What alchemy means in physics is to discover tractable solutions -- that is, to distill a workable solution where none appears to exist

The Emerald Tablet of Thoth (Hermes) and its meaning

A note on Leonardo Alchemy of da Vinci Vitruvius Man. In search of 3 vs 4



With minor exceptions, alchemy is found worldwide. It is enticing to call alchemy the predecessor to chemistry, metallurgy and medicine -- and well it may have been. Yet, a better way of saying it is that alchemy spawned these and other pursuits while alchemy continues to have a life of its own. Alchemy's utility is in its non-causal, associative qualities. When alchemy talks about transforming lead to gold, the alchemist is also interested in the change from being "led," (being dependent, on-a-leash, a follower, heavy, soft, or sinker) to becoming gold — a leader with non-corruptible qualities.

Alchemy never has a single message; more supporting nuances there are the better. The art of alchemy, for example, is to associate the donkey and the ass, all puns intended. Concurrency is sought and appreciated. Alchemy in modern times is closer to public relations, marketing and advertising than it is to hard sciences. Today's alchemy is similar to brain storming -- for the "thinking outside the box" proposition is very much the alchemical way of doing business -- that is, find innovative solutions inside and outside of the established context.

Alchemy deals with infinities. The power of alchemy is in ferreting out and marshalling forces no one thought were there -- as when an unusual political campaign strategy suddenly works. Alchemical texts call this the application of will. The 'will' is a fairly complex topic that has its origin with intent but -- as there is no physical force used by an alchemist -- the manifestation of the will can also be called the magic.

Traditionally, alchemy sets the most significant and the most difficult goals. For example, the creation of life itself is one of alchemy's goals. You could wake up one day and say, "How would I organize the spherical galaxy?" Now, that's alchemy. Alchemy is discredited along two arguments: 1) It is all too theoretical or "iffy," and 2) It is impossible.

Alchemy, almost by definition, deals with things most people would consider impossible and, therefore, alchemy's outcome is a solution and never a proof of impossibility. In the geometry of the compass and straightedge, an alchemist could deliver a formula yielding all angles that are divisible by three -- whereas a scientist delivers the proof that angles in general are not divisible by three. An alchemist works and delivers the proof that absolute spatial distance can and must be determined -- if de Broglie's wavelength is to find broader applications.

Alchemy comes from the word CHEMA or CHEMES, meaning process or processes. The word 'schema' is related. The addition of AL is the Arabicized version, not unlike alcohol or algebra, while more recently it is the McSandwich or Email or iPhone [and you thought I was going to say Al Gore]. The best translation for alchemy is operations. Other translations are transformations and transmutations. Words 'method' and 'procedure' are too narrow. If you are familiar with the Chinese Book of Changes -- well, that's another translation and the 'Book of ..' indicates not only plurality but concurrency as well. (Self-test:-) If you don't mind I did not scrutinize the word CHEMA, you are doing well. Alchemy is more about the right and broad feel than about the academic pointy precision. It is the broadness and interconnectedness that give alchemy its power and utility.

Alchemy 's innate workings

The results of alchemy workings can be broad and at times unknown. If your goal is to reduce defects (in a factory or in your personality), the results may be positive but on reflection you may be able to name but a few of the reasons for your success and even think of being lucky. The thing is that the reduction in defects is (and must be) accompanied by many other changes that are relevant but not necessarily obvious. And so you want to loosen up to allow many, many other changes to happen as well. It is for this reason that alchemy has two basic and intermingled grades: that of changing yourself and that of changing other things.

Changing oneself is easier said than done. Inherently, you start with your innate potential and build on that. Knowing what is innate to you is not necessarily known to you and so the first step is Calcination. The idea is that even the most obvious "what are your strengths" question is not easy to answer -- even by you. There are seven steps to alchemy, roughly corresponding to your chakras. The seven steps are and are not hierarchial and as you proceed in the upward direction you have to revisit the lower steps and do some supplemental work. Intrinsically, you feed back new knowledge to other levels, including the lower ones, and by so doing you are broadening your powers along many dimensions. You will then be able to engage and leverage your innate talents and that is how you will be able to affect the external environment.

