Month: November 2022

The Evolution of Multidimensionality

Posted on by japineda

Scientists root the concept of dimensions in the idea of describing space. However, the scientific sense of space as an “extended” void with dimensions did not arise until well into the 17th century; not until Galileo and Descartes made space the cornerstone of modern physics as something physical with a geometry. By the end of the 17th century, Isaac Newton had expanded the vision to encompass the entire universe, which now became a potentially infinite three-dimensional vacuum.

Interestingly, it was the work of artists several hundred years earlier that foresaw and likely undergirded this scientific breakthrough. In the 14th to 16th centuries, Giotto, Paolo Uccello and Piero della Francesca developed the techniques of what came to be known as perspective—a style originally termed “geometric figuring.” By exploring geometric principles, these painters gradually learned how to draw images of objects in three-dimensional space. By doing so, they reprogrammed European minds to see space in a Euclidean fashion.

Descartes’ contribution was to make images of mathematical relations and formalize the concept of a “dimension.” He did it in terms of a rectangular grid marked with an x and y axis, and a coordinate system. The Cartesian plane is a two-dimensional space because we need only two coordinates to identify any point within it. With this framework, Descartes linked geometric shapes and equations. Thus, we can describe a circle with a radius of 1 by the equation x2 + y2 =1. Later, this framework became the basis for the calculus developed by Isaac Newton and G W Leibniz.

How does this concept of space affect our lived experience? Imagine living in a Cartesian two-dimensional world in which you are only aware of length and width. You see two objects approach each other at tremendous speed in this flat-plane world. The inevitable outcome will be a crash, you think. When nothing happens and the two objects appear to pass through each other untouched and continue on the other side, you think—it’s a miracle!

The Cartesian plane makes it easy to imagine adding another axis (x, y, z), which now allows us the ability to describe the surface of a sphere (x2 + y2 + z2 = 1) and thus describe forms in three-dimensional space.

Imagine that you are now seeing the same two objects coming towards each other, but able to see them in three dimensions, not only length and width, but also depth. You see the two objects, which are planes, approach each other at tremendous speed. But because you can see that one is significantly above the other, you know they are safe. It is patently obvious and definitely not a miracle there is no crash. All because you can see into this third dimension.

In 1905, an unknown physicist named Albert Einstein published a paper describing the real world as a four-dimensional setting. In his “special theory of relativity,” Einstein added time to the three classical dimensions of space. Scientists mathematically accommodated this new idea easily since all one has to do is add a new “time” coordinate axis within the Cartesian framework.

Events in our world seem to occur in four dimensions (length, width, depth, and time) and we can see into all of them. Hence, when the same two objects, which we recognize as planes, approach each other at tremendous speed and at the same height, there would be a crash, except the two planes are flying in the same space but at different times. Again, it is obvious there is no crash because of our ability to perceive differences in time. This ability, to see in four dimensions, makes interactions between objects appear natural and obvious, whereas for those seeing in fewer dimensions, they would seem miraculous or paradoxical.

Einstein’s Theory of General Relativity says we live in four dimensions. String Theory, developed in the 1960s, in contrast, says it’s at least 10. In 1919, Theodor Kaluza discovered that adding a fifth dimension to Einstein’s equations could account for the interactions of both electromagnetism and gravity, the fundamental forces that govern how objects or particles interact. The problem was that, unlike the previous four, this fifth dimension did not relate directly to our sensory experience. It was just there in the mathematics. More recently, String Theory scientists have shown that an additional five dimensions account for weak and strong nuclear forces, the two additional fundamental forces of nature. Thus, with 10 dimensions, String Theory can account for ALL the fundamental forces and ALL their interactions. Unfortunately, we have no way of relating our lived experience to this mathematical multidimensional accountability.

We look out at our complex world and try to figure out why accidents happen? Why do young people die? What makes voters attracted to certain ideas? Why do we fall in love with this person and not that one? Why does only one person survive a plane crash? From our human perspective, these are difficult to answer and even incomprehensible questions because we don’t have full insight into the dimensions at work creating the dynamics of these interactions. If we did, it would be as obvious as the sun rising every morning.

Today we know physical interactions result from information exchanged by fundamental particles known as bosons, and mathematically accounted for in 4-D space by Einstein’s equations. Experiments with bosons, however, suggest there may be forms of matter and energy vital to the cosmos that are not yet known to science. There may, in fact, be additional fundamental forces of nature and distinct dimensions of information.

