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Sci Rev – II

it is November 18, 2025, as I begin this post. But now, as I continue, time has passed during which I’ve been trying to make sense out of the confusion which inevitably accompanies the early stages of a scientific revolution. It is now past Thanksgiving. That’s how it goes these days: Writing this blog is easily displaced by the many activities of my life and that is OK because occasions do arise when the busyness subsides and I can write and rewrite until what’s written feels right and can be posted.

In considering this revolution in our understanding of the cosmos one realization that I’ve had is the fact that this has been the only major scientific revolution in my lifetime, so it is a new experience for me and, in fact, for anyone who is concerned with it. The major revolution of our times, the quantum revolution, began to be resolved in 1925 and by the time I was born in 1929 the revolution was well on the way to completion. At that time the neutron hadn’t been discovered nor the positron (both discovered in 1932), but by the time I took chemistry in high school during the 1945-46 academic year the existence of these was well established, the neutron discovery leading to the atomic bomb, which had ended World War II just before that school term had begun. By the time I was trying to do physics during the early 1970’s, its cutting edge had moved on to understanding the elementary particles and “resonances” as they were experimentally discovered by increasingly energetic particle accelerators. I had a fairly good idea of what was going on as I understood how various representations of group SU3 made patterns which fit the new discoveries. In the early 70’s there were many puzzles, but nothing that called fundamental scientific realities into question. By the early 2020’s it had been 40 years or so since the “standard model” of particle physics came into being, and during those 40 years, its predictions were confirmed time and again with little hint of revolution on the horizon. In cosmology and astrophysics there were the puzzles of dark matter and dark energy, but no discoveries that were helpful in solving these puzzles. The physics and astronomy community was awaiting and hoping for a scientific revolution. Now, finally and suddenly, it is happening.

Since I have no access to any scientific journals (and likely wouldn’t understand their contents even if I did) my information about the new revolution comes from winnowing through writings on YouTube searching for gems among all the vague sensationalism. In addition, I can search the internet in the hopes of finding reliable sources and learning about subjects which are relevant for understanding what is happening.

Let me begin to make sense of this revolution by considering the cosmic microwave background radiation (CMB). This radiation has been well studied and it is difficult to find any weak links in its story. The radiation begins as high temperature black body radiation and as the universe expands, the radiation keeps the characteristic spectrum of black body radiation at an ever lowering temperature which stands today at 2.7 degrees above absolute zero. A beginning temperature for the radiation can be calculated by considering a typical ionization energy of atoms. A piece of well known background knowledge in atomic physics is that the ionization energy needed to free hydrogen’s single electron from its nucleus is 13.6 electron volts. If protons and electrons are in an environment where the average kinetic energy of particle motion is above this value, they are constantly bombarded by particles having more energy than needed to keep them apart: hydrogen atoms cannot exist.

In the latter part of the 19th century Ludwig Boltzmann discovered the remarkable connection between the average kinetic energy E of molecular motion and temperature T as measured by thermometers. A crude statement of his law is E = kT, the constant k being Boltzmann’s constant. Expressed in electron volts per degree Kelvin it has a value of 8.617 x 10¯⁵. To find the temperature below which hydrogen atoms can exist, you merely need to reach for your cell phone and its calculator. Enter 13.6, the divide symbol, and then 8.62. Pressing “=” gives 1.58 after rounding. Now move the decimal point 5 places to the right and get 158,000 degrees Kelvin or Celsius. (At this temperature the 273 degrees between the two is inconsequential.)

Above this temperature of around 160,000 degrees only the constituents of atoms exist in a plasma which bounces light around and is opaque. After the expansion of the universe lowers the temperature below this value, atoms form (mostly hydrogen) and space becomes transparent to the black body radiation of the former plasma and to any other radiating bodies which might be present. I’ve mentioned already in the first post about this revolution what astronomers expected; namely the very beginnings of galaxy formation, rather than well developed galaxies and primordial black holes mentioned in the last paragraph of the previous post. The latter are truly interesting because they suggest that the black holes in the center of galaxies, came about before the galaxies actually formed. The presence of black holes would speed up galaxy formation, but certainly not to the extent that JWST observed.

There are two obvious ways to avoid the dilemma posed by the impossible existence of mature galaxies and primeval black holes in an era when they shouldn’t exist. The first, and seemingly the less radical, is to push back the big bang by several billion years and assume that the early rapid inflation expansion didn’t occur, allowing time for developments before the cooling to energies allowing atom formation with its resulting transparency. If a tremendous amount of dark matter particles were created in the primeval explosion, these could cluster and form black holes. If energies remained in the mev range over a billions of years, there would be time for complex nuclei to form, much in the way we believe they form in stars. For this scenario to occur, the expansion rate of the universe would need to be slow enough to delay cooling. Since the recent conclusion that the Hubble constant for the universe expansion rate, isn’t a constant at all, but a field with different values throughout the universe, the idea of an expansion at a slow rate in the early days of the universe isn’t impossible. Let us call this scenario (with apologies to Texas) the Lone Star Universe.

A second way our of the dilemma is to assume that our universe didn’t arise our of nothingness, but issued instead, from the collapse of a predecessor universe into a “big crunch” with rebound. This scenario postpones the account of how a universe could arise out of nothingness to a day when we have a deeper understanding of physics. With this idea we avoid the idea of a singularity, always a troubling notion in physics, imagining instead a condensation of the prior universe only to the extent that its matter would be raised above a temperature where atomic nuclei would disintegrate into elementary particles including many we have not found yet. As this proto universe rebounds and expands, its elementary particles would decay into stable ones, including perhaps axions of dark matter. An interesting question concerns the fate of the massive black holes that formerly existed in the center of the old universe’s galaxies. Assuming that black holes are already compressed as much as possible, there could be no force which could disrupt them. A problem arises because if the volume of our universe in its early days is limited, billions of black holes from the previous universe would likely collide and coalesce forming galaxy centers larger that those we observe. If we can sweep this problem under a rug, we have a ready explanation of the primeval black holes and well formed galaxies that JWST has observed.

Of course, both scenarios outlined above are quite speculative. These days as the fact of a revolution is becoming more and more accepted, it is the hay day of the experimentalist making astronomical observations, finding the hard evidence that will ultimately lead to a new picture of reality for our universe. Much of this work now revolves around the expansion rate of the universe, the Hubble “no longer constant”. Since much of of our current picture assumes that this rate of expansion is everywhere the same, the shattering of this assumption is finally making it clear that we really are in the midst of a scientific revolution quite apart from the findings of the James Webb Space Telescope. I’ll mow bring this post to a conclusion and continue to search for interesting findings which will occur in the future. Back to Top

A Scientific Revolution

Crisis in fundamental science is disconcerting because it shakes up and disintegrates the very foundation of what we take to be reality. In Kuhn’s Structure of Scientific Revolutions while various revolutions are closely analyzed, we, as readers, know how these turned out because they were historic with a known future. Experiencing an actual revolution, not knowing what the future will bring, is similar to a Zen experience in which the foundations of everyday reality are ripped apart. We are, in a sense, left floating in space in an unknown galaxy in which there are no directions, no up-and-downs, no supports. One can learn to welcome this sort of experience because one knows that we humans, for all our factual knowledge, are ignorant of an actual fundamental reality; and experiencing this ignorance is a signpost on the way to enlightenment, assuming such exists.

