The Courage of Your Convictions

It is really easier to say nothing. You are under no obligation to say anything. If you must voice an opinion against some nonsense, it is enough to say that you disagree and leave it at that. Moreover, a postmodernist or someone similar will tell you that right and wrong are only cultural constructs. Of course that assertion itself is a cultural construct. And even a scientist will remind you that our ideas about truth have changed as new facts have been discovered and new theories developed to explain them. It was not always so. There was a time when a scientist would truly go to the ends of the Earth to prove a theory. 

Today, scientists are not alone in accepting a false theory of induction which asserts that we can only approach but never know the truth. 

From Susan M. Lea and John Robert Burke, Physics: the Nature of Things (Thomson Brooks/Cole; 1997). 

“Physics is an experimental science that prides itself in getting close to reality through laboratory testing of theory. … How can we be certain that the experimental process of dissecting nature into component part is ultimately correct? We can’t! Belief in experimental science depends on one’s worldview.” -- page 12.

 

“Consistency with experiment and usefulness in understanding nature are the properties of a good physical theory. The word truth is conspicuously absent. Aristotle… Kepler and Galileo… Newtonian physics, [were] thought absolutely true for 250 years. In the twentieth century, we have learned that Newtonian physics is not exact but stands as an excellent approximation. Absolute truth is elusive. We continue to seek greater depth in our understanding, greater elegance in our theories, and greater precision in our experiments. Whether truth can be achieved in some approximate sense by this process is unanswerable. We believe in physics because we know we can organize our knowledge and employ it to describe the behavior of nature with greater accuracy using only a small number of fundamental ideas.” -- page 14

Not all scientists are timid.

“As a scientist, Sagan speculated freely, sometimes wildly, and outraged his more cautious colleagues. ... He anticipated some interesting scientific discoveries, although sometimes (and oddly) for the wrong reasons. ... The price of fame is a big head, and Sagan’s grew mighty big; eyewitness testimony to this effect abounds.... Most scientists, by contrast, are rarely so self-assured. To them, Truth is a like a blob of mercury—it’s hard to pin down. Sagan’s air of omniscience made him seem sometimes slightly inhuman, more like Mr. Spock than Mr. Wizard.” ) Carl Sagan: A Life by Keay Davison, John Wiley & Sons, 1999, pages xiii- xiv passim.

 

When the American Astronomical Society sought to present Margaret Burbidge with the Annie Jump Cannon Award in May 1971, she rejected their offer.  

[quote] In a letter to AAS secretary Laurence Frederick, Burbidge wrote, “I believe that it is high time that discrimination in favor of, as well as against women in professional life be removed, and a prize restricted to women is in this category.” Underlying that official statement was the suspicion that the Cannon Award had kept women from receiving other recognition. In conclusion, Burbidge wrote, “It would be interesting to know, however, how often our names have been excluded from consideration for professorships, directorships . . . because we are women.” 

At that time, AAS offered two other awards—the Henry Norris Russell Lectureship, which honored an astronomer’s long and distinguished career, and the Helen B. Warner Prize, for astronomers no more than 35 years old. No woman had received the Russell. Burbidge was the only woman to have won the Warner Prize, in 1959, and she had shared it with her husband Geoffrey for their work on stellar nucleosynthesis.

From Physics Today 27 Feb 2018 in People & History: The award rejection that shook astronomy by Roberta Humphreys at https://physicstoday.scitation.org/do/10.1063/pt.6.4.20180227a/full/

Interviewed by Joe Rogan (YouTube here) Neil deGrasse Tyson said that while the dictionary definition of “atheist” applies to him, the functional definition does not. Functionally, he said, an atheist is someone who feels compelled to argue with religious people. He also said that he often uses the word “God” in the vernacular sense, as when he wished an astronaut friend, Godspeed, echoing “Godspeed, John Glenn.” 

