How Do You Know?

How Do You Know?

Our modern times have brought us many great advancements. We find ourselves living longer, becoming more globally connected, and enjoying medical ingenuities, such as antibiotics, blood transfusions, and artificial organs. There are many amazing necessities and niceties that are enjoyed by the human race in varying degrees because of Science. Science has given us a lot to be thankful for. Or has it?

In recent years, there have been debates, and at times heated arguments, over the likes of genetically modified foods, vaccinations, and global warming. Even the effectivenessFlat Earth of Western medicine has cropped up in many personal conversations over the years. Ideas such as Flat Earth have come back to the scene in modern discussions and often with contention.

Once thought for certain by the general populace, many scientific concepts are met with skepticism. But before you believe this blog is about winning you over to one side or the other, I ask you read on, because it not. There is something greater underneath these debates, and it has everything to do with you.

When researching the Philosophy of Science the other day, I came upon a very intriguing
question: How do you know your knowledge is authentic?

What a wonderful question, and it has given me more than a pause. Now before we reduce this question to reducto adsurdum, and say how can we really ever know anything, let’s try to accept the question for what it is: an invitation to know ourselves a little bit better.

Knowledge. It is a formidable due to its ubiquitous nature. It is an invading species that finds life in the uninhabitable regions of our brain. It plants its roots and digs deep so it cannot be easily removed, often without our realizing it.

Thus, when we allow “knowledge” to pass our acceptance filters and impregnate itself in our world view, it becomes almost impossible to remove. Especially if it comes from an authority – like science, religion, or a person of a particular importance. But are these sources enough to make an idea become an organism of knowledge?

One of the greatest lessons science has taught me is that it is only at its best when it is being challenged, and I find that this true of human knowledge in general. Authenticity cannot exist if challenge is not present. Growth is a product of conflict, not peace. Knowledge that is real will survive and become stronger; the ideas that do not deserve to be uprooted and replaced with a more genuine concept.

How do you know your knowledge is real? We listen and we give the other side their due. This is a very Masonic and scientific principle. In doing so, the only danger we will face is the danger of becoming more authentic in what we know. That doesn’t sound so bad, does it?

 

Is Death Necessary? Or Inevitable?

Is Death Necessary? Or Inevitable?

Death. A foregone conclusion to this life. Maybe. What does science say?

“Now he has departed from this strange world a little ahead of me, Albert Einstein wrote in a condolence letter, upon the death of his close friend Michele Besso in 1955, “that signifies nothing. For those of us who believe in physics, the distinction between past, present, and future is only a stubbornly persistent illusion.” Einstein was on to something, according to a contemporary scientist.

A theory… a philosophy, really, called “Biocentrism,” explores this question and many other fundamental reality-based questions. Introduced in 2010 by Robert Lanza, a scientist, doctor, and “influential thinker” who felt that consciousness is a problem for not only biologists, but physicists as well. Nothing, according to Lanza, can explain the “molecules of consciousness bouncing around in our brain.”

Biocentrism is sometimes the view or belief that the rights and needs of humans are not more important than those of other living things. This is not that theory of philosophy; it is something entirely different.

The theory postulated by Lanza is that nothing exists outside of consciousness and life. Biology is the great creator. In Lanza’s view, we humans have become very good at understanding the mechanics of our universe. We look at the rotations of planets, and we know chemical properties and can explain how apples fall from trees.

What we can’t explain is why. Why does the universe work as it does? Why can we not explain yet why we have consciousness, or what we should be doing with it? Biocentrism explains the why.

“I regard consciousness as fundamental. I regard matter as derivative from consciousness.” Said Max Planck, Nobel Prize-winning physicist, “We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.”

Lanza, with biocentrism, seeks to explain the difference between what we all perceive to be an objective reality versus a life-centric reality.

“If a tree falls in the forest, does it make a sound?”

Objective reality says, why yes, of course it does. Biocentrism reality says, not unless brainthere is an ear nearby. The science is lengthy but makes a point – without the ear to hear, the sound does not really exist. The tree falling creates puffs of air which stimulate aneardrum that translates the shift of air into a sort of sound. The sound is entirely held within our brains. The sound requires life and consciousness to comprehend it. The human must remove themselves from the equation to see the validity of the argument, and put themselves back in to understand the human place in creating the universe.

