[FOM] On Physical Church-Turing Thesis

José Félix Costa fgc at math.ist.utl.pt
Thu Feb 12 05:10:25 EST 2004

Dmytro asks:

Do you have a reference for infinite travel in finite time in Newtonian

In internet one can find a !short description of the proof! by Saari and
Xia. I am sending it as attached file. The main reference to Jeff Xia's
proof of Poincare conjecture is

The existence of noncollision singularities in Newtonian systems
by Zhihong Xia
The Annals of Mathematics, Second Series, Volume 135, Issue 3 (May, 1992),

Again, if wanted, then I can send a full list of references. The first
author I know who discussed computational implications of these results is
the (USA) Physicist Frank Tipler. Further results show that the set of
initial conditions that can code for universal Turing machine has measure

Best regards,


J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm
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