Celebratio Mathematica

Den­nis John­son was born in Los Angeles on 19 Novem­ber 1938. His par­ents, Elouise and Wil­bur John­son were of Scotch-Ir­ish and Swedish des­cent. His par­ents had di­vorced by the time Den­nis was six. He was a bit of a trouble­maker and his re­la­tions with his new step­fath­er were some­times strained. Den­nis has two half-sib­lings, Ju­dith, born in 1944, and Don, born in 1948 on Den­nis’ 10th birth­day.

Den­nis lived between Cren­shaw and West­ern Av­en­ues un­til his sopho­more year at Canoga High School in the San Fernando Val­ley. That was fol­lowed by two years at Phil­lips Ex­eter Academy in Ex­eter, New Hamph­sire. Den­nis began col­lege in 1956 with four quar­ters at Cali­for­nia In­sti­tute of Tech­no­logy but de­cided to trans­fer to Uni­versity of Cali­for­nia, Los Angeles, partly for mu­sic­al reas­ons.

Den­nis is con­sidered by some to be the founder of min­im­al­ism in mu­sic, and this story is well told in [e2]. His ob­it­u­ary in the New York Times (see nytimes.com/2019/01/09/ob­it­u­ar­ies/den­nis-john­son-dead.html) gave spe­cial em­phas­is to his mu­sic­al work, and his four-hour-long com­pos­i­tion Novem­ber is con­sidered a mod­ern mas­ter­piece.1

Even­tu­ally Den­nis settled down in­to math­em­at­ics and wrote a Ph.D. thes­is en­titled “The ho­mo­logy of loc­ally fi­nite CW com­plexes” with Nick Gross­man as ad­viser, fin­ish­ing in 1968. Know­ing Den­nis, I’d guess that the re­search was in­de­pend­ently done. And it was good enough that Den­nis got a two-year post-doc at the In­sti­tute for Ad­vanced Study from 1968 un­til 1970.

I was an as­sist­ant pro­fess­or at UCLA while Den­nis was a grad stu­dent, and I must have seen him, but all I re­call hear­ing about him was that he be­lieved that the Chinese had once known the art of mak­ing them­selves in­vis­ible, but had lost it down through the ages. When I asked him about this years later he thought a bit and then said he could ima­gine how that story might have got­ten star­ted.

I spent fall 1968 and also fall 1969 at the IAS, and I think it was the lat­ter year when a few of us, prob­ably John Wood and Bill Cas­sel­man, were dis­cuss­ing rock climb­ing and plan­ning a trip to Ral­ph Stover State Park, the loc­al prac­tice area just over the state line in Pennsylvania. Den­nis over­heard us and asked to come along. That’s when I really got to know Den­nis, and it was the start of an in­tense ten years of rock climb­ing and then white­wa­ter kayak­ing to­geth­er.

Den­nis re­turned to Los Angeles and rather than pur­sue an aca­dem­ic ca­reer, he took a job in­volving plan­et­ary ex­plor­a­tion at the Jet Propul­sion Labor­at­ory in Pas­adena. He also took up rock climb­ing with his usu­al in­tens­ity and en­thu­si­asm. The best loc­al prac­tice climb­ing in the area was at Stony Point in the north­w­est San Fernando Val­ley, where there was a nice bunch of house-sized sand­stone boulders. Fur­ther away was Tahquitz Rock near Mount San Jacinto. Tahquitz was where the soon-to-be-fam­ous climber Roy­al Rob­bins learned the sport, star­ted the decim­al sys­tem for rat­ing climbs, and put up some of the hard­est routes of the time. Some 10–15 years later, Den­nis climbed al­most all of those clas­sic routes, e.g., In­nom­in­ate, Chingadera, and oth­ers. I joined him on some of the climbs, and he came up to Yosemite after I went to Berke­ley in 1972 and joined Mike Freed­man and me on oth­er climbs.

Both Den­nis and Mike had in­de­pend­ently tried the clas­sic North­w­est Face of Half Dome and failed through in­suf­fi­cient plan­ning. In 1975 they de­cided on an­oth­er try and took me along for ad­di­tion­al com­mon sense. We spent four days on the climb, haul­ing eight gal­lons of wa­ter and ad­di­tion­al gear, and were un­event­fully suc­cess­ful. They were the stronger climbers, but gave me the last two (easi­er) pitches as a con­sol­a­tion prize. (The read­er can view Half Dome’s fam­ous “Thank God Ledge” from above in the this You­Tube video.)

Rich Miller (fine to­po­lo­gist, Ph.D. stu­dent of Jim Kister and a con­tem­por­ary of Bob Ed­wards) had mean­while come to Cali­for­nia in the early 1970s. He’d had some kayak­ing ex­per­i­ence and knew how to make a kayak from a mold. In 1975 he en­cour­aged me to make one from a Mark IV mold, us­ing fiber­glass cloth and a res­in. We did so, and Den­nis heard about this so we made an­oth­er for him. That star­ted five great years of white­wa­ter kayak­ing with Den­nis. (Rich did not pur­sue the sport, for his in­terests lay in con­struct­ing things, such as very good vi­ol­ins, wind surfers with hy­dro­foils, etc.)

