So, what should be one’s path of life, considering the fact that ultimately any life is essentially meaningless. We all vanish into the mists of eternity sooner or later and even if one is remembered for a time, such has no meaning for an eclipsed consciousness. Taking the vanishing of consciousness as an axiom (see first post), the conclusion is that one must find one’s life meaning in the here and now of one’s day to day existence. This idea is the conclusion of the existentialism movement, which arose during and after World War II. Though not consciously adopting this position, I have unconsciously followed it, rejecting paths of fame and fortune, seeking instead a path towards ultimate understanding, tempered by a lazy drift into whatever presented itself.

Thus, in 1948 as I entered the spring quarter of my freshman year at Stanford, having had no opportunity of taking any math courses, but with a compelling desire to learn calculus, I audited a beginning 3-hour course in differential calculus, finding it enjoyable and understandable. That summer I went back to Honolulu and had a summer job with the Experiment Station of the Hawaiian Sugar Plantation Association in the nearby Makiki district. My job was to drive to various plantations on Oahu, pick up samples of juice from crushed sugar cane, help analyze these samples for sugar content using polarized light, and clean up the glass ware dirtied from the tests. In my spare time I read ahead in the calculus text from the Stanford course, learning integral calculus. I set myself the problem of finding the formula for the volume of a hypersphere of 4 dimensions, having picked up my Freshman roommate Roger Shepard’s musings about 4 dimensional hypercubes, and examining his models of such projected into 3 dimensions. Reading about multiple integration in my calculus book didn’t seem helpful so I came up with the idea of how to add a dimension to the calculation for the “contents” first of a point, then a line, then a circle, then a sphere and finally a hypersphere. The final calculation of the latter involved integrating a sine squared, which I managed to do as an indefinite integral. (I missed the simple trick, learned much later for calculating a squared sine as a definite integral.) The satisfying answer was ½ π²r⁴, with pi actually being squared.

Also, I had a brush with danger that summer as a hurricane wandered within a couple hundred miles to the east of the islands. Sandy Beach, mentioned elsewhere in this blog, faced directly towards this hurricane. I shared a ride to the beach with some of my high school classmates and we marveled as the waves crashed into the water as it shallowed near the shore and then ran far up the beach. As these waves approached the shore, with their height and thickness they resembled rows of army barracks. From some irrational prompting of ego I decided I would try swim through the lethal shore break to the outside. All I had to do was to dive into an outflowing current from a retreating wave timing the dive with an appropriate interval between the descents of the tons of water as the waves broke. It was unthinkable to be caught under the descending wall. At the time it was before Titus Kinimaka had his femur broken by being under a somewhat stronger crashing wall at Waimea, but I knew that being caught by the descending break, though probably OK, could easily be fatal. Nevertheless, I timed what I thought to be a good undertow and dove in only to find that the current had stalled as I approached the impact zone. I stood up as the next wave approached, and as it was too late to retreat, I made a desperate swim and last second dive. I made it under the wall of descending water as some of it it hit my thighs. From past experience with smaller waves I knew that if it had hit my waist I would have been sucked back into the chaos. Out past the break I awaited a lull before attempting to go in, knowing that waves ordinarily come in sets of at most 8 or 10 waves. However, hurricane waves are different and minutes went by with no break in the succession of monsters. Amidst the fear, I kept my composure and finally there was a lull and I caught a small wave with only a ten-foot face and rode it up the beach to safety.

Back at Stanford, now a sophomore, I realized that I didn’t want to major in chemistry after all. Besides the summer job at the HSPA, I’d taken a course in qualitative analysis and found the actual practice of chemistry was unsatisfying. I took an intermediate course in electricity and magnetism, and, unhappy that the mathematical theory was slighted, I didn’t study and received a poor grade. I think it was a D, one slight step above failing. Since I really enjoyed math and figured I could learn physics later, I switched my major to math, a fun subject without a laboratory component. In Part I of this memoir I mentioned how I met Sherman Lehman and graduated successfully with a B. S degree in math.

In the summer after graduation, 1951, as recounted above, I spent the summer climbing with Nick Clinch, Richard Irvin and my brother George. Perhaps I will later go into details about our adventures that summer in the Tetons and Canadian Rockies, subsequent to our ascent of Teewinot by the Emerson route, talking about our climbs and close calls; and how our experiences made me into a competent mountaineer with the intuitive ability for judging situations in the mountains or in wilderness.

In the Fall I was back at Stanford, fulfilling the course requirement for a Masters degree in math. This academic year is easy to sluff over because my memory of what courses I took is blank. What I do remember is my concern about what I should do for a thesis. I was drifting and didn’t know what to do about it. I was rescued in Spring quarter by Professor Pólya who suggested that he would be my advisor and supply me with a research topic. I had met Pólya earlier at the time Sherman and I were preparing to take the Putnam exam, a test for aspiring mathematics students. I didn’t do well in the exam even though one of the problems was to find the volume of a 4 dimensional sphere, exactly the problem described above. Mostly, I was relaxed about tests and exams but on some occasions, of which this was one, I became completely paralyzed. In the debrief after the exam I started to explain how I had previously solved this problem, but before I got very far, Pólya cut me off. He obviously understood my method instantly, probably having worked it out at some point. Because of various episodes in the tutoring for the Putnam exam and my method of finding the 4 d sphere volume, Pólya had an exaggerated idea of my mathematics abilities and thought I should get my Masters.

Accordingly, I spent the Summer of 1952 at Stanford writing the thesis. By the end of the Summer it was finished and accepted. It missed