 

On the other hand, Richard Dawkins advocates for militant atheism. Granting that religious people can be good, he refuses to relinquish the epistemological high ground. Not only does God not exist, as good as many people seem to be, only religion specifically allows and encourages them to be bad. Arguing against that proposition some people point to the atheists of communist governments—the USSR, Cambodia, and China--who carried out atrocities against people holding religious beliefs. However, despite claims to “scientific socialism” political Marxism-Leninism is really another religion: it has books of sole truth, a priesthood, and intense internal battles over dogma, none of which can be empirically verified. Whatever failings that scientists have as individuals—to err is human—they do not bomb each other’s classrooms and cafes. 

It is not a lack of standards or a want of values. Right and wrong exist and we can know them. Only physical force is forbidden. As the US Supreme Court ruled on the legality of polygamy in Utah (Reynolds vs. the United States 18 US 145; 1879):You are free to believe whatever you want; you are not free to do whatever you want. Personally, I believe that SCOTUS was in error on the wider issue. As long as no one was coerced, they were all free to do whatever they wanted. The fundamental truth remains, however: The strength and resiliency of an open society is a consequence of the interactions—even acrimonious debate—among people advancing their own ideas.

 

It is infamously known in astronomy that Cecilia Payne changed her doctoral dissertation to agree with the (widely accepted) theory of her advisor Harlow Shapley and astronomers generally that the elements are distributed in the stars very much as they are on and within the Earth. Payne found that hydrogen is a million times more abundant in the stars. Similarly, 80 years later, confronted with doubts from the highest authorities, Bruce Campbell and Gordon Walker retracted their claim to have found the first evidence of an exoplanet. Nonetheless, it remains foundational to the scientific method that you have to know when you were wrong. How you know is as much a matter of introspection as it is of epistemology. 

 

PREVIOUSLY ON NECESSARY FACTS

 

Karl Popper and His Enemies 

Karl Marx and the Dustbin of History 

The Scientific Method 

The Scientific Method (Revisited)

 

Merry Newtonmas 2022

The first recorded Newtonmas is credited to the Newton Kai at Tokyo University, circa 1891. Physics students had been celebrating with a party of their own in their undergraduate years. As they became graduate students, they brought some of their professors into the circle. The report is in Nature, Volume 46 Number 1193 Page 459, published 8 September 1892. So that party had been convened the Christmas before. 

 

I do not remember my flash of inspiration back in 1982. However, I was enrolled in physics at Lansing Community College and was the physics lab aide. Our professor for that class was Dr. Alan Saaf who more than once called a McDonald’s Quarter Pounder a “Newtonburger.”[1] So, Newtonmas could have been a logical leap. I sent out Newtonmas cards several times in the 1980s and recorded a Newtonmas greeting as a “Community Commentary” for WKAR-FM, the public broadcaster of Michigan State University in 1983 or 84.

 

For that, I built up the imagery of a little boy born in a small village across the sea who would grow up to bring light to the world. When I quoted the poet's eulogy – Nature and nature's laws lay hid in night; God said "Let Newton be" and all was light.—I emphasized the word Pope and then announced that Sir Isaac Newton was born on December 25, 1642, the same year that Galileo died.

 

Michael Shermer and the Skeptic Society have been celebrating Newtonmas for at least 25 years by now. Richard Dawkins touted it in 2007. And it was an element in an opening scene of Big Bang Theory Season 3 Episode 11, “Maternal Congruence.” 

 

Why do we not have Galileomas or Keplermas? Sir Isaac Newton stands as perhaps the most accomplished scientist in the modern world. At his level would be only Aristotle or only Archimedes. As much as we owe to everyone who invented something new, not every savant earns the same honors as Newton. 

 

He invented the calculus to prove his physics. He did that with geometry. When Richard P. Feynman attempted to recreate that work from scratch, he found that he could not. We  rely on algebra and calculus and have forgotten much. Newton’s physics demonstrated that the laws on Earth are the same as they are in Heaven. Heaven is not perfect; Earth is not flawed. Force equals mass multiplied by the second change in distances over times and the path of an object acting under central force motion always fits to a curve sliced from a cone. 

