Introduction

Reading about a method of house division is more or less the same as playing telephone tag (or broken telephone), game in which messages are whispered from person to person for the original and final messages to be compared thereafter. Most authors have incurred descriptive errors, but no description has had the greater amount of errors than that of the Placidean mechanism of action, that is, the method of house division popularised (not necessarily developed) by the Benedictine monk Placidus of Titis (1603-1668), who was inspired by the primary directions of Ptolemy (second century). After all, it is the same method with two different applications: while the one regards prognoses, the other horoscope measurement or construction (i.e. erecting the chart). Brilliant English practitioner and talented drummer Michael Wackford argued (2006): “Unfortunately, the standard definitions of the house system that bears Placidus name have often been repeated incomprehensibly (or wrongly), and some authors, in misleading themselves as well as their readers, have caused several corrupt variations to gain currency.”

However, even Michael could not offer a sufficiently clear explanation of the method for the readers in the article wherein he wrote the above (although he did not provide a “corrupt” description in any way whatsoever either, and understood Placidus well). This is why we would like to provide more clarity with as little technicality as possible. The following may be considered an even simpler explanation than that provided in an illustration in a recent paper. Let us begin by referring to an interesting comment made by another astrologer, Anthony Louis.

Two Christmases ago (2022), Anthony was able to conclude: “[…] astrological house systems should be consistent with the prevailing scientific worldview of the epoch in which they are used. In other words, the astrological houses of a natal chart must necessarily divide the spacetime around us at the moment of birth”. And adds: “The Placidus system is consistent with Ptolemy’s description […] which takes into account both space and time, anticipating Einstein’s notions of space-time and the non-Euclidean geometries of the 19th century, implicit in Ptolemy’s original writings in the 2nd century CE.”

He can only be found to be entirely correct. But what does that mean in plain English or for those without any physical knowledge at all? If you were to look up the key word «proper time» in a dictionary of Physics or even in Google, you will learn that the path of an object is that which it takes pursuant to spacetime displacement («worldline»), not just spatial, but space according to time, and that it is unique to its “own clock”, the clock “it carries along with it”.

The Key

Why is this relevant to house division or the timekeeping (Placidean) method? Because, just as each segment of the ecliptic (i.e. sign) has a specific time of oblique ascension at a specific latitude (the same as the sun would have had at the same latitude when it occupied that sign or segment), so does each of its degrees (the same as the sun would have had at the same latitude when it occupied that degree) in its journey from the horizon (Asc) to the midheaven (MC) and from here to the opposite point of the horizon (Des).

The Key’s Cause

Both rotation (day) and revolution (year) can be considered two inertial frames of reference as long as we remain at the same latitude and the same longitude, for the different times of oblique ascension will remain the same for all signs or segments (i.e. months) and degrees (i.e. days). As Galileo would have suggested, all inertial frames of reference were created equal.

The tilt of a non-inertial or moving frame of reference (Earth) relative to an inertial frame of reference (ecliptic) is responsible for the first form of relativity known to us, tropical astrology, in addition to the other two (special relativity, or velocity, and general relativity, or gravity). Put simply: each day (i.e in or at each degree) the sun has a slightly different ascensional time than the previous day and the day that follows. The time differences become greater as greater the distance between the segments of the ecliptic (e.g. between July and January, instead of between July 20 and August 21 or between July 20 and July 21) and that of the observer from the equator. In physics, it is known as the «equation of time». It is the relativity that governs tropical astrology and its natural method of house measurement, the timekeeping method (Placidus, or relative houses, for it recognises *different fixed ascensional times*, as seen in an illustration below).

The Key’s Implications

So it would seem obvious, of course, that the amount of time that the sun would invest in travelling from the ASC to the MC and from here to the DES would be different according to both the position of the observer and the month of the year, and that this has decided the oblique ascensional times of all twelve segments of the ecliptic and their individual degrees at (almost) all latitudes on the globe, for these times correspond to the times of ascension of the sun when it occupied said twelve segments or their degrees throughout the year at (almost) all latitudes. It is or should also be obvious that, even when the sun no longer occupies a given segment, it will always preserve or retain the same ascensional time as it had when the sun occupied it (it will also retain the same properties: element, polarity or electric charge, and behaviour or modality. See the molecular theory of the ecliptic).

