Dream Numbers

This post is a little different from my usual content that is often prompted by an analysis of the number associated with my diurnal age. This post is prompted by a dream that I had involving a shipping container that, unlike most such containers, was gun metal in colour. It seemed totally sealed but I found a tiny opening and lit a match (or used the torch on my phone) to peer within. I saw a woman peering back at me.

She invited me in and the front face of the container disappeared so that access was now possible. She said that there were 37 people inside. Two of those were adolescent boys, one noticeably shorter than the other. It seemed that one of them was 17 but I wasn't sure which one. I pointed to the taller boy and then, quite audibly in my dream, said "seventeen?". The woman, and the mother of the two boys, smiled and clarified the situation. She said that they were twins (clearly not identical) and had been born on a Saturday. They were both 17.

After some thinking about these numbers, I realised that both 17 and 37 are 4\(k\)+1 primes and thus form the hypotenuse of right angled triangles with associated integer sides, connected by Pythagoras' Theorem:$$ \begin{align} 17^2&=8^2+15^2\\37^2&=12^2+35^2 \end{align}$$Thus we end up with a set of six numbers:$$8, 12, 15, 17, 35, 37$$Being 4\( k\)+1 primes of course, we can also write:$$ \begin{align} 17&=1^2+4^2\\37&=1^2+6^2 \end{align}$$This generates a set of five numbers:$$1, 4, 6, 17, 37$$I tend to go with the set of six numbers as they are easily associated with the Saturday night draw in the Australian lottery system. 

Being in Indonesia, I can't participate in this lottery, not even using a VPN, so I passed these numbers on to my daughter-in-law who lives in Melbourne. I suggested that she try them out. Whether she does or doesn't, I'll report back on what numbers came up in the Saturday night draw at the end of this post. I won't make the post public until after Saturday night in case anyone tries to "cash in" on my dream numbers!

LATE SATURDAY NIGHT

Well my daughter-in-law did submit the six numbers and, not surprisingly, my dream numbers did not prove precognitive. In fact I only succeeded in selecting one of the winning numbers and therefore not even a minor prize was won. See Figure 1. Nor did my other possible numbers (1, 4 and 6) make an appearance. Of course, the numbers could have been meant for Saturday April 2nd, the day before my birthday and a day that marks the 73rd solar return (when the Sun returns to the exact position that it occupied at the time of my birth).

Figure 1

Here are links to my two previous posts on the mathematics of Lotto:

• Lotto Simulations on October 20th 2018
• Lotto Loser on June 10th 2019

Of course the numbers 17 and 37 that I dreamed of may have had nothing to do with Lotto. In fact, Figure 2 gives an insight into a completely different interpretation of the numbers.

Figure 2

A shipping container is characterised by its square cross-section and so the 17 could refer to the side of this square and the 37 could refer to its length of the prism. Only two numbers are needed to define its dimensions.  When the front of the container is open and you look at it front on, the far end seems to be smaller than the open front end.  This corresponds to the twins being both 17 and yet one appearing larger than the other. 

What are the characteristics of this 17 x 17 x 37 rectangular prism? It has a volume of 10693 cubic units and a surface area of 3094 square units. If the front end is open, then the surface area is 2805 square units. How Saturday fits in with this view of things I don't know. Saturday is the sixth day of the week if we count Monday as 1, Tuesday as 2 etc. A rectangular prism does indeed have six sides.

Saturday is Saturn's day and each planet has an associated magic square. The one for Saturn is shown in Figure 3. The numbers associated with Saturn are 3, 9, 15 and 45 because the magic square is 3 x 3, there are 9 squares, the numbers in each row, column and main diagonal add to 15 and the total of all nine numbers is 45.

Figure 3

I've written about magic squares before. Here are links to these posts:

• Ultramagic Squares on November 12th 2021
• Prime Semi-Magic Squares on May 17th 2021
• Magic Squares on September 21st 2020
• Anti-Magic Squares on July 17th 2018

Other sources quote Saturn as being associated with the number 8. See Figure 4.

