Exegesis Volume 2 Issue #31

Exegesis Digest Wed, 09 Jul 1997


Date: Mon, 7 Jul 1997 22:33:04 +0000
From: Francis G. Kostella
Subject: Regarding PTSB, mathematics, etc.

On 18 Jun 97 DR GONZALO PENA TAMEZ wrote:

> [you] say that the fact
> that you do away with the
> Axiom of Beginnings does
> not imply that the natal
> chart is radical

I believe that there is room for confusion in the manner in which you paraphrase me above, so let me attempt to be perfectly clear. I did not say that doing away with the "Axiom" does not imply that a nativity is radical. That seems the exact opposite of what I did say, so I'm not even sure I am parsing that sentence correctly. Let me quote myself (from my last reply, with PTSB being "Ptolemy's Theory of Seeds and Beginnings", AKA the "Axiom of Beginnings"):

||  Thus far, most of your
||  arguments are arguments
||  FOR radicality, as if PTSB
||  and radicality were the same
||  thing. The proposition states
||  that charts are radical without
||  PTSB, so let us drop PTSB
||  and deal with radicality directly
||  . . .
||  This is critical: Radicality is
||  necessary to astrology, "Seeds
||  and Beginnings" are not. One
||  can have Radicality without
||  "Seeds and Beginnings" (as
||  shown by many examples).

What I am saying seems to be the exact opposite of the way you phrase it. I am saying that nativities ARE radical already, there is no need to append to the existing radicality that which you call your "Axiom". I do not recall making any claims about any charts that are not radical, nor have I made claims about anything causing non-radicality. Indeed, the basis of ALL the claims I have made has been that charts are radical, and all of my examples have been radical charts.

I repeat: I am only talking about radical charts. I have not addressed non-radical charts at all, to think that I have done so is to completely misunderstand.

> and here you are only
> introducing heavy
> neptunian fuzz, probably
> even tongue-in-cheek, as
> some listers have suggested
> to me in their personal
> communications.

Other readers may infer what they wish about my writing, and if they are confused or find me or my purposes confusing, then they should take advantage of this open forum and ask me directly. (I've publicly declared my motives as desiring to build stronger astrology theory discussions on the internet.) However, our discussion thus far has been too great an amount of work for me to be a simple hoax or some sort of joke on my part (you must admit that your messages are rather long, and thus I need to read and reread them and consider them well before replying, all this is very time-consuming). Perhaps some people are misdirected by my statement that I do not expect others to easily believe or adopt an astrology lacking PTSB as some sort of "tongue-in-cheek" denial of my own position. However, I am not being "tongue-in-cheek" nor am I attempting to confuse the issue and introduce "fuzz", Neptunian or otherwise.

Please understand that from my perspective dropping PTSB from astrology is an improvement that gives us a superior astrology. From my perspective, the need for PTSB is a "heavy neptunian fuzz" that we can do without. From my perspective, an astrology that lacks PTSB is a stronger astrology, one that does not fall prey to quite so many attacks, one that does not so easily offend the modern intellect, one with a firmer foundation on which to build, one that is built to survive the next century. From my perspective, tossing out PTSB allows us to bypass the "heavy neptunian fuzz" of determinism which is a thorn in the side of astrology. Finally, I believe that what I am suggesting here is much more like Plutonian "cleansing" than Neptunian fuzzing.

> Elsewhere I have
> made the point that
> astrology is like Physics
> before Newton.  Astrology
> is waiting for a
> mathematical genius to
> come do for the
> Tetrabiblos what Newton
> did for the Almagest. 

I am unwilling to totally dismiss that concept as there is an extremely remote chance that it is possibly true. However, if one bothers to delve into the field known as "the history and philosophy of science" one discovers that areas of study that eventually become what we label scientific have characteristics that are missing in astrology. The most damning aspect being that we astrologers never reject ANYTHING and tolerate the use of ANY idea in astrology. A "true" scientific field, on the other hand, totally reconstitutes itself along new lines every so often and discards those ideas which no longer fit the common conception of the field, and those participants who do not concur are ejected or marginalized. Astrologers try to accommodate every approach and every idea and every technique. And all this despite the fact that astrology predates nearly every other field now labeled scientific, and has had thousands of years in which to perfect itself into a science.

We already have had "our science" made solidly mathematical, it is called "astronomy", and they prefer to not have anything to do with us as what we do has very little to do with modern scientific principles and methods. We're the part they overlooked or rejected. In short, we're not going to be let into that club because we don't follow the rules of the club. Astrological reasoning is not the same as scientific reasoning. Pretending that simply adding some mathematics to astrology makes it into a science is to misunderstand the natures of both science and astrology.

