Theosophy and Science Contrasted
Jan 2000, May 2013
Part 1 of 5
Part 1: Astronomical cycles
1. The tilt of the axis
2. The four seasons
3. Precession of the equinoxes
4. The changing polestar
5. Apsidal motion
Part 2: Science, psychics, and myths
1. Axial shift
2. Polar wander
3. Crustal slippage
4. Psychic predictions
5. Ancient traditions
Part 3: Poleshifts and theosophy
1. The gradual inversion of the poles
2. From eternal spring to age of horror
3. Axial disturbances and geological cataclysms
4. Cataclysms and the precessional cycle
5. Earth in motion
Part 4: Climate change
1. The climate system
2. Climate and axial tilt
3. The climate record
Part 5: Appendices
1. The zodiac and precession
2. The zodiac and cataclysms
3. Herodotus and the Egyptians
4. Three axial inversions?
5. The Dendera zodiacs
6. Sampson Arnold Mackey
PART 1: ASTRONOMICAL CYCLES
1. The tilt of the axis
The rhythms of life on earth are largely regulated by the two fundamental motions of our planet: its daily rotation on its axis and its annual revolution around the sun. The earth rotates once every 23 hours 56 minutes and 4 seconds – the earth-day. Since the earth rotates on its axis from west to east, or anticlockwise as viewed from above the north pole, the sun appears to rise in the east and set in the west. The earth revolves around the sun from west to east (anticlockwise) about once every 365.25 days – the earth-year.
As a spinning sphere (or rather oblate spheroid), the earth possesses a rotation axis, whose two ends mark the north and south geographic poles, with the equator being situated midway between them. If the earth stood perfectly upright on its axis – i.e. if its axis formed an angle of 90° with the plane of its orbit around the sun (the ecliptic) – the equator would lie in the plane of the ecliptic. The sun would then always shine above the equator, and all regions of the earth between the two poles would enjoy a constant alternation of 12 hours’ daylight and 12 hours’ darkness.
The earth’s axis, however, is not perpendicular to the ecliptic. At present the equator is tilted at an angle of about 23.4° in relation to the ecliptic, and the earth’s axis makes an angle of 23.4° with a line drawn perpendicular to the ecliptic; in other words, the obliquity of the ecliptic is 23.4°. The tilt of the earth’s axis gives rise to two important parallels of latitude in each hemisphere: the tropics and the polar circles: the tropics of Cancer and Capricorn currently lie 23.4° north and south of the equator respectively, and the arctic and antarctic circles lie at 66.6° north and south latitude respectively (i.e. 23.4° from the north and south poles). These boundaries divide the earth’s surface into three distinct zones: the tropical or torrid zone (the region between the two tropics); the temperate zones (the region in each hemisphere between the tropics and the polar circles); and the frigid or polar zones (the region in each hemisphere inside the polar circles). The polar zones do not enjoy a regular alternation of day and night throughout the year; the sun is below the horizon for between one day (at the polar circles) and six months (at the poles) each year. In the tropical zone the sun is vertically overhead sometime each year, whereas in the temperate and polar zones, the sun is always at some angle less than 90°.
Fig. 1. The tilt of the earth’s axis.
The existence of the four seasons is due mainly to the earth’s tilt and, to a lesser extent, to the ellipticity of the earth’s orbit (i.e. the extent to which it departs from a perfect circle). If the earth’s axis stood upright, there would therefore be no distinct seasons.
To describe the positions and motions of astronomical objects, they are considered to lie on an imaginary sphere surrounding the earth, known as the celestial sphere. The north and south celestial poles are the projection onto the celestial sphere of the earth’s north and south geographic poles, and the celestial equator is the projection of the earth’s equator. The north and south poles of the ecliptic are the projection of a line perpendicular to the ecliptic. It does not matter whether this line is projected into space from the earth or from the sun, since the celestial sphere is conceived as being so far away that the ecliptic pole will fall on a unique point. The north and south celestial poles are 23.4° from the north and south ecliptic poles respectively. If the earth’s axis was upright instead of tilted, the celestial poles would coincide with the ecliptic poles. The north ecliptic pole lies in the constellation Draco, while the north celestial pole lies very close to Alpha Ursae Minoris, the current polestar.
