tag:blogger.com,1999:blog-3722233.post4214365156853800764..comments2024-03-28T14:56:46.834-05:00Comments on Computational Complexity: Cancer SucksLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3722233.post-75963956251051102602015-10-05T03:34:43.331-05:002015-10-05T03:34:43.331-05:00Small-f foundations for small-h hope
Sustaining h...<b>Small-f foundations for small-h hope</b><br /><br />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.<br /><br />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.<br /><br /><b>The War for Hope</b> Past generations have sought hope in the <b><a href="https://en.wikipedia.org/wiki/War_on_Cancer#Progress" rel="nofollow">War on Cancer</a></b> … 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.<br /><br /><b>Rising tides</b> 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:<br />-----------<br />"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."<br />-----------<br /><b>Hopeful readings</b> 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 <i>Why Is There Philosophy of Mathematics At All?</i> (2014).<br /><br /><b>Conclusion</b> 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.<br /><br />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.John Sidleshttps://www.blogger.com/profile/16286860374431298556noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-11819519102928188682015-10-05T03:10:04.226-05:002015-10-05T03:10:04.226-05:00May be $P=NP\iff\mathsf{cancer}\mbox{ }\mathsf{cur...May be $P=NP\iff\mathsf{cancer}\mbox{ }\mathsf{cure}$?Anonymousnoreply@blogger.com