Oftentimes, people get ideas on what to do and are very proud and happy about the ideas being their own ideas. Such is not usually the case and through alchemy you will discover those ideas that are truly yours and, consequently, work them for your benefit. (Just because you do something for your own benefit does not mean you are no longer altruistic -- you could be -- but through alchemy you discover how altruism benefits you as well, if that is where your strength lies.) Alchemy could easily be thought of being close to Zen, for many contradicting ideas and actions do find a resolution and even an application. Alchemy, it seems, is not debatable in the strict rational format, for going back and forth on fine details is putting aside and forgetting other variables that could be relevant. Yet, I have as yet to meet an alchemist who would be reluctant to talk.

Alchemy in math and physics


The traveling salesman problem is that of a non-polynomial class and is akin to code-breaking. While 1) we know that the solution exists and 2) we know the length of time it will take to obtain a solution, the alchemist cannot recommend a solution that calls for intractable processes. Because the current processes (really methods) to obtain a solution to non-polynomial problems are indeed intractable, such "solution" takes so much time it is for all practical purposes unusable and cannot be applied. If an alchemist is to figure out a solution that can be applied, he or she must come up with a tractable solution. An alchemist cannot and does not use intractable methods and does not recommend intractable solutions, for intractability is not a solution. Scientists, on the other hand, wallow in intractability and every time you hear how many millions of years it takes to get to another solar system -- that's the scientific mindset of the left brain talking -- talking about things that are not only impractical but that ignore the simple fact that the scientists' solutions are not usable. In making things worse, scientists are quick to claim that their methods are the only available methods and 'if we cannot get there from here, they (or anybody) cannot get here from there.' Not so. Tractable operations are available and intractable methods should always be filed in the dead end category. One can surely spend a lot of money pursuing a ball lightning research at a university, but -- by accepting intractable methods -- it just will never be understood there. Alchemically, difficult pursuits are not addressed with 'if-then' methods, for such methods are used by the left brain (and by the present computer) and the 'if-then' method is intractable when solving non-polynomial problems. In fact, the way to tell an alchemist apart from a scientist is that an alchemist does not use 'if' much but a scientist uses it often. (Can you call yourself a leader if you require something else to happen first?)

Operations of the Sun, Moon, and Stars

This is the basic triptych of alchemy. Alchemists tend to specialize -- oftentimes subconsciously -- in one of these three pursuits. Each component needs to develop different skills even though they are all related and issue from the same laws of the universe. For example, for an alchemist engaged in the Operations of the Sun the association with gold would then include work on the golden proportion.

    The Operations of the Sun is about the creation of the tangible universe and the Pythagorean Tetracts is the most fitting symbol here. (See the interpretation of the Emerald Tablet below.) The atomic and molecular structures are in focus and the atom can be created as well as dissolved. High art would be the creation of a planet and its insertion into an orbit with the goal of growing or stabilizing a solar system. Yes, the planet also needs to be terraformed with mountains (near-pyramid constructs) for the spiritual knowledge to continue increasing. For some life forms (read ours), water, gasses, and salts need to be made in situ.

    The Operations of the Moon deal with the understanding of the virtual domain. The virtual domain contains organized energy that is intelligence. The emphasis here is on predicting the future and the extraction of the needed intelligence from the universe. The most relevant symbol here is the AUM. High art is the creation of spiritual entities, although creating a space in your home infused with positive and harmonious spirit is accessible to anyone. However, because a spirit is a subjective creation, there is no barrier to creating any spirit, including a destructive one. So, while you cannot be forbidden to do what you may want to do, consider that 1) the intelligence out there is infinite and it may turn your creation against you and 2) even if you get what you want, it may be at the expense of what you need, and 3) creating a spirit to your specific requirements may not do it for you -- and it just might have qualities you don't like. So, if you create a spirit that is always nice, don't expect much of a useful advice from it. Oh, and don't expect it will just go away if you get tired of it. Basically, the existence or creation of spiritual entities is highly overrated, for there could be spiritual entities out there that are rather dumb or specialized in ways you don't care for or do not want.