Fig. 2. The celestial sphere.
2. The four seasons
The inclination of the earth’s axis gives rise to four important points in the earth’s orbit, which mark the beginning and end of the four seasons: at the vernal (or spring) equinox, the sun is above the equator; it then appears to move northwards and rises higher and higher in the sky (in the northern hemisphere) until the summer solstice, when it is above the tropic of Cancer; it then appears to move back towards the equator until the autumnal equinox, when it is again above the equator; finally it proceeds southwards until the winter solstice, when it is above the tropic of Capricorn. In reality, of course, it is the earth that revolves around the sun, not the sun around the earth. In the northern hemisphere, the vernal equinox falls on 20 March, the summer solstice on 20/21 June, the autumn equinox on 22/23 September, and the winter solstice on 21/22 December. In the southern hemisphere spring and autumn, and summer and winter are reversed.
Although, astronomically, each season lasts three months, for non-astronomers it is more sensible over most of the northern hemisphere to think in terms of a four-month winter (December to March), a two-month spring (April/May), a fourth-month summer (June to September), and a two-month autumn (October/November). A lag of a month or more occurs between the time of maximum and minimum solar radiation and the warmest and coldest months, because the earth takes time to respond to changes in the amount of incoming solar energy.
The two equinoctial points are the points (or nodes) where the ecliptic intersects the celestial equator. The equinoxes are therefore the two days of the year when the sun is directly above the earth’s equator. Equinox means ‘equal night’, and at the equinoxes day and night everywhere are about 12 hours long.
Fig. 3. The four seasons.
At the summer solstice (in the northern hemisphere) the sun reaches its northernmost point and rises to its highest point in the sky, and therefore the day reaches its maximum length, while at the winter solstice, the sun reaches its southernmost point, appears at its lowest point in the sky, and therefore the night reaches its maximum length. The sun’s rays fall vertically on the equator at the equinoxes, and vertically on the tropic of Cancer and the tropic of Capricorn at the summer and winter solstices respectively. The tropics are therefore that region of the earth on which the sun’s rays fall vertically at some point of the year, while at all other places on the earth the sun’s rays arrive at an oblique angle, so that they receive less heat.
At the equinoxes the sun’s declination is 0° as it is then traversing the celestial equator (declination is the number of degrees north or south of the celestial equator). It therefore rises and sets due east and due west all over the globe. In the northern hemisphere, the sun rises to the north of east in the summer and to the south of east in winter, reaching its northernmost and southernmost positions at the summer and winter solstices respectively, when it has its greatest declination of 23.4° north or south. The distance from due east and west of the point on the horizon where the sun rises and sets depends not only on the time of year but also on the latitude in question – the higher the latitude the greater the distance.1
The inclination of the earth’s axis means that different parts of the earth receive different amounts of solar radiation, and it is the main cause of the seasonal rhythms. A secondary factor is that the earth follows an elliptical orbit around the sun, so that its distance from the sun varies. At present the earth reaches perihelion – the point in its orbit closest to the sun (147 million km) – on 2-5 January, i.e. during winter in the northern hemisphere, and it reaches aphelion – the point in its orbit furthest from the sun (152 million km) – on 3-6 July, i.e. during summer in the northern hemisphere. This means that the northern hemisphere has milder winters but cooler summers than the southern hemisphere, though the effect is moderated by the heat stored in the greater expanse of oceans in the southern hemisphere. The amount of solar radiation intercepted by the earth at perihelion is about 7% higher than at aphelion.
1. The sun’s maximum annual deviation (Δ) north or south of the E-W line is given by the equation:
sin Δ = sin ε / cos l
where ε = obliquity of ecliptic, and l = latitude of observer. On the equator (lat. 0°) the total swing along the eastern horizon is therefore equal to twice the tilt of the earth’s axis. For any other latitude, it is greater.