In cosmology our reality until this year was that the universe had an age of around 13.8 billion years, beginning with a “big bang” which created the universe including its space and time out of nothingness. See the post Weird Stuff: Cosmology, etc. for the story of how this picture came about. As of now (Mid-2025) this picture must be abandoned and things are about to become really weird.. It is too soon to know what will replace the “big bang” theory. Fortunately, what we know about the universe has not been completely discredited: There are still stars, galaxies, neutron stars, black holes, supernovas and the rest of the amazing entities that we observe with optical telescopes on earth and the Hubble telescope in space. General Relativity still seems to predict accurately though, these days, it is far from being taken for granted. What’s new is that data is coming in from the James Webb space telescope. This miracle instrument was a huge dare which has panned out. (When a scientific project screws up, there’s a lot of publicity and adverse comment. When a daring project which has every expectation of failure works out, it gets the “ho-hum” treatment at least by the general public.) This JWST (James Webb Space Telescope) was designed to be revolutionary and has lived up to its goal. For a complete detailed description, one should consult Wikipedia. The telescope has a mirror too large to be launched in one piece by our present rockets. Instead, over the years since its launch on Christmas day, 2021, the mirror was unfolded and then assembled to an unholy precision out in space from 18 hexagonal pieces. It sits at a distance further out than the moon, circling around what is called a Lagrange point where gravity from the sun, earth, and moon balance out. The telescope became operational in early 2024 and has now been accumulating data for over a year. The telescope is sensitive to long-wave infrared, in a range running from a visible 600 nanometer reddish-orange to a mid-infrared at 28,500 nm. This range allows the telescope to see back to a realm where objects are red-shifted beyond the limits of human vision; objects existing in what we supposed were the early times in the universe after its temperature cooled to where it became transparent. Infrared is heat radiation. The telescope must accordingly be cooled to a temperature below 50 Kelvin (-223 degrees Celsius) so its own thermal radiation won’t wipe out the signal it is detecting.

Cosmologists and astronomers were exited to see what the new JWST telescope would reveal in the eight-hundred million year gap between the time when the universe became transparent 200 million years after the “Big Bang” and the time about 1000 miillion years after the bang (a billion years) that the Hubble telescope could see back to. The prevailing picture at the time around 2023 before JWST became active was that as hydrogen, helium, and a few lithium atoms formed, they would clump under gravity’s influence and would become the first stars as the pressure and temperature at their centers became sufficient to ignite a fusion reaction. The resulting stars, in turn, would cluster into blobs which would, after a 5 or 6 billion year process, form the galaxies that Hubble had been able to detect. The expectation was that there wouldn’t be all that much to detect in the gap.

Instead, the first startling thing JWST found were many huge, fully formed and structured galaxies. By measuring their red shift their ages were found to be only 3 to 5 or 6 hundred million years after the “Big Bang”, well within the gap. That they were really galaxies was confirmed by detecting the spectral lines of hydrogen. Galaxies which would take 5 or 6 billion years to form were found within a few hundred millions years of the purported “Big Bang”. Even more startling were primeval black holes such as exist at the center of galaxies. However, the star were missing and the black holes unclothed. Something was drastically wrong with the enormous amount of work which had established modern cosmology. And this was only the beginning. The revolution was under way.

I’ll bring this piece to an end and post it. I’ll have much to write about in the future. Back to Top

Supreme Fiction

Between 1993 and 2009 Microsoft published a multimedia Encyclopedia called Encarta which could be accessed from various early versions of Windows. During the mid 90’s while not actually programming I enjoyed computer games and read extensively in Encarta. Practically everything I read has vanished from my memory except for one striking prose essay by Wallace Stevens in which he mused about the idea of “supreme fiction.” Stevens must have written this at about the same time that he was composing his poetic masterpiece, Notes Toward a Supreme Fiction, published in 1942. In an earlier post, Into the Morass, Part I, I quoted some lines from the poem, lines which almost always lead me into an epiphany as they have, just now as I reread the post. (link) At the time of that post I mentioned that Stevens thought deeply about the idea of a supreme fiction and that I would myself consider this idea at a later time. Of course, at the time of the earlier post, October, 2016, I was recollecting the Stevens essay which would be a basis for any further thoughts on my part. But now that the time has come for my thoughts, the Stevens essay is missing and I’m on my own except for the poem and my imagination.

It seems that by 2009 Encarta was overwhelmed by the popularity and the sheer mass of articles in Wikipedia, the online encyclopedia which revolutionizes research in this day and age. Unfortunately, when Encarta was put to death, the Stevens essay did not make a transition to Wikipedia. I unsuccessfully searched the internet for the essay and then wondered if archaeological remnants of Encarta could be dug up and rendered meaningful. I found that Encarta, if it exists at all, cannot be accessed by Windows 10 to say nothing about Apple’s iOS. Resurrection is doubtless possible, but I no longer have either the time, temper, energy, will or ability for such an enterprise. I searched Amazon and found a book of Wallace Stevens essays, which I bought. The crucial essay is not there and there is nothing about fiction, supreme or otherwise. Literary critics have made the lame suggestion that poetry at large is the supreme fiction Stevens is driving towards. However, the title of the poem, “Notes Toward …” indicates to me that the actual images in the lines of the poem itself point the way to a wordless ecstasy of meaning for the phrase.

For me, reasons for considering “supreme fiction” go beyond the ideas of Wallace Stevens. The attraction is in the craziness of the locution itself, a Zen like phrase which comes out of the West and accordingly, in my mind anyway, allows a different vista of freedom from the milieu of the East.

”Supreme” and “fiction” jar against each other. Although they are certainly not exact opposites, they seem to have an Aristotelian kind of opposition allowing no softening middle between them. If something is “Supreme”, doesn’t that ultimate pinnacle argue for its “reality”. However, I would suggest that being “fiction” exalts the “supreme” beyond any possible mundane reality into a reality that is transcendent.

In the midst of the unbounded expanse of time in which our awareness exists, each day we have a “today” which we attempt to pinpoint in that unimaginable vastness by a formula such as July 29, 2024. On that today I hiked west on the Park Meadow trail from its trailhead on the Three Creeks road south of Sisters, Oregon. The forest along this trail was destroyed by the Pole Creek fire a few years back. Around two and a half miles in I came to a runnel of water called Snow Creek. Being alone and 95, I walked up and down the creek seeking a safe crossing, but found no passage I would risk in my lackadaisical mood. On the way back, about a mile from the trailhead, there was an area where, amid the devastation, the fire left a few clusters of trees, “swags of pines”, as Stevens puts it, mostly Lodgepole. I stopped for a rest and noticed that the tree next to me had the five needle packets of a rare, surviving White Bark Pine. The tree was tall and healthy: a beautiful specimen. I think that this tree will have to be the supreme fiction for today. Perhaps I’ll find another tomorrow. Back to Top

Time and Tide I

What is the significance, if any, of being briefly alive and aware in the early twenty-first century?

The immediate focus of this question is on our time right now; but in imagining this significance, it is essential to place ourselves in the context of history, beginning with the creation 13.8 billion years ago, out of an unknown nothingness, something we call our universe and within it a ticking clock embodying time and thus the possibility of history, the trace time leaves in space. This history has many aspects: the early physical aspect involving the creation of forces, fields, and particles; the coalescing of particles into simple atoms as the primordial plasma cools and transparency ensues; the accumulation of hydrogen, helium and a trace of lithium into stars. Following is the area of cosmology, the story of star generations with their life and supernova deaths creating complex atoms beyond the first three kinds and their galaxies revolving around massive black holes. Then comes geology, considering the ages of our planet with the creation of life, stratigraphy, continental drift, and various eras as life becomes complex and finally the accident of early forms of pre-humans. Then anthropology studies the evidence left by early forms of humanity until ultimately writing develops and traditional history begins.

Traditional history has countless themes, all possible subjects of future consideration: the wars, the technology, the growth of culture, the empires, the human urge to create art and music, the understanding of how it was in the past; and finally, that we are here looking back at all of this history, knowing the wonder of the whole story, but knowing also that we are still fundamentally animals with our emotions controlling our formidable intellects. Perhaps the significance of our time is that the universe could throw up a being whose very existence could be, for us, anyway, an event of significance in the universe.

As a first example of our human story and its possible significance I’ll consider how we humans have used our inventive brains to increase the carrying capacity of our environment to the extent that the environment itself becomes endangered by our very numbers and activities. In considering how any animal’s population fluctuates in response to changes in the ecosystem in which it lives one encounters many simplified stories of overpopulation, followed by a crash, followed by a recovery and a new overpopulation. Such life stories of a single species are actually the exception, however. And even in a so-called typical case one is apt to find that there is a complexity within the apparently simple story. The bio-sciences are not as straightforward as the physical sciences I’m more accustomed to, which is, in fact, to me one of their main attractions. Thus, it is not surprising that the story of human population growth is not simple. Even a broad-brush narrative such as I am giving here, has its somewhat paradoxical wrinkles. I’ll start this account by considering an interesting book. In this part of hoalablog I will often make a practice of bringing up and talking about books I’ve read, not so much reviewing them as using them as a launching pad for discussion or as a source of relevant ideas.

