- June 10, 2018
- June 9, 2019
- June 14, 2020
- June 13, 2021
- June 12, 2022

By Nicole Yunger Halpern '11

Mr. President:

February 2011. The time: Earlier in the morning than you want to know. The location: A quiet little nook in the physics building. Cold enough for a sweater, surrounded by office doors and whiteboards and posters full of physics gobbledygook. The event: Revelatory. Lit up my week like the homecoming bonfire.

In February 2011, I … I learned to use this mathematical doodad called the tensor product.

You're probably thinking, "Nicole, you need friends!" I have at least one friend. Sarah Siegel drove here from Boston to celebrate my commencement. When we were in kindergarten, Sarah and I used to refuse to leave each other's houses. Suppose you wanted to describe Sarah and me using a certain type of physics. Why not? You'd create a mathematical object that represents me and a mathematical object that represents Sarah. You can think of numbers or equations as mathematical objects. Mathematical objects of a different type would represent Sarah and me. You'd stick these objects together using mathematical glue. That glue is a tensor product.

Tensor products connect things. In February, tensor products connected me to an understanding of a physics lesson. In February, heaven help me, I started seeing the world in terms of tensors products. Connections. Lines that cross and circles that envelop. Connections between neurons in my brain, as I learned about tensor products. Connections between me and those of you who tolerate me despite my fixation on tensor products—your friendships. At the end of freshman spring, two of my floormates rolled my suitcases to the bus stop. I have two hands; I could have rolled them. But you insisted. Thank you, fellow Dartmouth students, for insisting, for connecting me to bus stops, for connecting with me.

Graduate students, too. One of you grad students TA'd my first Dartmouth physics course. One lab involved magnetic fields, things we represent with arrows. The arrows involved in this lab pointed all over the place. I didn’t understand which arrow pointed in which direction or why. This TA brought me back into the lab to show me which apparatus did what—He took me back into the lab without my asking him to, on two different days. Grad students, some of you have unreasonable patience. Thank you for your patience, for advising me, for having lunch with me…and for noticing my algebra errors.

I have made many errors. I ask many questions. Dartmouth faculty: Thank you for connecting me to answers. One professor said I have an infinite supply of questions. This professor taught me a physics course whose name I find intimidating. In the course, we distinguished among three technical terms: small numbers, large numbers, and very large numbers. If this professor said I have an infinite supply of questions, you know I can stretch office hours into office days. Sometimes, after interrogating a professor for an hour, I've looked at my watch and asked, "Shall I kick myself out of your office now?" Often I hear the response, "No, I have time for another question or two." For much of my understanding, my major, my questions, my ability to answer, I blame Dartmouth's faculty.

I blame my family for more. Who else has sacrificed to send me to Dartmouth? Who else has taught me self-discipline? With whom else can I connect before nine o’clock on Sunday mornings? Thank you for connecting me with love, with support, and with the occasional box of clementines.

At Dartmouth, we've built connections. We’ve developed tools for articulating connections—interpersonal skills, circuit-wiring skills, writing skills, familiarity with tensor products. I am grateful for these connections and these tools. I hope you’ve built connections worth maintaining. I hope you maintain them; I hope you build more. I hope I haven't awoken suppressed memories filling my speech with mathematics. I hope that if tensor products intrigue any of you, you connect with the friendly faculty and students in our physics department.

One could do worse than see the world in terms of tensor products.

Thank you.