3. Precession of the equinoxes
The vernal and autumnal equinoxes occur at the two points in the earth’s orbit where the earth’s axis forms an exact right angle with a line joining the centre of the earth and sun, as viewed from directly above or below the earth. The summer solstice occurs at the point in the earth’s orbit where its north pole is tilted directly towards the sun, and the winter solstice occurs at that point where it is tilted directly away from the sun.
If the earth’s axis always pointed to exactly the same point in space, the vernal equinox would occur at the same point in the earth’s orbit every year, and the earth would move through a full circle of 360° between successive equinoxes. However the earth’s axis gyrates very slowly clockwise (viewed from above the north pole), describing a conical movement round the vertical, rather like the axis of a spinning top, and traces a complete circle among the stars about once every 26,000 years. According to modern science, this is caused by the gravitational pull of the moon and sun and, to a lesser extent, the planets on the earth’s slight equatorial bulge. The result is that the vernal equinox occurs a fraction of a degree before the earth reaches the point in its orbit where the equinox occurred the year before. This phenomenon is known as the precession of the equinoxes (though it might just as well be called the precession of the solstices). The vernal equinox precesses at an average rate of about 50 arc-seconds (1/72°) per year, and it therefore occurs about twenty minutes earlier every year. This means that the earth does not revolve through 360° between two successive vernal equinoxes but only 359 71/72 degrees (or 359 degrees, 59 minutes and 10 seconds). The actual rate of precession fluctuates around the average figure of 50". The annual rate of precession for the year 2000 (epoch J2000.0) is 50.288".
Fig. 4. The long-term wobble, or precession, of the earth’s axis.
The sidereal year is the time the earth takes to make one 360° revolution around the sun, measured between two successive conjunctions of a particular star, and is currently equal to 365.256363 days. The tropical year (also called the solar or equinoctial year) is the time the earth takes to make one revolution around the sun, measured between two successive vernal equinoxes, and is currently equal to 365.242190 days. In other words, at present the tropical year is about 20.4 minutes shorter than the sidereal year.
The zodiac is a zone or belt of the celestial sphere, extending about 8 degrees on either side of the ecliptic, and divided into twelve portions or constellations. During each annual revolution around the sun, the earth passes through each constellation of the zodiac from west to east, at the rate of approximately one degree per day. At the moment of the vernal equinox, a line from the centre of the earth through the sun and extended outwards will cross the circle of the zodiac at the equinoctial point – one of the two points where the celestial equator intersects the ecliptic. Since each successive vernal equinox occurs when the earth is slightly to the west of its orbital position at the last vernal equinox, the vernal equinoctial point advances slowly westward, so that from equinox to equinox the earth moves ‘backwards’ through the constellations of the zodiac (i.e. in the opposite direction to that in which it orbits the sun). At an average rate of precession of 50 arc-seconds a year, the sun enters a new constellation (covering an average of 30 degrees of arc) every 2160 years (a period known in theosophy as the messianic cycle), and takes 25,920 years to complete a full circuit of the zodiac.1 A precessional cycle is also known as the Great Year or Platonic Year.
There is an important distinction between the constellations (or houses) of the zodiac and the signs of the zodiac.2 The constellations are groups of stars encircling the earth at a distance of many light-years. They are sometimes said to be ‘fixed’, though every star actually has its own proper motion, so that over long periods of time the stars of a constellation alter their position in relation to one another. The signs of the zodiac, on the other hand, are regions of space permeating and surrounding the earth. The vernal equinoctial point is the point on the celestial equator which the sun crosses at the vernal equinox, and the corresponding point on the earth’s equator is defined as the beginning of the sign Aries – whatever the constellation in which this occurs. As the vernal equinoctial point gradually shifts around the celestial equator during a precessional cycle, the signs shift around the earth’s equator accordingly. The signs are therefore not fixed, while the constellations (relatively speaking) are.