When I first began to write this piece, I remembered reading this book, but I had completely forgotten the name of the author or the title of the book. The book concerned the story of the early industrial revolution, invention, and the steam engine which was its centerpiece. It was a readable book and I knew it would be relevant. In a “what-the-hell” moment I googled “industrial revolution”, in what seemed to me a futile quest. To my surprise one of Google’s featured books was The Most Powerful Idea in the World: A Story of Steam, Industry and Invention by William Rosen. I read a review or two in Amazon, and upon dipping into the book via Amazon’s “look inside” feature, it became clear that this was indeed the book I was trying to remember. Idle curiosity then led me to figure out when I had read it. I checked out the Bend Library and it wasn’t there. I didn’t own it and it wasn’t in my Kindle library so I must have found it in the Eugene library and read it before 2013, the year we moved to Bend. The book was published in 2010, so this thought is plausible.

The main theme of Rosen’s book is the story of how humanity escaped what has been called “the Malthusian Trap”. This phrase refers to the theory expounded in Robert Malthus’s influential book, An Essay on the Principle of Population, published in 1798. Malthus’s idea is that population growth is inherently exponential while food supplies will only increase linearly. The result is that any increase in food supply is overwhelmed by population growth which means that a large portion of the population will always be on the brink of starvation. (An example of exponential growth is a doubling series – 1, 2, 4, 8, 16, 32, … while the corresponding linear series is – 0, 1, 2, 3, 4, 5, … .) I remember learning about Malthus as I sloughed through Stanford University’s famous course A History of Western Civilization¹ in the academic year 1947- 48. At that time, I was lazy and bored by history so I skipped most of the reading and simply took notes and paid close attention in class to the young, charismatic professor, managing to pass the course and come away with some knowledge. Besides Plato’s Phaedo, one selection I did read was an excerpt from Malthus’s book. His idea was new to me and I was impressed by his logic.

Going back to the early history of homo sapiens, starting some 2 to 3 hundred thousand years ago I suspect that Malthus’s ideas don’t apply to our situation as hunter-gatherers during that era. In a hunter-gatherer society the population is kept under control, more or less, in the same manner as for any other animal. We have abundance and starvation, war with other tribes and always accidents and disease, keeping a largely static population and an undisturbed environment. We did cause a few environmental problems during this era; notably the extinction of some megafauna, but though this is probably regrettable, these extinctions posed no massive environmental threat. With the advent of agriculture some 6 or 7 thousand years ago we gained control of our food supply and fell into a Malthusian trap. Rosen estimates that in the 7600 years between 6000 B.C and 1600 A.D world population increased from 5 to 500 million, with a doubling every thousand years or so. Although this population increase is large in absolute terms, the annual fractional increase is only about 0.000606. (I won’t get into the details of how one comes up with that number. God forbid that one brings serious math into history; or, for that matter, history into physics, chemistry or engineering. However, see a brief appendix at the end of this piece for details.) During this era of agriculture being the dominant economic activity, there was a food supply that could support a slowly increasing population. Although life was miserable for most people as per Malthus, a surplus of food, unevenly distributed, gave rise to occupations besides farming. Over these thousands of years, the food surplus allowed technology and culture to grow. Finally, in the west the scientific revolution occurred during the late 16th century onwards. However, this revolution did not allow us to escape the Malthus dictum. Life for most remained marginal and precarious.

Rosen’s Most Powerful Idea goes into the history of the steam engine in great detail telling of Thomas Newcomen’s first commercially successful engine of 1712 used for pumping water from coal mines, followed by decades of incremental improvements until in 1764 James Watt made a huge breakthrough which brought on the industrial revolution’s full flower. The engine was used in factories and most notably in steam locomotives, enabling railways to spread in England, the United States, and the Continent. Still later in the century steam largely replaced sail on ocean vessels. Rosen considers that the “most powerful idea” of the times during which the steam engine was developed and applied, was the patent system which democratized invention, adopted in England during the mid-1700’s. With the patent system both the incentive and the mechanism were in place for anyone to reap the rewards of invention. According to Rosen it was the flourishing of invention which lay behind the industrial revolution and ultimately expanded the economy, breaking us out of the Malthusian trap.

It should be noted that this breaking of the trap was not immediate. In the early years of the 1800’s as textile factories replaced skilled workers with the less skilled who could produce more under miserable working conditions with lower wages, the Luddite movement arose. Later, after parliament passed a reform act in 1832 which did not extend voting rights to those without property, the chartist movement came into being. Nevertheless, as the nineteenth century wore on, a tremendous number of new niches appeared in the ecology of the economy and a significant middle class arose in Europe and America. Between around 1860 to 1940 while the population grew rapidly, this growth did not seriously impact the environment. I can recall the life my parents lived in the late 1930s, a time, at least in Hawaii, when a peak was reached in enlightened employment practices. My Dad went to work as an accountant in the morning at 8 am. He had a half-hour off for lunch and finished the day at 4 pm, giving him ample time to swim at Waikiki for an hour or so before dinner with his wife and kids. He and my mother could afford to build two homes before the war came to us on Dec. 7, 1941. Around 1944 in school, I learned that the world population was now 2 billion, so there had been a substantial increase during the 344 years since1600 when the population was around 500 million.

Of course, after the war there was a population explosion and by now in 2024 there are numerous worrisome environmental impacts. We can summarize human population growth in a “big picture” way by saying that after the agricultural revolution, human numbers grew slowly with numerous ups and downs for 7000 years or so, subject to Malthus’s Law. The histories of this period neglect the miserable condition of the great mass of humanity, concentrating on the wars, the culture, and the innovations of a small fraction. With the industrial revolution, at least in the West, there was a breakout from the Malthusian Trap, which allowed a better life for many within a rapidly increasing population, driven by invention, but without the danger of the imminent extinction of humanity if not all of life. After World War II, the population grew frightfully fast with an increasingly better life for those in “first world” countries; but with the invention of the atomic bomb and the sheer numbers of people threatening the environment we now do face threats of extinction.

Some numbers substantiate the story above. I’ve already pointed out that during the agricultural era the world population increased from 5 to 500 million with an average doubling time of 1000 years and a fractional growth rate of 0.000606 per year. From 1600 to 1944 the world population increased from 500 million to 2 billion. Population doubled twice in those 344 years, giving a doubling time of 172 years and an annual fractional rate of increase of 0.00402. Finally, in the 80 years since 1944, population has again doubled twice, reaching 8 billion in 2023, giving a doubling time of 40 years and an annual rate of 0.017. To obtain an annual percent increase, commonly found in contemporary studies of population growth, one simply multiplies these annual fractional rates by 100.

Fortunately, the situation is not quite as dire as the last figures would suggest. It seems that one assumption made by Malthus is incorrect: as people’s affluence increases in a modern society, the extra wealth does not result in population growth. Instead, the cost of raising children goes up, the child mortality rate goes down, and birth control becomes available. There is also in many areas the possibility of abortion. As a result, the rate of population growth has gone negative in many first world countries and even in many third world countries the rate, though positive, is going down. The situation since WWII has been extensively considered and one can find many results on the internet. For example, the link

https://www.macrotrends.net/global-metrics/countries/WLD/world/population-growth-rate

has graphs of world population and the percentage growth rate from 1950 to 2024 and projections into the future. According to the year-by-year growth rate, the highest growth of 2.2% occurred in 1963, while in 1991 the decreasing rate dropped below the average, 1.7%, I calculated. The current growth rate, according to this study, is 0.9%.

Projections into the future are, of course, controversial. This particular estimate is about average for the few studies I’ve looked at. It projects the growth rate for the world to go negative in 2086 with a maximum world population of 10.43 billion at that time.