 

That would be enough. But Newton did more. 

 

He served two terms in Parliament, representing Cambridge University (1689-1702). He was president of the Royal Society (1703-1727). He found another proof for the Binomial Theorem (also known as Pascal’s Triangle). He found a clever shortcut for rapidly approximating square roots. 

His work in optics was fundamental to understanding light and, in truth, the entire electromagnetic spectrum. That work also led to the development of spectroscopy. Newton’s work in optics led to his invention of the reflecting telescope, which (unlike a refractor) introduces no chromatic aberration. 

 

While he was Warden and Master of the British Royal Mint for 30 years, he had himself sworn as a justice of the peace. He went disguised into the pubs where criminals exchanged wares and gossip. With the information he gathered, he arrested, interrogated, and prosecuted counterfeiters. The execution of the notorious William Chaloner hallmarked Newton’s labors to protect England’s money. Chaloner was a master criminal who even testified before Parliament in his efforts to rob from the Royal Mint with impunity. Clever as he apparently was, Chaloner was no match for Newton. 

 

In fact, no one was. 

 

Newton’s Principial Mathematica was more than the birth of modern astronomy or physics or science or mathematics. The Constitution of the United States with its balances of powers is a translation of the principles of physical science to the social world. You can get an ought from an is.

 

General Biographies of Sir Isaac Newton

Berlinski, David. Newton's Gift: How Sir Isaac Newton Unlocked the System of the World. New York: Free Press, Simon and Schuster, 2000.

Calligas, Elini (editor), Coincraft's 1998 Standard Catalogue of English and UK Coins 1066 to Date.London: Coincraft, 1998.

Keynes, Milo. “The Personality of Isaac Newton,” Notes and Records of the Royal Society (49), London: The Royal Society, 1995.

Marotta, Michael. “Sir Isaac Newton: Warden and Master of the Mint,” The Numismatist, Vol. 114, no. 11 (November 2001), p. 1302-1308, 1363 : ill., port. (George Heath Literary Award, Second Place, 2002)

Newman, E. G. V. “The Gold Metallurgy of Isaac Newton.” The Gold Bulletin Vol 8. No. 3, London: The World Gold Council, 1975.

Trowbridge, Richard J. Queen Anne, 1702-1714 Mystery Farthings. Long Beach: Coins of the British World, 1970.

Westfall, Richard S. Never at Rest: a Biography of Isaac Newton. Cambridge: Cambridge University Press, 1980.

White, Michael. Isaac Newton: The Last Sorceror. Reading, Mass.: Helix Books, Perseus Books, 1997.

www.newtonproject.sussex.ac.uk/, The Newton Project, Professor Rob Iliffe Director, University of Sussex, East Sussex - BN1 9SH

 

Newton at the Mint

(Sir John Craig was Deputy Master and Comptroller of the British Royal Mint.)

Craig, Sir John. Newton at the Mint. Cambridge: University Press, 1946.

Craig, Sit John. “Isaac Newton - Crime Investigator,” Nature 182, (19 July 1958), pages 149-152. 

Craig, Sir John. “Isaac Newton and the Counterfeiters.”  Notes and Records of the Royal Society (18;2), London: 1963, pages 136-145. 

www.royalmint.com/museum/newton Web site pages of the British Royal Mint. 

Shaw, W. A., F. B. A., Select Tracts and Documents illustrative of English Monetary History 1626-1730.  London: Clement Wilson, 1896; reprinted, London: George Harding, 1935.

 

Newton versus the Counterfeiters

Levenson, Thomas. 2009. Newton and the Counterfeiter: The Unknown Detective Career of the World's Greatest Scientist. Boston and New York: Houghton Mifflin, Harcourt.

Sources cited by Sir John Craig, Notes and Records of the Royal Society. (18;2), London: 1963, pages 136-145. 