Since Aries is traditionally regarded as the first sign and constellation of the zodiac, a precessional cycle could be said to begin when the first point of the sign of Aries coincides with the first point of the constellation Aries (i.e. when the earth, the sun, and the first point of the constellation Aries are in a straight line at the moment of the vernal equinox). This does not occur at the beginning of the Age of Aries, but at the end, for the following reason. Since the earth revolves around the sun from west to east, the westernmost point of each constellation (each assumed to cover 30° of arc) is counted as 0° of that constellation (and 30° of the preceding constellation); the first point of Aries (0° Aries) is therefore also 30° Pisces. However, the equinoctial point precesses in the opposite direction – from east to west. Thus when, in the course of precession, the sun leaves the constellation Taurus and enters Aries, it enters the 30th degree of Aries, and does not coincide with the first point of the constellation Aries until the end of the Age of Aries.
According to H.P. Blavatsky, the Age of Taurus ended and the Age of Aries began in 2410 BCE, the Piscean Age began in 255 BCE, and the Aquarian Age began at the end of the 19th century. These dates assume that each constellation spans 30°. It will be many centuries before the equinoctial point enters the actual constellation of Aquarius.3
Fig. 5. The precession of the equinoxes. Position A shows the first point of the sign Aries coinciding with the first point of the constellation Aries. A quarter of a precessional cycle later (6480 years), it coincides with the first point of Capricorn (position B), then Libra (position C), and Cancer (position D). After a total of 25,920 years, the earth returns to position A.4
1. H.P. Blavatsky gives the length of the precessional cycle as 25,868 years, equivalent to 50.10 arc-seconds per year (H.P. Blavatsky, The Secret Doctrine, Theos. Univ. Press (TUP), 1977 (1888), 2:330fn). However, she also says that 25,920 years is the ‘exact period of revolution of the heavens’ (H.P. Blavatsky Collected Writings, Theos. Publ. House, 1950-91, 14:360). In 945 BCE (before Christian era) the Hindus calculated the rate of precession to be 48.57 arc-seconds per year (see The Theosophist, Sept. 1881, p. 263). On the basis of the current rate of increase in precession (0.0002 arc-seconds a year), the annual rate of precession would have been 50.10" around 1060 CE, and 49.699" in 945 BCE.
Blavatsky sometimes refers to the precessional cycle as the ‘sidereal year’ or ‘tropical year’. Nowadays these terms have different meanings, as noted above in the text.
2. G. de Purucker, Fountain-Source of Occultism, TUP, 1974, pp. 125, 139-42.
3. Blavatsky Collected Writings, 8:174. See Appendix 1: The zodiac and precession.
4. Fountain-Source of Occultism, p. 672.
4. The changing polestar
The north and south celestial poles are the points on the celestial sphere directly above and below the earth’s north and south geographic poles respectively. The north and south ecliptic poles are the points directly above and below a line drawn perpendicular to the ecliptic. The celestial poles are often situated in wide open space, but at other times they come close to, and occasionally coincide with, a star, which is then called the polestar. In the northern hemisphere, the present polestar (Polaris) is the star at the end of Ursa Minor’s tail. In the southern hemisphere, there is currently no bright star near the celestial pole; the southern polestar, Sigma Octantis, is only of the 5th magnitude, whereas Polaris is of the 2nd magnitude.
An observer on the earth’s surface sees only half the celestial sphere at any one time. The visible half is bounded by the observer’s horizon, a plane that cuts the celestial sphere 90° from the observer’s zenith (the point on the celestial sphere directly above him or her). As seen from the equator, true polestars lie on the horizon while all other stars rise at right angles to the horizon, remaining above it for 12 hours. As viewed from either of the poles, a polestar remains stationary overhead while all other stars move in circles parallel to the horizon, remaining permanently above it. At intermediate latitudes, the apparent motion of the stars lies between these two extremes: some stars rise and set, but others circle around the poles without setting and are known as circumpolar stars. At a latitude of 25°N, for example, the north celestial pole lies 25° above the north horizon and therefore all stars within 25° of the celestial pole are circumpolar, while all other stars visible from that latitude rise and set. Since the earth rotates in an anticlockwise direction, the stars appear to revolve around the celestial poles in a clockwise direction, completing one revolution every day.