  • The First Principle of Biocentrism is that “what we perceive as reality is a process that requires our consciousness.” Or, said slightly differently, requires “any” consciousness. If I ask you, where is the universe, most might answer, “out there.” What many struggle with is that we are part of the same universe; what is out there is what is in here.                                                                                                                                                                     
  • The Second Principle of Biocentrism is that “internal and external perceptions are intertwined; they are different sides of the same coin and cannot be separated.”

In a complex explanation, Lanza says the general idea is that our brains create the reality we see. In this book, “Biocentrism: How Life and Consciousness are the Keys to Understanding the True Nature of the Universe,” Lanza explains all of this in an answer to the question: “Where is the Universe?”

In total, there are seven principles to Biocentrism, according to Lanza.

  • The most interesting one, in relation to death, is the Fourth Principle of Biocentrismwithout consciousness, “matter” dwells in an undetermined state of probability.

Any universe that could have preceded consciousness only existed in a probability state. This seems to state that we, as are in that undetermined state of probability, and that our matter never really “goes away” but is folded into and part of the ongoing reality of the universe. Our consciousness separates from matter but doesn’t cease to exist because it’s all part of the same consciousness. This reminds me of Neil Gaiman’s story, “American Gods.” Gods exist and thrive because of our consciousness of them.

Life creates the Universe. The Universe (Darwinism, the Big Bang, etc) did not create life. We’ve got it backwards.

Mind. Blown.

It seems like such a simple turn of phrase, one which everyone can identify with. Lanza brings to bear all the science and experiential anecdotes to back it up. He picks us up, biocentrism-turning-the-universe-outside-inkicking and screaming, from seeing the universe one way and to standing on our heads, viewing it another. These theories harken back to the ideals of Eastern Philosophies and Freemasonry.

Freemasons, Buddhists, and Taoists seek balance and unification, we see an understanding of nature and science, and a middle path. For the Buddhist, our consciousness allows us to connect with the One – the whole. For the Taoist, the focus is a seamless flow of life – where there are no individuals but a single existence. For the Freemason, we seek unity and harmony, and the idea that as a unit, we are also creators. None of this is incompatible with Lanza’s scientific and philosophical approach to how the universe, physics, works.

So, to the original questions: “Do we die?” and Is it inevitable?” 

According to Lanza, we are already dead, alive, past, future, and creators right now. The limitations are in our own perceptions and ideas of reality. All of it is right now because we, and all matter, are conscious. Lanza himself addressed this question in a Psychology Today article, located here.

Perhaps if more people could look at the universe from this new paradigm, we would become the creators we already are; we create and destroy together, whether we believe it or not.


  1. For a really good read, try out Lanza’s book on Biocentrism and his follow-on book, “Beyond Biocentrism.”
  2. For an interesting Buddhist view of Biocentrism, look to “The Endless Further,” a Buddhist’s blog.

When Did We Stop?

When Did We Stop?

It is easy for life to sweep us away on the current of self-importance. I don’t think we mean to; it just happens to be the way our culture works. Fast and busy and “me” centered. This way of life isn’t just an adult thing. We have shown our children how to do it. They, too, are pounded with the every day commitments we give them and allow. This way of living is like a fierce version of the Tango but at a pace it was never intended to be danced at.

This is my life as well; I made the same choice you did, to be a part of this me-speed machine.

Two events recently occurred that has made me slow my dance steps down and see those around me better: the launch of Falcon Heavy and a philosophical discussion on whether we should migrate to Mars.

The only word that I can give to the launching of Falcon Heavy is wonder. Watching the launch left my mouth open but with no words. There was something eerie when the sideFalcon Heavy boosters landed on Earth again. This shouldn’t be happening, I told myself. Side boosters don’t come back, they just don’t. Again, the wonderment had me re-watching several times over until the busy day I had, had dragged my eye lids closed.

Two weeks later the philosophical debate on whether humans should migrate to Mars coincidently dove-tailed with the SpaceX’s launch. The discussion was an interesting juxtaposition to my earlier experience of watching the Falcon Heavy launch. I entered the discussion, as I do monthly, with great enthusiasm about the topic. How could I not with this particular idea? We were going to talk about the possible expansion of our kind. To me, the feeling I had could be analogous to what people must have felt when travel to the New World seemed impossibly possible. The feeling was akin to infectious hope sprinkled with reservation. The New World, that is Mars, seems so alien, so inhospitable, could we ever truly make a life there?