Indeed, different exchanges of information mediate human interactions. These involve intangible dimensions of unity, beauty, sociality, persistence, love, entanglement, etc. Information in these dimensions affects social interactions and relates more directly to our life. Imagine, for example, two individuals running at each other at full speed and crashing. Without contextual information, how do you understand the action? Is it two angry opponents on a battlefield trying to kill one another? Or, is it two players on opposite teams tackling one another in a game of American football? Knowing the intangible dimensions of the interaction and the information provided gives us an obvious answer.

Preliminary attempts by psychologist Sarah Hoppler and her colleagues (2022) give us hope that a combination of factors can describe social encounters. These researchers have identified six dimensions (actor, partner, relation, activities, context, and evaluation) with three levels of abstraction, based on how people describe their social interactions. They have shown their approach to depict and account for all conceivable sorts of situations in social interactions, irrespective of whether described abstractly or in great detail.

It might be useful, therefore, to ask whether there are limits to our comprehension of additional dimensions of information? Science tells us that physical dimensions may be so tiny and fleeting that we currently can’t detect them. However, in terms of intangible sources of the human experience, we may not be as helpless. We can sense and intentionally improve some of these dimensions (love, sociality, persistence); others we sense and learn to appreciate (beauty, unity); but a vast majority are, for now, still beyond our comprehension (entanglement).

We are still discovering, evolving, and quantifying the full capacity of our human experience. If we accept Pierre Teilhard de Chardin’s statement that “We are not human beings having a spiritual experience; we are spiritual beings having a human experience,” then the voyage of discovery of our multidimensional nature is unlimited and ought to be infinitely enjoyable.

What Is Genius?

Posted on by japineda

Leonardo da Vinci — Albert Einstein

We define genius as original and exceptional insight while performing some art or endeavor that surpasses expectations, sets new standards for future works, establishes better methods of operation, or remains outside the capabilities of competitors. Prior to doing some background reading on the subject, I assumed that at such heights of intelligence, there is little room for fallibility, errors, flubs, mistakes, wrong guesses, etc. I discovered this was wrong, and it made me reconsider what genius really means. It’s not what we’ve been told by mythmakers.

Let’s consider two well-known and uncontested cases of genius, Leonardo da Vinci and Albert Einstein. For many of us, they represent the epitome of creativity in arts and science and a full-flowering of the human potential. Leonardo da Vinci is the embodiment of the Renaissance man. He was a painter, artist, engineer, architect, scientist, inventor, cartographer, anatomist, botanist, and writer. His active imagination conceptualized the tank, the helicopter, the flying machine, the parachute, and the self-powered vehicle. He was a man far ahead of his time and many of his visionary inventions became real only centuries later.

As an engineer, Leonardo sensed more than most how the design of machines informed by mathematical laws of physics is better than relying just on practice. He was the first to design separate interchangeable components deployed in a variety of complex devices. And no one drew machines with more attention to detail and reality. His insatiable curiosity about nature undergirded his efforts to devise flying machines. He sought not only to imitate flying birds, but to understand and apply the principles of flight to endow man with the ability to fly on his own. His genius lay in his mastery of engineering principles, design, and natural law.

Walter Isaacson, author of “Leonardo da Vinci,” describes how Leonardo integrated science with his artistic genius. “Leonardo spent many pages in his notebook dissecting the human face to figure out every muscle and nerve that touched the lips. On one of those pages you see a faint sketch at the top of the beginning of the smile of the Mona Lisa. Leonardo kept that painting from 1503, when he started it, to his deathbed in 1519, trying to get every aspect exactly right in layer after layer. During that period, he dissected the human eye on cadavers and could understand that the center of the retina sees detail, but the edges see shadows and shapes better. If you look directly at the Mona Lisa smile, the corners of the lips turn downward slightly, but shadows and light make it seem like it’s turning upwards. As you move your eyes across her face, the smile flickers on and off.”

While one can sense the inexhaustible work, energy, curiosity, and creative drive behind Leonardo’s genius, the stories insinuate his creativity unfolded naturally, perfectly, and inevitably. But, much of this reality is mixed with mythology since Leonardo created an endless succession of untested contraptions, unpublished studies, and unfinished artworks. There was no inevitability to his creations. There was a lot of fudge work and many, many steps before the final product. It would appear his genius rested on having an active and creative mind. What motivated such a mind? Undoubtedly, it depended on several personality attributes, but foremost among these was curiosity, his defining trait. Everything seemed to interest Leonardo. Maybe genius is simply an unrelenting curiosity that in its wake happens unexpectedly upon original, novel, and unique insights. The genius is that all that preparation and work allows one to recognize those marvelous coincidences.