The gyration of the earth’s axis that produces the precession of the equinoxes involves a slow change in the direction in which the axis points in space (the tilt, according to modern astronomy, remaining more or less the same). The axis slowly sweeps an approximate circle, with a radius of about 23.5° around the poles of the ecliptic in the course of a precessional cycle. Since the polestar is simply the star closest to the celestial poles at any given time, a series of different stars take on the role of polestar during a precessional cycle. Alpha Draconis (Thuban) was closest to the north celestial pole around 2700 BCE. The north celestial pole currently points to within 1° of Polaris, and will point closest to it in 2100. In 12,000 years the star closest to the north celestial pole will be Vega, the brightest star in the Lyre.
According to modern science, the tilt of the earth’s axis does not remain exactly the same but gradually varies within very narrow limits owing to gravitational perturbations caused by the sun, moon and planets (especially Jupiter, Mars, and Venus). It has been established by observation that the tilt is steadily decreasing by around 0.47 arc-seconds a year (about a hundredth of a degree per century). On 1 January 1950 the obliquity was 23°26'45", and on 1 January 2000 it was 23°26'21". On the basis of calculations of gravitational perturbations, scientists theorize that the tilt oscillates between about 22.1° and 24.5° over a period of about 41,000 years.1 The slight variation in the tilt of the earth’s axis means that the curve described by the earth’s north pole around the north ecliptic pole is not a perfect circle.2
According to theosophy,3 on the other hand, the axis gradually inverts through a full 360 degrees, at an average rate of 4 degrees per precessional cycle (0.56 arc-seconds per year), and therefore traces not a circle but a spiral around the poles of the ecliptic. In addition, sudden axial disturbances occur from time to time, resulting in major cataclysms.4 Scientists would dismiss the idea of a gradual inversion of the poles as impossible because they do not know of any force that could produce such an effect. Then again, they cannot explain what causes the earth to rotate on its axis – but it keeps on turning just the same!
Fig. 6. The changing polestar. Theosophy postulates that the earth’s axis does not trace a circle around the ecliptic pole but a spiral.
1. A. Berger & M.F. Loutre, ‘Insolation values for the climate of the last 10 million years’, Quaternary Science Reviews, vol. 10, 1991, pp. 297-317.
2. Furthermore, the ‘circle’ is not smooth but wavy owing to the phenomenon of nutation, a ‘nodding’ movement of the earth’s axis with a period of 18.6 years and an amplitude of 9.2 arc-seconds. Its chief cause lies in the fact that the moon’s orbital plane is inclined at about 5° to the earth’s orbital plane and precesses around it in 18.6 years (‘ideal’ figure: 18 years). The ‘circle’ described in a complete precessional cycle therefore has about 1440 waves (= 25,920/18). (It is interesting to note that there are 1440 minutes in a day, and a human being breathes an average of 18 times a minute: 18 x 1440 = 25,920.) The approximate circle (with superimposed nutation) is traced in an anticlockwise direction as viewed from the earth, or in a clockwise direction as viewed from the north ecliptic pole.
3. H.P. Blavatsky, The Secret Doctrine, TUP, 1977 (1888), 2:331, 357, 407-8, 768; G. de Purucker, Fountain-Source of Occultism, TUP, 1974, pp. 346-7; Samson Arnold Mackey, Mythological Astronomy of the Ancients Demonstrated (1822/23), Wizards Bookshelf, 1973.
4. The Secret Doctrine, 1:369, 2:144-5, 274, 314, 330, 350; W.Q. Judge, The Ocean of Theosophy, TUP, 1973 (1893), pp. 135-6, 140.
5. Apsidal motion
The sun occupies one of the two foci of the ellipse of the earth’s orbit. A line drawn through the point of the earth’s closest approach to the sun (perihelion) and farthest retreat (aphelion) – the two apsides – passes through the sun and is called the line of apsides or major axis of the orbit. Perihelion currently occurs in early January, when the earth is in Sagittarius, and aphelion in early July, when the earth is in Gemini. The line of apsides precesses slowly eastward (anticlockwise) due to the gravitational attraction of the other planets. The average rate of apsidal (or perihelion) precession is 12 arc-seconds (1/300°) per year, or 108,000 years for a complete rotation,1 the present rate being 11.45 arc-seconds per year.
In addition to the sidereal and tropical years already mentioned, the rotation of the line of apsides gives rise to a third type of year – the anomalistic or orbital year, which is measured between two successive passages of the earth through perihelion. It is currently 365.259635 mean solar days long, or about 4.7 minutes longer than the sidereal year.
Taking 50 arc-seconds per year as the average rate of the precession of the equinoxes, and 12 arc-seconds per year as the average rate of apsidal precession, the earth revolves around the sun:
• 360° - 50" in one tropical year;
• 360° in one sidereal year;
• 360° + 12" in one anomalistic year.
Since the vernal equinox advances westward, while perihelion advances slowly eastward, the combination of these two movements – the precession of the equinoxes and the rotation of the line of apsides – gives rise to a third cycle, lasting about 21,000 years.2 This cycle is called climatic precession, to distinguish it from the astronomical precession of the equinoxes. Whatever the earth’s position in relation to the apsides at the time, say, of the vernal equinox in a particular year, it will return to the same relative position at the equinox not in 25,920 years but in only about 21,000 years, due to the movement of the apsides themselves. During this period the earth precesses westward about 290°, while the line of apsides advances eastward about 70°: 290° + 70° = 360°.3
According to astronomical calculations, climatic precession has an average period of 21,000 years, but allegedly comprises two main periods of about 23,000 and 19,000 years.4
1. G. de Purucker, Fountain-Source of Occultism, TUP, 1974, p. 140fn. 108,000 years is equal to a quarter of the period of the kali-yuga (432,000 years). 108 is roughly the average distance between the sun and earth in terms of solar diameters, the average distance between the surfaces of the moon and earth in terms of lunar diameters, and the diameter of the sun in terms of earth diameters (actual figures: 107.5, 108.1, and 109.1 respectively).
2. Using the figure of 50" for the precession of the equinoxes and 12" for apsidal motion, the combined movement is equal to 62" (62/3600°) a year, or 20,903.226 years for a complete cycle. Blavatsky gives a figure of 50.10" for the precession of the equinoxes and 11.24" for the rotation of the line of apsides (equivalent to 115,302 years for a complete circuit), these figures being taken from the Encyclopaedia Britannica (The Secret Doctrine, 2:330fn; note the [deliberate?] mistake involving minutes and seconds).
3. Suppose that, in a particular year, the vernal equinoctial point enters the constellation Aries at the same time as the earth is at perihelion. Using the ‘ideal’ figures, it would take 6 complete apsidal rotations or 25 precessional cycles – a period of 648,000 years – before such an event occurred again, 648,000 being the lowest common multiple of 108,000 and 25,920. Perihelion will next coincide with the equinoctial point (i.e. the longitude of perihelion will be 0°) around the year 6440 (aom.giss.nasa.gov).
4. A. Berger et al. (eds.), Milankovitch and Climate, Reidel, 1984, p. 35; A. Berger & M.F. Loutre, ‘Insolation values for the climate of the last 10 million years’, Quaternary Science Reviews, vol. 10, 1991, pp. 297-317. These two periodicities, along with the 41,000-year obliquity cycle and the approximately 100,000-year eccentricity cycle, are said to have been confirmed by the discovery of similar periodicities in studies of the Pleistocene climate record. This claim is considered in part 4, section 1.
Poleshifts: Part 2