From this follows that the amount of time spent by a sign or an ecliptic degree in rising above the horizon in the Caribbean *varies relative to both the observer in New York or in Kodiak and to each day or month (i.e. each degree or sign, respectively) at the same latitude*, for in both cases they conduct their observations from different frames of reference (not to mention that, far from the equator, they also move or rotate slower than the observer located in the Caribbean due to the circumference of the Earth, but this variable was exposed very briefly in the paper referred to earlier).

If this is so, how, then, can it be so difficult or require so much effort (almost as much as it takes the sun to lift its buttocks in a polar region, if I may be humorous) to explain to astrologists, if not to the entire astrological community, that we know of oblique ascensional times (i.e. of the ascensional time of each sign and its particular degrees) because of the very sun and/or the seasons? So that it can be recognised that, when we measure a region of the sky (i.e. house), we are to remain loyal to all times simultaneously and uninterruptedly.

The fact that the sun has vacated the rest of the degrees of the circumference does not deprive them of their ascensional times, does it? This implies recognising that the degree occupied by, say, the twelfth or eleventh cusp (or that the exact region of the horizon occupied by the degree in question) represents a different ascensional time than that of the ASC (Alcabitius) and that of the MC (Koch). That is why our sky is flooded with imaginary diurnal lines and it is our task to discern the point of intersection between these and the zodiacal belt (i.e. ecliptic).

It is very simple (although relativistic).  After the second century, Placidus should have been, for this reason, the only method to had been taken into account (spatial measurements ignore, as described above, time, and must therefore be discarded).

Each sixth of the diurnal arc (i.e. each Placidean cuspal degree) represents the path travelled by a different zodiacal degree, which bears its own clock, speed, or time of ascension. Therefore, each length of time constitutes one, two, three, four, or five sixths of the time that would have elapsed since the sun’s rise if it had occupied that degree of the ecliptic (i.e. all five cuspal degrees constitute five different trisections). When we measure the houses of an astrograph, the sun does not occupy all the degrees simultaneously, but these bear with them the time established by the sun the first time it rose or dawned with them during the year. We thus measure the time of all simultaneously and uninterruptedly in order to determine the house cusps as accurately as possible. Such measurement, however, is not trigonometric, but physical.

Astrographical Measurement

This motion — or spacetime displacement — applies to all degrees simultaneously, even if you find yourself interested in one only (say, the ascending degree, in the case of an Alcabitius-based measurement, or the culminating degree, in that of a Koch-based one). That is, they all move at the same time (because of rotation). One, then, cannot divide the amount of time of the ascending degree (Alcabitius) or that of the midheaven (Koch) into three equal parts in order to apply it to the intermediate cusps (different degrees/ascensional times) indistinctly, but to the corresponding cusp (degree). The degrees of the two intermediate cusps have their own ascensional time or clock (see «proper time» again), namely, that which the sun established the first time it rose or dawned with it. Just as we do not apply to the ASC or the MC a third of the length of time of the degree of the twelfth or eleventh cusp, so we shall not apply to these cusps a third of the length of time of the Asc or the MC. It would do us good to recognise the true path or length of time («proper time») of the two different ecliptic points or degrees which actually occupy or mark these regions of the horizon. Although the Asc and MC are measured trigonometrically, we have not failed to respect their clocks. That being so, why not bother to do the same for the rest, even if it represents a challenge that triangulation only can overcome?

Seasonal or Planetary Hours

The reader should also know that this will not change the truth about planetary or seasonal hours. On the contrary: it will confirm them. That is, said truth (seasonal hours) is able to exist and remain the same perpetually thanks to the reality that has been described above: you will be able to establish the seasonal hours (diurnal or nocturnal) of whatever degree of the ecliptic you choose, meaning each — seasonal — hour will constitute one twelfth of the total amount of time that the sun would have spent in the visible (diurnal hours) or invisible (nocturnal hours) sky if it had occupied that degree of the circumference. Because of this, any Placidus-measured house cusp (i.e. degree) will necessarily appear in the next cusp every two seasonal hours (i.e. of said degree). Let this be the only proportional feature of the Placidus measurement, for each house will measure a different amount or length of time (each is relative to another, necessarily).