It was after this debate that I have felt my mouth go dry with disappointment and my inner Tango stumble with the memory of a statement made earlier in the discussion, “What did schlepping to the Moon ever get us?” I shouldn’t judge I know… but I did. This question has forced me to understand the alternative purpose that Elon Musk had when he sent his Tesla roadster into space. He didn’t use his car solely as payload… he used it to get our attention.

I have to ask; I have to know. When did we stop looking up? When did we stop finding continual inspiration in the stars and unimaginable possibilities in worlds that seem saturns_shadowunreachable? I cannot help but to understand Elon Musk’s strategy. He needed to pull our eyes off the ground by wowing us with his fancy car whizzing around Earth’s orbit because a rocket that brings us one step literally closer to Mars, wasn’t and isn’t enough.

My hope has been temporarily dampened, but it still remains because it is possible to change the rhythm by which we live to include the stars. Space exploration isn’t about man schlepping through the cosmos; it is about us making a bigger place for ourselves in that inky black sky. And the possibility that we are closer than ever to doing just this gives oxygen to that small flicker of hope.

 

Masonic Soul Food

Masonic Soul Food

“What is a Soul? What is Spirit? What is Energy?” We begin to engage in conversations about such esoteric terms as soul, energy, and spirit without being cognizant that we are not speaking the same language. The words may be the same but meanings span the spectrum. We can debate these questions all night, all month, and for the rest of our lives and never come to understanding. Do people really know what they mean when they talk about energy, soul, or spirit? While these are common discussions amongst Freemasons, they are sometimes the most difficult subjects on which to remain impartial and fair.

Humans seem to have a lot invested in the idea of their souls, and in other people’s souls, too.

Many  people join Masonic groups so they can “have an energetic experience” or “touch something mystical.” Some talk about experiencing something that touches their soul or provides a spiritual meaning to their lives. Some Freemasons mention how they “love the energy of Lodge” or how it’s our job to “raise the vibration of our material world and send out ‘healing’ energy.” Many people start their Freemasonic career looking for something mystical, something secret that only they have learned, that no one else knows, that provides them a conduit to perhaps special insight that no one else has. Because Freemasonry deals with the questions of life and death, the neophyte may be looking for Freemasonry to unlock all those special secrets and have the answers. They use terms like soul, spirit, and energy without defining them for themselves and in their communications with others.

energy1It seems that many times, the conversations are about what people want to believe rather than reasoned conclusions. Discussion and debate are the way we educate ourselves and grow. Transformation requires thought.

To those who let go of preconceived desires and wishes, Freemasonry is transformative in many ways. It does discuss these questions of life and death. It leaves the aspirant to mull over symbols and meaning and yes, come up with personal insights on perhaps souls and spirit and energy. Freemasonry provides us the opportunity to to convert from a polarizing human nature to one of balance. We need to learn to deal with all aspects of our temperament in order to understand all the features of this life – material, emotional, mental, and spiritual.  It is this last realm, spiritual, that trips many up.

Most Freemasons accept the presence of a greater power, something undefined that connects us all to a single purpose. Most would agree with the idea of the multi-faceted nature of human existence, struggling with the balance of brain, mind, body, and this idea of “connectedness.” Many have experienced things they can’t explain, the nudges of intuition, and the sudden flashes of insight that seem “deep.” These are all valid experiences. It’s taking them from the experience to meaningful communication that humans struggle. We throw out a word like “soul” or “spirit” or “energy” and assume that the people we communicate with understand what they mean. Freemasons are philosophers,  and any good philosopher will not abide a discussion with random, undefined terms. When asked about souls, there are vague allusions to something energetic, mystical, unique, and connected to some form of god/goddess/force/Tao. A soul is what makes us individuals. A soul is something that is part of God. A soul is our energetic self.  “When our eyes met, our souls touched.”

What does any of that really mean?  For each individual who speaks on these subjects, there is a different answer. Pinning people down about souls and spirits and such can be quite agitating for people. Some people get downright angry.

Can we define any of it? Perhaps. Perhaps we can start with energy.

socratesUnless you wholeheartedly dismiss science, there can be no doubt for one second that we are energetic beings. Neurons use electrical impulses and neurotransmitters (chemicals) to enable our bodies to function in its entirety: to think, feel, heal, sense, breath – everything. Without energy, our hearts would not pump, we would cease to be able to think and process information, and we would die. Mitochondria, in a weird symbiotic relationship with us, enable us to live by helping us process the material world around us into energy. Every cell has mitochondria and every cell is able to produce energy of some sort. Life is energy.

