Further to Robert Marks on the math paradox that challenges physics because it may be unanswerable, Rob Sheldon writes to say,
Without reading the full paper, it sounds like a familiar problem in many-body QM, how do you add up all the distant interactions in an infinite crystal to find the energy of the system at a single point? Sometimes the interactions fade away, and the series converges. Sometimes the interactions stubbornly refuse to fade, and the series diverges. This paper is saying “there is no a-priori way to know if you have a convergent or divergent series.” I think for mathematicians, this is a Thales moment, when they get to tell the physicists that math really does have application to the world.
Thales moment?:
The ancient Greek philosopher Thales was born in Miletus in Greek Ionia. Aristotle, the major source for Thales’s philosophy and science, identified Thales as the first person to investigate the basic principles, the question of the originating substances of matter and, therefore, as the founder of the school of natural philosophy.
For me, this is a nice piece of work that proves why you need experimental physicists and not just computer simulations. One more reason to claim that physics is an empirical science.
See also: Rob Sheldon on the meaning of time
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