If astrology is going to become a science anew then it going to do so in a way unlike any other field has ever done so. My own investigations into systems of human knowledge suggests that astrology is not only lacking the requirements for being a science, it is lacking the requirements for being a "pre-science". However, we should not let that dishearten us, astrology is a system of knowledge of a different order than modern science. The problem, I think, is not that astrology is not a science, but that many of us believe that astrology must become scientific to be acceptable. And mainly for that reason we need to try and prop up astrology with grand empty theories and more and more mathematics and precision and computers and new techniques and research efforts, and so on. What we really need to do, I think, is look at what we do and try to see what is there plainly, and then take that as a starting place from which to understand the place of astrology in the modern world. That has been my purpose in suggesting that we drop PTSB from the canon, when one looks at what astrologers actually do, one sees that PTSB is not required to do astrology. Nobody depends on it in any critical way. If you ignore it, as most astrologers already do (except to pay it lip-service), nothing need change except the need to build up complex rationalizations in order to pay homage to PTSB. And the fewer complex rationalizations we introduce, the better for us in the long run, I think.

> We need to mathematize
> astrology, like Newton
> mathematized physics by
> discovering the derivative
> and the integral that
> allowed to handle motion
> with differential equations.

Newton had it easy, he was working with the simple behavior of physical forces, things which could be measured and quantified. But in astrology we work with EVERYTHING that is and only rarely those simple things covered by Newton's physics. The vast majority of astrologer's topics are not things that will ever be plugged into equations: the calculus of love? The integral of career? The derivative of good luck? The algebra of mundane events? Again, within the field of mathematics the concept that we can mathematically model things like this has been disproved: the universe is NOT a clockworks which we can model, our view is limited, perfect vision is impossible, we make a choice about what we will see and live with the consequences. Astrology is about imposing a human-scaled, human-centered framework on existence and there is no mathematics that deals with that.

I think a brief look at the history of mathematics in the last few centuries may be illuminating for those who have not studied the subject. Right after Lilly's day was the era of Newton and Leibniz, who put into place all of the mathematical pieces of the puzzle that gave the physical sciences the impetus that has carried them to the forefront of all areas of Western knowledge. Building upon this were Euler and others, right up to the French mathematicians of the revolutionary era, when Uranus was discovered. Like Lagrange and Laplace who developed sophisticated techniques that enabled sophisticated engineering and more scientific research. Essentially, they put into place a mathematics that could model the physical world to a great degree, and the student of calculus will recognize these men's names for all of the fundamental concepts they perfected.

Around the time when Neptune was uncovered and Marxism given birth, there were advances in "strange geometries" and new approaches to logic and eventually set theory and number theory. The 19th century is a VERY interesting era, and we can cleanly divide it in halves. During the first half we see nascent people's movements threatening monarchies all over Europe, along with strong scientific advances and formation on a variety of fronts. Then, in the middle of the century Neptune appears and we see science bearing fruit in a technology than enables Europe to "colonialize" large parts of the world, distracting those revolutionaries who were not crushed by means of a new form of nationalism. This latter half of the century is amazing in that boundary after boundary fell to science and Europe was flush with conquest, the mood seemed to be that all would fall before the progressive and modernizing scientific approach. A century ago there seems to have been a common conception in the sciences that all of the hard work had been done and that all that was required was a lot of "mopping up" which would take place in the 20th century. That is, the universe was a grand machine whose gears were fairly well understood and all that was need for complete understanding were the solutions to a few "small" problems. Many people are familiar with this story as it relates to physics and how Einstein's Relativity not only solved some of those "small" problems, but ultimately changed physics dramatically. Less well know is Hilbert's program and answering parts of it, Godel's proof, and the dramatic shift in thinking that it is still causing.

Around the turn of the century, the mathematician David Hilbert and his happy band of followers (and you understand that I'm oversimplifying dramatically, right?) put forth the proposition that since the universe was a clockworks, and all God's creation could be described in physical terms, and all creation could be reduced to algorithms, could we not then prove that it is possible to do so? That is, we assume the universe can be reduced to smaller parts which are easier to understand, and by use of an algorithm, a reproducible set of (ordered) steps, we can build a model of those parts of the universe we desire to understand. Then, by joining together these various parts we can get a thorough grasp of anything that exists. Indeed, a goal of the program was to essentially accumulate all of the foundation material into a "dictionary" that would form the basis for this work. The "small" problem (and you understand that I'm oversimplifying dramatically, right?) was that nobody was able to write a proof (or disproof) that it was possible to create a mathematical structure as was proposed that would maintain internal consistency. That is, you don't want a system where 1+1=2 AND 1+1=1 both become true at some point as that calls into question the fundamental assumptions, the axioms of the system.

