Today my goal is to make you feel hopeful using math. Are you with me?
In these challenging times, it’s easy to look at the news (the climate, rising facism, gun violence, all the big problems that make our hearts heavy) and imagine a straight line plotting our course inevitably towards doom. This is called determinism, and lots of things do work that way. If you push a ball at the top of a hill, it’s going to roll towards the bottom of the hill. If you spend all day Saturday cleaning your house, your house will be cleaner. If you never mow your lawn, the plants will take over. It’s generally cold in the winter here in the twin tiers, and hot in the summer. Except… this August it was in the 40s some nights. Because actually things are pretty complicated, and don’t always do what we think they are going to do.
There’s a theory in Math called “chaos theory.” Contrary to the name, this doesn’t mean things are truly chaotic, it means that some things are really sensitive to their “initial conditions” Here’s a cool example of that- in this video by Veritasium [pendulums start about 8’22’], 2 double pendulums were started at the same time, but slowly at first, and then more dramatically they take totally different paths.[i] you’ll notice if you watch carefully that it starts out with one yellow line, and then soon you’ll begin to see two different lines, yellow and green, the lines of two paths that started very similarly and then get very different. The narrator tells us that no matter how hard you try, you can never get the pendulums to do the same path twice. It’s that sensitive to tiny differences right at the start.
Edward Lorenz was a meteorology professor at MIT in the 1950s[ii] working on long term weather simulations on his computer. One time he wanted to re-run a simulation, and to save time (because computers used to take much longer to run back then) instead of starting over from the beginning he decided he would start partway through, and manually typed in the numbers from a printout at the point where he wanted to restart. Then he left the computer to run and went out to get a cup of coffee. When he came back, the new weather forecast was totally different. Why? It turned out the printout he was using to enter the numbers only went to 3 places after the decimal point, but the computer went to 6 places after the decimal point. So that tiny tiny rounding difference totally changed the results.[iii]
Lorenz wrote a famous paper back in 1963 explaining what he noticed, about how just those tiny differences in initial conditions grew over time, like we saw with those pendulums. When he presented the paper at a conference in 1972, he called it "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" and that is where the saying “butterfly effect” came from.
It turns out that what Lorenz discovered was useful not only in forecasting the weather, (turns out that’s part of the reason that any forecast longer than 8 days is notoriously inaccurate- perhaps you’ve noticed this? ) but also economics and biology and other stuff.
This idea took hold in our imaginations- there are may wonderful stories out there about how one tiny change, one tiny choice or accident set someone’s life off in a new direction. Do you have a moment like that? Do you ever ask yourself- what would have happened if I hadn’t gone for a walk that day? If I hadn’t bought that book, or made that u-turn in front of the library?
The idea of that little butterfly flapping their wings reminds us that not all actions have the same impact, that even tiny variations at a key moment can make a huge difference in outcomes.
There are tons of stories out there of these tiny changes with big impacts. Here’s one from Reddit:
“My husband- He found out after 18 years that his moms side of the family was Spanish, not Mexican. He found this interesting and changed his country to “Spain” on MySpace instead the US where he really was. Meanwhile in Australia, I was helping my friend find Spanish people to add as a friend as she was learning the language. I came across my now husband and decided to send him a friend request as well. We got along really well and met in person after 3 years. Have been together 11 years, married for 7. If he didn’t change his country to Spain (and only for a day or so) we’d never know each other existed.”Or this one:
“When I was in 8th grade (13 years old) I had a really long bus ride home so would pass the time by reading. One day I faced the very serious situation of nothing to read and a minute to grab something in the library, and for whatever reason I grabbed a book on astronomy. That book was amazing and grabbed me like nothing else had before. I remember being excited to realize every astronomer on Earth was 13 years old once too, and that was a career you could actually do, even if you were from Pittsburgh.Whenever you get discouraged, thinking “there’s only one way this can end” it’s important to remember, we don’t even really know what the weather’s going to be like 9 days from now.
Anyway, today I am a professional astronomer who studies gigantic space explosions for a living. There was a lot of work to get from that moment to this one, but I’m always grateful that I picked up that library book!”[iv]
I like to use this mathematical theory as a metaphor, a symbol that sometimes small actions can lead to unexpected outcomes. Once I was sharing with a spiritual director friend about something I felt SURE was going to go a certain way- the pattern seemed clear. And she asked “have you made room for the God of surprise?”