This study and others however, neglect the numerous threats our current times provide. A recent New Yorker article (June 10, 2024) examines a University of Chicago course entitled “Are we Doomed?”, which considers various scenarios of disaster. After many guest lectures and discussions, students in the course considered that the most serious threat would be the break-out of nuclear war. Climate change they concluded had the main effect of increasing the risk of nuclear war. There are many other threats. I’ve just read an interesting book, The Blue Machine: How the Ocean Works, by Helen Czerski, a physicist turned oceanographer. Most of the book simply considers the workings of the “blue machine” as far as we know them; but the last chapter considers the threats oceans face, using the knowledge explored earlier. Collapse of ocean life support systems, however, is only one of many environmental threats. I could doubtless write an entire piece about threats to our existence using Czerski’s book as a touchstone as well as another favorite, The Ministry for the Future by Kim Stanley Robinson. Perhaps I will.

It seems clear to me that the story of human world population growth, which I’ve told here, is indeed one matter of significance for an aware person of the early twenty-first century.

Appendix – Calculating Population Growth Rates

The basic equation for annual population growth is

P_{next year} = (1 + r) times P_{this year},

Where the P’s are population numbers and r is the rate of annual increase per year.

This equation has to be applied hundreds or thousands of years at a time when one considers population growth over long periods of time. The calculation is similar to that of investing when one wants to know the compound interest rate, knowing what one’s principal amount is at the beginning and end of a time period. With interest, one compounds daily and uses an Excel spread sheet with its automated repeat feature. With the population equation above, the built-in compounding time is one year.

Fortunately, there is a simple highly accurate approximation in any case of compound growth; namely, the exponential growth equation

P_{time t}= P_{time 0} e^rt

Where P is the population, r is the rate, t is the time period and e the base of nature logarithms with a value of 2.718… . Note that the quantity rt is dimensionless, r being a rate and t being a time; e.g. a rate is a fraction per year and t is a time in years. One can, in fact argue that the exponential growth rate equation defines r rather than the equation at the top.

To use the growth equation, make an algebraic rearrangement and then take the natural logarithm, ln, of both sides, obtaining

rt = ln (P_t/ P_{t zero})

In our first calculation the ratio of the P’s is 100 with a natural log of 4.605. (In one’s calculator turn it sideways to bring up the ln function.) Enter 100 and tap ln. Then divide by 7600, the number of years to get an r of 0.000606. Back to Top

See Post History I ↩︎

More Thoughts I

August 17, 2023 marked two years since the last post on Hoalablog. The blog, I thought, had come to an end with the Ramblings I post. Ramblings II is somewhat lightweight but perhaps adds some insight. Although I have posted nothing since August 17, 2021, my spiritual journey continues, as it will, until time does in awareness. The blog has been kept alive and I have intentions of editing it, perhaps changing the order of posts trying for more coherence, and perhaps writing more, of which this might be a first installment. As is obvious to anyone who pokes around in this blog, the main impetus for writing has been my conviction that western thought badly needs a deep, absolute, underlying functional spirituality, atheistic and lacking any doctrines whatsoever. In many of the previous posts I have looked into Zen Buddhism as such and have pointed out that it could fulfill this role, silently informing all of Western thought and culture. Recently I have realized that I could do better in coming at what I’m proposing by adopting, as much as is possible, a “pure” Western point of view, ignoring as much as possible the Eastern ideas and traditions which lay behind Zen. Of course, there is a question of what I really mean about a Western or an Eastern or a what-have-you point of view in these times where there is basically one vast world culture. This culture, does however, have different flavors, one of which may be labeled Western as the predominating and historic culture of Europe and the American continents.

This mainstream Western thought and culture is vast and intricate. It stretches from cosmology and mathematics, physics, chemistry and the practical sciences of engineering, medicine, psychology, sociology, philosophy and economics; to arts such as architecture, writing, painting, sculpture, music, and to various sports. However, beyond the local epiphanies that these might engender there is a spiritual vacuum. It seems that as we have discarded God and religion, we have also discredited the very idea of a deep spiritual underpinning. We have created an empty cathedral. However, when I posed the idea of a Zen flavoring for Western thought to my good friend Roger Shepard, he was appalled that I would entertain any such idea. Roger is with us no more but he is still a rather well-known experimental psychologist, formerly a professor at Stanford University. He was also a talented artist and musical composer. In his last years he became immersed in the puzzles of human consciousness and he pursued a mathematical understanding of quantum mechanics and its mysteries in order to understand if it might possibly throw some light on consciousness. (He was somewhat skeptical that I had made any progress whatever in Quantum Measurement theory). As a scientist Roger was hard-core and the very idea of any spirituality seemed to him a hark back to religious ideas inevitably akin to a mindless distraction. Such would, in his mind, be a regression having no place whatever in science, philosophy or serious Western thought. I bring up Roger and his attitude towards spirituality because I believe that this attitude is widely shared among those who I think of as an audience for this blog.

I share Roger’s attitude towards flaky ideas in science or elsewhere, but believe that meaningful spirituality can be a part of human reality. As a beginning to what I have to say I’d like to move beyond the dichotomy of God vs. Atheism with its excluded middle. This dichotomy inhabits a limited framework which deserves total shattering. Beyond the shattered shards is the great emptiness and I want to see all of us living beyond even the great emptiness in a realm suffused with meaning. This sense of meaning lacks any verbal or material expression. For such we turn to the cathedral itself hoping to find it filled as expressions of Western thought and culture connect to that great wordless glory beyond. Perhaps “glory” is not a good word to use. I’m reminded of the time while living in Alabama that our group of friends came into possession of a Christian fundamentalist document about religious experiences. The saying that stuck in my mind was, “I’m under the spout where the glory comes out.” We loved the Kitschy aspects of this saying; however, if one ignores the Kitsch, one notes that the “spout” can hardly be taken for the Deity and the saying must be regarded as meaningless metaphor: The “glory” flows out of nowhere. Nonetheless, on further consideration I think the word is probably tainted so I will avoid it as much as I’m able in referring to an ultimate experience.

Roger Shepard’s convictions about spirituality remind me that there is an ongoing conflict between science and common culture. Many scientists fear that the entire basis of rationality and empirical thought will give way to a superstitious and feckless society which wanders into chaos and war. On the other side, many thoughtful people think that science, for all its progress and practicality, lacks a soul; that it fails to bring us comfort in the face of a mortality subject to the capricious flows of chance, ignorance and evil in our world. In a way I am wading into the center of this conflict and I am exposed to attack from both sides. However, if I go, for a moment, into attack mode myself, I can point out that, on the one hand, there exists a superstition-free spirituality which poses no threat to rationality or science; and, on the other, science is deep and meaningful, that it demands creativity, which is always a struggle and that scientists, like artists, do better if they can slip into the “zone”, whether realized or not. Science is indeed, at least incipiently, spiritual, though many scientists would deny it.

It’s clear to me that our culture has the grounds for germinating a spirituality not simply in science (which indeed may be a hard nut to crack) but in our society at large and in many of the various strands of Western culture which I detailed above. The key, as I see it, is the idea and experience of “being in the zone”, a Western trope for various ineffable Zen like experiences. So far, the expression is mostly used in athletic endeavors such as football and surfing. In football it manifests in the competition between ends on offense and the secondary on defense. The seemingly impossible feats which occur when a quarterback throws a pass make the game worth watching in spite of incessant interruptions of commercials, timeouts, penalties, two-minute warnings and other breaks in the game, to say nothing about twinges of conscience which occur from knowing of its inevitable concussions and other life-shortening injuries it engenders.

The feats which occur in surfing are equally incredible. On Oahu’s North Shore a famous winter break is the Pipeline, originally called Bonsai Beach after the Japanese suicide charges of World War II. When I was growing up, I’d heard of it, but it had never been surfed. The reason it seemed impossible and dangerous was its perfect tube breaking with lethal force into three feet of water over a jumbled coral reef. First surfed in 1961, it was indeed the scene of many serious injuries and fatalities. Gerry Lopez, a young surfer born in 1948 in Honolulu, became the first master rider of the Pipeline, riding its tube with a relaxed nonchalance. He was known as Mr. Pipeline. In his book, Surf Is Where You Find It, he mentions that when surfing pipeline, it is a good idea to be in the zone before dropping in. Curiously enough, Gerry now lives in the town where I live and recently gave a talk promoting a new edition of his book. I, along with my wife and friends, were fortunate enough to attend. Gerry spoke about the importance of the Hawaiian aloha spirit and mentioned also that he had spent years in Yoga practice and meditation. Other surfers seldom speak of being in the zone, but are masters at riding waves three or four times as large as those at Pipeline. These waves don’t break on shallow coral reefs so are possibly not as dangerous as pipeline, but their sheer power, capable of snapping a femur like a matchstick, makes surfing them unthinkable for anyone who has experienced the power of smaller waves.