Figure 4: source

I seem to be going off on a tangent here so I'll stop. It has occurred to me that 17 and 37 are both reversible primes since 71 and 73 are also prime. Currently, at age 72, I'm stuck between these two primes although in less than two weeks I'll be 73. 

Let's not forget that 71 and 73 are also twin primes which fits in very nicely with the twin element in the dream. Additionally, my 73rd solar return occurs on April 2nd 2022, a Saturday. The solar return marks the return of the Sun to the same zodiacal position (12°47'07" Aries) at the time of my birth. My birthday actually occurs on April 3rd.

The shipping container may just be a symbolic representation of life on the physical plane. I am reminded of Carl Jung's description of his Near Death Experience in his autobiography "Memories, Dreams, Reflections" :

In reality, a good three weeks were still to pass before I could truly make up my mind to live again. I could not eat because all food repelled me. The view of city and mountains from my sick-bed seemed to me like a painted curtain with black holes in it, or a tattered sheet of newspaper full of photographs that meant nothing. Disappointed, I thought, "Now I must return to the 'box system' again." For it seemed to me as if behind the horizon of the cosmos a three-dimensional world had been artificially built up, in which each person sat by himself in a little box. And now I should have to convince myself all over again that this was important! Life and the whole world struck me as a prison, and it bothered me beyond measure that I should again be finding all that quite in order. I had been so glad to shed it all, and now it had come about that I along with everyone else would again be hung up in a box by a thread.

He continued:

It is impossible to convey the beauty and intensity of emotion during those visions. They were the most tremendous things I have ever experienced. And what a contrast the day was: I was tormented and on edge; everything irritated me; everything was too material, too crude and clumsy, terribly limited both spatially and spiritually. It was all an imprisonment, for reasons impossible to divine, and yet it had a kind of hypnotic power, a cogency, as if it were reality itself, for all that I had clearly perceived its emptiness. Although my belief in the world returned to returned to me, I have never since entirely freed myself of the impression that this life is a segment of existence which is enacted in a three-dimensional boxlike universe especially set up for it.

So perhaps my dream primes 17 and 37 are meant to be interpreted as the twin primes 71 and 73 with Saturday April 2nd marking my astrological coming of age 73. I realise I'm straying too far into the metaphysical here and it would be better to continue this train of thought in my blog "Mystical Meanderings".

The Fine-Structure Constant

 Yesterday I came across Quanta Magazine article titled:

Physicists Nail Down the ‘Magic Number’ That Shapes the Universe

The article continued:

... the fine-structure constant, denoted by the Greek letter α (alpha), comes very close to the ratio 1/137 ... The constant is everywhere because it characterises the strength of the electromagnetic force affecting charged particles such as electrons and protons. “In our everyday world, everything is either gravity or electromagnetism. And that’s why alpha is so important,” said Holger Müller, a physicist at the University of California, Berkeley. Because 1/137 is small, electromagnetism is weak; as a consequence, charged particles form airy atoms whose electrons orbit at a distance and easily hop away, enabling chemical bonds. On the other hand, the constant is also just big enough: Physicists have argued that if it were something like 1/138, stars would not be able to create carbon, and life as we know it wouldn’t exist.

Today, in a new paper in the journal Nature, a team of four physicists led by Saïda Guellati-Khélifa at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet of the fine-structure constant. The team measured the constant’s value to the 11th decimal place, reporting that \( \alpha \) = 1/137.03599920611. (The last two digits are uncertain.) With a margin of error of just 81 parts per trillion, the new measurement is nearly three times more precise than the previous best measurement in 2018 by Müller’s group at Berkeley, the main competition. (Guellati-Khélifa made the most precise measurement before Müller’s in 2011.) Müller said of his rival’s new measurement of alpha, “A factor of three is a big deal. Let’s not be shy about calling this a big accomplishment.”