    The Operations of the Stars deal with the navigation in the virtual domain. This involves mapping the universe, the superluminal transfer among desired destinations, as well as the technical aspects of ship building and force creation. The virtual domain works by logical association and the vision (seeing) is not the same as in the visible universe. You'd then feel comfortable speaking of a black (or cold) sun, for example, and in fact you might go right through it. You could call the vision 'warping the space ahead' but that's just to impress the left brainers. The most relevant symbol is the Hunab Ku. High art is, well, "where do you want to go?"

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This design is called the Adventure of The Black Sun.

Circle squaring

Applicable to both math and physics, the squaring of a circle is one of the central aspects of alchemy workings. It leads to metaphysics and more specifically to the virtual domain where quantum mechanics lives. Charles Dawson wrote Alice in Wonderland under the pseudonym Lewis Caroll. Being an accomplished mathematician he attempted to square a circle, gave up, and spent some time documenting the futility of this effort. In his notes he writes: ".. More than a score of letters were interchanged before I became sadly convinced that I had no chance." Well, Dawson could have tried the alchemical approach toward the squaring of a circle. The mathematical tools today stand a bit outside of what is really happening in nature and only rarely do the math guys lead -- with the exceptions of Dirichlet (photon wavefunction), Riemann (orbitals via primes), Gauss (public key crypto via modulo math).

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A good example on mathematical and thinking tools goes back to Euclid and to his proof that irrational numbers cannot be created by rationing of real numbers. The unavailability of a rationing method, however, cannot stop the alchemist from dealing with irrationals! You and I can construct the square root of two using the Pythagorean Theorem in short order. So what if it cannot be done algebraically by rationing -- it can be done geometrically and exactly at that. The idea is not to dwell on ways and means that show something to be impossible, for that is but one way that happens to be a dud. Euclid, it seems, is treating incommensurables as a dead end (at worst) or a loose end (possibly) or in the context of geometric superiority over arithmetic [I'd like that]. Transcendentals, being a unique subset of incommensurables, do present a challenge because the infinite addition mechanism needs to be found (think QM superposition), but the scientist would like to have you throw the boat away because he cannot move the boat with the paddle he has. Here, then, is where the insight comes in. Self-test:-) If you think numbers are no big deal then you just walk away. If you think numbers are not the fundamental root, you will never think the stone can be shaped without hammer or heat.

Western alchemy is the only one that recognizes and speaks about the mystery of 'Three versus Four.'


So there is this guy who knows you like numbers and he comes up to you -- or proclaims from a podium: "You know, the old Greeks found out that when it comes to doubling a square, you cannot do it with numbers!"

How many seconds did it take you to answer with something similar to: "The fastest supercomputer today cannot do it but most people can (do it geometrically)."

Then again, if you are in a mature company, you might come back with: "Well, the Greeks were infatuated with magnitudes .. and that could be the problem."

Leonardo's alchemy

 Alchemy of da Vinci Vitruvius Man. In search of 3 vs 4 While Leonardo da Vinci attracts much attention, his 'Three vs. Four' separation is based on Vitruvius' thoughts. In a human, the separation between three and four is at the navel that is the point of the couplex (Chinese dantien and Japanese hara). The couplex is created (issues) from geometry of the upper and the lower body and has a transformative function, which deals with the conversion of thoughts to motion. The workings of the couplex, then, go well beyond the clinical description of the navel. (Perhaps Rene Descartes would have been fruitful here if he didn't get spooked by the Inquisition. Rene picks the object in the brain he thinks is responsible for thought-to-motion conversion -- and gives it a paisley shape, which is pretty close logically.)

