delivered by Andrew Bergdahl, Chair, Math Department
Good morning everyone. My name is Andrew Bergdahl; I’m a math teacher and a dorm parent at a school near here. This is my first year at Stoneleigh Burnham, and I am pleased and excited that you asked me to speak today; thank you. Parents and guardians, welcome. To my colleagues, the faculty and staff, well done.
Seniors, you sit now at the inflection point of a imploding gyre of effort, time, and intention; an orbit bound to its focus by willpower and shaped by countless hands but tracing a single curve; at this moment poised to close the Mӧbius band circuit of your first ambitions and place a heavy blanket over the parrot cage of the maddening mixed metaphor we call high school.
This is a time when you’re going to receive a lot of advice. You’ve crossed a threshold today, and your relationship with everyone in your life has changed, whether you realize it or not. You will be given advice, by teachers who previously gave you instruction. You will be offered advice, by coaches who before told you where to run and how high to jump. You will hear advice, from family and friends of family who until today were content just to watch you grow. You will endure advice, from your parents, who can feel their authority over you waning, whether you leave the house or not, and you will receive with this advice the burden of applying it to your own life.
We want to give you advice because we see the threshold you’ve crossed, we’ve seen it coming and we’ve held our breath for you these last few weeks. It’s a cliff’s edge that each of us has been over, ourselves. We see, in retrospect, the new journey you are facing now, and we want so badly to tell you everything you could possibly want to know about life on the other side. In my case, this will take the form of a math lesson. You have no one to blame but yourselves.
In 1931, Kurt Gӧdel, an Austrian-American mathematician, settled an important question in logic when he proved the necessary incompleteness of set theory. The result of Gӧdel’s work was to show that any complex logical system must contain statements that are impossible to prove or to disprove, regardless of how true they might be. This is the reality we live in. Truth and provability are not guaranteed to go hand in hand, and uncertainty is an inevitable feature of life. Mathematically. Imagine now trying to raise children in such a reality, and thank your parents one more time.
By the middle of the 20th century, Gӧdel was one of the closest friends of Albert Einstein, another Austrian mathematician who became a naturalized American citizen. Like Gӧdel, Einstein spent his career defining the logical underpinnings of everything that is. His special theory of relativity explains the relationship between time and space, and has allowed for incredible new understandings in cosmology.
We now know that the universe is expanding. It’s not just that galaxies are drifting apart in space; the fabric of spacetime is itself expanding, carrying all of us along with it. The universe is only 13.8 billion years old, yet it is as wide as you would expect from light traveling for trillions of years! The longer we wait, the greater the distance between us and the next planetary civilization over.
That’s not even the weirdest part of all this. The universe is actually expanding at an accelerating rate. Things are flying apart faster and faster, and there are huge swaths of the universe we can never see, because they are retreating from us faster than the speed of the light they might send back toward us. See, everyone says that the speed of light is the fastest thing there is, but that’s not quite accurate. Light just happens to be capable of traveling as fast as anything can, but the speed limit it obeys is actually the speed of information. A cause on one end of the universe can only lead to an effect on the other end so quickly. And as the expansion of the universe outpaces the speed of information, transmitting knowledge from one place to another becomes like trying to walk up the down escalator.
So there’s an upper limit on how fast light, or information, or advice, can reach someone. When light travels across the expanding fabric of spacetime, it gets stretched out along with everything else. This is called red-shift, because a stretched out light wave is going to be closer to the red end of the spectrum. The very act of trying to transmit information, deforms it.
When I graduated high school, I received plenty of advice. Some of it was what you would expect: Work hard, be brave, socks before shoes. Good advice, but maybe it didn’t need to be said. The rest was what I can call very specific advice, often stated emphatically and with personal context given as justification. Everyone told me not to choose a major too quickly at college, except those who told me the opposite. Some people wanted me to choose a safe career in a stable field, while others said it was time to pursue my most ambitious dreams, I assume because they themselves either had, or hadn’t. I was lovingly told by the mother of a childhood friend that I was very creative, very smart, but too lazy. She told me I very easily could have been the person to write the book Captain Underpants, had I put my mind to it, and implicit in this was the question, Why hadn’t I? A priest told me to purchase a little canister of compressed air. I could go downtown, and walk from one business to the next, offering to use my canister of air to blow the dust out of their keyboards. To be fair, it was the end of a millennium, and we were all really excited about computers.
All of this wisdom was deeply dependent on the experiences of the people sharing it. Ultimately, I followed some of the advice I was given, but not on purpose. My life came together the way it did, and it really doesn’t resemble that of other members of my family, or a priest who was born in the nineteen-fifties, or Dav Pilkey. The most venerable person on this planet has experienced some portion of one human lifetime. What is that? How many uncountable trillions of lifetimes must be possible in this world, and all sequestered by generation, and culture, and genetics, and wealth, and ethnicity, and circumstance and inclination. Our galaxy will never receive information from the vast majority of the universe we’re a part of, and no one person will ever know enough to be an expert about another.
And what this means, class of 2019, is that you are the experts. We have instructed, and coached, and parented you, and we have done the very best we could. But any advice you receive from me does not come from an expert, and should be assumed to be badly red-shifted. You are the experts, this is your world, and it is yours to save or spend.
And the world needs you. The world needs experts who are going to bring new ideas to the fight for the environment, and rationality, and human dignity. I’ll do my best to help, I’ll keep voting and stuff, but you can not expect me to understand the world with my last-millennium brain. I am, I say this seriously, I am legitimately scared of Tik Tok.
So, welcome to the world, experts. We’re glad you’re here. You have a lot to do, so let me just tell you one more thing, before we’re done. Not advice; an observation.
Experts lead, but with humility. The more an expert learns in their field of study, the more they realize the infinite gulf of what they don’t know. They also see how much they are needed by the rest of us, and so they take charge, because they know they have to.
An expert has an open mind, and actively explores the possibility that they might be wrong, every step of their lives. This is not weakness, it is imperative.
Experts are marked by curiosity. About everything. This leads them to find one another. Experts don’t compete, they collaborate, and every important work has been finished this way.
Stoneleigh-Burnham, class of 2019. Thank you for sitting on your inflection points long enough for me to talk to you today. It has been a pleasure getting to know you this year. Congratulations.