It gave me pause- “have you made room for the god of surprise?” well that conversation happened in January of 2020, and nothing turned out quite how I had expected.
In the Hebrew scriptures, the book of Isaiah 43:19 God says to the prophet Isiah
See, I am doing a new thing!There are many similarities between the time that the book of Isiah was written, about 700 years BC, vast income inequality, oppression of the poor[v] and corruption in high places, and yet Isiah reassures us that God is doing a new thing, making a way in the wilderness.
Now it springs up; do you not perceive it?
I am making a way in the wilderness
and streams in the wasteland.
Now we Unitarian Universalists are theists, atheists, agnostics, so if scripture doesn’t give you comfort, remember those 2 pendulums, and how even something as simple as a double pendulum doesn’t take the same path twice. It’s not all written in stone, and while the die may be cast at the first instant, the way it begins to roll is wildly unpredictable.
Oh no, you might be thinking, that’s too much pressure! What if I do something tiny that breaks earth? Remember how during the Covid lock-down, a lot of us thought the world had changed forever, in massive ways. And it turned out that some things did change, but other things moved back towards their old familiar forms. For example, here we are, sitting in these same maroon chairs in this same building we’ve been meeting in for 34 years, but who could have predicted that we’d have friends and members joining us on Zoom?
It turns out Chaos is not the only force at work. Thomas Cotterill wrote in his blog in 2013[vi]
“At the ecosystem level, life is subject to endless dampening effects that limit the impact of changes. There are checks and balances. No virus or bacterium can run amok completely; organisms have immune systems. No species multiplies endlessly; predator numbers increase to exploit the increased food supply. Life forms are limited to specific environments. Nothing lives forever. Localized damage may occur, but the web of life is resilient and adapts. It is capable, not only of resisting change, but of repairing itself, re-establishing a pre-existing status quo.”I find that comforting too. We are living in a time of great change, but Cotterill reminds us that things tend to bounce back. Nature is resilient, nature can repair itself. Nature tends to return to balance when it is thrown off balance.
For example, the ocean is sometimes described as the planet’s thermostat[vii] because it holds a lot of heat. This is why, when I lived near the San Francisco Bay, it never got quite as hot or quite as cold there as it did over the hills. That’s because there is a powerful stabilizing impact of a giant body of water that hovers in the 50s (in the winter) and 60s in the summer. Not that change never happens in the ocean, but it’s an example of a stabilizing force that slows down big temperature changes for places nearby.
It is often comforting to me, when I worry about the fate of the world, to remember that We are all part of the web of life, and when one part of the web weakens the other threads hold.
For folks who draw comfort form scripture, there is another passage in the book of Isaiah 46:4 (NIV) where God says:
Even to your old age and gray hairsThe power of chaos, of disruption is tempered by the web of life, by large stable forces like the ocean.
I am [God], I am [God] who will sustain you.
I have made you and I will carry you;
I will sustain you and I will rescue you.”
And theologically, both are sacred -- the power that allows new thing that springs up, and the power that sustains and carries us -- both are within the power and promises of the divine.
And we are part of that too. Perhaps in some moment we might be part of a tiny action that changes the path of our own lives, or someone we never even meet. In some other moment we may be part of the web that holds our family, our congregation, our ecosystem in place when some the ripples of some initial condition, large or small, flutters like a butterfly. In all of it, we are never alone.
References
[i] https://www.youtube.com/watch?v=fDek6cYijxI Veritasium, the science of the butterfly effect
[ii] https://www.technologyreview.com/2011/02/22/196987/when-the-butterfly-effect-took-flight/
[iii] This podcast was a big help to me in understanding this topic https://www.iheart.com/podcast/1333-mind-jungle-podcast-273448494/episode/the-butterfly-effect-how-one-tiny-action-changes-everything-273448498
[iv] https://www.reddit.com/r/AskReddit/comments/jzfe7v/whats_the_craziest_butterfly_effect_that_happened/?chainedPosts=t3_ttsdgn
[v] https://rsc.byu.edu/covenant-compassion/poor-needy-book-isaiah
[vi] https://thomascotterill.ca/2013/04/10/debunking-the-butterfly-effect/
[vii] https://ocean-climate.org/en/the-role-of-the-ocean-in-climate-dynamics/