Besides sports I wonder whether or not the experience of being in the zone has spread to other activities which offer instances of seemingly superhuman performances. What comes to mind are the number of outstanding piano players, several of whom have grown up in China, Japan and Korea where one might expect a lurking tradition of transcendental Zen mastery. Among many whose incredible performances one finds on YouTube, I will mention two: Yuja Wang and Yunchan Lim. Yuja Wang (see Wikipedia), was born in Beijing in 1987. She studied piano in China starting at age 6. She came to the US at age 15 and studied at the Curtis Institute of Music, graduating in 2008. Yuchan Lim was born and studied in South Korea, which has become a hotbed of Western classical music. In 2022, at age 18, he won the Van Cliburn Piano Competition, and since then has embarked on a sensational career. Both of these pianists have incredible technical abilities, but, in addition, have the ability to enter into the soul of whatever they play. Yunchan’s sensational playing of Liszt etudes and Rachmaninov’s 3^rd piano concerto was doubtless instrumental in his winning the Cliburn. However, it was his performance of Mozart’s piano concerto 22 which carried me away. Yuja Wang in concert flaunts her femininity as if to say, “Look here! It’s a beautiful woman who is giving this transcendental performance.”

I wonder if, in fact, “being in the zone” is more common in the West than one would suspect and that it indeed constitutes a slow tide filling the cathedral. I like the “zone” expression because it does not have a sharp meaning, but is, instead rather muddy to the point of meaninglessness. I’ll finish this post by pointing out the dangers of language in the context of (I almost said “spiritual” growth). In reading over this post, I notice that the words “spiritual” and “spirituality” frequently occur. In fact, these like “glory” are tainted words. I think that Roger Shepard has a point: the word “spiritual” inevitably suggests mystical ideas which can lead to concrete religious ideas which, in turn, inevitably lead to grasping and fanaticism. What all of this means is that it is impossible to talk in conventional language about what I am proposing without using “tainted” words. I hope that people reading or rereading this post will keep in mind that it is meaningless unless they find their “zone”.

Add on: April 29, 2024

It is now, as I begin to write, 11:30 A.M. on an April Wednesday in the year 2024. At the moment I have nothing more to say about Zen, Western or otherwise, but I still want to continue writing in Hoalablog so I need a new, overarching, unifying theme, worthy of exploration, which theme might encompass anything I want to say, whether insightful or mundane. Actually, within the last month or two I’ve come up with such a theme and on our recent trip across the country to view the 2024 eclipse from a friend’s backyard in St. Albans, Vermont, I had plenty of time to ruminate on its suitability and to realize that it is seemingly what’s needed. This theme, phrased as a question, is:

What is the significance, if any, of being briefly alive and aware in the early twenty-first century?

Our present knowledge or speculation about the stretch of time our moment occupies is that it begins some 13.8 billion years ago with the creation of a ticking clock, so to speak; and continues indefinitely into an infinite future. Of course, the clock is simply a part of an entire universe in which happenings play out; one of which is the birth and growing up of each of us. Nevertheless I like the emphasis on the question being that of time. So, onto the next theme! Back to Top

Ramblings II

In the last post I inadvertently used the epithet “IT” for the name of an imagined new slant on a Zen grounded in Western Culture; or, perhaps not just Western Culture but the complex enriched, modern World Culture which has itself grown out of Western Culture. This new embodiment needs a name. “IT” won’t do, as it just doesn’t have the proper ring, cachet or heft of existing names, Dhyana, Ch’an, Zen. Dhyana, beginning as simply a name for meditation can now be taken as the name of the “almost Zen” of Mahayana Buddhism as it grew under the tutelage of Nagarjuna and his kin. Ch’an is the Chinese name while Zen is the Japanese pronunciation of Ch’an which became the label for the Japanese embodiment. Finding a good label is tough; and I don’t feel that I have the talent for it. Consider the physicist Murray Gell-Mann, who did have that talent. Gell-Mann came up with the name quark as a label for simple particles within the various nucleons, mesons, and resonances of the strong interaction. Independently of Gell-Mann the physicist George Zweig had had the same daring idea, that there were actual “real material” particles belonging to the fundamental triplet representation of the SU3 group. Zweig named his particles “aces”, while Gell-Mann preferred “kworks”. Fooling around in Joyce’s Finnegan’s Wake, Gell-Mann found the phrase “three quarks for Muster Mark” on page 383. Thinking that one of Joyce’s meanings might be a bar order, “three quarts for Mister Mork” Gell-Mann proposed “quark” pronounced “kwork” as a tortured rendition of “quart”. The page 383 is significant since the next higher representation of SU3 has 8 members which are even more “real” than the quarks because they can exist on the “outside” as hadrons and make tracks in a bubble chamber. The “eight-fold way” has been taken over from Buddhism for the SU3 interpretation in which there are 8 particles which can be “seen”. An older, discarded 3-fold Sakata model used the hadrons proton, neutron and Lambda as a fundamental triplet.

Although the likelihood that I have Gell-Mann’s talent for labelling is vanishingly small, I really must give it a try; so, I will propose the Hawaiian pidgin Da Kine. This expression works rather well because it is a corruption of the English “the kind”, but in Pidgin the meaning has changed in that da kine’s reference is deliberately vague or ambiguous. Often the phrase is used when one does not feel like being specific. When I now use “da kine”, maybe it refers to this new kind of Western religiosity, or maybe it’s merely a meaningless redundancy. It could refer to anything. An example of the flavor I’m talking about occurs in William Finnegan’s wonderful, Pulitzer-prize winning memoir, Barbarian Days. The author and his buddy, Bryan, in a vain attempt to keep secret their discovery of a world class surfing spot, Tavarua, in Fiji, never say its name, but refer to it as “da kine”. A problem with da kine is, of course, that is a very common expression in Hawaii and, in fact, there is a company with the name Da Kine. One faces a possible copyright infringement complaint; however, if “Wind Surfer” and “Kleenex” couldn’t defend their copyrights, I doubt that “Da Kine” can either. In any case one might well end up with an even better name than Da Kine.

It is pretty clear to me that we do need a new name. Consider the existing names Dhyana, Ch’an, and Zen. Dhyana has a lofty, abstract, almost philosophical connotation of the jewel in the lotus, while in Chinese culture there is the wonderful idea of taking serious things lightly and light things seriously. This particular sensibility, it seems to me, is missing in Japanese culture; not that there isn’t a wonderful sense of humor in certain Japanese productions. I remember in the late fall of 1974 when my first marriage had dissolved, I was quite distraught, and visited my parents in Honolulu. They lived on Kulamanu Place right around the corner from where William Finnegan lived on his first Hawaiian visit, not that that has any relevance. What does have relevance is that Hawaiian television in those days featured Japanese science fiction cartoons. These were deliberately and deliciously corny, with a wonderful sense of humor. I still remember one in which the villain was named “Blue Electric Eel”. He could take on a human form and when he was in a crowd about to perpetrate some villainy, the scene would move down and show his blue suede shoes, just before all hell broke loose with, if I remember, many sparks and short circuits. With world western culture there are so many strands that I won’t pick out any particular one. The whole culture is da kine. What is clear that this new world culture needs a new word for its penumbra and its specifics, and I’m proposing da kine.