The couplex is the point of separation and the point of joining between Three and Four. Leonardo combines Three (Vitruvius Man legs together) and Four (legs apart) inside one circle but Three and Four cannot be combined within one context -- and the circle is the delimiter of context. Leonardo also takes the navel as the center of such circle, which is okay (it is a point). Leonardo thus combines '3 vs. 4' within the human body as a whole while superposing it with 'square vs. circle.' This is "okay" and reflects Leonardo's (or Vitruvius') intense search for mapping of cosmic geometries onto man.

The '3 vs. 4' is the original Western alchemical mystery, which is different from the 'square vs. circle' problem. '3 vs. 4' deals with 'real vs. virtual' or 'tangible vs. intangible' or 'matter vs. spirit,' while the 'square vs. circle' deals with linear (straight, Euclidean) and curving (transcendental, Riemann) geometries that are applicable at the atomic level and, also, for the intercept of cosmic energies. '3 vs. 4', moreover, cannot be combined within one circle because the real and virtual duality remains separate.

'3 vs. 4' and 'square vs. circle' cannot be equated or mutually "mapped" but they both exist side by side and they are both existential to man. In a way of a comment, Leonardo -- or those who come after him -- need to separate '3' and '4' and then the squaring of a circle is (should be shown as) happening in both the upper (Four) and the lower (Three) individual components of the human body.

Leonardo makes a significant step above Aristotle while illuminating the mysteries of numbers and geometry in the artistic (right brain) context rather than in the written (and at times exhaustive) textual modality. But it also happens that the power of dominating ideas allows the truth to come through even though some technical aspects might not be just right.

The reflection of cosmos in the human geometries is shown here {April, 2006}. The joining and separation is at the couplex (at the "navel") where both circles touch. Four is shown above, Three is shown below: Couplex is -- and must be -- at a single point

When it comes to the intercept of cosmic energies, then your thoughts, your inherent body geometries, and exercise (motion that happens in a particular geometric and mental framework) come to the forefront. Yes, think Tai Chi and Martial Arts. These exercises are not just about fighting -- they are about your health, too. The basic notion is that of the 'squaring of a circle.' Technically, incoming energies (not just light), have geometric associations and they need to be folded within the circle or sphere (geometry that is symmetrical about a point) if they are to "stick around." The word 'energy' is but a rudimentary expression -- for actual knowledge is contained within cosmic energies.

The '3 vs. 4' is an issue with much depth and breadth. (In the East, for example, dantien generally stops with Yin and Yang with some extensions to Chi and the meridians.) The idea is that the human not only emulates the cosmos but through the shapes and geometries the human becomes the receiving structure for 'all there is.' The human (and some animals') brain has a similar arrangement where the 3 vs. 4 separation is at the Corpus Callosum. The book Quantum Pythagoreans derives and names the couplex and applies it to the transformative action between both halves of our brain.

The 3 vs. 4 is a construct that is applicable to many concepts such as stability, organization, and creation.

Cosmologists maintain that the utility of stargazing is in applying the cosmic discoveries down here on earth, and claim that is how 'as above, so below -- as below, so above' saying formed. Alchemists, however, understand (or want to understand) infinities, and the 'above' and 'below' stuff is also about gods. The 'above' and 'below' goes well beyond "heaven" and "earth" -- it is a mystery of its own and Thoth is not even subtle about it.

Occultists maintain that some relationships are virtual and cannot be observed but that the relationship's existence can be visualized, computed, and possibly realized (manifested).

Alchemists studying matter find the mathematical computability foundation of atoms compelling and invigorating so much the alchemists' credo may well become 'as inside, so above.'