In the great droughts of 1976–77 and 1977–78, we did not do so much river run­ning, but we did learn on our own how to run low-wa­ter rivers. We also dis­covered that our homemade boats were brittle, and ten­ded to break after hit­ting rocks. So we bor­rowed the mold again and used Kevlar and epoxy. Kevlar is ex­tremely tough and epoxy worked much bet­ter than the earli­er res­in, so our kayaks did not break. But they did de­vel­op soft spots, and thus re­quired re­peated ap­plic­a­tions of ex­tra ma­ter­i­al to stiffen them up.

In 1978, the first plastic boats ap­peared. They were called Hol­low­forms and were made out of the equi­val­ent of garbage-can plastic, and so were quite tough. If bent, they simply re­turned to their ori­gin­al shape. With this de­vel­op­ment, the sport sud­denly opened up and rivers that were pre­vi­ously un­run­nable (from a mul­ti­tude of rocks) be­came doable.

It was quite ex­cit­ing to be in on the be­gin­ning. Or­din­ary people like us could, with a bit of de­term­in­a­tion and dar­ing, do first des­cents of ser­i­ous rivers. Over the course of two days in May 1980, we des­cen­ded the up­per por­tion of Mill Creek, fed by snows on Mt. Lassen. It was a fant­ast­ic run, and when we fin­ished I de­clared this was go­ing to be our best run ever, for it was so un­likely that we would be able to match it in the fu­ture. This de­clar­a­tion has held up.

Three of our com­pet­it­ors for first des­cents were Lars Hol­beck, Richard Mont­gomery (UC­SC geo­met­er now, but a high school stu­dent then), and Chuck Stan­ley, and they out­did us. Hol­beck and Stan­ley ed­ited the “Bible” of white­wa­ter kayak­ing in Cali­for­nia, Guide to the best white­wa­ter in the state of Cali­for­nia [e1]. Their de­scrip­tion of the Mill Creek run starts out:

Check out that gradi­ent. This has to be some of the steep­est run­nable white­wa­ter in Cali­for­nia. The av­er­age gradi­ent over the 17 miles is 135 feet per mile, in­clud­ing 5 miles av­er­aging 200 fpm. When I first looked at this run on the topo maps, I thought, “No way; no how; like nev­er!” I was shocked when I heard that Den­nis John­son and Rob Kirby ran this sec­tion in 1980 with no port­ages!

Our oth­er most not­able first des­cents were both legs of the Clavey River, a trib­u­tary which, when it hits the Tuolumne River, causes Clavey Falls, the hard­est rap­id on the clas­sic “T”. Den­nis and I took three days to run the lower half of the Clavey, and port­aged 23 times, so you might say we only ran/walked the run. In the “Bible”, Hol­beck writes:

Be­fore 1984, the Clavey was shrouded in mys­tery. In 1980, Den­nis John­son, that tight-lipped pi­on­eer of many “secret” runs, ran the two sec­tions of the Clavey with Rob Kirby. […] Al­legedly they took two days on the 8.8-mile lower run, port­aged over 20 times, and sub­sisted on only a few pea­nut but­ter sand­wiches.

Hol­beck et al. even­tu­ally gave it a try in 1984, and be­ing bet­ter boat­ers, ran it with few­er port­ages. His com­ment about Den­nis be­ing tight-lipped and secret refers to an im­port­ant part of Den­nis’ kayak­ing philo­sophy. He felt that there was something pure and mys­tic­al about a first des­cent. If you heard that a sec­tion of a river had been done, then you knew it was pos­sible, that it had no death traps, that this vir­gin river had been de­flowered. So Den­nis did not want to rob oth­ers of the joy he felt in a first des­cent, and thus tried to keep them secret, some­times suc­cess­fully.

Den­nis burned out on kayak­ing in May 1981. The in­tense joy of kayak­ing could not keep in­creas­ing, and he only came back to so­cial kayak­ing dec­ades later.

In the time span that cor­res­ponds roughly to those kayak­ing years, Den­nis did his most not­able work in to­po­logy, par­tic­u­larly on the Torelli sub­group of the map­ping class group of a sur­face. (This is the sub­group of dif­feo­morph­isms that in­duce the iden­tity on ho­mo­logy groups, and is gen­er­ated by Dehn twists on curves that bound or op­pos­ite twists on pairs of curves that co-bound.) Andy Put­man, re­spond­ing to a Math Over­flow ques­tion, re­ferred to Den­nis and his work with these words: “ ‘A Sur­vey of the Torelli Group’ by Den­nis John­son (the crazy geni­us be­hind much of the found­a­tion­al work on the Torelli group).”

Den­nis might drive 1000 miles on a four-day week­end from his three-day-a-week job at the JPL, and dur­ing that time he thought hard and suc­cess­fully about to­po­logy. Whenev­er we met, and dur­ing shuttle runs from take-out to put-in for some river or oth­er, he would tell me with genu­ine pas­sion and in­tens­ity about his math­em­at­ic­al work.

After 1981 I didn’t see Den­nis much, but I know he con­tin­ued rock climb­ing, some­times with Mark Feighn. He be­came in­ter­ested in restor­ing old si­lent films, par­tic­u­larly those star­ring Clara Bow, the “It” girl. He moved to Oak­land in time for the fam­ous 1991 Oak­land Hills fire, which burned up his stu­dio apart­ment and his trove of kayak­ing pho­tos.

Very sadly, de­men­tia en­vel­oped him in his later years. Den­nis stayed for a time in as­sisted liv­ing in the East Bay — healthy, skinny, not speak­ing or re­cog­niz­ing people, but ap­par­ently en­joy­ing mu­sic. He died peace­fully on Decem­ber 20, 2018.