Another, more concrete theme of da kine sensibility is that it originated as an outgrowth of traditional Buddhism. I wonder what sort of novel insight Buddhist thought could confer on Western history, culture, philosophy and religion, to say nothing about contemporary affairs. Going beyond any historical distinctions in Buddhism such as its split into Theravada and Mahayana forms, I think that the idea of “attachment” and a goal of its relaxation or lessening, is curiously underemphasized in our culture. I remember an incident that occurred some years ago when for a time I attended a “Bohm dialogue” group, dedicated to the idea of a selfless descent into creating and following interesting threads of conversion without an agenda, pretty much identical to an eighteenth-century French salon, but perhaps with a higher expectation of generating deep new insights. During a discussion of a topic, now forgotten, one person brought up the idea of “gnosis” which he considered to be knowledge and understanding of a religious doctrine, in a manner so absolute as to be impervious to refutation. What struck me at the time was that this constituted a grasping, so rock solid and with such a diamond hardness that it might well be called adamantine. What struck me even more was that this person implied that he admired this gnosis and that its “knowledge” should be taken seriously , in part, simply because it was held with such mystic conviction. At the time I was quite shocked because I had been immersed in Buddhist thought for some twenty to thirty years and didn’t realize that “grasping” could be taken in a way other than “undesirable”.

A day or so ago to learn more I looked up in Wikipedia the word “gnosis” and read about its considerable history, beginning in ancient Greece as simply a word translated as “knowledge”. Then in later Hellenistic times there were sects which were called gnostic, and in still later times it led in various modern European languages to words for two kinds of knowledge. It would seem that gnosis is a mystic kind of insight into belief, but in no part of this article was there a hint of the idea of “grasping”, a concept seemingly foreign in Western thought if applied to doctrines or ideas.

Of course, the modern scientific revolution, starting somewhere around the early seventeenth century, did implicitly bring in the idea of letting go or “ungrasping”. Scientists are supposed to have convictions, but be willing to change them when evidence rules against them. However, anyone who is at all knowledgeable about scientific history knows that this ideal is far from being followed by scientists in practice. The physicist Planck, who elucidated the first quantum mechanical phenomenon I’ve discussed in earlier posts, was not at all happy with what he discovered and only slowly accepted the idea that he had truly found something revolutionary and new. However, Planck, I think it was, reflecting on the continued opposition of older scientists to his and later discoveries said something to the effect that no amount of experimental evidence would ever cause these physicists to change their opposition; but fortunately, they would eventually die off, leaving the new, field of quantum theory, to be developed by scientists who would pay attention to the experiments which definitively demonstrated the reality of quantum phenomena.

The point is that science does have a way of eventually dealing with adamantine grasping, whether through grudging acceptance or the dying off of stubborn opposing scientists. In recent times, as I’ve discussed before, Karl Popper’s idea of “refutation” has been enormously clarifying for the philosophy of science. “Refutation” directly implies the necessity for ungrasping as a theory is disproved. Popper’s idea has furthermore diffused into areas outside of science as a touchstone of rational thought. However, the idea of refutation becomes muddy as one moves away from science into areas where refutation becomes more and more difficult or impossible. One then needs to grapple with the whole idea of “grasping” especially with what I’ve called adamantine grasping or the grasping implied by “gnosis”, impervious to any change of mind regardless of evidence or argument. For it seems clear that a tendency to grasp beliefs is ingrained in we humans, and likely has some positive survival value in many situations. However, increasingly there does seem to be a need to cope with its negative consequences; a need underappreciated in Western thought. Back to Top

Ramblings I

I had thought it was time to write a summary of what this blog was all about and, after the summary, write no more. However, after many tries, I could never even make a start and, in addition, I lost all desire to write. Today I had a better idea: just ramble and perhaps find a Zen place. Of course, there are many Zen spaces, none well defined, all possibly controversial, since the concept of a Zen place has no referent and is from a conventional, rational Western point of view meaningless nonsense.

However, the whole point of this blog is that there IS such a space; and from this place all the various Western sciences, arts, and what-have-you’s can be stitched into a meaningful fabric in which each piece gives its body to the other bodies, creating in our minds, at least, a tapestry which goes beyond any of its pieces. And beyond this tapestry there is the pure religion which tells one that one’s life is not meaningless; that our lives, though arising out of nothingness and snuffed out into pure oblivion have some kind of eternal significance, beyond verbal expression.

Actually, Zen is a poor name for this tapestry, this pursuit, this vision, and this religious understanding, but my imagination is too limited to come up with a better name. One problem, as I see it, is that the term Zen, is irredeemably Eastern and irredeemably stitched into Eastern culture at least in the minds of Westerners unfamiliar with it. One seemingly needs an Eastern mind to sense what it might be. Luckily, for me growing up in Hawaii, I somehow came to admire and love an Eastern outlook, Japanese and Chinese, tempered by an underlying Hawaiian vision, and could “aha” an inkling of what this religion, beyond all religions and cultures might be. However, any name for it is misleading, a word for what cannot be named. In attempting to link “IT” to Western culture, I don’t imply that Western culture is in any sense special or beyond any other world culture. I simply feel that there is a big lack in Western culture of a religion that can complete, link and top off the various strands of the culture. Such a religion (identical to Zen) can, in my opinion fill the bill in a way that traditional Western religions cannot.

As you, my ideal reader coming from a Western culture and upbringing, journey to an understanding of this religion I have a couple of thoughts at the moment that could be useful. One concerns the idea of “enlightenment”. In earlier posts I’ve suggested that I prefer the Soto idea of gradual enlightenment rather than the Rinzai ideal of sudden enlightenment. However, I would go a little further, regardless of whether you’re a Rinzai guy or a Soto woman (or vice versa), and use an idea and an image from analytic geometry, a very Western form of thought. This is the idea of an asymptote. Consider a hyperbola, one of the conic sections. This two-dimensional figure has four arms, each one of which, as it travels out forever from the center of the figure approaches closer and closer to a straight line called its asymptote. In my analogy consider enlightenment the asymptote and our journey towards enlightenment a curve which comes closer and closer to the asymptote without ever touching it. At some point one gets so close to the enlightenment asymptote that one more and more senses and takes on its properties without ever touching it. If one takes this idea as an axiom, one never needs to consider whether or not one is enlightened. You’re not and neither am I nor anyone else. Just keep up your meditation and striving, coming nearer and nearer to the ideal.

Another thought concerns the concept of “ego”, “self”, or “me”. Does such exist? Are we “attached” to our ego or self in a Buddhist sense? In our journey, can we lose this attachment? Does it help to realize that one’s ego or self doesn’t really exist? “I” don’t think so. The self may be a fiction; but our attachment is very real, and it’s the attachment, the clinging that is the problem. Consider also that “I”, “you”, “self”, “we” are simply words in a language and we’re dealing with realities which are inexpressible in that language. As we practice over the years we may hope and sense that the attachment is weakening. However, it actually can give one a sense of “peace” to realize that the “attachment” will likely never go away and that one can drop worrying about it. The practice is important, but don’t expect it to do more than, at times, weaken our attachment. Another thought is that these “self” words, though meaningless, are actually useful. When I encounter you, I hope I have the ability to look at you and “see” who you are; see in a deeper sense beyond your persona, your background, education, and the objective facts of your life. I want to see this fictional “you” and have “you” feel that you have been seen and understood. Back to Top

Weird stuff: Astronomy, cosmology and Zen

In this post I tell another story of how science, in going beyond what we can imagine, stretches our imagination to encompass new possibilities of the “real”. There are several important themes here, mostly implicit in this account. There is the fact that scientific measurement is often boring in the extreme, seemingly meaningless, especially when it consists of large tables of numbers. However, out of these tables come new mind-blowing meanings, as sublime as great poetry. In addition, there is the human side of science: how people are ensnared by the mysteries facing us and pursue the tedious day to day work which mostly goes nowhere. But enough. Let’s to the story.

