Professor and Director of the Intelligent Systems Laboratory (ISL)
Tel#: (718) 982-2814 - Email: Erlan.Feria@csi.cuny.edu
On November 10th, 2014 the New York Times reported on major prizes given to scientists [1]. Of the contributions leading to these prizes some physicists made use of mathematical dualities that are said to "offer physicists the chance of going around intractable problems of calculation in one system by solving the easier equations in another." This New York Times article also reports that the use of these dualities has become "a cottage industry in physics today." In my seminar I will be reviewing work on the universal cybernetics (UC) duality principle, which I discovered in 1978 in control theory while conducting graduate research on cybernetics [2]. UC is the study of control and communications in living and non-living systems. Its duality principle states that, "synergistic physical and mathematical dualities naturally arise in efficient system designs." The UC duality principle uses both mathematical and physical dualities for going around intractable problems of calculation not only in physics [3] but also in control [2], radar [4] and biological lifespan [5]. The very latest solutions derived by the UC duality principle will be reviewed, inclusive of the nascent linger thermo theory [3], which has inherently led to a sensible and straightforward relationship between biological lifespan and specific heat-capacity.
Statistical physics bridges for latency information theory (LIT) are revealed that include the discovery of the time dual of thermodynamics [1] - [4]. LIT is the universal guidance theory for efficient system designs that has inherently surfaced from the confluence of five ideas. They are: 1) The source entropy and channel capacity performance bounds of Shannon’s mathematical theory of communication; 2) The latency time (LT) certainty of Einstein’s relativity theory; 3) The information space (IS) uncertainty of Heisenberg’s quantum physics; 4) The black hole Hawking radiation and its Boltzmann thermodynamics entropy S in SI J/K; and 5) The author’s 1978 conjecture of a structural-physical LT-certainty/IS-uncertainty duality for stochastic control. LIT is characterized by a four quadrants revolution with two mathematical-intelligence quadrants and two physical-life ones. Each quadrant of LIT is assumed to be physically independent of the others and guides its designs with an entropy if it is IS-uncertain and an ectropy if it is LT-certain. While LIT’s physical-life quadrants I and III address the efficient use of life time by physical signal movers and of life space by physical signal retainers, respectively, its mathematical-intelligence quadrants II and IV address the efficient use of intelligence space by mathematical signal sources and of processing time by mathematical signal processors, respectively. The theoretical and practical relevance of LIT has already been demonstrated using real-world control, adaptive radar, physics and biochemistry applications. Seven results are stated next that relate to the revelation of statistical physics bridges for LIT. They are: 1) Thermodynamics, a special case of statistical physics, has a time dual that has been named lingerdynamics; 2) Lingerdynamics has a dimensionless lingerdynamics-ectropy Z that is the LT-certainty dual of a dimensionless thermodynamics-entropy, and like thermodynamics has four physical laws that drive the Universe; 3) S advances a bridge between quadrant II’s source-entropy H in bit units and quadrant III’s retainer-entropy N in SI m^2 units; 4) Z advances a bridge between quadrant I’s mover-ectropy A in SI secs and quadrant IV’s processor-ectropy K in binary operator (bor) units; 5) Statistical physics bridges are discovered between the LIT entropies and the LIT ectropies; 6) Half of the statistical physics bridges between the LIT entropies and LIT ectropies are found to be medium independent, thus yielding the same entropy-ectropy relationships for black holes, ideal gases, biological systems, etc.; and 7) A medium independent quadratic relationship T=dT(M/dM)^2 is revealed that relates the lifespan T of a retained mass M to the ratio of M to the fractional mass dM that escapes it every dT seconds, e.g., for a human with M = 70 kg, expected lifespan of T=83.9 years (or 2.65 Gsec), dT=1 day (or 86.4 ksec), its daily escaping mass is given by dM=0.4 kg. In turn, this requires him/her to consume 2,000 kcal per day (i.e., 5,000 kcal/kg times 0.4 kg) to replace the 0.4 kg lost from day to day which correlates well with expectations.
Guidance theory for intelligence and life system designs will be discussed along with three fundamental and overlapping enabling dualities. The duality entities are: 1) physical passing of time uncertainty and physical configuration of space certainty; 2) channel mediated communication and sensor mediated recognition; and 3) mathematical intelligence and physical life. The first uncertainty/certainty duality occurred to me in 1978 with the objective of both physically justifying and mathematically enabling the extension to quantized control of a separation between state estimation and processor control appearing in the seminal 1960 ASME publication by Rudolf E. Kalman on linear quadratic Gaussian (LQG) control. This novel approach was advanced in my Ph.D. dissertation of 1981 and a 1985 article in the International Journal of Controls, and given the name Matched Processors since it was the ‘certainty’ quantized control dual of Matched Filters in ‘uncertainty’ digital communications. Recently the other two dualities have been found to surface from the first. Six years ago in 2003, after spending several years in the development of a novel predictive-transform methodology for multidimensional signal modeling and compression, I started researching knowledge-aided radar for DARPA. My investigations for this radar project made me aware of the need for a design methodology addressing the joint compression of prior-knowledge synthetic aperture radar (SAR) imagery and the compression of the processing time of a covariance evaluator for this imagery. This was an extraordinarily complex problem to tackle. After many failed attempts it occurred to me, once again, to invoke the ‘liberating’ physical uncertainty/certainty duality revelation of years past. This realization has presently led me to the discovery of a novel latency theory for recognition systems that is the time dual of information theory, which guides channel and source integrated (CSI) coder designs for communication systems. While the units of information theory are mathematical binary digit (bit) units of a ‘passing of time uncertainty nature’ the units of latency theory are mathematical binary operator (bor) units of a ‘configuration of space certainty nature.’ As reported in two April 2009 SPIE papers and a January 2009 IEEE Signal Processing Society DSP & SPE Workshop paper available in my website http://feria.csi.cuny.edu , latency theory and information theory form together a latency information theory (LIT) that guides sourced intelligence-space and processing intelligence-time system designs. The most recent LIT discovery has been that radar systems can achieve outstanding signal to interference plus noise ratio (SINR) performances without the need of SAR imagery as prior-knowledge. This result can be readily verified with Matlab programs that simulate radar models used by DARPA. A ‘physical life’ dual which guides motion life-time and retention life-space system designs has been further revealed for the ‘mathematical intelligence’ LIT. Among several physical life LIT duality revelations is a dual for the ‘speed of light in a vacuum.’ This dual is the ‘pace of dark in a black hole’ of 6.1123 x 10^63 seconds per cubic meter that appears in a newly discovered ‘retainer-entropy’ that surfaces as the recognition dual of Claude E. Shannon’s ‘source-entropy’ in communications. Moreover, if a physical uncertainty/certainty duality is valid for the entire spacetime evolution of our universe, this would imply that any quantum-gravity theory must agree with it. A natural inference is then that a satisfactory quantum-gravity theory may already exist that is formed from the integration of existing gravity motion theories of a configuration of space certainty nature and quantum retention theories of a passing of time uncertainty nature. In turn, this also leads us to the realization that the ‘certainty’ advocacy of Albert Einstein for motion and the ‘uncertainty’ one of Werner Heisenberg for retention are both valid, and complementary in nature. An outline of the aforementioned research in the form of a genial four quadrants LIT revolution, exhibiting two mathematical and two physical fundamental methodologies in science, will be covered in this seminar with the details advanced in the sited references.