Chaloner, William: Proposals.. ... to prevent clipping and counterfeiting, II.2.I694/5: Against raising £1,000,000 for the great recoinage, c. 3.1695: The defects.. ... of the Mint, 1697: Appeal after arrestc . I8.2.I698. (Four pamphlets.)

Middlesex Sessions Roll for 1699, containing original indictments at the Old Bailey, in the County of Middlesex Record Office, London. now in the London Metropolitan Archives.

Newton MSS. in the library of the Royal Mint; 5 large volumes of those papers from Newton's residence which were sorted by Conduitt as 'Mint'. 

Depositions about and letters from criminals, 1697-1704; one volume in the Royal Mint Library. 

Anon. GuzmanR edivivus, a short view of the life of William Chaloner, the notorious Coyner, who was executed at Tyburn on Wednesday the 22nd of March 1698/9; with a brief acount of his trial, behaviour and last speech. London: J. Hayns, 1699. 

Reasons Humbly Offered Against Pass an Act for Raising Ten Hundred Thousand Pounds by William Chaloner, 1694.

Proposals Humbly Offered, for Passing an Act to Prevent Clipping and Counterfeiting of Money, by William Chaloner, London, 1694.

 

[1] Just to note, 1 N = 0.2248 lbf and 0.25 lbf = 1.112 N. Dr. Saaf came to physics at LCC via astronomy at the University of Chicago. So, he probably would have accepted an order of magnitude approximation if the theory were useful.

 

PREVIOUSLY ON NECESSARY FACTS

Newton versus the Counterfeiter 

Merry Newtonmas 2021 

Of Watches and Beaches and Atheists 

 

LIKE SOMETHING OUT OF ATLAS SHRUGGED

Ayn Rand kept a "Horror File" of current news reports validating the worst aspects of her fictional universe in Atlas Shrugged. She said that she did that because often, in casual discussions at social occasions, someone would assert, "No one really believes those things!" or "No really says that." Well, yes, someone does and not just a random person but someone with social capital and personal status. 

Personally, I believe that from both an engineering standpoint and a market perspective, newer energy sources will eclipse oil and coal just as they outshone hardwood and charcoal. At the same time, I also believe in spontaneous order very well enucniated in Leonard E. Reed's essay, "I, Pencil" (Foundation for Economic Education here). 

Furthermore shutting off the oil that supplies you with heat and light and transportation will not deliver to me a solar-powered car, or a plasma power plant for my home.

More to the point, I believe that the people who oppose the production and delivery of oil today do not care if you have heat, light, and transportation (or food). They have them. So, they are satisified. And they have the leisure time to engage in an anti-industrial revolution. 

PREVIOUSLY ON NECESSARY FACTS

Jerry Emanuelson's Algebraic Proof of Ricardo's Law of Association

What is Legal Tender?

Money is Speech

Debt: The Seed of Civilization

The Great Gatsby an Alternate View and an Alternate History

The family is reading The Great Gatsby. It is something new for us. About 12 years ago our daughter and I read The Sun Also Rises. After that I read For Whom the Bell Tolls on my own. My wife and I have read some of the same books—I read four Rex Stouts for her; she read some cyberpunk scifi for me—but we never read together like a book club. 

About page 44 for me, Laurel asked about study guides and I examined four online, from the New York State Regents Examination Preparation down to GradeSaver and Shmoop. The Regents want you to know your tropes but the criticisms are all pretty much the same about the decadence of the Roaring Twenties. For the academic critics parallels to America today are impossible to ignore. I can take a different view. I can find in The Great Gatsby the hints and tendrils of new virtues then and now, supplanting Victorian sensibilities, which I can contend are also misunderstood by critical theorists from sociology and literature today.

 

Consider Jordan Baker. She earns an independent income as a golf pro, competing in tournaments. That would have been impossible before World War I. We easily accept that Nick Carraway sells bonds, but that, too, did not exist until about the 1820s. It could have been explained to a medieval banker or merchant factor. They bought and sold paper. Gaining understanding from a noble, knight, or peasant would have been difficult. Industrial capitalism of the mid-19^th century created the bonds markets to finance canals, railroads, etc. The soubriquet nouveau riche was an insult. It should have been a compliment, speaking to the creation of new wealth. 

