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 (1643), 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 observation¹. 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.

Footnotes

¹While observation and measurement lie at the heart, “theory” comprises the soul. For science to be a living being, it needs both.

²If 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.