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There’s no such thing as sign cusps

Washington-Idaho borderAt school I always got Fs in physics.  Literally. And I always got As in chemistry.  But I do remember a physics teacher telling us that light could be both a single wave and many particles. Don’t ask me to explain or justify this view.  Though it does underline the point that a single phenomenon can be seen in two different ways.

Astrology can certainly be seen in two ways – the wave model and the box model.  When I first started studying astrology, in the 1980s, the wave model was very much in vogue.  The angular separation between planets was important, and one could see horoscopes in terms of harmonics and midpoints.  However, the box model was always there in the background.  Planets work differently in different signs, and the move from one sign to another makes a big difference.

If you’re new to astrology, then you should know that the dates given for sign changes are approximate, and they require an exact time.  For example, the Sun moved from Aries to Taurus at 9.27 pm GMT on April 19 2017, at 3.12 am GMT on April 20 2018 and at 8.55 am GMT on April 20 2019.  These times are given to the minute, but actually the switch-over happened at a precise time.  Before this precise time you are an Aries, after you are a Taurus.

A sign change isn’t just about signs.  A bank of essential dignities change.  The Sun in the last degree of Aries is in the sign of Mars, the exaltation of itself, the triplicity of itself or Jupiter, the term of Saturn and the face of Venus.  The moment it moves into Taurus, it is in the sign of Venus, the exaltation of the Moon, the triplicity of the Moon or Venus, the term of Venus and the face of Mercury.  Furthermore, it moves from being in a Fire sign to an Earth sign, from a masculine sign to a feminine one.  There are no fuzzy borders.  The network of rulerships have changed in an instant.

I suppose it is rather like travelling on the borderlands of Washington and Idaho.  Imagine you are in Washington State, travelling North East up East Appleway Avenue (see the map at the top of this article).  Just before you cross the Idaho state line, the Washington police pull you over.  They notice that you have an ounce of marijuana on your back seat, in a sealed bag.  They check your drivers license, see that you’re over 21 and not under the influence, and wave you on your way.  You cross the state line, and you’re stopped again, this time by the Idaho police.  They find the marijuana, you get arrested, you go to court, and you’re convicted of misdemeanour drug possession, with a $500 fine plus costs – and if it is your second offence you’ve a good chance of going to prison.  This underlines the fact that when you drive across the border between Washington and Idaho everything changes.  Marijuana is no longer legal for recreational use, and you find yourself criminalized.  In terms of drug laws, there is no such thing as being on the cusp, with your possession of marijuana slowly becoming more criminal as you glide across the state line.  You’re either in Washington or Idaho, you’re either an Aries or a Taurus.

We can also look at the problem mathematically.  Let’s imagine the Sun moving through Aries getting closer and close to zero degrees Taurus.  We’ll give the Sun a number.  When it is at 5 degrees Aries it is 25 degrees short of Taurus, so we’ll give it the number minus 25.  At 15 degrees Aries it is -15, at 25 Aries -5, at 29 Aries -1, at 29 30 Aries -0.5, at 29 45 Aries -.25, and at 0 Taurus it is zero.  When the Sun moves into Taurus, and the numbers become positive.  At 5 Taurus it is +5, at 15 Taurus + 15.

Now what we’ll do is take the reciprocal of this number – in other words dividing 1 by this number.  So the reciprocal of 5 is 1/5 which is 0.2.  We can draw a graph of this:

30 degrees either side of zero Taurus.

At zero degrees Taurus the graph goes crazy.  This is because you are finding the reciprocal of increasingly small numbers – which turn into large numbers, when they are divided into 1.  At zero degress Taurus, you are dividing 1 by zero, which is mathematically impossible – you have an undefined solution to the problem.  And this is what happens at the supposed cusp – you are effectively dividing by zero.  This means that there is no rational cusp, you are either on one side of zero degrees Taurus or the other.

If you are using signs in your astrology, then by definition you are accepting a box model of astrology.  You are accepting that you are in one state or another.  You cannot be in two places at one time, you cannot merge two sets of meanings.  Of course if you don’t like the box model, there are other forms of astrology available.  You can use harmonic and midpoint astrology. Or you can play around with the Gauquelin system.  However, I do believe that if you drop the signs from your astrology you are missing a great deal.

{ 2 comments… add one }
  • Ian Delaney November 14, 2020, 3:25 pm

    Hello again Archie,

    Your article has got me wondering if this is one subject where astrology has made things unnecessarily complicated – rather like pondering the question as to how many angels can dance on the head of a pin!

    I recall David Hamblin in his 1983 book “Harmonic Charts” addressing the issue of the waves vs boxes model. My impression is that he didn’t really arrive at any firm conclusions and since the book was more of an exploratory investigation, I think he was attempting to ask serious questions about what we normally take for granted. This also encouraged my own thinking that perhaps astrology is not what we always suppose it to be.

    I wonder if the box and waves models are that not mutually exclusive. In other words, the box version of astrological reality is one that we can apply quite easily to signs, whereas the waves model as proposed by John Addey is more applicable in the realm of aspects. If one views signs and aspects as two separate measurements, instead of mixing up apples and oranges, then presumably everything assumes its rightful place.

    I suppose that ultimately, one gets to the point where you have to say “this is where things begin, and this is where things end”, so there has to be a precisely defined point which demarcates the location of a celestial body. Astrology really has done a not so good job of tying itself up in knots!

    • Archie Dunlop November 14, 2020, 5:46 pm

      Midpoints and harmonics aside, there is an argument that the box model constrains the wave model. In horary astrology, we have aspects, but sign changes can weaken them. In Indian astrology, the box and and wave model can exist at the same time. For example, when calculating exaltational strength. The Moon has 3 Taurus as its degree of maximum exaltation, 3 Scorpio its degree of maximum fall. The close the Moon gets to its degree of maximum exaltation the stronger it gets, and I believe at 3 Taurus/Scorpio the effect of exaltation is neutral. Likewise in Indian astrology, aspects take place on the basis of signs, with angular separation not being very important.

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