Like da Vinci, Albert Einstein reached the pinnacle of admiration in the modern era as the iconic symbol of genius. His most famous equation is E = mc2. Einstein, however, doubted how important this was and dismissed notions it might one day be at the heart of an alternative energy source. In 1934, he declared that “there is not the slightest indication” that atomic energy will ever be possible. Today his equation is at the heart of over 400 nuclear power stations, which are about to become the world’s leading source of non-carbon-based energy.

Einstein thought his biggest mistake was refusing to believe his equations that predicted the expansion of the Universe. While some astronomers favored the notion that many objects in the sky were actually “island universes” located well outside the Milky Way, most astronomers of his time thought that the Milky Way represented the full extent of the Universe. Einstein sided with this erroneous view, and when he applied his General Relativity theory to the entire universe, he had to add a special type of fudge factor into his equations, a cosmological constant, to make it static and eternal. Unfortunately, later evidence showed that, in fact, the Universe was and is still expanding equally and uniformly in all directions on large cosmic scales. In the 1930s, Einstein referred to his introduction of the cosmological constant to keep the Universe static as his “greatest blunder.”

Today we know that Einstein actually missed out on predicting something even bigger: the existence of dark energy. In the mid-1990s, 40 years after Einstein’s death, astronomers showed his misplaced faith on his beautiful equations. Studies of exploding stars in distant galaxies revealed the Universe isn’t just expanding, it’s expanding at an ever-faster rate. The cause for this is a force stronger than gravity, but acting in the opposite direction—and with no obvious origin. This is the mysterious dark energy. Einstein’s theory can accommodate it, but at the price of reintroducing the same ugly fudge-factor Einstein loathed. Most theorists believe dark energy has its origins in the quantum laws of the sub-atomic world, which allow even apparently empty space to be seething with energy. Einstein’s antipathy for quantum theory made it unlikely he would have incorporated it into his most cherished work.

In fact, Einstein had to be dragged kicking and screaming to the idea that the Universe began in a Big Bang. After learning from the Belgian mathematician Georges Lemaître that General Relativity (GR) predicts the creation of the Universe, he dismissively replied: “Your calculations are correct, but your physics is abominable.” It’s easy to see why he believed this since the GR equations go haywire at the moment of the Big Bang, giving literally infinite results. What’s needed is something extra to bring the theory back under control. Theorists now believe they know what that something extra is—and, regrettably for Einstein, it’s the very thing he couldn’t accept: quantum theory. Recent calculations by theorists in the US and Europe have shown that combining GR with quantum theory results in a theory of ‘quantum gravity’ that gives insights not only into the Big Bang but also what came before it.

Although Einstein played a major role in developing quantum theory, he became increasingly suspicious of its fuzzy, ‘probabilistic’ view of particles, which seemed to prevent even their position and speed being known with complete precision. He summed up his view by saying, “God does not throw dice.” But today, most physicists believe Einstein was wrong. Throughout his career, Einstein had an almost religious belief in the fundamental unity of the Universe, and spent decades searching for the one true Theory of Everything (ToE), which would describe the Universe and everything in it. His failure did not deter others, and over half a century after his death, the quest for the ToE continues. The bad news is that there may be at least 10,500 ToEs, and no obvious way of deciding between them. There’s now a growing suspicion that the whole idea of just one true ToE may be a mistake—and that Einstein was naïve to spend his life looking for it.

These brief highlights of Albert Einstein’s miscues and false steps in his theorizing, amidst the many times he proved to be right, reinforce what my argument about genius is. It is not a natural, perfectly linear, and inevitable unfolding that occurs in the mind of one person. Rather, it reflects circuitous thinking, hard work, and an unrelenting drive that makes mistake after mistake. Yet, somewhere along this messy path, this creativity and uncompromising drive falls upon and discovers, perhaps unexpectedly, a heretofore unknown jewel of creation.

Unless special circumstances occur, such as injuries or neglect, most children embody the driving curiosity and energy of genius. My argument is that everyone is born with equal potential to realize such a trait. While it is unimpeded in an Einstein or da Vinci, it is blocked, obstructed, unencouraged, derailed in the vast majority of us. It is up to our society at large to identify these reasons and avoid this human misfortune. As Walter Bowman Russell, an American Renaissance man in his own right, put it in 1946, “Mediocrity is self-inflicted; genius is self-bestowed. The choice is yours.”