If you could prove that this approach could work, then you essentially had proved that all those barriers to understanding the clockworks universe would fall to science, and that human knowledge could be melded into mathematical form, so a number of people tried to solve this "small" problem. Hilbert put forth this problem (among a list of others) in 1900, but it was not until 1931 (right after the discovery of Pluto) that Kurt Godel answered the problem with a proof that the problem would never be dismissed. Godel's work is rather obscure, but in essence, what he showed was that beyond the simplest (and most useless) system, there was no way to eliminate statements that could not be shown to be true or false, and since there are these undecidable statements, one can never be certain that contradictions will not arise. In short, you can't model the universe with mathematics and expect that model to be consistent and ever-expanding. Which makes sense when you think about it, as the universe is not mathematical, the universe just IS. Rather, we project our mathematics onto the universe. There's no reason to assume that human conceptualizations can or must encompass the entire universe. Our map of the universe is, after all, only a map, not the actual universe.

In any case, Godel kicked the legs out from under the idea of putting all creation into a mathematical "box" and tying a bow on it because the box will always leak. The idea that all that is can be reduced to a few axioms and a few equations is now a doubtful proposition. In some ways it is a sort of relativity in that mathematical systems have a local framework and not a universal framework. In some other ways it is a statement that things are not simple, surprise.

So, what's the point of my little historical observation? Only this, that science has limits to its (albeit very great) reach. That after a century or so of exponential growth of scientific knowledge, science has not only NOT fit the pieces together, it has created many, many more pieces. And that physics has not only NOT conquered metaphysics but seems less capable that ever of even perceiving, let along addressing, the issues of metaphysics.

I believe that the problems of astrology are not a lack of mathematical rigor, we have more mathematical technology available than we can ever use effectively without a stronger theory foundation. Mathematics is the least of our worries. We need to do more work on theory, we need to make ethical stances about the behavior of astrologers, we need to find a place to stand in the modern cultural and intellectual realm where we can have significant discourse with other fields. We need to develop a deeper understanding of the human heart-mind, and pray that we become wise. Mathematics will not accomplish these things for us, but it will give some of us the satisfying feeling that we are involved in a grand scientific process, and it will give others a convenient shield for their pronouncements, a mock authority to blame for ill-luck.

In short, the worst thing we could possibly do is start believing that mathematics will "save" astrology. If there is a fault in astrology it is in the astrologers and not the mathematics of astrologers.

We are not so different than the ancient astrologers, we face many of the same dilemmas and issues, but we now have no role "at court" and are not taken quite so seriously as we once were. The desire for scientific respectability is a only a veiled desire for social respectability. There's nothing wrong with wanting recognition for hard work, but to pretend that astrology is something other than astrology is improper. It is much better to openly show oneself as the foreigner in a different country than to try to ineptly disguise oneself as a native over and over again and constantly be caught at it and despised for the poor attempt.

> the concept of Inception,
> implying the Axiom of
> Beginnings, was a central
> concept of Hellenistic
> astrology:  the allotment
> of fate occurred at
> katarcheh, a seed moment,
> a commencement 

First, I must note that it is you who suggests that "inception" IMPLIES your "Axiom". Secondly, I'm glad you raised the issue of the katarche as this is one of the central themes in Cornelius' book which I've wanted to raise but thus far had not found convenient to do so. His take on the meaning of katarche is very different that the one you present. Here's some relevant material from "The Moment of Astrology", from the chapter titled, "Katarche: The Line of Descent from Augury" (starting from p136):

| In the early authors, an
| astrological forecast of
| the horary type was named
| by the Greek term katarche.
| A literal translation of this
| word is `beginning', which
| seems to present another
| facet of the all-pervasive
| doctrine of origin. A rendering
| that is more faithful to the
| astrological usage is `initiative'.
| This accurately conveys the
| idea of human action and
| purpose, as contrasted with
| a natural origin.

He then goes on to show historical records of the usage of the term, mostly associated with horaries and elections. His use of katarche is a critical concept in his thesis and he spends a great deal of effort delving into the meaning:

| It is common for words of wide
| currency to take on a specific
| technical meaning within a
| particular discipline. The specific
| meaning frequently has a close
| semantic relationship with other
| non-technical uses. In astrology,
| such words as `election' and
| `rulership' are typical instances.
| The same is true of the word
| `katarche' when employed as a
| technical term in early Greek
| astrology.
| Let us look at the non-astrological
| meanings of the term. The word
| carries several meanings
| depending on context. The most
| general of these is `beginning'. It
| may also refer to 'primacy,
| sovereignty, and basis'; `the part
| of the sacrificial victim first offered';
| and `to begin the rites of sacrifice'.
| This last usage appears to be the
| most ancient, dating back to Homer.
| The word `katarche' thus carries
| a semantic thread of sacred
| primacy and authority. 

