b'18 GLOBAL UNION OF SCIENTISTS FOR PEACE SCIENTIFIC SOLUTIONS TO VIOLENCE AND GLOBAL CONFLICT 19samadhi. This maximally expanded state of awareness is the direct experience/realization of what mathematics calls the Universe of Setsi.e., consciousness beyond comprehension. In the language of physics, it corresponds to the direct conscious experience of the unified fieldthe fundamental unity at the basis of creation.Modern physiological science has identified this state of samadhi as a fourth major state of human consciousness, physiologically and subjectively distinct from waking, dreaming, and deep sleep. Neu-rophysiologically, this experience is marked by the onset of global EEG coherence and increased alpha power, indicating peak orderliness of brain functioning and utilization of the total brain.This fourth state of consciousness is universally accessible today through specific, highly developed technologies of consciousness derived from the Vedic tradition. Among these technologies, the Transcendental Meditation program and more advanced TM-Sidhi program of Maharishi Mahesh Yogi are the most extensively researched and widely practiced technologies in the world for accessing this fourth statewhich in turn leads to the many physiological, psychological, behavioral, and sociologi-cal benefits described elsewhere in this brochure.The key scientific point here is that when human awareness is maximally expandedwhen humanFigure 2: The hierarchical structure of mathematical logic. The natural numbers (or counting num-awareness opens to, and identifies itself with, the unbounded, universal unified fieldthen the naturebers) are the most familiar, concrete, and intuitively accessible numerical system, well suited to day-to-and reach of this state of consciousness is non-localized, and transpersonal. At that fundamental, spa- day human interactions. The addition of the number 0 (the additive identity) by early Indian mathemati-tially unbounded, unified level of reality, we are all, in essence, unified: we are all intimately and intri- cians elevates the natural numbers to the whole numbersa slightly more complete and logically more cately connected as one universal field of consciousnessthe unified field. powerful framework, if somewhat more abstract. The addition of negative numbers to form the integers To state this succinctly, at its deepest, most expanded level, consciousness is a field. And field effectsresults in a system that is closed under subtractioni.e., in which the operation of subtraction can, for of consciousnessi.e., long-range, society-wide effects of consciousnessare to be expected, andthe first time, be properly defined. The addition of fractions results in the rational numbers, in which the indeed have been observed and reported in the extensive published research on collective conscious- operation of division can be properly defined. The resulting, more complete and powerful mathemati-ness presented in this brochure. cal framework is suitable for accounting and most other practical purposes and endeavors. All the above four numerical systems constitute infinite sets of the same size. Between any two fractions there are an In this (or any) field model of consciousness, it follows that the radiated powerand resulting societalinfinite number of irrational numbers that cannot be expressed as fractions. The addition of these irratio-effectsemanating from a group of meditators will grow as the square of the number of meditatorsnal numbers fills out the gaps in the number line, and constitutes what are called the real numbers, or the in the group (i.e., grow quadratically, as opposed to linearly). This is because the amplitude (height) ofcontinuum. The real numbers constitute a higher order of infinity than the rational numbers, and are key a wave is equal to the sum of all the contributing waves that occupy a common space. Yet the powerto the formulation of calculus and for comprehending and pursuing the physical sciences, such as clas-of that resulting, combined wave is proportional to the square of the height of that wave. This is why,sical mechanics. Still more abstract than the inexpressible irrational numbers are the imaginary numbers, for example, the volume of two loudspeakers playing monaural sound in close proximity to each otherwhich, when added to the reals, give rise to the complex numbers. The complex numbers are essential for is two-squaredor four timesthe sound of a single loudspeaker. It is also why the intensity of laserformulating quantum mechanics and for understanding the world at the molecular and atomic levels. light grows as the square of the number of photons in the beam. This is a universal principle of waveAfter the complex numbers come what are called function spaces, limits of function spaces, and products of behavior, known as constructive interference. The resulting N-squared growth of the coherent influencefunction spaces, all representing progressively higher orders of infinity. These are necessary for the proper of a meditating group is well documented in the published literature. This N-squared effect makes itformulation and understanding of physics at the quantum-field-theoretic and deeper levels. Beyond the highly practical to generate a substantial peace-creating effect with even a relatively small number oflargest possible infinity that can be conceived by the human intellect lies the Universe of Sets, an infinity meditating participants when they are gathered in a group. which transcends all mathematically definable infinities, and includes them all.'