Thursday, September 17, 2020

Hail to the Spartan Victors?

I do not remember where I was driving when I saw this banner. The incongruity prompted me to stop and take a picture. I found it again in my archives but it had been edited and the date was too current now. 

We mostly lived in Michigan for about 30 years off and on from 1977 to 2011, almost 20 years continuously from 1979 to 1999. The hometown rivalries are between the Michigan State University Spartans (green and white) and the University of Michigan Wolverines (blue and maize). 

Never much for team sports and certainly not college football, the fact is that we lived in and around Lansing until 1999. My daughter and I made good use of the MSU campus. I had a community library card. We skated the grounds, rented canoes, and explored buildings when classes were out. 

But Laurel’s freshman year was at the U of M before we met. She returned to work at the University and take a graduate class when we were living in Ann Arbor and attending Eastern Michigan University 2005-2010. So, our loyalties are somewhat conflicted.


But, as I said, I don’t follow sports. So, there was one time I was working for a software firm in Lansing and some of the programmers were MSU graduates; everyone else was an MSU fan. I caught a cold the week of Thanksgiving and missed a day of work that Wednesday and spent the weekend in bed recuperating. The Michigan-Michigan State game was televised (oddly) and I caught snatches of the last quarter as I surfed the channels. When the game was over, the Green and White band came out and played “Hail to the Victors.” 

 The next Monday, they were talking about the game, and going to school, and learning the MSU fight song at orientation. And I said, “Hail to the Victors” and they said, “WHAT?!?!” And I explained that I caught the end of the game and the Spartan band played “Hail to the Victors.” And they said, “That’s because we lost. The band salutes the winner by playing their song.” Oh…


Hook ‘em Horns! 

Good-Bye Redskins 

Why a Level Playing Field? 

Big Bang Theory: More Friends than Seinfeld 


Tuesday, September 8, 2020

Pencil Notes: Reflections on Henry Petroski’s "The Pencil"

“Yet, perhaps in part because specialization was no doubt as common in ancient times as it is today, the written history of engineering is sparse. Even the most able and articulate of ancient engineers, whether they were known as artisans, craftsmen, architects, or master builders, might have had no more time or inclination or reason to articulate what it is they did and how they did it than do some of the most able of today’s engineers.” – page 17

That is why they hire technical writers. To me, it is a right-brain/left-brain situation. Engineers tend to be right brain thinkers. Technical writers bring that with them, also, the ability to read, edit, and create drawings, whether architectural plans or software flowcharts. Ultimately, though, the images get verbal explanations. That may explain why so many technical writers are women: the left and right hemispheres of the brain are connected by the corpus collosum, which tends to be more highly developed in females than in males.


It is difficult to be certain how this or that better design for a brush, plow, house, or sword evolved from its predecessors, for the process was at best sketched metaphorically in pencil and seldom if ever copied in pen. It is because of this that the ideas and artifacts of technology—the processes and products of engineering—are so very different from the creations and theories of literature, philosophy, and science. … The classics, even if superseded in factual or theoretical sophistication are considered models of thinking from which one can today still benefit by emulation, or at least inspiration. […] Curators of technological artifacts, industrial archaeologists, and historians of technology represent rather new careers…” – pages 20-21

  1. First, that is why we have industrial archaeology now, to recover and understand those earlier activities and artifacts. 
  2. Second, we have lost some mathematics. Richard P. Feynman wanted to demonstrate to his class how Newton proved Kepler’s laws, and he wanted to do it in Newton’s own language. He could not. Feynman could not recreate the geometry that was fundamental to the Principia. We have become so dependent on algebra and calculus that we have forgotten the admittedly more cumbersome tools of earlier mathematics.
  3. We also lost the machinery of the Antikythera Mechanism. It would be almost 1500 years before clocks were again so complicated, accurate, and precise.
  4. Fourth, and to Petroski’s point, antiquarians do inform the present. Though we had advanced past the hand-hammered methods of coinage, it is famous that President Theodore Roosevelt commissioned Augustus Saint-Gaudens to give America coinage as compelling as that of the ancient Greeks. 

Professional Coin Grading Service "Coin Facts" website
TOP: Half Dollar of Charles Barber imitating the work
of Oscar Roty for France. BOTTOM: Something better. 

“[Sir Isaac Newton’s] seashore metaphor allows that one shell (theory) may be prettier (more elegant) than another, and perhaps the searcher becomes less fond of the old shells as prettier ones are found, but the implication is still that the truths are whole in the ocean and it is just a matter of time before they are found thrown up on the shore.

“While pencils may be helpful in formulating abstract theories of motion and gravitation, abstract theories do not make pencils.” – page 74.


The history of modern physics may refute that. The mathematics describing atomic and nuclear processes energy became the design specifications. We did not tinker our way to nuclear power.


Of all the revelations and insights here, I was captivated by the story of Henry David Thoreau (Chapter 9: An American Pencil-Making Family). We recently watched the most recent remake of Little Women (Greta Gerwig director). We see Jo March’s ink-stained fingers and we watch her on the floor, scribbling in pen. But we all also know that the family was connected with the Transcendentalists, among them Henry David Thoreau. But who knew that his family made pencils? In his list of supplies taken to Walden Pond, mostly likely written with the pencil he carried, Thoreau omitted the pencil. Thoreau also billed himself as a surveyor and civil engineer, two professions that even in 1840 depended on good, reliable graphite pencils. 


I wrote here last week about the passage on pages 223-225 describing how engineers often were trained to draw by copying architectural treatments. It is, of course, how architects learned to draw. That opened up a new vista on an early passage in The Fountainhead. That being as it may, it is nonetheless true that to learn science, we recreate the important experiments of the past. We just do not slavishly recreate them with archaic beakers, wires, and flyball governors. I believe that it is a valid criticism of physics in particular, stated in Thomas Kuhn’s Structure of Scientific Revolutions, that we are handed science as a completed artifact and do not trouble ourselves much with discarded paradigms—or why we discarded them. (My review for this blog is here.)


“One desirable quality is often gained at the expense of another, for how the properties of complicated materials will change with changing ingredients and methods of preparation, whether they be pencil leads or concrete, is not always easily predictable. While a new mixture might give a stronger material, it might also give a more brittle one that will be greatly weakened by a small crack.”—page 236


“The stories of the Munroes and the Thoreaus and their pencils illustrate in microcosm the often conflicting objectives of real-world engineering and business: making pencils as fine as possible as an end in itself; making pencils better in quality or price than other pencil makers; making pencils secretly in order to have an advantage over the competition; making pencils overtly to conceal a more profitable business; making pencils for the social and cultural good of artists, engineers, and writers of all kinds. There is no such thing as pure engineering, whether in the artifact or in the abstract—for that would be nothing but irresponsibility or a mere hobby. Engineering, far from being applied science is scientific business.” – page 276-277.

It reminded me of the discussions among Austrian economists over what entrepreneurship essentially is. (See NecessaryFacts here.) Being rationalists  they seek one or a few axioms from which all of the remainder can be derived by pure reason. Do entrepreneurs bring new inventions to market? Do they arbitrage risk? Do they carry goods from where they have lower value to where they are valued more? Do they drive each other out of business by any means possible? Do they find cooperation where others find conflict? Do they take advantage of the unwary or do they profit from intelligent decisions? Mises pointed out at some length that the entrepreneur can be so self-centered that they invest all of their resources in a lost cause when a rational person would just get any good-paying job and keep it. There is no such thing as pure entrepreneurship unless it is a hobby. 


In 1933 [the Lead Pencil Institute] has ten members who together manufactured 90 percent of all American pencils. Thus the institute effectively represented the entire industry, which at that time included thirteen firms. They were roughly in order of size: Eagle Pencil Company, New York, N.Y.

Eberhard Faber Pencil Company, Brooklyn, N.Y.

American Lead Pencil Company, Hoboken, N.J.

Joseph Dixon Crucible Company, Jersey City, N.J.

Wallace Pencil Company. Brentwood, Mo.

General Pencil Company, Jersey City, N.J.

Musgrave Pencil Company, Shelbyville, Tenn.

Red Cedar Pencil Company. Lewisburg, Tenn.

Mohican Pencil Company, Philadelphia, Pa.

Blaisdell Pencil Company, Philadelphia, Pa.

Richard Best Pencil Company, Irvington, N.J.

Empire Pencil Company, New York, N.Y.

National Pencil Company, Shelbyville, Tenn.

(Page 293)


I found it disappointing that Petroski quoted John Middleton Murray at length on the poetry of being a pencil, but never mentions “I Pencil” by Leonard E. Reed.


The old meets the new. These pencil extenders are built
from STL files provided to 3-D printers

“Who today but a frugal draftsman would use a pencil down to such a stub? But our pencils, unlike many of those of the Victorians, have lead from end to end, and some engineers and draftsmen, when a good pencil’s stub is too small to hold even in a pencil extender, have been known to cut away the last of the wood case and use the left in their compasses.” – page 354


Previously on NecessaryFacts

Imaginary Numbers are Real but Pegasus is not 

Forbidden Planet 

Spoken American Grammar 

The Map that Changed the World 

Monday, September 7, 2020

The Pencil: History, Design, and Circumstance

The book opens and closes with the fact that the pencil’s ubiquity rendered it invisible. On pages 5 and 346 the author tells of being unable to find old pencils in antique stores or museums. Shops that specialize in classic craftsman’s tools keep the compasses, but throw out the pencils. They value the carpenter’s levels, but discard the trade’s signature pencils. They curate the surveyor’s drafting pens, but not the pencils that laid out the guidelines that made inking possible. If that is received as incongruous, then consider that very little engineering is ever recorded. The work is the story. How it came to be is locked and lost in the mind of the inventor. The engineering drawing delivers its thousands of words. The engineer seldom records any of the words that gave birth to the plans and procedures. And as central as is the precision drawing, the pencil that made it has been ignored.

The Pencil: A History of Design and Circumstance by Henry Petroski (Alfred A. Knopf, 1990) is a paean to engineering with the pencil as its metonym. Being a professor of civil engineering, the author frequently compares the creation of pencils with the development of bridges. The allusion is not deep. The focus is the pencil, not the truss or suspension, though both are mentioned as needed for context.

We are told too easily that scientific theories become applied as engineered structures or machines. In truth, it is the other way around: theories explain what engineers develop by intuition, insight, trial and error, craft, and trade secret. When those are formalized into mathematics, then engineering science can improve the product or the process by analysis, seeking and eliminating limitations, flaws, defects, and oversights.


People were happy with metallic scribers made of lead, tin, or silver, and pens cut from reeds or feathers. The discovery in the 16th century of “black lead” or “plumbago” or “British lead” that we now call “graphite” radically altered writing and drawing, both for fine art and engineering. For three hundred years, the best graphite came from a single district in England. France’s wars with England led to the Conté crayon, a secret mixture of clay and graphite. Closed out of France, German firms developed their own secret formulas with graphite from Bavaria and Bohemia. Suitable graphite was found in New England and pencils were the family business for Henry David Thoreau. A new lode was discovered in China, giving rise to the yellow color we assume for the default and trade names such as “Mongol.” 

Alongside the rapid successive innovations of the 19th and 20th centuries, pencils were still sharpened with penknives. The first pencil sharpeners date to the 1890s and did not achieve the forms we accept today until after the 1930s. (Wikipedia has more to say about their development.) Into the 1980s, if not still a practice today, drafters at their drawing boards sharpened their pencils with sandpaper. I had mechanical drawing classes in junior high school (1962) and college (1978 and 1984) and that is how I was taught. 


Through all of that and into our time, the challenges have been to make consistent pencil leads in predictable grades, tough, strong, resilient, pliant, black (or other colors), and cheap; and do so by the millions, eventually billions. Graphite mixed with clay will not make a pencil. Only a few species of trees—mostly cedars—will do. The wood must be treated. The leads must be prepared. They are both in their ways shaped, formed, baked, boiled, heated, coated, stripped, and glued. While mechanical pencils—known since the 18thcentury—solve the problem of the wooden casing, they bring their own limitations. 

As a result of this book, I have been buying pencils, driving to office supply and art supply stores, giving long minutes to reading the pencils themselves, comparing their imprinted names and grades with the notecard I made for the purpose. I think that for myself, a 2-½ H or F would be best, but I cannot find them locally. Amazon has two brands, Mirado and Ticonderoga. I may have to give in and buy there.



Start the Presses! 

Art & Copy 

For the Glory of Old Lincoln High 

Dealers Make the Show: Armadillocon 41 Day 3 Part 2 


Monday, August 31, 2020

The Fountainhead: an exploded view of one scene

We lose the past too easily. Ayn Rand was born in 1905. In The Fountainhead, anyone of mature professional status 1922-1942 would have been a generation older. Rand studied in an architect’s office, working for free in order to understand the craft and the business. I was pleasantly surprised to be informed by another book of an underlying tradition in engineering design. It was an eye-opener.

From The Fountainhead:

“You will kindly explain yourself,” [said the Dean].

“If you wish. I want to be an architect, not an archaeologist. I see no purpose in doing Renaissance villas. Why learn to design them, when I will never build them?” [replied Howard Roark].

“My dear boy, the great style of the Renaissance is far from dead. Houses of that style are being erected every day.”

“They are. And they will be. But not by me.”

“Come, come, now, don’t be childish.”

“I came here to learn building. When I was given a project, its only value to me was to learn to solve it as I would solve a real one in the future. I did them the way I’ll build them. I’ve learned all I could learn here—in the structural sciences of which you don’t approve. One more year of drawing Italian post cards would give me nothing.” 


From The Pencil: A History of Design and Circumstance by Henry Petroski, Alfred A. Knoff, 1990:

Although orthographic projection was used in Albrecht Dürer’s 1525 book on the geometry of drawing, and theoretic foundations were laid down in Gaspard Monge’s 1795 book on descriptive geometry, the techniques and conventions derived from the work of these pioneers did not become universally employed in what has come to be known as mechanical or engineering drawing until the nineteenth century, when it became virtually indispensable for conveying information to machine shops and iron foundries. Up until about the middle of the nineteenth century, engineering drawing was learned in the long tradition of architectural drawing, and many early machines, such as large steam engines, were designed with iron structural elements cast in the forms of columns of the classical orders. Functional brackets were adorned with the classical motifs that students had learned in drawing classes, which consisted largely of copying increasingly complex architectural drawings, and one can only speculate on how much of what came to be known as Victorian architecture and structure was influenced by this practice. 


Through the middle of the nineteenth century architectural drawing was learned by most, though not all, draughtsmen by tracing. Hence technique was learned at the expense of theory. …  The mid-nineteenth century state of the art of engineering drawing was recorded succinctly in the preface to one of the earliest textbooks on the subject, An Elementary Treatise on Orthographic Projection, Being a New Method of Teaching the Science of Mechanical Engineering by William Binns. According to Binns…:

“… the usual mode of teaching… is from the ‘flat’—that is, from copy—the practice being to lay before each student of the class a drawing of some part or parts of a structure which he is requested to copy. This being done, another drawing, probably more elaborate, is laid before him; and the same course is pursued until he becomes tolerably expert with his instruments and brushes, and eventually able to make a very creditable or even highly finished drawing from copy. If, however, at the end of one or two years of practice the copyist is asked to make an end elevation, a side elevation and longitudinal section of his black-lead pencil, or a transverse section of the box containing his instruments, the chances are that he can do neither the one or the other.”



The Genius of Design 

Science Fair: A National Geographic Film 

Absolutes and Objectives 

There Really Are “Civil” Engineers 




Tuesday, August 18, 2020

Neighborhood Book Kiosks

The first one in my neighborhood appeared in February and I thought that it was unique. I saw another one a bit farther from home. It finally occurred to me that this is a phenomenon. I like it as an example of spontaneous order, an axiom in Austrian economics. Reading on Wikipedia revealed that other people think the same way that I do. And not everyone else is happy with us.  

This is the one in my neighborhood.
It has four sides with two panels of books and it rotates.
(I don't know who owns the easement.)

From The Atlantic

U.S. -- The Danger of Being Neighborly Without a Permit

All over America, people have put small "give one, take one" book exchanges in front of their homes. Then they were told to tear them down.

Conor Friedersdorf

February 20, 2015

Since 2009, when a Wisconsin man built a little, free library to honor his late mother, who loved books, copycats inspired by his example have put thousands of Little Free Libraries all over the U.S. and beyond. ... 

I wish that I was writing merely to extol this trend. Alas, a subset of Americans are determined to regulate every last aspect of community life. Due to selection bias, they are overrepresented among local politicians and bureaucrats. And so they have power, despite their small-mindedness, inflexibility, and lack of common sense so extreme that they've taken to cracking down on Little Free Libraries, of all things.


[Texans are a little more open to letting people do the right thing without permission from the government. Wells Branch is a neighborhood on the north side of Austin. Dell, HP, and others have campuses there.]


WBNA | Wells Branch Neighborhood Association

Little Free Library Boxes

Welcome to the Little Free Libraries Summer Scavenger Hunt!


Did you know there are currently 14 Little Free Libraries throughout Wells Branch?  LFLs are free book exchanges where anyone can “take a book, return a book.”  Join us in June for a LFL Scavenger Hunt.  You’ll have the opportunity to visit our neighborhood LFLs, find some great (free!) summer reads, and earn a chance to win a Barnes & Noble gift card.


Posted to Nextdoor dot com serving our wider subdivision

[ I found out that the Little Free Library boxes were not the first of their kind. “Book Crossings” appeared about the turn of the millennium.] 


Leaving reading materials in public places when no longer needed has long been a silent means of communication and sociability amongst bibliophiles. Ron Hornbaker conceived the idea for what is now known as BookCrossing in March 2001[2] and enlisted business partners and co-founders Bruce and Heather Pedersen[3] to launch on April 21, 2001.[4]


After two years the website had over 113,000 members and by 2004 it was prominent enough to be referenced in an episode of the Australian soap opera Neighbours.[5] The same year it appeared as a new word in the Concise Oxford Dictionary,[6] although as of 2017 only Collins of the major online dictionaries retained it as a word.[7][8][9][10]


On a busy backroad I take to the freeway.
It serves walkers well.
(Again, it seems to be on the property owner's
public easement.)

[From Wikipedia] Closely allied with the BookCrossing concept, the original public bookcases were conceived as artistic acts.[1] Very early examples are the creations of performance artist duo Clegg & Guttmann in 1991. Collections of bookcases were conceived as "free open-air libraries" in Darmstadt and Hannover in Germany in the late 1990s.[2]


Controversy and criticism[edit]

In 2003, BookCrossing was criticized by the astrologer and novelist Jessica Adams, who claimed that books were being "devalued" by the website as BookCrossing could lead to lower sales of books and, therefore, the reduction in royalties being paid to authors.[20] Most BookCrossers dispute this argument, however. They claim that the website introduces readers to authors and genres that they have not read before, that the website encourages more people to take up or reclaim reading as a hobby, and that some members, having read a book that they have enjoyed, will buy extra copies to distribute through BookCrossing.[21]


Another busy side road. 
You have to step up onto the property for this.

In March 2005, Caroline Martin, managing director of the publisher Harper Press, said in a speech that "book publishing as a whole has its very own potential Napster crisis in the growing practice of bookcrossing".[22] BookCrossers rebutted the link to Napster, saying that while music filesharing involves duplicating audio files countless times, BookCrossing doesn't involve duplicating books (and also does not involve violating copyright, as books can be sold or given away freely without permission of the publisher being needed). When BookCrossing was first launched, the founder of BookCrossing, Ron Hornbaker, originally wondered if people would make this comparison.[23]


[A related link on Wikipedia]

Give-away shops, freeshops, free stores or swap shops are stores where all goods are free. They are similar to charity shops, with mostly second-hand items—only everything is available at no cost. Whether it is a book, a piece of furniture, a garment or a household item, it is all freely given away, although some operate a one-in, one-out–type policy (swap shops). The free store is a form of constructive direct action that provides a shopping alternative to a monetary framework, allowing people to exchange goods and services outside of a money-based economy.


A neighbor told me about a different one.
I found this instead.
(Clearly on the front lawn.) 

[More from following the links in Wikipedia write-ups]

The anarchist 1960s countercultural group the Diggers[1] opened free stores which simply gave away their stock, provided free food, distributed free drugs, gave away money, organized free music concerts, and performed works of political art.[2] The Diggers took their name from the original English Diggers led by Gerrard Winstanley[3] and sought to create a mini-society free of money and capitalism.[4] Although free stores have not been uncommon in the United States since the 1960s, the freegan movement has inspired the establishment of more free stores.


Previously on Necessary Facts

Laissez-faire Criminology 

Spanish Coins on American Notes 

A Culture of Reality, Reason, and Freedom 

Tokens of Capitalism 


Saturday, August 8, 2020

Measuring Your Universe: Alan Hirshfeld’s Astronomy Activity Manual

This guide to hands-on learning instilled me with a sense of confidence about my ability to perform the basic mathematics of astronomy. The exercises start with measuring shadows to track the sun as evidenced by stone age monuments. Before the last one, the learner estimates the expansion rate of the universe according to Hubble’s Law. The learning does not end there. Prof. Hirshfeld is a good instructor, and the assignments come full circle. Having started with the Sun and Moon, the book ends by assigning the calculations to estimate the relative masses of Sirius and its dwarf companion. (Just to note: This is from the first edition of the book (2009); the second edition (2018) is a bit different; and a third edition is promised.)

The stars are pretty at any magnification. It is most important to understand what you are looking at. Following these structured exercises, I gained an intuitive understanding of how astronomy developed historically, and (more importantly) of my location in the universe.

First Edition. 2009.

It starts with the gnomon, basically a vertical stick in the ground. At the end of the shadow, you place a stone. In Chapter 2, several thousand years or generations later, you come to the conclusion that the angle of the Sun in the sky at mid-day is directly related to the length of the shadow relative to the height of the stick. Theta equals arctan(L over H). 


Hirshfeld provides good, simple explanations of the math, though not in depth. At the back is a tutorial on basic trigonometry. Neither is a substitute for a semester of trig. Hirshfeld just gives you the number 57.3 without telling you where it came from. Similarly, it is true that although you do not need much mathematics to benefit from the hands-on calculations, you do need some. Even so, Hirshfeld steps you through work that you will come back to again. The same basic formulas are applied repeatedly to new problems from measuring the diameter of the Earth to measuring the distances to the Moon and Sun and then to the stars.  


Even if you are completely math-phobic, you can still get a lot out this by at least reading through the exercises to appreciate how the Greeks, Galileo, Kepler, Newton, and the astronomers of the 19th and 20th centuries came to their conclusions. If all of the arithmetic and algebra is “digital” then “Activity 15: Picturing the Universe—How Photography Revolutionized Astronomy” is “analog.” 


I put off the central exercise of “Activity 14: Parallax” until I finished the rest of the book. I could have just worked through it on paper, but I wanted to set up a yardstick in the doorway between the kitchen and the living room in order to take my own measurements. Alan Hirshfeld is the author of Parallax: The Race to Measure the Cosmos; W. H. Freeman & Co., 2001. So, I wanted to give him his due and take my time with the work before reading the book.


Activity  1  The World's First Skywatcher - YOU!

Activity  2  Shadowland

Activity  3  Shadowland - the Sequel

Activity  4  Shadowland Follow-up

Activity  5  The Phases of the Moon

Activity  6  Eratosthenes Measures the Earth

Activity  7  Aristarchus Measures the Size and Distance of the Moon

Activity  8  Aristarchus Measures the Size and Distance of the Sun

Activity  9  The Copernican Cosmos

Activity  10  Kepler's Third Law

Activity  11  Isaac Newton and the Moon

Activity  12  Galileo Measures a Mountain - on the Moon!

Activity  13  Precision Astronomy After Galileo - Stellar Aberration

Activity  14  Precision Astronomy After Galileo - Stellar Parallax

Activity  15  Picturing the Universe - How Photography Revolutionized Astronomy

Activity  16  How Bright is That Star? A Tutorial on the Magnitude System

Activity  17  The Realm of the Spiral Nebulae

Activity  18  Hubble's Law - in the Kitchen and in the Universe

Activity  19  The Herzsprung-Russell Diagram

Activity  20  Binary Stars and Stellar Motions.

Appendix  Mathbits


In the second edition, Activity 19 is about Dark Matter. In fact, while I found the second half the H-R Diagram helpful, the introduction about height and shoes sizes was obvious. Perhaps plotting the land speeds and weights of various mammals would have been more analogous to the relationships between spectral types and luminosities. The second edition also replaced the work on Sirius A Sirius B with your own reflective essay. I believe that was a loss. The reflective essay could help the instructor modify the class. I still think that it would have been best left as extra credit. The H-R diagram is important to modern astronomy.

Although I have a calculator on my iPhone and my computer, I bought a new one just for this, a basic scientific TI-30Xa. It was $8.95 which is like 89 cents in 1978 dollars when we bought our first TI-30 calculators. The universe may not be expanding, but the money supply is. Still, I worked several of these in my head by approximation, 3 for pi, and so on. 



In Support of the Entry-Level Telescope 


Defending the Hobby-Killer Telescope 

Problems with Pop Sci from Sky & Telescope (Part 1)


Problems with Pop Sci from Sky & Telescope (Part 2)