), and start from where I’d left off, for my next session a few days later.

In the past, I would have wasted my energy carrying around a half-formed idea in my mind for days. I would have felt like I had nothing to show after all my exhausting brain work. Now, when I start, I allow myself not to have every step figured out. I have the statements that I know to be true, guesses about which ones will get me to closer to the conclusion, and an instinctive idea of how the proof will end up. I build from there, just like I would do for a fiction piece.

My New Approach and Why It Works

Photo by Ashim D’Silva on Unsplash

The most striking difference in my new approach is how easily-flowing the experience of writing math proofs is compared to my past experience. Instead of feeling like my brain is about to burst and I can’t stop until it releases some of the pressure, I feel relaxed, I pause, flip back in my notebook and enjoy the progress.

I invite you to write down everything you know. Don’t just keep it in your head, write down your current knowledge of the problem, what you expect to happen, and the things you think might be relevant but aren’t sure. You’ll avoid frustration and the unfulfilled expectations of having “The Answer” at the end of your session.

Freeing up the brain-space you were using to think those thoughts will enable you to take unimaginable next steps. Let your notes build on each other on the page and become something that your mind alone could not create. You will be surprised to find the boundaries of your knowledge expanding in ways you could not predict or control.

In my next installment, I will take you through how these ideas can be applied to blogging. In the meantime, write your ideas down and let me know what happens next!

Originally appeared in Evidence Of…

The Two Kinds of Incremental Progress

The kind that leads somewhere and the kind that doesn’t

Photo by Brannon Naito on Unsplash

I’ve been struggling to organize my home office for years. I’ve made a variety of resolutions to ‘finally’ buy the right chair or invent an organization scheme for my notes, tidy a little bit each evening — none of it stuck.

I did tidy in small increments as planned. But I ended up cleaning the same layer or clutter over and over as it built back up, never getting any closer to the comfortable, organized office I needed.

Taking a tiny step in a process that seems overwhelming is one of the best ways to start. However, all types of incremental change are not equally effective.

I’ve often come across this pattern of incremental changes that don’t add up to anything, on a small scale my own life, and also broadly in social groups, companies and society. It applies to nutrition, lifestyle, social change and technological change — any area where we apply effort, yet nothing seems to be happening and so our attempts fizzle out.

What do you need to make incremental change lead you where you want to go?

Increments of the right size and shape

Making changes to your behavior, however small, has costs in effort and discomfort. If you make a change so small that its effect is imperceptible, that effort and discomfort will appear to have been wasted.

If no perceptible change occurs over a period of time, you sap your motivation and train your brain to think that change is futile.

Sometimes, making a small change has a positive effect that is quickly reversed by the erosion of normal living. For example, taking 10 minutes a day for a hobby helps you de-stress, but the effect is quickly wiped out by the usual stresses of work life, now exacerbated by trying to add this time to your schedule. Finding the correct amount time for the hobby will ensure that the time spent has a net-positive effect, and counter-intuitively, this amount of time may be longer than the bare minimum. This is what I mean by choosing the ‘right size’ of increment.

By the right ‘shape’ of increment, I mean that the change might need to span several areas of your life to have a net positive effect. Changing just one area might cause problems in another area, so the incremental change might have to include two changes, one to counteract the problem caused by the other. An example of this is when your new hobby affects your sleep cycle, and so you have to modify your sleep habits in tandem.


For incremental change to do any good, its effects have to accumulate over time. That can only happen if you do it often enough for the benefit of one action to carry over to the next.

Each time you take an action, there needs to be a next action in the pipeline. And it has to happen before the insight, motivation boost, or shrinking of the task from the previous action wears off.

You don’t necessarily need to work on the change every day, but there needs to be a clear trigger that will cause you to return to the task. It could be a calendar reminder, a milestone, or time of day that reminds you that you need to continue working toward the end goal.

It helps to keep a notebook or digital document where you write down your observations from each action, so that you can pick up where you left off.

Course corrections

Each increment gives new insights. It can be tempting to just ignore whether any of the actions are working and just keep doing the same thing, especially if the change isn’t your top priority.

However, continuing to take an action that has no perceivable benefit is counterproductive, because it’s demotivating. So the additional effort of diagnosing what’s not working and updating your plan will save effort in the long run. Just spinning your wheels for months is far worse than having to spend a few hours assessing progress.

Escalating commitment

Change has to start small because you don’t know the whole road map. So it makes sense to make things easy on yourself when you are just starting out and figuring things out.

However, once you get past that point, and the changes get bigger, the reaction force pushing you back to the old equilibrium gets stronger. As you make new activities a bigger part of your day, the disruption becomes uncomfortable. At this point, you can’t make the changes easy on yourself any more. You have to commit to working through the difficulty.

The same effect is noticeable on a broader scale in society, as recent events have shown. After a movement for social change makes progress, the backlash from society grows and opposes the progress made. At that point, continuing to do what you have always done is not sufficient.

To keep from reversing the progress you made, you have to increase your commitment and effort the longer you go.

I eventually did break out of my home office organizing rut when I had a reason to spend some concentrated effort setting up — I moved to a new house. I finally tackled several interdependent issues at once: the lack of storage space, the lack of a scheme for organizing notes, and wrong-sized furniture. Beyond a point, I couldn’t tidy until I had places to put things, and I couldn’t buy shelving until I had an organizing scheme.

The change was still incremental, because I had to break it into several sessions, but the increments got bigger.

Each increment couldn’t be a bit of random rearranging. It had to be enough organizing to make an appreciable difference (the right size of increment), so that I’d experience the improvement and come back to it motivated. I had to revisit the process often enough to keep up with the clutter of daily use (continuity).

And when I identified issues in the setup, I had to figure what was wrong (course correction) and spend some concentrated effort doing the tiresome work of moving furniture around (escalating commitment), even though I’d much rather just try to work within the clutter.

There are two kinds of incremental progress. The kind that goes around in circles, re-treading the same ground until it dies out, and the kind that builds in momentum and grows in effect. To create the latter, you have to line up the increments just so. Haphazard plodding won’t do.

Even if you set up your changes to have all the factors I listed above, the initial feeling that nothing much is happening is common and likely. When you give yourself the best chance of success, you can wait out the slow start with optimism that all your effort will add up over the long run.

Originally appeared on Medium.