(Roughly) Daily

Posts Tagged ‘astronomy

“The earth is what we all have in common”*…

Explore a catalog of NASA images and animations of our home planet: “Visible Earth,” from @NASAEarth.

* Wendell Berry


As we peruse our planet, we might recall that it was on this date in 1965 that NASA turned on planetary science mode on the Mariner IV spacecraft (which had been launched on November 28, 1964 from Cape Canaveral) as it flew by Mars. Over the next two days, Mariner IV captured the first “close up” pictures (21 in all) of the planets surface. The images taken during the flyby were stored in the on-board tape recorder; each individual photograph took approximately six hours to be transmitted back to Earth.

While waiting for the image data to be computer processed, the team used a pastel set from an art supply store to hand-color (paint-by-numbers style) a numerical printout of the raw pixels. The resulting image provided early verification that the camera was functioning. The hand drawn image compared favorably with the processed image when it became available.

The first digital image from Mars, hand-colored (source)

Written by (Roughly) Daily

July 14, 2023 at 1:00 am

“The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.”*…

The Pythagoreans believed that the motions of the heavenly bodies, with just the right ratios of their distances from a central fire, made pleasant music — a concept that evolved into the “music of the spheres.”

As Tom Siegfried explains, the “music of the spheres” was born from the effort to use numbers to explain the universe…

If you’ve ever heard the phrase “the music of the spheres,” your first thought probably wasn’t about mathematics.

But in its historical origin, the music of the spheres actually was all about math. In fact, that phrase represents a watershed in the history of math’s relationship with science.

In its earliest forms, as practiced in ancient Egypt and Mesopotamia, math was mainly a practical tool for facilitating human interactions. Math was important for calculating the area of a farmer’s field, for keeping track of workers’ wages, for specifying the right amount of ingredients when making bread or beer. Nobody used math to investigate the nature of physical reality.

Not until ancient Greek philosophers began to seek scientific explanations for natural phenomena (without recourse to myths) did anybody bother to wonder how math would help. And the first of those Greeks to seriously put math to use for that purpose was the mysterious religious cult leader Pythagoras of Samos.

It was Pythagoras who turned math from a mere tool for practical purposes into the key to unlocking the mysteries of the universe. As the historian Geoffrey Lloyd noted, “The Pythagoreans were … the first theorists to have attempted deliberately to give the knowledge of nature a quantitative, mathematical foundation.”…

More at: “How Pythagoras turned math into a tool for understanding reality,” from @tom_siegfried in @ScienceNews.

Apposite: Walter Murch’s ideas on “planetary harmony” (and Lawrence Weschler’s book on him and them)

* Henri Poincare


As we seek beauty, we might recall that it was on this date in 1595 that Johann Kepler (and here) published Mysterium cosmographicum (Mystery of the Cosmos), in which he described an invisible underlying structure determining the six known planets in their orbits.  Kepler thought as a mathematician, devising a structure based on only five convex regular solids; the path of each planet lay on a sphere separated from its neighbors by touching an inscribed polyhedron.

It was a beautiful, an elegant model– and one that fit the orbital data available at the time.  It was of course, nonetheless, wrong.

Detailed view of Kepler’s inner sphere


“Mathematics has not a foot to stand on which is not purely metaphysical”*…

Battle of Maida 1806, part of the the invasion and occupation of Naples by Napoleon’s French Empire (source)

Lest we forget…

A forgotten episode in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.

In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination…

Massimo Mazzotti with an adaptation from his new book, Reactionary Mathematics: A Genealogy of Purity: “Foundational Anxieties, Modern Mathematics, and the Political Imagination,” @maxmazzotti in @LAReviewofBooks.

* Thomas De Quincey


As we count on it, we might send carefully-calculated birthday greetings to Regiomontanus (or Johannes Müller von Königsberg, as he was christened); he was born on this date in 1436. A mathematician, astrologer, and astronomer of the German Renaissance, he and his work were instrumental in the development of Copernican heliocentrism during his lifetime and in the decades following his death.