The Emerald Tablet

There is much about The Emerald Tablet on the Internet and in the Secret Teachings of All Ages by Manly P. Hall. The author of the Emerald Tablet text is said to be Hermes or Thoth (same person, different cultural contexts). As you may suspect, the authorship and stewardship is subject to much spin over the centuries as different cultures and religions wished to be associated with the tablet. Below is the full text of the tablet, which is followed by a personal commentary. If there is something that is encoded or cryptic it is The Emerald Tablet. After reading several interpretations, none of them struck me as "just right" and this is not necessarily bad, for you may also be enticed on your own interpretation that is relevant to your needs. The tablet itself may or may not exist, though it is likely that it did exist at one time. The eyewitness description is certainly intriguing, for the tablet is made from emerald and the text is in bas relief. The precious stone that is emerald is not the intriguing part. Rather, emerald is a crystal that some think may become "liquefied" through thought. The bas relief is interesting in that the standing waves can only exist across space and under specific geometric formations -- that is, writings that are engraved into matter are not as rich in geometries that support standing waves.

The full text of The Emerald Tablet

True, without falsehood, certain and most true, that which is above is as that which is below, and that which is below is as that which is above, for the performance of the miracles of the One Thing.

And as all things are from One, by the mediation of One, so all things have their birth from this One Thing by adaptation. The Sun is its father, the Moon its mother, and the Wind carries it in its belly, its nurse is the Earth. This is the father of all perfection, or consummation of the whole world. Its power is integrating, if it be turned into earth.

Thou shalt separate the earth from the fire, the subtle from the gross, suavely, and with great ingenuity. It ascends from earth to heaven and descends again to earth, and receives the power of the superiors and of the inferiors. So thou hast the glory of the whole world; therefore let all obscurity flee before thee.

This is the strong force of all forces, overcoming every subtle and penetrating every solid thing. So the world was created. Hence were all wonderful adaptations, of which this is the manner. Therefore am I called Hermes Trismegistus (or Trismigestus), having the three parts of the philosophy of the whole world. What I have to tell is completed, concerning the Operation of the Sun.

I've read several translations and rephrasings of The Emerald Tablet done by Hermeticists and people the likes of Blavatsky and Newton. I like the one above the best, the translation by Starrus and Reeves. SelfTest:) If you think Starrus and Reeves are not real names, you are doing well. Perhaps 'stars' & the 'field of reeves' (ancient Egyptians). If you know the reeve is The One you don't have to read on.

The Emerald Tablet with interpretation and commentary {summer, 2009}

True, without falsehood, certain and most true, that which is above is as that which is below, and that which is below is as that which is above, for the performance of the miracles of the One Thing.

    The aspect of above, below, and its equivalence is simply not understood by any interpreter or commentator I have come across. The misinterpretation of this paragraph is widespread and runs along the lines that the "above" is either saintly or aristocratic that tells the "below" what to do. In a better refinement it is thought of as the heaven and earth, mind and matter, or creative and ordered .. that is, a duality. The duality is composed of qualitatively different components having the intangible aspects (subjective, informal, indirect, volatile, relational, virtual, feminine, "vertical") and the tangible aspects (order, hierarchy, repeatable, formal, real, masculine, "horizontal"). While the duality does indeed exist, the Tablet's intro paragraph is not about that. The above and below refers to the cosmic and the atomic aka the macro and the micro. However, the important statement here is that the world of macro (above) and the world of micro (below) are the same in that they each contain the duality of the intangible and the tangible.

And as all things are from One, by the mediation of One, so all things have their birth from this One Thing by adaptation. The Sun is its father, the Moon its mother, and the Wind carries it in its belly, its nurse is the Earth. This is the father of all perfection, or consummation of the whole world. Its power is integrating, if it be turned into earth.

    This paragraph deals with the duality but it is is also about the increase in organization (intelligence). I see the One as the zero-dimensional point through which the infinity is available and through which all births -- that is creations, occur. From the first paragraph we know that such creations may be in the macro and/or in the micro worlds. With a Pythagorean slant I call the One Thing the top dot of Tetractys. The adaptation deals with the transformative action between components of the duality that increases organization. The transformative action is ongoing and must be occurring through the zero-dimensional point, for that is the only way a duality can interface. Sun is the tangible, Moon the intangible. The Wind is the energized ether (intelligence, knowledge), which maintains its cohesion in a particular context the Tablet calls a belly. Here, the belly is the delimiter of context (such as a circle or sphere) holding the like-like knowledge/intelligence in a cohesion, while the wind is the like-like etheric attraction and rearrangement associated with the creation of a new context. The 'father of all perfection' refers to the mechanism of improvement via transformations (Egyptian Shu, geometric diagonal or "stairway"). If the intelligence stays and continues to be associated with the nurse Earth then the earth's intelligence is increasing as all knowledge continues to be integrated. It is likely that 'if it be turned into earth' calls for building and creating real things in addition to integrating knowledge. It is also likely that not all knowledge remains Earth bound.