Over the last one-hundred years or so we as humans have been vouchsafed through science an overarching view of the universe we inhabit. At the beginning of that last century, around 1920, we knew that the stars were incredibly far away, but figured that the entire universe was embodied in the enormity of what we now call our galaxy. Only eighty-two years before that in 1838 had the first accurate distance to a star been calculated using the phenomenon of parallax, a shift in the apparent position of nearer objects relative to those further away when observed from different viewpoints. A simple way to observe and understand parallax, is to hold up a finger at arm’s length in front of one’s nose, close one eye and then the other. The apparent position of one’s finger jumps back and forth relative to a background further away. One half the angle of the shift defines the parallax. One uses half of the shift because the direction straight out from one’s nose towards the outstretched finger defines a base direction for where one is looking. A line to the finger from either eye meets the straight-out line at the parallax angel. Knowing this angle and the distance between one’s eyes, one can calculate the distance to one’s finger using simple trigonometry. That calculation would be pointless; however, one realizes, using the same idea, that instead of the distance between one’s eyes, one can take the distance between opposite sides of the earth’s orbit around the sun and by measuring the apparent shift in position of nearby stars relative to those further away, one can calculate the distance to those nearby stars.

The fact that there should be parallax in the heavens was understood in ancient times, was known to many in the sixteenth century and could be used to calculate the distance to the moon, around 10 times the circumference of the earth. The seminal transitional figure, Tycho Brahe, 1546 – 1601, excited by the new theory of Copernicus (1543), but still under the thrall of the classic Ptolemaic view, realized that only by measuring the angular position of both the “fixed” and the “wandering stars”, called planets, might he be able to tell what was really going on in the heavens. Tycho thus became obsessed with measuring, so was among the first in history to intuit and practice what we now realize lies at the heart of science, careful measurement and observation ¹. Tycho was a Danish nobleman and used his own and other money to finance the construction of instruments such as quadrants and sextants, each like a piece of a giant protractor. During his life he measured hundreds of stellar positions as well as those of the planets. The telescope’s invention lay in the future, but Tycho could measure angles to around a minute of arc, one sixtieth of a degree, about thirty times smaller than the moon’s diameter as seen from earth. Probably influenced by ancient Greek ideas of an earth surrounded by crystalline² spheres carrying successively, the moon, the sun, each of the five planets, and then the fixed stars, Tycho imagined that the stars were not much farther away than the planets. If Copernicus was right and the earth had a circular orbit around a fixed sun, Tycho should easily be able to detect the parallax shift in at least a few stars over a six-month period as the earth swung around the sun in its orbit. Finding such a shift would confirm Copernicus and simultaneously give an idea of the distance to the stars in terms of the roughly known distance to the sun.

Over a year’s time Tycho could detect not the slightest parallax in any candidate star. This meant one of two things. Either the earth and the stars were fixed in the cosmos, OR the stars were unimaginably far away. The latter possibility was to Tycho unthinkable so he guessed the former and made up a model in which the five planets circled the sun, while the whole shebang of sun and planets, circled the central, spinning fixed earth and her moon inside the sphere of the fixed stars. Tycho’s theory was messy, but saved at least part of Copernicus’s beautiful picture. Tycho’s guess was wrong, as so many scientific guesses are. In fact, wrong guesses are an important part of science even though they mostly are forgotten and ignored by history. In Tycho’s case although his guess was wrong, his measurements proved crucial to Kepler’s laws of planetary motion, and with the contributions of Galileo and Newton, a Copernican model made more sense, although it took over another 100 years for stellar parallax to be detected and yet another 100 years before it was actually measured by Friedrich Bessel in 1838. Before its detection in the early 1700’s there were still die-hard anti-Copernicans who could use the lack of stellar parallax as the primary evidence for their views. It seemed to them impossible that stars could be so distant. As it turns out, the parallax of the nearest star is less than an arc second, more than 60 times smaller than Tycho Brahe could detect. An arc second is the angle subtended by a quarter 3.3 miles away and the stellar shift is at most about half of that. (See Wikipedia’s article, “Stellar Parallax”.)

It’s worth doing some simple math in a short paragraph to show how the distance to nearby stars is calculated and find its value. (Feel free to skim.) It turns out that one doesn’t even need to use trig, because if the parallax angle is small, one can use the formula s = r times ø, relating the arc length s on a circle to its radius r and the angle ø which s subtends. In the astronomical situation r is the distance to the star, s is the radius of the earth’s orbit around the sun, 93,000,000 miles or so, and ø is the parallax angle. The angle ø needs to be in radians, an angular unit = π/180 times the angle in degrees. These days with a smart phone one can easily grind out the calculation. Let’s take ø to be half a second of arc. We need that half second to be in degrees so we can then multiply by π/180 and have it in radians. So, .5 times 1 /60 x 1/60 = .5/3600 = 0.000138888 degrees. Multiply that by π and divide by 180 and we have our half second as 0.00000242407 radians. Divide 1 by this angle and we find that a nearby star is 413,000 times as distant as our sun; namely 38,400,000,000,000 miles away. Astronomers like to cut these big numbers down to size. If we used an entire second rather than a half as our parallax, the distance would be half as much. Astronomers name this latter distance a parallax second, abbreviated as a parsec, pc. Our hypothetical star is 2 parsecs away and there are, in fact, stars that are that close to us. There are none as close as a parsec. Another distance unit in popular usage is the light year, the distance light goes in a year’s time, traveling 186,000 miles or so each second throughout the year. You can whip out your phone and show that a parsec is about 3.26 lightyears. It is worth contemplating for a moment the magnitude of this distance to our near neighbor stars. Light gets to the moon in a couple of seconds, to the sun in half a minute, but takes 5 years or so to reach nearby stars, 2 parsecs away. We will see below that typical distances in our universe are measured in mega parsecs, a million times as large. As a means for measuring cosmic distances parallax is quite limited. The satellite Hipparcos, aloft 1989 – 1993, could detect a parallax of 0.001 arcseconds (like measuring the diameter of a quarter in New York as observed from San Francisco), so could measure the distance to stars one-thousand parsecs away. Helpful, for stars in our immediate neighborhood, but worthless further out.

As the twentieth century dawned it was clear that most stars were unfathomly far away and that any parallax they possessed was infinitesimal. Enter into our story Henrietta Swan Leavitt, 1867 – 1921. Around 1892 as a college senior she took an astronomy course and became incorrigibly fascinated. As a woman traditional routes to becoming an astronomer were closed to her. Instead she was able to wrangle her way as a volunteer at the Harvard Observatory. Around 1900 photographic plates came into being and were soon put to use in astronomy. The relative brightness of stars could be measured with greater precision on these plates than by naked eye observation and Henrietta, was put to work measuring the brightness of thousands of stars. Imagine the tedium of this work, day after day, year after year, with only a slight inkling of what use this data would ever have. However, in the early 1900’s while measuring the relative brightness of 1777 so-called Cepheid variable stars, Henrietta noticed something; namely, that there was a relationship between the brightness and dimness period of these stars and their relative brightness at its peak. She made a graph of the data and pointed out her finding to her boss, the astronomer, Edward Pickering. As a woman she could not publish her finding, but Pickering could and did in 1912, giving her credit for the discovery. The stars whose brightness she measured were in the large Magellanic Cloud, a nebula, so were at an unknown distance. The brightness was only relative. However, people soon realized that there were nearby Cepheids within parallax range. With an absolute measure of brightness established one could potentially reach out, finding the distance to stars much further away than could previously be measured. Ms. Leavitt pointed this out before she succumbed to breast cancer in 1921. Her finding was easily worth a Nobel prize, but there were three reasons she could not be considered. 1, Nobel’s are only given to living persons; 2, Astronomers were ineligible in those days; and 3, She was a woman.

By 1924, using parallax, the distance to several nearby Cepheids had been measured and the time was ripe for momentous discoveries. The first of these was made by Edwin Hubble using the newly built 100-inch Wilson telescope above Pasadena, California. (When I lived in Pasadena in 1953-4, I would hike up to the observatory on weekends and occasionally be amused by the spectacle of California drivers skidding around in a rare snowfall.) By the end of 1924 Hubble had been able to detect and measure the brightness of several Cepheids in the Andromeda and other nearby “nebulae”. Clearly, the distance to these stars was much greater than to any star in our milky way galaxy and the “nebulae” were, in fact, “island universes”, each consisting of a several hundred billion or so stars. Hubble thus settled a controversy since some influential astronomers at the time thought that the nebulae were simply large star clusters inside our milky way. As a distance measure, astronomers still cling to the parsec, an established convention, but now mostly in the form of a kilo or mega pc, a thousand or million times the distance mentioned in the last paragraph. For example, our nearest neighbor galaxy, according to the Wikipedia article “Andromeda Galaxy”, lies at a distance from us of 778 kpc or 2.54 million light years.

