## Thursday, October 01, 2015

### Cancer Sucks

Karsten Schwan said the title quote when we were gathered as a faculty two years ago mourning the Georgia Tech School of Computer Science faculty member Mary Jean Harrold who died from the disease. Karsten just lost his own battle with cancer monday morning and my department is now mourning another great faculty member.

Just a few months ago, Alberto Apostolico, an algorithms professor at Georgia Tech, also passed away from cancer

I went back through the obituaries in the blog and we lost quite a few to cancer, often way too young, including Mihai PătraşcuBenoît MandelbrotPartha NiyogiIngo Wegener, Clemens Lautemann and Carl Smith. I just taught Lautemann's proof that BPP is in Σp2∩Πp2 in class yesterday.

With apologies to Einstein, God does play dice with people's lives, taking them at random in this cruel way. Maybe someday we'll find a way to cure or mitigate this terrible disease but for now all I can say is Cancer Sucks.

1. May be $P=NP\iff\mathsf{cancer}\mbox{ }\mathsf{cure}$?

2. Small-f foundations for small-h hope

Sustaining hope is no easy task at any stage of life, and few experiences exhaust our capacity for hope so entirely as disorders like metastatic cancer, schizophrenia, and alzheimer's.

There's no shortage of writings on these diseases, but not many of these works offer much comfort to children grappling with the impending loss of a parent, or to parents grappling with the impending loss of a child.

The War for Hope  Past generations have sought hope in the War on Cancer … note the large-W and large-C. Yet needless to say, this large-W War has not been Won, in that the Enemies Cancer, Schizophrenia, and Alzheimers have not been Defeated.

Rising tides  Nowadays the STEM community — mathematicians especially — is slowly turning away from Large-Letter Enterprises, and embracing instead small-m mathematics as a small-f foundation for (among other things) the small-h hope of healing. The hope is that the small-f foundations of small-m mathematics can immerse our ignorance — not only our mathematical ignorance, but our medical ignorance too — in rising tides of understanding:
-----------
"The unknown thing to be known appeared to me [Grothendieck] as some stretch of earth or hard marl, resisting penetration … the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it … yet it finally surrounds the resistant substance."
-----------
Hopeful readings  Some hope-inducing student-friendly readings are the works of the philosopher John Hacking, in particular Hacking's short (and much-cited) article "Do We See Through a Microscope?" (1985) and his longer (and well-reviewed) book Why Is There Philosophy of Mathematics At All? (2014).

Conclusion  What we are seeing nowadays, through our increasingly capable 21st century microscopes, is providing us with increasing medical hopes of effective treatments for presently intractable disorders; moreover the small-p philosophy of small-m mathematics is helping to speed the day of our hopes' fulfillment, by immersing our microscopic observations in a rising tide of small-p performative small-u understanding.

Complexity theory too has a crucial role to play in this hopeful enterprise: not so much the (large-C) Complexity Theory that seeks the Holy Grail of provably separating PvsNP, but rather the small-c complexity theory that seeks to understand why so many formally hard problems — like structural mechanisms of metastatic cancer, schizophrenia, and alzheimer's — are hopefully solvable.