The Comment from Tony (2022) and Mike (1994)

Thus, when Tony refers to Placidus as the most compatible with spacetime or Einstein’s notion of time and space, he also gets it right, as does Michael Wackford when he explains (1994) that this method is the most natural. So much so, we have to appeal not to the man-made or human-made tool we know as mathematics (trigonometry), but rather an unbiased observation of the sky, that is, physics.

House Systems: An Intrinsically Unnecessary Debate

However much this can be considered to be clear, unambiguous, or true, many have not understood the mechanism of action of the Placidean (or relative) measurement of the houses and the vast majority of astrologists concentrate only on stating or pointing out the fact that Placidus trisects or divides the semiarch into three parts equally on the basis of time. But so does Alcabitius and Koch, and it would seem that they have found some difficulty in explaining the difference, that is, in explaining to themselves and their readers how, exactly, this is so: both Alcabitius and Koch conduct a timekeeping or Placidus measurement for a single degree of the ecliptic, while Placidus for all simultaneously, for it is aware of the relativity inherent in ascensional times (not necessarily relativity as we understand it today, of course, as it derives from a different form of time dilation, but almost). That is, degree by degree.

Can it be said, then, that if the community had understood this from the beginning, the only existing chart models would be that of whole signs, of equal houses, of Porphyry, (perhaps also of Alcabitius) and of Placidus? If we were to take into consideration the knowledge and tools available at the time, these would be the only measurements that would matter, whereby the most faithful to the sky would be, of course, the timekeeping method (i.e. Placidus). And ironically, as it precedes all (unnecessary) debates.

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This was originally presented in Time Dilation according to Tropical Astrology and Why the Placidus Measurement of Astrographic Regions is Compatible with Relativity Theory (Bustamante, D. 26 September 2024). We explained therein notions such as Lorentz transformations, time dilation, special relativity, and the zodiacal belt, among others.

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References

Carroll, Sean. (2022). The Biggest Ideas in the Universe. Space, Time, and Motion. Dutton. Penguin Publishing Group. New York.

Chatham, Rhys. (Abril 2, 2021). “Placidus versus Alcabitius House System.” Rhys Redmond Chatham Astrology. Retrieved from: https://rhysastrology.fr/placidus-vs-alcabitius/

Forest, Steven. (2023). “Why I Use Placidus Houses.” Forest Astrology. Retrieved from: https://www.forrestastrology.com/blogs/astrology/why-i-use-placidus-houses

Holden, Ralph. (repr. 2023). The Elements of House Division. Raven Dreams Press. Boulder, Colorado, USA.

Louis, Anthony. (December 28, 2022). “Space-Time and Astrological House Systems.” Anthony Louis Astrology Blog. Retrieved from: https://tonylouis.wordpress.com/2022/12/28/space-time-and-astrological-house-systems/

Louis, Anthony. (February 23, 2023). “William Lilly’s Squares [λ 90º] acting like Sextiles [λ 60º]!” Anthony Louis Astrology Blog. Retrieved from: https://tonylouis.wordpress.com/2023/02/23/william-lillys-squares-acting-like-sextiles/

Louis, Anthony. (September 5, 2024). “Can a sextile [60º] act like a square [90º]?” Anthony Louis Astrology Blog. Retrieved from: https://tonylouis.wordpress.com/2024/09/05/can-a-sexile-act-like-a-square/

Placidus de Titis. (1814) Primum Mobile. trans. John Cooper. David and Dickson. London, England, UK.

Ptolemy. (1940). Tetrabiblos. Loeb Classical Library. Harvard University Press. Boston, Massachussets. USA

Wackford, Michael. (1994, repr. 2006). “Placido and the semi-arc method of house division.” Skyscript. Retrieved from: https://www.skyscript.co.uk/placido.html