 

When I read this in college (1967), the only thing that I took away was that Daisy’s ineptitude as a driver symbolized her inability to manage her own life. I understand. But, really, no one could drive back then. Today, we have two or three generations raised in automobiles, conditioned to perceiving the world at 60 mph. And cars are much safer with seatbelts, airbags, impact resistant superstructures, automatic transmissions, power steering, and steel belted radial tires. We still kill 40,000 people a year, but the population is three times larger than it was in 1925. So, the symbolism stands: Daisy is a wreck. That being so, automobiles nonetheless deserve context.

 

World War I was the turning point. When I cannot get to sleep, I imagine that I have a time machine and box of Barbara Tuchman’s The Guns of August and William Shirer’s The Rise and Fall of the Third Reich. To whom would they go? What would be the reaction? I could have the books on a Kindle or iPad, itself a wonder to underscore the veracity of the claims. (And then I am asleep.) But what if…? Had World War I not destroyed the status quo of Europe, what would the world of 1940 have been like?

 

I like to think that we could have been on our way to the Moon. The Internet would exist via telephone, radio, television, and teletype. But would any woman earn an independent income playing golf? Would women vote? 

 

I am enjoying The Great Gatsby for F. Scott Fitzgerald’s writing. I underline phrases and block off paragraphs of narrative. That in itself is motivation and reward. 

PREVIOUSLY ON NECESSARY FACTS

 

Aaron Feldman: Buy the Book Before You Buy the Coin 

For the Glory of Old Lincoln High 

Dealers Make the Show: Amadillocon 41 Day 3 Part 2 

Soldier’s Heart by Elizabeth Samet 

Libraries of the Founders 

 

Lunar Eclipse 8 November 2022

This was the last total Lunar eclipse until 14 March 2025. I got out early and took my time. Other snapshots have gone better. 

These were taken with an iPhone 11 on a Celestron NexYZ adapter connected to an Explore Scientific 102 mm f/6.47 refractor with a Nagler 32-mm Plössl ocular at 20X. Snapshots with an iPhone 5 did not go well this time. I also relied on a Celestron 32-mm eyepiece. For both, the Neutral Density Filters (“Moon Filters”) were from Celestron. These are the best of 45 tries.

Snapshot 1 just before 50% in the penumbra.

I got out at 1:00 AM CST for the 2:00 AM start and set-up went well. I made time to observe naked eye and through the telescope between exchanges of attachments. At 4:50, I stopped adjusting the hardware and only observed. 

The photographs do not represent the image captured by the eye. Naked eye, the Moon was never completely dark. Totality did not look like this. Also, the color was never a full startling red, only a dusky red-gray. 

Snapshot 38 close to 50% in the penumbra.

As the Moon passed 50% into the penumbra, darkness brought out the stars, about 150 in all including the Hyades and Gemini. Through the telescope, I viewed Messier 42, Messier 41, and the Pleiades. Mars was high in the west and even at 20X the sky was clear enough and dark enough to show surface markings on the planet. Predicted clouds arrived at 5:20 AM.

 

The fans kept the dew off. 
Dew point and ambient were close all morning.

Also, as soon as it got noticeably dark, the world got quiet. Past 50%, I do not recall hearing an emergency vehicle siren for the remainder of the morning.

 

PREVIOUSLY ON NECESSARY FACTS

The Antikythera Device 

The Drunken Astronomers 

Eclipses? 