Okay, we’ve established we’re energetic beings, and by the nature of the material world, energetic beings are everywhere. We communicate with our senses and receive communication with our senses. Abraham Hicks said, “We talk with words but communicate with energy.” Cyndi Dale, author of “The Subtle Body: An Encyclopedia of your Energetic Body,” states that “energy is information that vibrates.” This latter definition is a little more trustworthy, it seems, than the former. We can test it. We can retest it. We can play with it and work to define examples. However, this is also where it gets tricky, right? Let’s take a page, well, a short paragraph from Wikipedia: “In physics, energy is the property that must be transferred to an object in order to perform work on or heat the object. It can be converted in form but not created or destroyed.”

BB_timelineWell, okay then, simple question: where did the energy that makes up us come from? Ouch, right? In a recent conversation, I posited this question to a fellow Freemason. He answered, “the stars.” I said okay, get me from B to A. He said “Stars created the elements that trapped the energy that went into making us.” I replied that I agreed, but then, what makes up the stars? He said it must be “the Big Bang.” Humans are the trapped energy of the material created during the Big Bang. To him, we all derive from the single moment that created time, matter, and energy. Physicist or philosopher, the topic of energy is where we converge. We can conclude from this that elements that make up the material world are trapped energy. Is this trapped “energy” spirit? Is that our “soul?”

If we are trapped energy of stars, as is everything around us, then we have far more in common with other matter than we think we do. If we are all made of the same matter, we should be able to recognize one another by way of transferring energy. Or, so one would think. What is interesting to note is that many psychologists and philosophers considered love to be a transference of energy. Freud dwelt on the physical aspects of love while Plato talks about spiritual or unselfish love; but one in the same, what we call love is, to them, a transference of energy. When we love something, we do put energy into it, and it into us. Perhaps this is the idea of spirit. Spirit, Plato said, that that way we communicate emotionally with other humans. Is this not love? So, love is spirit. We can also say love is energy.

So if love, life, and elements are all energy, can we draw any conclusions about the soul?

Many philosophers have tried to explain ‘soul.’ Just one example, Plotinus, the first Neo-Platonist, did his best to help us along in understanding that the soul doesn’t necessarily need a body; yet, without a body, it can’t exist in the “intelligible realms and express itself in the visible realms.” This concept tells us how he thought the soul expressed itself, but not what it is. In a very basic sense, Neoplatonists call the soul “consciousness” or “psyche.” Still, it’s unclear even in modern terms what consciousness is. If we thought defining “soul” in religion is difficult, try the philosophical bent…Truly angst-ridden. It seems that Plotinus and Plato are already agreed that there is a soul, even if they can’t agree on its definition. Maybe it’s something that we all have to debate on until we get to learn for sure. Maybe we’ll never learn for sure, at least not in this world. galaxy-wallpaper-preview-4

One solid conclusion is that the meaning of a soul does not seem to be the meaning of a soul for everyone, and spirit is not something we can agree upon, either. If nothing else, the myriad world religions would illustrate that. The phrase “our souls speak to each other” doesn’t mean much if you can’t really explain to someone else what it means. “We communicated ‘energetically’ is really worthless unless you can really understand clearly what you intend. It doesn’t even matter if you can explain it to someone else; do we even understand ourselves?  A wise Freemason once said that if you can explain something to a five-year-old, and the five-year-old gets it, then you really understand the concept of it. Simple terms, clearly defined, done. We definitely need more five-year-olds around us to keep us honest and clear.

Freemason, scientist, philosopher, or physicist: regardless of what you believe about soul, spirit, energy, or anything else esoteric, definitions are important and personal understanding moreso. The exploration of life’s meaning is, whether we agree on terms or not, something we all share.

Why are we here? Because we’re here. Roll the bones.” – Neal Peart

diceroll

Know Thyself: The Ship of Thieves

Know Thyself: The Ship of Thieves

“I am not the person I was.” We hear that a lot, especially when it comes to growing older and, one hopes, wiser. Indeed, we’re not the same person we were. Over the course of time, our cells die, regenerate, add, delete, change, morph, and eventually we have all new cells. But we retain our name, our memories, our lives. Are we not the same person?

One would argue that of course we are. Or are we? Really?