“There is only one good, knowledge, and one evil, ignorance”*…

The School of Athens (1509–1511) by Raphael, depicting famous classical Greek philosophers (source)

If only it were that simple. Trevor Klee unpacks the travails of Galileo to illustrate the way that abstractions become practical “knowledge”…

… We’re all generally looking for the newest study, or the most up-to-date review. At the very least, we certainly aren’t looking through ancient texts for scientific truths.

This might seem obvious to you. Of course you’d never look at an old paper. That old paper was probably done with worse instruments and worse methods. Just because something’s old or was written by someone whose name you recognize doesn’t mean that it’s truthful.

But why is it obvious to you? Because you live in a world that philosophy built. The standards for truth that you imbibed as a child are not natural standards of truth. If you had been an educated person in 1200s Europe, your standard for truth would have been what has stood the test of time. You would have lived among the ruins of Rome and studied the anatomy texts of the Greek, known that your society could produce neither of those, and concluded that they knew something that your society could not. Your best hope would then be to simply copy them as best as possible.

This was less true by the time Galileo was alive. This is why an educated man like Galileo would have entertained the idea that he knew better than the ancient Greeks, and why his ideas found some purchase among his fellow academicians (including the then Pope, actually). But still, there was a prominent train of thought that promoted the idea that a citation from Aristotle was worth more than a direct observation from a telescope.

But you live in a different world now. You live in a world in which the science of tomorrow is better than the science of today, and our societal capabilities advance every year. We can build everything the ancients did and stuff they never even imagined possible. So you respect tradition less, and respect what is actually measured most accurately in the physical world more.

Today, this battle over truth is so far in the past that we don’t even know it was ever a battle. The closest we come to this line of reasoning is when new age medicine appeals to “ancient wisdom”, but even they feel compelled to quote studies. Even more modern battles are mostly settled, like the importance of randomized, double-blinded controlled studies over non-randomized, non-controlled studies.

The reason we mark battles is not just for fun or historical curiosity. It’s to remind us that what we take for granted was actually fought for by generations before us. And, it’s to make sure that we know the importance of teaching these lessons so thoroughly that future generations take them for granted as well. A world in which nobody would dream of established theory overturning actual empirical evidence is a better world than the one that Galileo lived in…

On the importance of understanding the roots of our understanding: “You live in a world that philosophy built,” from @trevor_klee via @ByrneHobart.

Apposite (in an amusing way): “Going Against The Grain Weevils,” on Aristotle’s Generation of Animals and household pests.

* Socrates, from Diogenes Laertius, Lives and Opinions of Eminent Philosophers (probably early third century BCE)


As we examine epistemology, we might send elegantly phrased and eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of (what he called) the Rubaiyat of Omar Khayyam, Fitzgerald’s attribution of the book’s poetry to Omar (as opposed to the aphorisms and other quotes in the volume) is now questionable to many scholars (who believe those verses to be by several different Persian authors).

In any case, Omar was unquestionably one of the major philosophers, mathematicians and astronomers of the medieval period.  He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle.  His astronomical observations contributed to the reform of the Persian calendar.  And he made important contributions to mechanics, geography, mineralogy, music, climatology and Islamic theology.


Written by (Roughly) Daily

May 15, 2023 at 1:00 am

“It is well to remember that the entire universe, with one trifling exception, is composed of others”*…

This artist’s impression shows the temperate planet Ross 128 b, with its red dwarf parent star in the background. Credit: ESO/M. Kornmesser

For centuries, scientific discoveries have suggested humanity occupies no privileged place in the universe. But as Mario Livio argues, studies of worlds beyond our solar system could place meaningful new limits on our existential mediocrity…

When the Polish polymath Nicolaus Copernicus proposed in 1543 that the sun, rather than the Earth, was the center of our solar system, he did more than resurrect the “heliocentric” model that had been devised (and largely forgotten) some 18 centuries earlier by the Greek astronomer Aristarchus of Samos. Copernicus—or, rather, the “Copernican principle” that bears his name—tells us that we humans are nothing special. Or, at least, that the planet on which we live is not central to anything outside of us; instead, it’s just another ordinary world revolving around a star.