He then goes on to the meaning of the Latin words which have become the English words `auspice' and `augury', and . . .

| It remains to be added that
| auspicium is, by the usage of at
| least one modern authority, a
| valid translation for the
| astrological `katarche'.

Rather than quoting the entire chapter, I will let those who are interested read it in full themselves and summarize here as well as I am able. Cornelius claims that the roots of the astrological `katarche' are in the ancient rites of augury and divination. Further, he suggests that the historical record shows that the use of divination was primarily concerned not with the reading of (rigid, deterministic) fate, per se, but with asking the gods about the appropriate actions to take at THIS time, this moment, the katarchic moment as he calls it. A moment when one may interact, rather be a passive recipient of a pronouncement. Then:

| The katarche, unlike the natal
| moment as ordinarily understood,
| does not require a theoretical
| structure to support it. It has no
| need of a law of astrological
| influence [. . .] Since it is not held
| within the boundary of the doctrine
| of origin [PTSB], where a literal
| beginning is the definitive
| theoretical requirement, the
| katarche finds expression through
| a range of possible moments for
| which a horoscope may be judged.
| This range naturally includes
| beginnings as a pre-eminent
| possibility. However, which
| moment is taken up in each
| particular case depends entirely
| on the astrologer, in the light of
| the circumstances. It is not to be
| predetermined by any fixed rule,
| unless the astrologer has chosen
| to follow a convention [. . .]

It is not some "birth" that counts for a katarche:

| One moment is not theoretically
| more important than any other --
| it is the moment that comes
| forward in the particular
| circumstance that count.

That is, it is not the "birth" of the question that is judged, it is the time when the moment presents itself to astrologer (perhaps the receipt of the question for a particular astrologer, perhaps another moment for another astrologer) that is the katarchic moment. As Cornelius says, it is "the moments `significantly presented' and therefore `spontaneously associated'" where we take a katarche. And, very importantly, it is an event that is marked by the participation of the astrologer. He points out that we moderns can most clearly see the ancient katarchic approach at play in horaries, where the astrologer is an active participant, who even shows up in the horary at times. And this, I note, is in contrast to the approach of a modern nativity, which seems to be seen as an abstract description of psychology, personality, character, fate, etc. -- and no need for the astrologer to enter the picture.

This idea of katarche requiring the participation of the astrologer (as the keeper or creator of the templum, the place or "space" where a question can be answered) is one of the more critical issues facing astrology today. The idea of the scientific mechanization of astrology is flawed because it ultimately seeks to destroy the katarchic moment as it desires removing the astrologer from the moment. The goal of science is not to interact with the individual on a personal basis, but to reduce all to easily reproducible, demonstrable "facts", to remove significance and replace it with generic pronouncements. To turn all astrology into something exactly like beginners reading astrology "cookbooks" and making pronouncements, the worst of all possible worlds for astrology. Borg astrology.

The idea that we can simply replace the astrologer with a set of mathematical algorithms is not only a bad idea because it seeks to dehumanize astrology, but it is impossible to prove that this can even ever be done (and my intuition hints that a disproof is likely). One important aspect of the mathematical study of algorithms is that one can prove that an algorithm is correct, or conversely, prove an algorithm incorrect and thus saving oneself a great deal of wasted effort. If one is claiming that all of astrology can be reduced to algorithms, then desiring it or claiming that it can be done is not enough, one should be able to show a proof that it can be done. Lacking that, one should proceed cautiously.

> That's why I have given
> this principle the rank of
> Axiom

I reiterate: the status of being an axiom requires that you NOT be able to do astrology if that assumption is removed. I've demonstrated that not only can you do astrology without that assumption, but that many branches of astrology require that you abandon that assumption. Therefore, it is NOT an axiom. QED.

And since we've been discussing this topic, I've encountered a great many more types of charts that do not require PTSB. One more example: decumbitures are drawn for the moment of taking to one's bed when one is ill, but that is certainly not the START or BIRTH of the illness. It is the katarchic moment significantly presented to the astrologer. Lilly says that if that moment is not known, then take the time when the patient's urine is brought to the physician or astrologer, and the illness definitely does not begin when THAT occurs.

> I will continue replying
> to your comments and
> objections in future
> postings as time allows it...

Indeed, but I feel we have may have reached a plateau in our conversation, perhaps others would care to add their thoughts to the discussion thus far. I'm starting to feel that I've monopolized the conversation and that my proper role as the moderator should be to patrol the boundaries of the discussion. Since we've begun this conversation on this topic the readership of the list has nearly doubled, yet, for the last few weeks, only you and I are bothering to speak up. Let us give others a chance to express their views.

> My very long article on _The
> Prediction of Death and the
> Alchochoden_ can now be
> accessed [ at ]
> the Zodiacal Zephyre.

And for those who are unfamiliar with this excellent web site, the URL is:




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