We cling to our identities like dryer sheets to hot cotton shirts. In our minds, we are who we always have been. We are that twelve-year-old child who swam in the lake as well as that adult who had their first job in fast food. We remember events, creations, or possessions and claim them to be ours.

Conversely, we claim our “self” to exist because of those things. We do not change, or if we do, it is at a glacial pace. We affix our identity in time and space, and like an astronaut, place a flag on it and proclaim it to be ours, to be “true” identity: knowing who we are.Theseus_Helene_Staatliche_Antikensammlungen_2309_n2

In a recent conversation with a fellow Mason, I was discussing the Ship of Theseus. The paradox is quickly explained in this video: The Paradox of the Ship of Theseus. In essence, the question is this: at what point does the ship cease to become Theseus’ ship and become something else?

If we take one plank from the ship and replace it, we generally can agree that the ship is still Theseus’ ship. At what point, however, do you fix enough broken pieces that the ship becomes something else? My colleague was convinced that the ship remained and always remained Theseus’ ship. For him, the idea of identity stays with the generally recognized “thing” even if the sum of its parts is not original.

Conversely, the argument is this: if I am a thief, and I slowly steal the pieces of Theseus’ ship, replace them with identical parts,  take the original parts, and put them together in my backyard, who has the ship of Theseus? The original owner, or me?

My friend said that the original owner did. I disagree. If I take a painting from the Louvre, and replace it with an identical painting, and everyone recognizes it as the “painting,” who has the “real” painting? In my colleague’s eyes, then, have I really stolen anything?

identityI contend that I have, if nothing else, I have stolen the certainty of the Ship of Theseus. I have stolen, or potentially stolen, the idea of the ship. But these painful musings do have a purpose: they help us work out our identity – the answers to the question of: Who am I?

A brilliant article on this is found on Brainpickings. I would encourage you to watch the other short videos on this site: not only is the one on Who Am I thought-provoking, but there are links to life’s other huge questions. How do I know I exist? What is the Nature of Reality? But, I digress.

The question is, at what point is our self no longer “us?” Is it when all the cells in our body have replaced themselves? What about new neural pathways or brain cells? If we replace a leg or arm or heart, are we the same person? 

Freemasons live by an adage of “Know Thyself,” which also adorned the Oracle of Delphi  at the Temple of Apollo. We must first understand what it is that makes up our “self” and when does that “self” become something else. I think this is a life long exploration and, since the self is constantly undergoing change, are we always who we were? Perhaps not.

But then, where did “we” go? Does our identity persist? If it does so, how? What makes us, us?fingerprint

I asked my fellow Mason about clones, which sent us down an entirely different path, discussing identical twins, and the like. Does time make a difference? If a plank is rotten on Theseus’ ship, and it is replaced, does that make identity linger, as opposed to replacing a “new” plank? If I change my mind about how I feel about something, am I still the same person? What if I create new habits? What then?

We are ever seeking to understand our true natures; yet, our true nature is ever-changing. Freemasonry teaches us about the cycles of life, death, rebirth, nature. and science. It teaches us all of Life’s Mysteries. If stagnation is death and change is life, how can we ever be the same person moment to moment? Perhaps that is the mystery that we must ever follow: a constant, persistent discovery of who we are, and what we are doing.

Astronomy and the Quadrivium

Astronomy and the Quadrivium

Perhaps your first thought, as was mine, is: “How can Astronomy be an ‘art?'” Furthermore, how can Astronomy be called a ‘liberal’ art? From a very interesting (and worth exploring) website called “Arts of Liberty,” we have a snippet for explanation:

“To call astronomy an ‘art’ can come as a shock to a modern reader… Perhaps without thinking much about it, we think of “science” as being a genuine and exact knowledge, whereas ‘art’ is more expressive, or touchy-feely.  But, that is not quite adequate, since medicine is also an ‘art,’ and it is anything but touchy-feely… And while ‘science’ and ‘art’ do not appear to be synonyms, it could very well be that the same discipline can be called both a ‘science’ and an ‘art,’ although for different reasons.

To understand this properly requires us to consider a sense of the word ‘science’ not in common use today.  The word ‘science’ comes from the Latin word scientia, which meant a very exact knowledge, a rigorous and sure knowledge of things deduced from self-evident truths.  The ancient Greeks would have called such knowledge epistémé...  