As can be seen, even with the latest refinements to the value of \( \alpha \), the value is still very close to 1/137 and so the attention tends to focus on the number 137 itself rather than its reciprocal. The question is asked: what makes 137 so special? The physicists Richard Feynmann and Wolfgang Pauli were intrigued by this the fine-structure constant. Here is a short but informative video about the constant:

We learn from the video that the constant is dimensionless and that it can be expressed in terms of three other fundamental constants. We can write:$$ \alpha=\frac{e^2}{\hbar \,c} \approx \frac{1}{137.03599920611}$$where \(e\) is the charge on the electron, \( \hbar\) is Plank's constant divided by 2\(\pi\) and \(c\) is the speed of light. It's important to note the \(e\) in this formula is not the famous mathematical constant that is sometimes called Euler's number. Another way to write the previous result is as:$$\alpha^{-1} =\frac{\hbar \,c}{e^2}\approx 137.03599920611$$There is an interesting concluding quote from this source:

In his essay, “Pauli (Wolfgang) 1900-1958,” Charles Enz (Pauli’s last assistant) writes; “This number 137 symbolised for Pauli the link with the magic world of the alchemists which has so much fascinated him.”. Recalling his preoccupation with the fine-structure constant and research on synchronicity with Carl Jung, Pauli was moved upon finding his room number was 137 at the Red Cross hospital during his last days when pineal activation can happen in transition.

 The abstract for this source states that:

Wolfgang Pauli was influenced by Carl Jung and the Platonism of Arnold Sommerfeld, who introduced the fine-structure constant. Pauli’s vision of a World Clock is related to the symbolic form of the Emerald Tablet of Hermes and Plato’s geometric allegory otherwise known as the Cosmological Circle attributed to ancient tradition. With this vision Pauli revealed geometric clues to the mystery of the fine-structure constant that determines the strength of the electromagnetic interaction. A Platonic interpretation of the World Clock and the Cosmological Circle provides an explanation that includes the geometric structure of the pineal gland described by the golden ratio. In his experience of archetypal images Pauli encounters the synchronicity of events that contribute to his quest for physical symmetry relevant to the development of quantum electrodynamics.

The article is largely incomprehensible to me but it at least shows that this constant touches on many other areas outside of particle physics. Arthur I Miller has written a book titled 137 in the paperback. On the author's website, he writes:

In Deciphering the Cosmic Number I explore how Carl Jung analysed the dream imagery of one of his most famous patients, the ground-breaking physicist Wolfgang Pauli. Pauli’s unconventional and wild life brought him to the brink of a mental breakdown. He obsessed over how he had made his greatest discovery, feeling that he had tapped into something beyond physics.

It’s the story of two mavericks – Pauli, a scientist who – unlike his peers – was fascinated by the inner reaches of his own psyche and not afraid to dabble in the occult; and Jung, the famous psychologist who nevertheless was sure that science held answers to some of the questions that tormented him. Both made enormous and lasting contributions to their fields. But in their many conversations over dinner and wine at Jung’s Gothic mansion on the shores of Lake Zurich, they went much further, striking sparks off each other as they explored the middle ground between their two subjects.

They deliberated at great length over whether there was a number that everything in the universe hinged on, that explained everything – a primal number that provided insight into the equations of the soul. Might it be three as in the Trinity? Or four as argued in alchemical texts? Could it be the weird number 137, which on the one hand described the DNA of light and on the other is the sum of the Hebrew letters of the word “Kabbalah”?

Deciphering the Cosmic Number is a tale of an extraordinary friendship between two equally brilliant yet very different men. Jung’s and Pauli’s was a truly unique meeting of the minds. It was, as Jung wrote, to lead both of them into “the no-man’s land between Physics and the Psychology of the Unconscious…the most fascinating yet the darkest hunting ground of our times.”

There is a radio interview, first broadcast on 2nd May, 2009, in which Arthur I Miller is talking to Gene Heinemeyer about Deciphering the Cosmic Number: link.

I found a link to an article that provides a more mathematical treatment of the constant. The author cites various quartic equations that have a close approximation of the constant as a root. Two of these are:$$x^4-136x^3-136x^2-818x+1=0 \text{ with }x=137.03599916816339$$ $$x^4-137x^3-10x^2+697x-365=0 \text{ with }x=137.03599916836927$$Here is the abstract for this article:

The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant.

I have little idea what all that means but it shows the interconnectedness of this constant. 

UPDATE: February 4th 2022

Here is another informative YouTube video about topic: