Monday, September 26, 2011

Crazy 8

Mathematician, Keith Devlin, a frequent guest on NPR, entitled his popular book, Mathematics: The Science of Patterns, very appropriately because mathematics is truly concerned with the discovery and celebration of patterns.

A few days ago I noticed what appeared to be a symmetry pattern embedded in the eight recognized planets (poor Pluto, once the ninth planet, got the boot a few years ago). To help remember the planets outward from the sun, many mnemonics have been created such as My Very Energetic Mother Just Served Us Noodles.

As the above diagram shows the asteroid belt located between the orbits of Mars and Jupiter divides these eight planets into two groups of four each. Almost 12,000 asteroids have been given names, and over 96,000 asteroids have been assigned numbers for identification purposes.

The four planets inside the belt (left of it in the diagram) are commonly referred to by astrologers as the personal planets. Jupiter and Saturn are sometimes termed the social planets, while Uranus and Neptune are called the transpersonal.

When I began looking at pairs of planets symmetrically located about the asteroid belt, indicated by color coding, some curiosities emerged.


  • The initial letters of these two planets’ names, M and N, are the two middle letters in the alphabet, so as a pair they divide the alphabet into two equal parts.
  • Both Roman gods these two planets are named after carried staffs. Mercury held the caduceus and Neptune a trident.
  • There is a similarity in their glyphs in that each is topped by a semi-circle.
  • In astrology Mercury is associated with the rational, conscious mind and Neptune with the intuitive, unconscious mind.


  • Once again we have initial letters, U and V, which are successive in the alphabet.
  • These are the only two planets whose final syllables (-nus) match.
  • The mythological Venus is the Roman equivalent to the Greek Aphrodite. Greek mythology tells us Aphrodite was born from the genitals of Uranus after he was castrated by his son.
  • Flip over the glyph of Uranus, remove the parallel bars, and you have the Venus glyph.

  • To me, the most striking parallel by far is that these are the only two planets that rotate in a clockwise fashion. All the other rotate counterclockwise.


  • In astrology Saturn is strongly linked to time, and sometimes termed, “Father Time.” Are we obsessed with time here on earth? Several years ago the Oxford dictionary announced that the word ‘time” is the most often used noun in the English language.
  • Saturn’s orbital period is approximately 29.5 years which is a nice numerical match to the orbital period of the earth’s only satellite. The moon’s orbital period is about 29.5 days.
  • Our planet is the only one of the eight known to support life, but oddly one of Saturn’s moons, Enceladus, has often been regarded as a potential base for microbial life.
  • Tellus is a Latin word meaning "earth," and Terra, the root of the word, “terrestrial,” was the Roman earth goddess. Although it’s a more subtle occurrence, if we use either of these two alternative names for Earth, we again have successive letters in S and T.
  • Saturn is frequently referred to as the Lord of Karma, and is closely associated with karma in astrology. It is not unusual to find references in astrological and esoteric literature discussing a link between our planet and karma as well. Many believe that by our callous abuse of Mother Earth we are incurring a collective, karmic debt that by cosmic law will have to be paid for in the future. The esoteric astrologer, Alice Bailey, has written, “Great waves of karmic impact have beaten upon our Earth.” We humans often joke nervously about karma on our planet with phrases like “What goes ‘round, comes ‘round.”


  • For many people, especially those who lived through the 60s, the pairing of these two planets brings a line from the song Aquarius to mind: “When the Moon is in the seventh house, and Jupiter aligns with Mars”
  • A similarity that is marginal but still bears mentioning is that the mythological gods, Mars and Jupiter, the latter being the Roman version of Zeus, were powerful gods with a distinctly masculine, dominating energy. Mars was the God of War, and Zeus threw the terrifying thunderbolts.

It may all mean nothing, but it’s something to think about when you’re bored.

Tuesday, September 6, 2011

It's 9/6 Today, a Topsy-Turvy Date

A strobogrammatic number in one that remains the same number when it is rotated 180 degrees. The strobogrammatic digits are considered to be 0, 1, and 8, even though in the case of 1, the rotated form is not exactly the same as the original. If we write today’s date (minus the year) in the common month/day format, we have 9/6 which is then a “strobogrammatic date.” If you can’t visualize that write “9/6” on a piece of paper and then rotate the paper 180 degrees. Clearly, this date has a “sister” in 6/9 (June 9) which is also strobogrammatic.

The 6th astrological sign is Virgo, and we are currently transiting through that sign so today’s day of the month (6th) makes a nice alignment. There’s even more harmony. If you are familiar with the Tarot you probably know that each of the 22 cards in the Major Arcana is associated with either an astrological sign, a planet, or a luminary (Sun or Moon). The 9th card is “The Hermit,” and the astrological correspondence is Virgo, which is the 6th astrological sign. Now we have 9 and 6 joining hands once more.

Sunday, September 4, 2011

The Most Magical of Magic Squares

If you’ll pardon some personal history, it’s time to explain why I have included what is known as an order 4 magic square on this blog. The generic term magic square usually refers to a square grid filled with consecutive numbers beginning with 1, and having the property that the sum of the numbers in each row, each column and each of the two diagonals is the same. The total is called the magic constant for the magic square. In the magic square I have included the magic constant is 34 as can easily be verified. Magic squares of any size from order 3 upward can be formed and all of them have the above mentioned property, but some are even more special. Yet, none is as special as the order 4. For example the four numbers in the corners sum to 34, as do the four numbers in the center, and several other symmetrically located sets of four numbers.

When I was in high school my mathematics teacher would give us students one problem each week for which we could earn extra credit. One week he drew a blank 4 x 4 grid on the blackboard and challenged us to go home and fill such a grid with the first 16 numbers in such a way that the sum of the numbers in each row, column and in the two diagonals was the same. At home I struggled and struggled for hours on end until I finally got it. Although that moment was marked with elation, even more significantly in terms of my future, it represented a birth. I was hooked. Numbers were not just numbers anymore. They had personalities. They were pure magic.

Years later I began to claim “ownership” of this square and the number 16. The fact that I was born on the 16th of the month was no longer simply random. I counted the number of letters in my full name and found it was also 16. Through the years this number has appeared in special ways at special times. For example when I was awarded my last teaching position, I found that the mathematics department was housed in a 16-sided building. Now how many buildings with 16 sides are there!