In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.

Important elements of games, movies, and other computer-generated content, shadows are crucial for enhancing realism and providing important visual cues. In recent years, there have been notable improvements in visual quality and speed, making high-quality realistic real-time shadows a reachable goal. Real-Time Shadows is a comprehensive guide to t

Christmas Day, 3:00 a.m., December 25, 2015 The final chapter in man’s search for truth began with a single event that took place in the wee hours of Christmas morning, 2015. A crippling blizzard of epic proportion had blanketed the entire northeastern corridor with an opaque shroud of ice and wind-driven snow. All ground and air transportation was at a complete standstill as residents throughout the Atlantic coastal area hunkered down in their homes awaiting a reprieve from nature’s fury. This explains why Ray Hodges was fast asleep at his desk in the air traffic control tower of Dulles International Airport. After doing absolutely nothing for the past six hours, he was bored stiff and had planned to rest his eyes for only a moment. Forty-five minutes later, Hodges was awakened by a high-pitched alarm warning him of an incoming bogey. The aircraft’s radar signature was that of a TWA Constellation, a prop-driven plane that he had not seen since the early 1960s. The anonymous intruder was flying dangerously close to the high value targets in Washington DC, and Hodges was required to establish immediate radio contact with the inbound aircraft. Using multiple radio frequencies, he tried to hail the pilot, with no response. This perilous situation prompted an urgent call to the Strategic Air Command at Andrews Air Base, and within minutes of notification, a squadron of F18 jets had surrounded the aircraft. The team leader contacted Hodges and reported that he too was unable to communicate with the pilot. Then the pilot said something that made Hodges’s skin crawl. “Dulles, there seems to be multiple objects protruding through the fuselage of the plane. Understand the visibility up here is marginal, but those objects look a lot like body parts.” Hodges instantly felt a gnawing pain centered in the pit of his stomach. Thus began one young man’s journey into the crypts of the unknown. It was a place where all reality was an illusion.

"Chronological explanation of physics from early history through current studies geared to lay readers with limited mathematical training"--

The Allegory of the Cave, or Plato's Cave, was presented by the Greek philosopher Plato in his work Republic (514a–520a) to compare "the effect of education (παιδεία) and the lack of it on our nature". It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates, narrated by the latter. The allegory is presented after the analogy of the sun (508b–509c) and the analogy of the divided line (509d–511e). All three are characterized in relation to dialectic at the end of Books VII and VIII (531d–534e). Plato has Socrates describe a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall from objects passing in front of a fire behind them, and give names to these shadows. The shadows are the prisoners' reality.

Presents the author's thesis that consciousness, in its manifestation in the human quality of understanding, is doing something that mere computation cannot; and attempts to understand how such non-computational action might arise within scientifically comprehensive physical laws.

Westerners often make the mistake of discounting the spiritual aspects of life as “not real”, imaginary, a mere reflection of what is experienced in the “real world” (by which they usually mean, the physical world that we experience with our five senses). Many claim that the concept of angels and demons are creations of our imagination, that God or the gods of other religions are mere projections that we create for ourselves. The argument goes like this: Humans look at physical reality and then create/imagine a shadow world, the spirit world, based upon our experience of ‘real life’. But what if the opposite is true? What if what we are experiencing with our five senses is really just a reflection in a pond? What if the “real” begins with the spiritual and then is reflected into the physical? If this hypothesis is true, if indeed what we see happening around us in the physical world begins in the spiritual world and is only later manifested where we can perceive it with our five senses, then that has profound implications for us in a practical sense. If true, this would mean that individual crimes, acts of evil and aggression, and perhaps even larger events, armed conflicts, terrorist strikes or man-made catastrophes that occur in our physical world might be avoided altogether...if we can stop them at the spiritual level. Likewise, what if good might blossom in our physical world as a result of intervention at the spiritual level? It certainly seems that we have evidence for both, in human experience and in the scriptures. Join Dr. Silas Gaines as he walks his readers through a scriptural, historical and personal journey to identify spiritual laws and principles that govern our current reality. Gaines aids us in highlighting spiritual laws woven into the Created Order of which we are often dangerously ignorant, and which often hold the keys to humanity flourishing in God’s plans and purposes. Gaines invites us to join in a journey that will open our eyes to new realities around us, and empower us to walk into our God-given destinies, impacting people and the world around us as we were born to do.