In the vocabulary of the ancients, an ‘art,’ like a science, meant a carefully reasoned-out knowledge, but more than that, it meant a knowledge of how to produce something.  Where there is no ‘product,’ there is no ‘art.’  So it is possible for a form of knowledge to be a ‘science’ but not an ‘art.’  For example, Aristotle considered the study of god to be a ‘science,’ a body of knowledge rigorously reasoned out from self-evident principles, but not an ‘art,’ because it did not teach us how to make gods, or how to do anything about god.”

Ptolemaicsystem-smallClaudius Ptolemy (100-170 CE) was a Greek mathematician living in Alexandria. His work The Amalgest was one of the most influential astronomical works until Galileo’s discoveries in the 17th C. The Amalgest documents many mathematical and astronomical treatises, including works by other mathematicians – works thought to be lost. The most significant piece of this Amalgest (total of 13 books), is the documentation of the geocentric model of the universe. Ptolemy’s work became the accepted theory of the structure of the planets and stars, with the Earth central to all.

This influenced not only astronomy and mathematics but also theology, philosophy, and fine art. Three centuries after it was written, Hypatia and her father Theon, genius mathematicians, added to the work with their own commentary, throwing in their thoughts of elliptical orbits, the procession of the equinoxes, revising Ptolemy’s Handy Tables, and introducing the sexigesimal calculation systems. It’s believed that this rendering of the Amalgest, with the Hypatia/Theon commentary, is the one that was used for the majority of the Middle Ages although no direct reference to Theon survives and Hypatia is mentioned only in a passing 10th C. reference.


And thus, the Quadrivium ends. I hope you’ve enjoyed my answer to the Bro.’s challenge of finding a significant event, work, or person who influenced each specific liberal art. The question was posed, should Freemason’s really learn the liberal arts? The answer, to me, should be obvious. Not only should we learn the liberal arts individually, but understand their context in the whole of being educated about the natural world. Human beings can be taught easily to survive; we cannot just “pick up” how to thrive, generate ideas, and create a better world.

An example of this “Freemasonic mindset” is James Madison, even though he was not a Freemason. In his early twenties, when the United States was in its infancy, he gave up much of his career and life to studying the histories and government of world cultures. He was relentless in his pursuit of the histories and knowledge of government administration, what worked, what didn’t; he studied philosophy, history, theology, art, classical literature, geography – the liberal arts and more. By the time he finished, and began his work in the new nation’s government, he was arguably the single biggest influencer in shaping the United States Constitution and the framework of our Democracy. By learning the past deeply, he was able to innovate and create a new world. To me, that is a main goal of the Service of Freemasons.

Mathematics and the Quadrivium

Mathematics and the Quadrivium

Personally, I struggled with Math in school. Faced with a math test, any math test, I froze, cried, banged my head against the desk, and ultimately gave up. I saw mathematics as an isolated “thing” to be conquered. You were either good at math, or you were not.

How little I knew, and how little I was taught, about true mathematics. More than numbers, factorials, and fractions, Mathematics is about relationships – of numbers: how they work with each other, work for us, against us, and can talk about any situation. There are mathematics of money, elections, government, science, music, agriculture, capitalism, socialism, any -ism. Math is language and structure: it is a bridge between all aspects of liberal art. Which leads us to the Bridges of Koenigsberg.

bridgesLeonhard Euler, a Swiss mathematician of the 18th Century solved, sort of, the problem of the Seven Bridges of Koenigsberg (Russia, at the time). Koenigsberg had two islands connected by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point (touching every edge only once). Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The bridges did not meet this condition and therefore, no solution could be found to the problem.

Yet, what this Eulerian circuit eventually did provide is the basis for modern topology , which has expanded into areas of quantum physics, cosmology, biology, computer eulernetworking, and computer programming. For example, the Eulerian cycle or path is used in CMOS circuit design to find an optimal logic gate layouts. For anyone wanting to read the paper outlining these paths in the original Latin, it can be found here.  English translations do exist. A good page on the history of topology is here.

Leonhard Euler was a fascinating individual in that he saw mathematics as something that infused all of life. Though his writings, he made applied mathematics accessible to the layman and his scholastic peers alike. An excellent and thorough biography, written by Walter Gautschi, can be downloaded in PDF form here. With a varied interest in all aspects of mathematics  (arithmetic, geometry, algebra, physics), music, anatomy, physiology, and astronomy, he truly was a man of the “Enlightenment.”  While he was not a Freemason from what I can tell, he seemed to hold much regard for the idea of true science, and creating a better world for his fellow man: a Freemason’s true ideals, to be sure.