Astrophotography and Me 

Observing with NASA: An Open Platform for Citizen Science 

Value and Worth

“What’s it worth?” Bill Bradford (Wikipedia here) asked me. That was about 1976 in his store, Liberty Coins, on Abbott Road in East Lansing. He continued: Is it worth what you paid for it? What you can sell it for? What it would cost to replace it? Over the years, I have considered the question. In 1990, I served on the board of ELFCO, the East Lansing Food Cooperative and chose the finance committee for my working task. There, I learned a lot from East Lansing entrepreneur Bruce Roth who sat on the board for many years and chaired the finance committee. Passed over for a job opportunity because I had no stronger experience in finance, I took a seminar in accounting for data processing at Lansing Community College. I do not remember if we did much with cost accounting but I do remember that you debit an asset to increase it. 

Some years earlier, the winter of 1972-1973, I sat in on a presentation on meta-ethics by Dr. William F. Schmidt in the home of Linda and Morris Tannehill. Bill Schmidt planned a futures trading company based on his algorithms for predicting change in the marketplace. He eventually had two satellite dishes feeding data. In 1993, I wrote computer programs for him because his IBM PC/AT computers (upgrades over the HP 9830s from too long before) were at their limit. (Necessary Facts here.).  I do not remember the content of his lecture that night and much of it was over my head at the time anyway. The essence was that in order to have values, you must have a standard of value.

 

To address that question, Ayn Rand posited an indestructible robot, asserting that as nothing could affect it, it could have no values. Any action or none at all would be equally consequential. (See “The Objectivist Ethics” in The Virtue of Selfishness. Ayn Rand Lexicon entry here: http://aynrandlexicon.com/lexicon/values.html)

 

Some years ago (2017), on vacation, I wrote out notes but never was able to wotk through the problems to a solution or a set of them. The essential problem is one of limits: by Rand’s standard, the farther you are from any threat, the more secure your life it, the less consequential your choices. She solves that problem with the open container of “Man qua man.”

 

The Objectivist ethics holds man’s life as the standard of value—and his own life as the ethical purpose of every individual man.

 

The difference between “standard” and “purpose” in this context is as follows: a “standard” is an abstract principle that serves as a measurement or gauge to guide a man’s choices in the achievement of a concrete, specific purpose. “That which is required for the survival of man qua man” is an abstract principle that applies to every individual man. The task of applying this principle to a concrete, specific purpose—the purpose of living a life proper to a rational being—belongs to every individual man, and the life he has to live is his own.

 

Man must choose his actions, values and goals by the standard of that which is proper to man—in order to achieve, maintain, fulfill and enjoy that ultimate value, that end in itself, which is his own life.

 

The standard of value of the Objectivist ethics—the standard by which one judges what is good or evil—is man’s life, or: that which is required for man’s survival qua man.

 

Since reason is man’s basic means of survival, that which is proper to the life of a rational being is the good; that which negates, opposes or destroys it is the evil.

 

“Man’s survival qua man” means the terms, methods, conditions and goals required for the survival of a rational being through the whole of his lifespan—in all those aspects of existence which are open to his choice.

 

("Standard of Value" paragraphs from "The Objectivist Ethics" in The Virtue of Selfishness. Ayn Rand Lexicon here: http://aynrandlexicon.com/lexicon/standard_of_value.html )

 

The statements are synonyms, tautologies, restatements in somewhat different words of the same assertion without evidence or demonstration. 

 

One of my favorite movie scenes (also in the book) is from 2010: The Year We Make Contact.  Curnaw and Floyd are homesick. “What I wouldn’t give for a hotdog at the Astrodome,” says Walter Curnaw. Floyd is taken aback “Astrodome?! You can’t grow good hotdogs indoors! Yankee Stadium. August. The hotdogs have been on the grill since opening day… The brown mustard.” 

 

But are they good for you? Are they pro-life? Are they appropriate to Man qua Man? Made from the lowest scraps of meat, spiced with artificial chemicals, each one is a cancer time bomb. 

 

An old joke goes that the doctor tells his patient that his health is at risk. Says the doctor, “Stop drinking, quit smoking, stop running around the bar scene chasing women.” The patient asks, “If I do that, will I live to be 100?” The doctor replies, “No. But it will seem like it.”

 

Aristotle’s Golden Mean offers some insight. Note first, that a problem underlies the concept of “eudaimonia” because it begs the question: What is the good life? In the Nicomachean Ethics, Aristotle gives a shopping list of attributes that a good person will have, such as a measured walk and tone of voice. That being as it may, the Problem of the Stadium Hot Dog does speak to Ayn Rand’s Indestructible Robot. If you are 17 years of age having one hotdog at one game is not going to kill you: you are closer to indestructible than destructible in that context. At the other extreme, if you are 75 years of age, diagnosed with incurable cancer and given a few years (at most), as destructible as you are, the hotdog will not be your demise: you might as well enjoy it. 

 

Rand does indicate a productive line of analysis: “… for the survival of a rational being through the whole of his lifespan …” For Rand, of course, “rational” meant more than volitional or self-aware, though those are requisites to her deeper meaning. The inclusion may be redundant because, for example, rocks have no values. However, I assert that cats do have values. It is easy to assert (being unable to ask them) that cats are not self-aware. Like dogs, horse, etc.,, they do not "have" emotions because they are their emotions. (Unlike horses and dogs, though, cats have three different names.) 

 

Back to the question at hand: the Problem of the Stadium Hotdog can best be evaluated in the context given: through the whole of your lifespan. 

 

What is a hotdog worth? Is it a mistake, an error in judgment? If so, what does it cost to remediate the problem? The fact of future value indicates that any investment now correcting a mistake in the present results in tremendous costs in lost returns on investment in the long future. 

No matter how small the interest rate—the rate of return being some measure of how your life will improve—compounding will make the final answer consequential. 

 

PREVIOUSLY ON NECESSARY FACTS

 

Morality and Ethics 

Choose Your Virtues

Understanding Objectivism 

A Good Place with Inadequate Philosophy 

Virgin Galactic VX01 VX03 

 

Footnotes on Number Theory

I love to watch the odometer. It is not always convenient to stop and take a picture. 

186285 miles were 1 Light Second

Kaprekar’s Constant

There’s a lot of these out there on YouTube. It is very popular in India, of course. 

Numberphile has it. I was disappointed that Mathologer did not. 

Take any four digits, as long as all four are not the same.

Order them highest to lowest and then lowest to highest. Subtract the smaller from the larger. Do it again. Soon, it reduces to 6174. Every time. I wonder how it works in different bases. 

Hidden Circle in Pi?

That is also a challenge that I have never pursued from Carl Sagan’s Contact.  He posits that if you extend pi out far enough-as I recall, in Base 11—you get a string of 1s and 0s that can be arrayed to display a circle. There’s always something else to do… but a computer program seems easy enough and it can run all night and probably not much longer with today’s MacBook, Dell, etc. 

Kaprekar's Constant from Numberphile

10 REM MIKE MAROTTA. FEB 5, 1987. NEWTON'S ALGORITHM FOR SQUARE ROOTS

19 LIMIT= .0001

20 PRINT "ENTER A NUMBER"

21 INPUT X

56 XN = X/2

60 R1 = (XN + X/XN)/2

70 IF ABS(XN-R1) < LIMIT THEN GOTO 80

75 XN = R1

76 GOTO 60

80 PRINT "THE SQUARE ROOT OF ";X;" = ";R1

 

Fast Square Root.
(She only does it for Primes.)

I first wrote this in the winter of 1976-1977, cadging time at the Michigan State University computer center when I was between terms at Lansing Community College. I used it again when I was employed (briefly) at the MSU campus bookstore. They had a Data General Nova for which the vendor delivered a “Business Basic” without algebraic functions. (“You don’t need them for business.”) I wanted to project economic order quantities, which does require finding a square root. I also wrote numerical expansions for natural and common logarithms and made the set into a library of callable functions.

Square Roots

YouTube has a ton of videos on calculating square roots by hand. In this day of cellphones, it is seldom necessary. But I found this video interesting and wrote a sticky note to hang on a monitor for a while. 

 

Another trick I use is based the binary search. Two or three iterations are usually enough. 

Sqrt(97) < 10. Guess 9.3. Square 9.3. Guess again. Richard P. Feynman has a story about beating a Japanese  abacus salesman in a bar in Brazil figuring like that in his head. “More digits! … More digits!”

 

PREVIOUSLY ON NECESSARY FACTS

 

Number Theory as an Adventure 

Nerd Nation: Natalie Portman, Danica McKellar, and Felicia Day 

The Man Who Loved Only Numbers 

Contradictions in the Patentability of Numbers 

Halloween 2022 on Brandi Circle

 We have dresseed for Halloween in years past. Being in costume makes it fun to give out treats. This year, among a dozen knickknacks, I bought elf years. I am not sure which character that wll be for.

The Werewolf wakes up at 2:30 PM and works until 9:30.
He will be working late for Halloween.

 

The giant and the dinosaur stand out. 

The Rider and Dragon need some walking around

 to be perceived within the very busy graveyard scene.

We are fixin' to start.

The things that go bump in the night are a little happier in this scene 
across from the werewolf.

Neatness counts. Nicely arrayed.

Marysville, Ohio, 2001

EOS North America, Pflugerville, Texas, 2019.

Selene, Miami Beach, 2015. Michael, Ann Arbor, 2008. 

With the mortgage meltdown and stock market collapse of 2008, 

I gave stock certificates to the adults in costume.

Previously on Necessary Facts

The Bloodless Corpse 

Fountain Pens

Like dressing for dinner, writing with a fountain pen helps you to be at your best. The direct descendent of the reed, it is the modern quill. A fountain pen requires focus on the line, the curve, and the mark. Even a quick note, soon to be discarded, carries importance, however briefly. 

 

The fountain pen requires maintenance and demands care and too easily leaves unwanted ink—sometimes alarmingly much—on fingers, papers, desk, and books. And it does not erase. A good ballpoint or roller ball will almost do as well on paper. Pencils have their virtues beyond erasability. The fountain pen needs no justification or excuse because it is the premier writing instrument.

Last year, I enrolled in several webinars about calligraphy that were sponsored by Mont Blanc. (I have a Meisterstück 4810 which was a present from an old and dear friend.) Following those, I unboxed my inventory and cleaned them up. Although I wanted the circa 1967 Sheaffer to be the everyday pen, its barrel was cracked and reinforced with scotch tape and the reservoirs fell off the connector pin. I bought new Sheaffers. One for calligraphy had an extremely lightweight body and never flowed well. I sent it back with a letter. They sent me another, much better. Another with promise of good heft does not accept the standard Sheaffer reservoir or any other from Sheaffer that I have found. So, it was back to ballpoints, rollerballs, gels, and fiber-tips. 

 

Taking the challenge again, I viewed YouTube videos from Gentleman’s Gazette and Figboot, and one from Prof. Richard McCutcheon, Dean of Arts at Thompson Rivers University. Then, I found a Figboot interview with Neil Degrasse Tyson. 

 

I cleaned the Mont Blanc and put a medium nib in another Sheaffer calligraphy pen. Yesterday, I went shopping. Jerry’s Artarama stopped carrying them. They sent me to Kinokuniya, a Japanese store. There, I found a Pilot that fills with a squeeze reservoir. I also bought an inexpensive Kawe Perkeo that accepts the “Euro” cartridges of which I have an unused box. I chose a red body for the Pilot and filled it with red ink (Mont Blanc). The Kawe nib is fine and the ink plain blue. The Mont Blanc and Sheaffer, both mediums, are black, though the Mont Blanc 585 nib is broader.  

 

PREVIOUSLY ON NECESSARY FACTS

 

The Pencil: History, Design, and Circumstance 

Pencil Notes: Reflections on Henry Petroski’s “The Pencil” 

Armadillocon 41 Day 3 Part 2 

Copy Rights and Wrongs