I. Introduction
ORGANIZATIONS such as NASA, ESA, and others have put substantial resources into space missions designed to study properties of the sun. A few examples of such missions are the Solar and Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE) and the Solar Dynamics Observatory (SDO). Many properties related to the occurrence of solar particle events are being studied such as the sun's magnetic topology and characteristics of radiation emitted during events in the hopes that some reliable predictor of events can be found. Despite this significant international effort, solar particle events can occur suddenly and without obvious warning. This is a serious difficulty for new space initiatives that plan to send manned spacecraft to the moon, Mars or interplanetary space. It can also be problematic for instrumentation as well as electronic and photonic subsystems. Thus, there is strong motivation to develop predictive methods for solar particle events. It is hoped that the apparent statistical character can be overcome and predictability achieved if precursor phenomena such as x-ray flares or magnetic topology signatures can be properly interpreted or if the underlying mechanisms are identified. This paper addresses the very basic question of whether deterministic predictions of solar particle events are possible (i.e., whether it is possible to predict their time of occurrence and magnitude).