There is an East-West perspective reversal in the symbology of masculine vs. feminine. In the Western tradition the exclusive, "hard rock" aspect of the earth is masculine while in the East the earth is feminine. The resolution is a matter of emphasis. Spiritually, earth is inclusive and thus feminine, but with the physical, or real, emphasis the earth is masculine. There are other gender reversals or "inconsistencies" such as air being masculine (ancient Egyptians, Chinese) and the Sun being masculine in the West but feminine in the East. But now you know that the 'above' and 'below' both contain the duality and you want to be careful when you generalize.

As a Pythagorean, even numbers are feminine while the odd numbers masculine -- and this is consistent throughout this planet and, well, the universe (think symmetry).

Thou shalt separate the earth from the fire, the subtle from the gross, suavely, and with great ingenuity. It ascends from earth to heaven and descends again to earth, and receives the power of the superiors and of the inferiors. So thou hast the glory of the whole world; therefore let all obscurity flee before thee.

    Here is where you are becoming the creator. By understanding the duality you also understand that the duality cannot be merged together and become undifferentiated "one" (if you try it in the micro you'll get antimatter). The separation of the world around you into the intangibles (fire, subtle, linkages) and the tangibles (earth, gross, things) is then your first step. This cannot be rushed, for cutting something in half does not separate the duality's components. The intangible component, moreover, contains a priority (independent/superior along one axis, dependent/inferior along another). Before knowing what has priority the intangibles must all be compared with all other intangibles -- and this gets into true infinity. The four-sided pyramid comes in to play, too. The heaven is the domain of all intangibles I call the virtual domain. What this paragraph does not say is that the priority may change -- either in time or with context or through your workings. What you may also discover is that your left brain deals with the tangibles while the right brain deals with the intangibles. In the end this paragraph promises the excitement of knowing everything and you can pat yourself on your back.

This is the strong force of all forces, overcoming every subtle and penetrating every solid thing. So the world was created. Hence were all wonderful adaptations, of which this is the manner. Therefore am I called Hermes Trismegistus, having the three parts of the philosophy of the whole world. What I have to tell is completed, concerning the Operation of the Sun.

    The knowledge of priority is needed for changing the intangibles. Ether readily passes through tangibles of matter but you need superior knowledge imparted onto ether before you can affect the solid thing that is matter. The Operation of the Sun refers to Man's Work, which tends to be left brain dominant and deals with real things including matter creation.

    There also exist the Operations of the Moon and the Operations of the Stars. If Hermes would like to be called Trismegistus, he should have said something about the other two Operations to be really thrice greatest.

    The bottom line is that The Emerald Tablet is the real deal.

The zero-dimensional point is also prominent in the AUM symbol that is commented on and interpreted on our Circle and Pi page.

We have a book review On Becoming An Alchemist by Catherine MacCoun.

 Book by Mike Ivsin
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In Quantum Pythagoreans the separation is followed by joining. The separation enables all individual elements to showcase their strengths while the joining creates systems -- or monads -- that continue to improve you and your universe.

The power of the Pythagorean foundation highlights the opportunities of applying new energy sources, and building atomic structures from scratch. Some applications are presented in considerable detail while others are ideas waiting to happen.

Much work is in the area of the couplex, for this point has been misunderstood in the West in the past. The book explains why it is a point -- that is, why couplex must have the geometric construct of a point. Couplex can also be found in the Great Pyramid.

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Last updated June 6, 2013

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