As the 1920’s wore on (remember: this is the time of the quantum revolution, the German hyperinflation and the inexorable growing foundation for Hitler’s rise) Edwin Hubble made another earthshaking discovery, measuring a Doppler shift in the spectra of various galaxies. One experiences a Doppler shift here on earth when an emergency vehicle with “lights and sirens”, passes by. The pitch of the siren suddenly lowers as the vehicle passes. Hubble found that the frequency of light from galaxies lowered (were Doppler shifted towards the red), the amount of shift being directly proportional to the estimated distance of the galaxies. What this meant was that the farther a galaxy was from us, the component of its velocity in our direction was always away and greater. Imagine in your mind being in the middle of all these galaxies. Anywhere you imagine being, you are always in an apparent center (so says general relativity) and all the galaxies are moving away. The number of threads in the fabric of the entire universe is increasing so distance measures are growing. The speculation this situation suggests is that at one time there was a beginning of this spread and that the entire universe exploded out of nothingness. This idea is called “the big bang” theory, “big bang” being an expression coined by Sir Fred Hoyle, a brilliant, creative, quirky British physicist and astronomer, who proposed a rival, steady-state theory of an eternal, expanding universe, kept homogeneous by the rare, occasional creation of a stable elementary particle. Hoyle claimed he was not being pejorative in his term, but with it he was implying that the very idea of a “big bang” was ridiculous. Among other things Hoyle wrote some interesting science-fiction novels, one at least, based on a possible rupture of space-time in the vicinity of earth. (October the First is Too Late.)

Hubble published the paper about his red-shift observations and some of their consequences in 1929. His ideas had been anticipated in greater detail and published in a somewhat obscure journal, two years earlier by Georges Lemaître, a priest, mathematician and physicist, then a part-time lecturer at the Catholic University of Louvain in Belgium, see Wikipedia. Lemaître, rediscovered a metric, predicting the expansion, in the equations of General Relativity. Also, he realized that Einstein’s solution for a static universe was untenable. Then, using red-shift observations in the literature, Lemaître made the first estimate of the Hubble constant (now renamed the Hubble-Lemaître constant). Lemaître was also the first to imagine the “big bang” arising from a densely packed “primeval atom” containing what was to become our entire universe. When Lemaître translated his paper to English in 1931 he left out his section about the Hubble constant because by then Hubble’s 1929 paper had come out and Lemaître figured that his own value was obsolete. Ironically, Hubble’s value was off by a factor of 10 or so. Nowadays we know that the constant(?) is about 70 although at the moment (7/14/2020) there are at least two different values which disagree, with a gap beyond their error estimates. The units of the “70” which I left out of the previous sentence are worth explaining briefly. (70, without units, has the same status as 48, mentioned in Douglas Adams Hitchhikers Guide to the Galaxy as the answer to “life, the universe and all that.”) To understand the Hubble expansion unit, imagine that we “look” out from our earthly center of the universe a megaparsec. We will find that out there, all the galaxies are moving away from us at an average speed of 70 kilometers per second. Go out another mpc and they’re going at 140, etc. The unit is thus a kilometer per second per megaparsec. Incidentally, the variation of galaxy velocities making up this average is small. The universe is incredibly homogeneous, a fact Hoyle could have used, had he known, in his long battle with the big bang.

Until fairly recently Hubble received the credit (for whatever it’s worth) of discovering the red shift and the big bang because of his well-publicized 1929 paper. Hubble did nothing dishonest in accepting his honors and fame, but also did nothing in the way of discouraging such. Why should he? Lemaître remained an obscure figure partly because he was not at all interested in self-promotion and possibly because he was a Catholic priest, with the baggage of being considered anti-science because of his religion.

As the 20^th century wore on, the picture suggested in the first third of the century fleshed out. People researched the different kinds of galaxies, realizing in the process that there are 100 billion or so in our universe to say nothing of quasars and “black holes”. Between 1963 and 1965 perhaps the most exciting astronomical discovery of the century occurred. I can remember my excitement in 1965, as a newly installed Associate Professor at Auburn University, when the news came out that a cosmic microwave radiation had been accidentally observed by Penzias and Wilson at a Bell Labs site, using a large so-called horn antenna. The signal was to them, when first detected, unwanted noise, and they tried in vain to get rid of it. Finally, they called Professor Dicke at Princeton, whose design was incorporated in their antenna. According to Wikipedia when Dicke got the call, he said to his team, “Boys, we’ve been scooped”. The radiation had been theoretically predicted and Dicke’s team was about to search for it. As the shape of the radiation spectrum was filled in, it fitted exactly, the formula that Planck had found in 1900, for black body radiation. Link to Black Body discovery. The temperature of the radiation was 2.7 degrees above absolute zero, having cooled from an incredible high temperature through the expansion of space from the time when the universe became transparent to electromagnetic radiation some 200,000 years after the big bang. This observation of cosmic black-body radiation was a striking confirmation of the big bang theory, and, in no way, could be twisted to be compatible with Hoyle’s rival theory. The decline of the Hoyle theory is a good example of Karl Popper’s idea of how science advances as I discussed in an earlier post. However, in science, nothing is ever really settled and continuous creation could easily again rear its [ugly?] head.

Towards the end of the 20^th century, as more and better measurements of the cosmic radiation were made, it became clear how remarkably homogeneous it was. How could this be? As the fabric of the universe expands, regions become separated in a way special relativity calls “spacelike”. No signal could pass back and forth to soothe out fluctuations. Thus, unlike a cooling liquid, there is no mechanism to bring about homogeneity. Between 1979 and 1981, a young physicist, Alan Guth, developed a theory of inflation. This was not an economic theory, but, instead, the idea, that in the early instants of the big bang, “negative vacuum pressure” caused a wild, exponential expansion of the infant universe. After the inflationary expansion stopped, the universe was much larger and the ordinary Hubble type of expansion took over. Recent satellite measurements of the remaining non homogeneity agree well with Guth’s theory. I must confess that an intuitive understanding of the math behind this theory is totally beyond me.

In more recent times, deep mysteries concerning dark matter, dark energy and the idea of a multiverse have arisen. At this point I will not talk about them, leaving a possible discussion for later. Instead I will ask, “what is the significance for a thinking, aware human being of what we have found out about the place in which we live?” Many have noted that the history of cosmic discovery is one which displaced the human race further and further from the central significance we thought we had in the scheme of things back in ancient and medieval times, a displacement towards utter insignificance and humiliation. I want to take an almost opposite point of view. I wish to disregard the finer points of the science and look at the universe in the largely non-quantitative way as I have described in the previous paragraphs. I want to consider our picture of the universe as an aesthetic object, an unbelievably magnificent work of art. I want to suggest that this picture of the universe is, as well, a gigantic Zen Mondo, making clear an ultimate religious view beyond any language in which it could be couched.

If I am able to proceed in this direction, I must switch to an entirely different language game. So, in the a later post, possibly the next, I need to go further into the meta-language concept as suggested and developed by Wittgenstein, Kuhn and Meagher. Back To Top

While observation and measurement lie at the heart, “theory” comprises the soul. For science to be a living being, it needs both. ↩︎
If you think that the moving crystalline spheres, giving off a kind of music, are unreasonable, consider the “luminiferous ether”, a medium in space, thought necessary, in the late nineteenth century, for carrying light waves. In order for light to have its observed speed, the ether would need to be massless and incredibly rigid yet allow astronomical bodies such as the earth, planets and stars to pass through it in a frictionless way. Perhaps, that is. Allowing the ether to be dragged along close to earth could explain why it was undetected by the Michelson-Morley experiment. As it turns out, the electromagnetic field is perfectly capable of existing in vacuum, unlike all the more familiar waves known at the time. This is another example where a “guess” was wrong and, in this case, adopted by an entire scientific community. ↩︎

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