BioSystems 64 (2002) 47–53 Extradimensional bypass Peter A. Cariani * Eaton Peabody Laboratory of Auditory Physiology, Department of Otology and Laryngology, Harard Medical School, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston, MA 02114, USA Received 3 May 2001; accepted 20 September 2001 Abstract We discuss the concept of extradimensional bypass as it was developed by the late theoretical biologist Michael Conrad. An evolving system that optimizes its performance by gradient ascent (hill climbing) can avoid being trapped in local maxima by increasing the effective dimensionality of its search space. Many local maxima may become saddle points in the higher dimensional space, such that gradient ascent can continue unimpeded. Extradimensional bypass as a concept has parallels in theories of open-ended learning and functional emergence, where new structural, functional, and informational primitives can increase the effective dimensionality of material systems. © 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Michael conrad; Theoretical biology; Biological cybernetics; Molecular computing; Adaptability; Self-organization; Evolution; Emergence; Dimensionality www.elsevier.com/locate/biosystems Some organizations are better suited to effectieeolutionary learning than others. If a specific combina - tion of simultaneous genetic ariation operations (e.g. mutations) are required to occur simultaneously, eolution proceeds too slowly for een small adances to occur on time scales as long as the age of the earth …. This is because, products of probabilities decrease rapidly. We can picture an adaptie landscape of peaks, alleys, and saddle points. If specific combinations of mutations are required, the landscape will be sparsely populated by isolated adaptie peaks, and consequently the eolution will stagnate. According to the extradimensional bypass principle it is possible to transform the landscape into one that is highly populated by saddle points by increasing the dimensionality of the adaptie surface in an appropriate way. Suppose that a mountain climber standing on top of an isolated peak could magically increase the dimensionality of his space. If the topographic features of the landscape satisfy suitable conditions, it would become increasingly likely that a traersable pathway to a neighboring peak would appear as new dimensions were introduced. Isolated peaks would be conerted to saddle points and additionally the density of acceptable locations [solutions] on the surface would increase … (Chen and Conrad (1994, p. 429)). * Tel.: +1-617-320-9717; fax: +1-413-618-4025; www.cariani.com. E-mail address: cariani@mac.com (P.A. Cariani). 0303-2647/02/$ - see front matter © 2002 Elsevier Science Ireland Ltd. All rights reserved. PII:S0303-2647(01)00174-5