Our apparent mediocrity has only ascended in the centuries that have passed since Copernicus’s suggestion. In the middle of the 19th century Charles Darwin realized that rather than being the “crown of creation,” humans are simply a natural product of evolution by means of natural selection. Early in the 20th century, astronomer Harlow Shapley deepened our Copernican cosmic demotion, showing that not only the Earth but the whole solar system lacks centrality, residing in the Milky Way’s sleepy outer suburbs rather than the comparatively bustling galactic center. A few years later, astronomer Edwin Hubble showed that galaxies other than the Milky Way exist, and current estimates put the total number of galaxies in the observable universe at a staggering trillion or more.

Since 1995 we have discovered that even within our own Milky Way roughly one of every five sunlike or smaller stars harbors an Earth-size world orbiting in a “Goldilocks” region (neither too hot nor too cold) where liquid water may persist on a rocky planetary surface. This suggests there are at least a few hundred million planets in the Milky Way alone that may in principle be habitable. In roughly the same span of time, observations of the big bang’s afterglow—the cosmic microwave background—have shown that even the ordinary atomic matter that forms planets and people alike constitutes no more than 5 percent of the cosmic mass and energy budget. With each advance in our knowledge, our entire existence retreats from any possible pinnacle, seemingly reduced to flotsam adrift at the universe’s margins.

Believe it or not, the Copernican principle doesn’t even end there. In recent years increasing numbers of physicists and cosmologists have begun to suspect—often against their most fervent hopes—that our entire universe may be but one member of a mind-numbingly huge ensemble of universes: a multiverse.

Interestingly though, if a multiverse truly exists, it also suggests that Copernican cosmic humility can only be taken so far.

The implications of the Copernican principle may sound depressing to anyone who prefers a view of the world regarding humankind as the central or most important element of existence, but notice that every step along the way in extending the Copernican principle represented a major human discovery. That is, each decrease in the sense of our own physical significance was the result of a huge expansion in our knowledge. The Copernican principle teaches us humility, yes, but it also reminds us to keep our curiosity and passion for exploration alive and vibrant…

Fascinating: “How Far Should We Take Our Cosmic Humility?“, from @Mario_Livio in @sciam.

* John Holmes (the poet)


As we ponder our place, we might send carefully-observed birthday greetings to Arno Penzias; he was born on this date in 1933. A physicist and radio astronomer, he and Robert Wilson, a collegue at Bell Labs, discovered the cosmic microwave background radiation, which helped establish the Big Bang theory of cosmology– work for which they shared the 1978 Nobel Prize in Physics.

MB radiation is something that anyone old enough to have watched broadcast (that’s to say, pre-cable/streaming) television) has seen:

The way a television works is relatively simple. A powerful electromagnetic wave is transmitted by a tower, where it can be received by a properly sized antenna oriented in the correct direction. That wave has additional signals superimposed atop it, corresponding to audio and visual information that had been encoded. By receiving that information and translating it into the proper format (speakers for producing sound and cathode rays for producing light), we were able to receive and enjoy broadcast programming right in the comfort of our own homes for the first time. Different channels broadcasted at different wavelengths, giving viewers multiple options simply by turning a dial.

Unless, that is, you turned the dial to channel 03.

Channel 03 was — and if you can dig up an old television set, still is — simply a signal that appears to us as “static” or “snow.” That “snow” you see on your television comes from a combination of all sorts of sources:

– human-made radio transmissions,

– the Sun,

– black holes,

– and all sorts of other directional astrophysical phenomena like pulsars, cosmic rays and more.

But if you were able to either block all of those other signals out, or simply took them into account and subtracted them out, a signal would still remain. It would only by about 1% of the total “snow” signal that you see, but there would be no way of removing it. When you watch channel 03, 1% of what you’re watching comes from the Big Bang’s leftover glow. You are literally watching the cosmic microwave background…

This Is How Your Old Television Set Can Prove The Big Bang
%d bloggers like this: