3.14159265

Today is Pi Day, and we commemorated the occasion by ordering an extra-large #2 (salami, mushrooms and sausage) from Toto's.

π is the Greek symbol for the value of a circle’s circumference divided by its diameter. Pi is the first irrational number (a real number that cannot be expressed as a ratio of integers) that I ever came across. The elementary-school arithmetic books only took pi out to four digits, i.e. 3.1416, but that felt unsatisfying. I looked up pi in the library and memorized it to eight digits,3.14159265. After high school I never had to use pi in a calculation, but I still know it, just like long-defunct telephone numbers.

BTW there was a lunar eclipse today. The congruence of the moon and pizza on the same day prompted me to play the 1953 Dean Martin hit while munching on Toto's #2.

When the moon hits your eye
Like a big pizza pie, that's amore
When the world seems to shine
Like you've had too much wine, that's amore

Spreading the Gospel of Net Present Value

Your humble blogger studied accounting and finance before the personal computer was invented.

The only electronic devices that we brought to class were calculators that performed basic arithmetic. And so it was that we labored over present value/future value problems, pencilling out intermediate solutions so we at least could get partial credit from the proctor.

After learning how the basic formulas were derived, we were taught how to use books of tables to bypass much of the repetitive drudgery in financial calculations. The future-value table below is from McGraw-Hill.

Until financial calculators and PC's came on the scene, such tables were used in finance for 3½ centuries(!) These tables seem extraordinarily crude today, but when they were first published in the 1600's, it sparked the widespread acceptance of "discounting" as an alternative payment. It wasn't businessmen or bankers who spread the word, but the Anglican church. [bold added]

In the early 1600s, the officials running Durham Cathedral, in England, had serious financial problems. Soaring prices had raised expenses. Most cathedral income came from renting land to tenant farmers, who had long leases so officials could not easily raise the rent. Instead, church leaders started charging periodic fees, but these often made tenants furious. And the 1600s, a time of religious schism, was not the moment to alienate church members.

Interest-calculation book from 1700.

But in 1626, Durham officials found a formula for fees that tenants would accept. If tenant farmers paid a fee equal to one year’s net value of the land, it earned them a seven-year lease. A fee equal to 7.75 years of net value earned a 21-year lease.

This was a form of discounting, the now-common technique for evaluating the present and future value of money by assuming a certain rate of return on that money. The Durham officials likely got their numbers from new books of discounting tables. Volumes like this had never existed before, but suddenly local church officials were applying the technique up and down England.

Spreading the "Gospel of Net Present Value" was one of the most important developments in capitalism. With apologies to the bard,

Neither a borrower or a lender be
But if you are either
Be mindful of the NPV.

Competitive Excel

The competitors take the stage in Las Vegas (WSJ)

Back in my day I was pretty good at building Excel spreadsheets. But I would never have come close to qualifying for the World Excel Championships, held December 7-9 in Las Vegas:

the omnipresent office spreadsheet software has spawned ranks of data geeks who see Excel as a sport. And here they were at the biggest table of them all: the Microsoft Excel World Championship, held at the HyperX Arena Las Vegas in the Luxor Hotel & Casino. (One floor down from a show by the comedian Carrot Top.)

...the thrills were off the charts at the main tournament, where rivals battled for the Excel championship over three 30-minute sessions that included both high drama and hexadecimals. Watching the action unfold on a giant screen, the live audience screamed cheers of encouragement and surprise and marveled at the rich data types, tables, monster functions, and the dreaded #ref error flashing before them.

Those who, er, excel at competitive Excel are able to identify classes of problems quickly (financial, statistical, dataset searching, etc.), select the functions (built-in algorithms like IRR and COVAR) that might be useful, and put together lines of calculation that produce the answers.

The above approach to spreadsheet building is frankly, anathema to accountants and many financial analysts. In real-world finance we have to build auditable spreadsheets that are reviewable by others. This means organizing linked spreadsheets so that one has the data inputs, others the calculations, and still others the reports. It also helps to write "notes" about what is going on in particular cells.

In Excel tournaments, where the object is to solve the problem in 30 minutes and there is no need, say, to have a work colleague run the calculations in the modeler's absence, many of these design techniques can be ignored.

That said, there is always a need for genius programmers that can get Excel to solve problems that seemed beyond the software's capabiities. At these tournaments it's nice they're finally getting some recognition.

Don't Hold Them Back Became Let's Give Them an Advantage

Katherine Johnson (1918-2020) received
the Presidential Medal of Freedom.

The 2016 film Hidden Figures was based on the true story of African-American women mathematicians who were crucial to the success of NASA's early missions. They had to overcome extreme race and sex discrimination, accompanied by condescending attitudes, to be taken seriously.

By the end of the movie their skill and reputation became so widely known at NASA that John Glenn insisted that the numbers be checked manually by Katherine Johnson, one of the "hidden figures," before his historic flight. She also performs emergency calculations to bring John Glenn home when one of his capsule's heat shields broke loose.

It's a popular theme in fiction and real life: the talents of a person who is discriminated against are so outstanding that the powers-that-be must call on the person to solve an important problem. Anti-discrimination narratives appeal to both the heart and the head: the former because the victims are treated unfairly and the latter because society's potential is unrealized by holding back skilled people.

60 years later the pendulum has shifted too far in the other direction. Anti-discrimination has given way to Diversity, Equity, and Inclusion (DEI) quotas. DEI is especially damaging in the technological contest with China: [bold added]

The Australian Strategic Policy Institute reported this year that China leads the U.S. in research on 37 of 44 critical technologies, including advanced aircraft engines, electric batteries, machine learning and synthetic biology. In a recent essay in Foreign Affairs, Dan Wang, an expert on China’s technology landscape, wrote that “China now rivals Japan, South Korea, and Taiwan in its mastery of the electronics supply chain.” In 2007, the Chinese added less than 4% of the value-added costs of iPhones made in that country. Now it’s more than 25%...

Given this challenge, you might imagine that America would re-emphasize the principles of objectivity and merit that made it the world’s leading scientific innovator. You would be mistaken.

Where it once was taken for granted that expanding knowledge was more important than a scientist’s sex or skin color, anyone adhering to that approach in the U.S. now must fend off charges that it is racist, patriarchal, colonial, or a tool of oppression. As a group of 29 scientists and academics contended in a recent paper for the Journal of Controversial Ideas, scientific progress in the West “is being hindered by a new, alarming clash between liberal epistemology and identity-based ideologies.”...

The U.S. will only find it harder to compete with China if activists and administrators are allowed to bully scientists into caring more about artificial diversity goals than about their work. To quote the 29 authors who stood up for merit, “for science to succeed, it must strive for the non-ideological pursuit of objective truth.”

In the liberal arts and social sciences, the DEI crowd can advocate for individual revealed truths and personal lived experiences. By contrast, those who work in STEM fields believe that there are objective truths, and the goal of science is to discover these truths. I am 100% sure that the mathematicians who worked for NASA would agree.

Reduce Inequality by Making Everyone Poor

(Image from Algebra I Review)

Back in the 1960's my school had two Algebra classes for 7th-grade kids who showed some aptitude in math, and the rest of our age group took Algebra in 8th grade.

It's a sign of how education has regressed that no one is offered Algebra I in San Francisco in middle school, even if a student is capable. Worse, the deliberate holding back is being done in the name of equity. [bold added]

For years, San Francisco public schools have been caught up in a bitter debate over the district’s math curriculum. A vocal group of parents has argued that the district’s decision to delay teaching Algebra I until high school hobbles children who are ready to take the math course in middle school. But some experts and district leaders have argued that pushing back algebra can level the playing field for kids who are struggling in math.

This is what happens when you put Progressive ideologues in charge of education. They reduce inequality (how that ever become the objective instead of encouraging children to develop their individual gifts is baffling) by hamstringing the top performers, as opposed to lifting up those on the bottom.

This ideology would have a talented musician play basic chords until the tone-deaf can catch up, or have track athletes wear ankle weights so the slower kids can keep pace.

Give the advanced kids as much as they can handle, and offer extra help to those who are struggling--and here's an idea--try to make it fun.

That's Amore

It's easy as π (3.14159265...) to calculate
the square inches of the 16" wheel

In honor of Pi day (3.14.23) we ordered pizza last night. Our favorite joint was closed on Tuesdays, so we ordered take-out from Velo City Pizza. (The name isn't as clever as the owner thinks.)

The #2 special--sausage, pepperoni, mushrooms, bell peppers, black olives--was delish. The crust was thin and crisp, the cheese and tomatoes didn't overwhelm, and the spicing was delicately complex.

The verdict was unanimous: we have a new favorite pizza place.

When you take the night off, that gives customers a chance to sample the competition.

Math Education Debate Goes as Expected

A policy debate about whether to teach Algebra in middle school has embroiled Berkeley and Stanford professors on opposite sides. Tweets by the professors and others have escalated into charges of racism and police harassment.

Background: non-white, non-Asian students have fallen behind in math, and the State has produced a 900(!)-page math framework to foster "educational equity." [bold added]

Jo Boaler

Stanford University Professor Jo Boaler has led the effort to rewrite the state’s math framework with a stated focus on students of color and English learners. Her work is now the catalyst for a proposed statewide math framework similar to San Francisco’s, which pushed Algebra 1 to ninth grade.

But Boaler’s work has drawn ire from those who want algebra as an option for eighth-graders and worry that without it, taking calculus in high school — which selective colleges often expect — becomes difficult...

Elizabeth Statmore

That debate boiled over Tuesday after a math teacher at San Francisco’s Lowell High School who opposes Boaler’s approach posted on Twitter a contract that seemed to show the professor made $5,000 an hour to train teachers in the Oxnard school district...

Yet the contract included not only Boaler’s fees, but her home address — which, Twitter notified the original poster, was a violation of the social media site’s policies. The Lowell teacher, Elizabeth Statmore, said she wasn’t aware the contract included a home address and deleted the posts.

After Elizabeth Statmore took down her tweet about Jo Boaler's fees, the personalization of the debate could have been defused. Then a Berkeley math professor got involved. (bold added]

Jelani Nelson

UC Berkeley Professor Jelani Nelson, who teachers electrical engineering and computer science, however, retweeted one of Statmore’s posts about the contract, criticizing Boaler for “alarmingly lucrative consulting deals.”

Nelson told The Chronicle Tuesday evening that he didn’t retweet the post that included the address.

Boaler said after his retweet that she contacted Nelson via email, notifying him that police and lawyers were taking up “the sharing of private details about me on social media.”

“I was shocked to see that you are taking part in spreading misinformation and harassing me online,” she wrote to him in an email.

Nelson, who is Black, then posted the email online, accusing Boaler, who is white, of unjustly calling the police on a Black person.

“A professor just threatened me with police. After BBQ Becky, Permit Patty, Golfcart Gail, and all the memes, we now have Retweet Rachel,” he posted on Twitter. “Public advisory: don’t call the cops on black people for no reason. Black people disagreeing with you on Twitter is not a crime.”

The people in this debate do upend a few stereotypes. Lowell teacher Elizabeth Statmore calls for more academic rigor, as does Jelani Nelson, despite his being quick to play the race card.

Nevertheless, it's a very sad commentary on the times that discussions over serious matters seem inevitably to be pulled toward the racial and sexual identity of the speakers, their biases, and motivations (which people who don't know them personally seem easily to ascertain). The accusations are blasted widely on Twitter, then the mob gets involved, resulting in threats to people and property. One can barely recall the substantive arguments.

After all that sturm und drang, a few changes have been made to the proposed framework:

After extensive feedback, the framework toned down some of the social justice language that inflamed critics. However, it changed from the current framework to suggest Algebra 1 in middle schools should be a local decision. The state Board of Education is expected to vote on the framework in July.

When your humble blogger went to school, Algebra in eighth grade was the norm; it was offered in seventh grade to "advanced" students. 55 years later, the educational establishment seems to be saying that Algebra in eighth grade is either too tough or shouldn't be taught for "social justice" reasons. I've long since ceased to be angry at the current state of affairs and am just sad.

The Other Dismal Science

(Image from the balance)

I never gave a thought to actuarial science until I went to business school. One of the smartest guys in the class had been an actuary, which I came to understand was too tough a career choice if I had to be as smart as he was and pass difficult, technical exams. (BTW, he's now CFO of a well-known company.)

Digression: so I became a CPA, which meant sitting for two days of exams and working for two years in the audit department of a CPA firm. The latter path was easier, and besides, I've never had to pay anybody to do my taxes.

Apparently, becoming an actuary is even tougher these days: [bold added]

Among people taking at least one exam from the Society of Actuaries—the field’s biggest U.S. credentialing body—15% eventually pass the multiple tests required to become an Associate, one of two designations allowing them to practice. Just 10% pass those and additional tests to become a Fellow, the group’s higher designation, which affords bigger responsibilities and salaries.

It’s such an arduous process that the number of test-takers has been declining in recent years, and the society is making changes to keep candidates from dropping out of the gantlet. It is also adding new “predictive analytics” tests to adjust to the massive amounts of data insurers now have...

There is no limit to how many times a candidate can take the tests. It took one man 50 years to become a Fellow, says Stuart Klugman, an official at the society. The society says a candidate typically takes seven to 10 years to become a Fellow. They must pass 10 exams plus other coursework and requirements.

Every profession is being inundated with oceans of data, and being familiar with data science has become essential to being an actuary. Knowing how to filter, analyze, and model the data is crucial to success. (We noted the importance of predictive analytics three years ago.)

If one is not thorough, knowledgeable about statistics, and honest, one can easily promulgate misinformation by biasing the data sets, selecting or not selecting variables to be analyzed, finding causation in correlation, and not "showing the work" so that results can be replicated.

Why must an actuary be honest? Because as the analyses become more complex, and as the demand for risk assessment (not only for insurance purposes) explodes, there are fewer people who are available to check the work; actuaries must be trusted not to force through results that please the powers that be.

I was glad that I didn't try to become an actuary.

Just for fun: the article presents a sample question involving rudimentary statistics and algebra. Without using a calculator, I could still solve it. (My high school self could have figured it out much more speedily but would also have snickered throughout at the phrase "blue balls.")

“An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn.”

NBA Finals: Unexpected and Interesting

Giannis Antentokounmpo and Chris Paul (nba.com)

The NBA playoffs have been a war of attrition, with teams trying to survive with their best players being knocked out of the playoffs. If every team was at full strength, we would probably be watching a Lakers-Nets final, but without Anthony Davis, Kyrie Irving, or James Harden both favorites lost in the early rounds. Nevertheless I'm watching.

Perennial All-Star and Hall of Fame shoo-in Chris Paul had never played in a conference final, much less in a championship.

He made the Phoenix Suns a sentimental favorite; at 36, the point guard is running out of chances to get a ring. However, I also feel sympathy for two-time MVP Giannis Antentokounmpo, a young, likeable, talented giant who has trouble making free throws (like a pro golfer who can drive the ball 350 yards but can't make a 5-foot putt).

So I like both the Phoenix Suns, who have never won a championship, and the Milwaukee Bucks, whose last title was 50 years ago. Both teams are flawed but seem evenly matched, and the last two games were decided in the final minute.

Now, a small complaint about modern sports commentary. Analysts bombard the audience with statistics, some interesting but many times not. If they're going to occupy our precious attention span, please don't waste it on triteness masquerading as insight.

Going into Saturday's game, reporters kept repeating the fact that in a series tied at 2-2

the team that wins Game 5 has gone on to win the series 72% of the time (21-8).

Note: Milwaukee won and holds a 3-2 lead in the series.

When kids are introduced to algebra and elementary statistics, they are asked to construct a simple coin-flip table and calculate the probability of getting heads twice in a row. There are four possible outcomes to two coin flips, so there's a one-in-four chance (25%) of getting heads twice.

But what's the probability of getting at least one head in the next two flips? Obviously, the answer is 3 out of 4, or 75%.

If the NBA finals has two evenly matched teams (almost by definition, if the games are split 2-2), then a simple statistical model in the absence of data would predict that the team that wins Game 5 goes on to win the championship 75% of the time. The actual result, 72%, is well within the range of expected outcomes in a population of 29 data points.

The surprise would be if the historical record produced a number higher than 80% or lower than 70%. Now that would be interesting.

[Update - 7/20/21: The Milwaukee Bucks won Game 6, making them NBA champions. Their victory adjusts the historical record slightly: teams that win Game 5 become champions 73.3% (22-8) of the time.]

STEM + A

(Graphic from poetsandquants)

Your humble blogger has always been in awe of the STEM (science, technology, engineering, and mathematics) professions. The feeling started in college; the classmates who majored in these courses were very smart and, frankly, worked harder than I did. They didn't necessarily become scientists or engineers; many became doctors, which requires lots of STEM.

Sufficient aptitude in math and statistics enabled me to enter the fields of accounting and business finance and, as they say, put food on the table. But I never thought that accountancy was as technically demanding as engineering, biochemistry, or computer programming.

However, some politicians do. The House of Representatives bill HR 3855 proposes [bold added]

To amend the Student Support and Academic Enrichment Grant program to promote career awareness in accounting as part of a well-rounded STEM educational experience.117th Congress (2021-2022)

(Image from Mindy Barker Assoc.)

Ever since STEM was identified as a national priority in the early 2000's, STEM education funding has steadily increased regardless of which party controls the White House or Congress.

It's great that accounting has been accorded some respect and that accounting education may soon be eligible for Federal support. There is an acute shortage of accountants relative to open positions.

Respect the green eyeshade!

Secure, Transparent, Auditable, and Reliable Voting

Homomorphic encryption: the picture helps a little

Protecting voting systems against hacking is difficult, and the principal reason is not government incompetence or corruption but the requirement of the secret ballot:

modern elections enshrine privacy at the cost of transparency, and try to compensate for the loss with a host of bureaucratic patches: voter-registration schemes to prevent people from voting twice, tally systems that ensure the number of voters matches the ballot total, and centralized polling places where rival election monitors can scrutinize the proceedings, all to impart legitimacy to a system of vanishing ballots.

“If you want to understand why elections are hard, it's because of the secret ballot,” says [MIT Comp Sci PhD Ben] Adida—that's the single variable “that introduces all of the operational complexity and trust.” Not for nothing did a leading technology conference recently declare voting the “hardest problem in IT security.”

A promising solution lies in homomorphic encryption, related to the same technology that produced bitcoin.

In 1987, [Microsoft cryptographer Josh] Benaloh's thesis at Yale spelled out how a homomorphically encrypted voting scheme would come to life. First, voters would need access to a machine that could perform advanced cryptography. When they cast their ballot, each digital vote would start out as a simple binary—1 for Biden, 0 for Trump—but its ciphertext might be thousands of characters long. Rather than send voters home with a binder full of hexadecimal gibberish, the computer would print the ciphertext as something much smaller: a hash code, much like how a URL is shortened into a Bit.ly. That would serve as the voter's unique receipt, which they would keep and carry away with them.

At the end of the night, when the computers stopped whirring, all those encrypted votes would be added together. A small number of election officials—the county clerk, the secretary of state—would possess a key that allowed them to decrypt the sum. They'd compare the columns of votes for each candidate and reveal the winner.

Thanks to the nature of the math involved, those resulting sums would also be verifiable by independent outside observers. After the election, all the encrypted votes could be posted on a public, online bulletin board for all to inspect. Using a set of mathematical operations called Chaum-Pedersen protocols, auditors would be able to crunch all those ciphertexts to arrive at what cryptographers call a non-interactive zero-knowledge proof: “Proof that the vote is correctly captured,” Benaloh explained, but without any way to know whose ballot said what.

But the thing that excited Benaloh most was what this scheme would mean for individual voters. When a voter left the polling place, clutching a receipt that bore their unique hash code, they could go home and perform a search for its twin among all the encrypted ballots on that massive public bulletin board. For the first time, elections would not only be verifiable, but people could be certain whether their specific vote had been counted, all without violating the secret ballot.

Even if STAR (secure, transparent, auditable, and reliable) machines could be produced, convincing election officials and the general public that they perform according to specifications will require extraordinary wisdom and patience. To non-experts--which are most of us--the mechanism looks like a black box, and everyone knows that black boxes 1) can be hacked and 2) have "back doors" built in by the makers.

Maybe homomorphic encryption will be too hard a sell and we should just go back to the way we used to do it. Yes, elections were stolen back then, but the methods weren't mysterious. And paper voting systems can have STAR qualities, too:

the reliance on paper in key states may strengthen voter confidence this year. Arizona, Florida, Georgia, Michigan, North Carolina, Pennsylvania, Virginia and Wisconsin all have voter-verified paper trails in place for November. This changes the total number of voters using a paper trail to almost 95 percent, according to voting experts. That’s up from 75 percent during the last presidential election.

In two or more weeks the votes will be tabulated. The continuity of the American experiment will depend upon 60 million voters trusting the process even though their candidate lost. Never in the past 160 years has that trust seemed so fragile.

Yes, Do This at Home

The quietest Saturday night, probably ever, at BJ's

It was Pi Day on Saturday, and BJ's Brewhouse was offering a mini-pizza for $3.14. The youngster and I decided to avail ourselves of the promotion, and besides, who knows how much longer we'll be permitted to dine out? (Not long, it turned out.)

I brought out the canister of Clorox tissues and wiped down our area. Hey, I wasn't the only one doing it. Hypochondriac, thy name is legion.

We feasted on our pies, made more enjoyable by a $10 coupon that expires on April 5th. It was fortunate that we used it.

Last night health authorities ordered residents of six Bay Area counties, including San Mateo, to "shelter in place": [bold added]

Six Bay Area counties announced “shelter in place” orders for all residents on Monday — the strictest measure of its kind yet in the continental United States — directing everyone to stay inside their homes and away from others as much as possible for the next three weeks in a desperate move to curb the rapid spread of coronavirus across the region.

The directive was set to begin at 12:01 a.m. Tuesday and involves San Francisco, Santa Clara, San Mateo, Marin, Contra Costa and Alameda counties — a combined population of more than 6.7 million. It is to stay in place until at least April 7. The three other Bay Area counties — Sonoma, Solano and Napa — did not issue similar mandates.

Just outside the Bay Area, Santa Cruz County late Monday also announced a “shelter in place” order for its 275,000 residents.

The orders — which are all similarly worded — fall just short of a full lockdown, which would forbid people from leaving their homes without explicit permission. The orders (read San Francisco’s here in its entirety at tinyurl.com/waddyqv) call for county and city sheriffs and police chiefs to “ensure compliance,” and local authorities said they would not “rush to enforce” the directives as residents adjusted to understand what activities are no longer allowed. Violation of the orders is considered a misdemeanor punishable by a fine or jail time.

Businesses that do not provide “essential” services must send workers home. Among those remaining open are grocery stores, pharmacies, restaurants for delivery only and hardware stores. Most workers are ordered to stay home, with exceptions including health care workers; police, fire and other emergency responders; and utility providers such as electricians, plumbers and sanitation workers. BART will run for essential travel, and airports are not closing.

I heard the news on the radio and rushed out to buy some replacement faucets and light fixtures at Home Depot. It was a relief to discover that hardware stores will remain open during the near-lockdown; any project, no matter how small, always involves more than one trip to Home Depot.

Zero

May, 2019: the Ride of Silence for traffic casualties (Chron)

Perhaps you haven't heard about Vision Zero, San Francisco's 2014 action plan to eliminate traffic deaths by 2024. It's not surprising that there's been little publicity: [bold added]

We’re five years into the 10-year goal. And yet just two-thirds into 2019, 22 people have lost their lives on the city’s streets. That’s one less than died in all of 2018 and two more than died in all of 2017. We’re on pace to surpass the 31 deaths in 2014, the year Vision Zero began....

One major factor is a dramatic drop in tickets issued to drivers by San Francisco police — a neglect that could be explained by too many unfilled vacancies in the department’s traffic division and ever-changing leadership of the crucial unit.

New figures obtained by The Chronicle show the San Francisco Police Department is ticketing far fewer drivers for illegal behavior behind the wheel than it did the year Vision Zero was adopted.

Ticket-writing for the most dangerous driving behaviors has fallen dramatically:

Vision Zero directs the Police Department to focus its enforcement on the five most dangerous driving behaviors: speeding, failing to stop at a red light, failing to stop at a stop sign, failing to give pedestrians the right of way, and failing to yield to pedestrians while turning.

The number of citations for those specific behaviors are also distressingly low. Of all the citations handed out in 2014, 30,613 were for those five violations. While that number climbed at first, it fell off dramatically in 2018. Last year, police officers handed out just 20,154 tickets for those five violations. In the first half of this year, they handed out just 10,267.

That's what one gets when politicians--in fact, any leaders--make big promises and don't put their time and more money behind them: zero.

A Good Movie Despite the Math

The camera sends a message. (Image from Medium)

One of my favorite movies of recent years is The Martian, the story of an astronaut who must survive on Mars for a year and a half with only a fraction of the food needed for survival.

A key plot point is how he and NASA can communicate armed only with a still camera that can rotate 360 degrees.

The astronaut can write brief messages to Earth on poster board, but how can Earth send messages to him? The answer: a circle with 16 positions corresponding to hexadecimals:

This is where hexadecimal or base 16 comes in. If we allow ourselves 16 number symbols, then our place values can multiply by 16 at each step. For example, the number 321 represents one unit, two 16s and three 256s, so it is the same as the decimal number 801.

The trouble is that hexadecimal requires 16 symbols, and our usual numerals only go from 0 to 9. The solution is usually to use the letters A, B, C, D, E and F for the extra symbols representing the decimal numbers 10 to 15.

This means that hexadecimal numbers can look like C9F, which represents F (i.e., 15) units, nine 16s and C (i.e., 12) 256s—that is, 3,231. In coding, for instance, colors can be represented as six-character strings in hexadecimal, which yields a total of more than 16 million possible colors, starting at 000000 for pure black and running through FFFFFF for pure white.

In hexadecimals, i.e., base-16, only two characters, FF, are necessary to count up to 255 (in our decimal system). 255 places are more than we need to translate hexadecimals into the standard letters, numbers, symbols, and control characters of the ASCII table.

More than 50 years after converting base-10 numbers into base-2, base-8, and base-12 (by hand, without calculator or computer, kids), I finally see why the teachers made us do it.

(From LookupTables.com)

No "Yes, But's" Allowed

At Northeastern University computer-science majors are required to take a course in theater and improv.

(GIPHY Image)

The course requires public speaking, lecturing on such nontechnical topics as family recipes. Students also learn to speak gibberish—“butuga dubuka manala phuthusa,” for instance.

The class is a way to “robot-proof” computer-science majors, helping them sharpen uniquely human skills, said Joseph E. Aoun, the university president

All the world's a stage, nerds, so you'd better get used to it.

As for liberal arts majors, laugh it up, fuzzballs, but a little science, technology, engineering, and math will get you on the good side of our future robot masters.

Home and Hope: Conversation Over Dinner

I piled the plate with the casserole and sat across from the mother and two kids. Volunteers for Home and Hope not only prepare dinner but engage in dinnertime conversation with the guests.

A.J. corrected his mother on her word usage. Disrespect by pre-teens toward parents is not unusual, but it's atypical to show it by means of vocabulary.

Do you like to read, A.J.? He shook his head.

"He likes math," said five-year-old Taylor, who immediately peppered him with addition problems using the biggest numbers she knew, i.e., "what's 100+50?" Addition being no sweat, a couple of questions about multiplication quickly showed that he had mastered those tables, too.

But math, in fact any subject, should be fun, not a test. I recounted the story about a famous mathematician who as a child was asked to calculate the total of the series

1+2+3+4+5....+100 = ??

(This is a familiar tale, but perhaps there are a few humanities majors reading this.) The child solved the problem quickly, confounding his teacher. How did he do it? A.J. puzzled for a minute, then shook his head.

Using pen and paper, I wrote the series in reverse order:

1+2+3+4+5....+100
100+99+98+97...+1

The total of the two series is 101+101+101+... one hundred times. So the solution is 100 x 101 divided by 2, or 5,050.

The mathematician was Carl Gauss, (1777-1855) who was seven when he came up with the answer.

A.J. enjoyed hearing about how kids in those days were pretty smart, too. If I see him again on Thursday night [update: i didn't--they had dinner elsewhere], we'll resume talking about how people, before computers, could still accomplish a lot by just using pen and paper.

We Know What We Are Talking About

The revelation that U.S. consumer debt is nearly a record $13.0 trillion made for fevered commentary, but Matt Drudge's blaring headline prompted a chuckle:

If you see the absurdity of showing the ".00", then you, dear reader, have a feeling for significant digits.

Here's an accounting joke that reflects the same concept:

An accountant visited the Natural History museum. While standing near the dinosaur, he said to his friend, “This dinosaur is 2 billion years and 10 months old.” “Where did you get this exact information?” the friend asked. “I was here 10 months ago, and the guide told me that the dinosaur is 2 billion years old.”

We give out precise information because people then think that we know what we are talking about.

Accountants Get Respect

In honor of April, a very taxing month, I rented The Accountant from Netflix. Ben Affleck stars as Chris Wolff, an adult high-functioning autistic with genius skills in accounting, martial arts, weaponry, and mathematics. He also has the problems of those afflicted with autism and Asperger's, such as difficulties socializing and adapting to unexpected events, and hypersensitivity to sight, sound, and touch.

There are several mysteries that propel the story: how did the Accountant acquire his skills, what is his relation to law enforcement, some of whom regard him as an arch-criminal, and what's going on with millions of dollars appearing and disappearing from Living Robotics, a company about to have an IPO?

There's a lot of violence and gunplay, and all the major mysteries are explained by the time the credits roll.

I enjoyed the movie not only because of the unusual characteristics of the protagonist but also because the writers took the risk of inserting some finance-geek dialogue. It's about time accountants got respect!

Financial statement analysis unearths the problem

A big reveal, though "not in a commensurate fashion" doesn't have the ring of "Luke, I am your father."

Finance Like We've Never Seen Before

Quantitative finance: a grind to mostly
everyone, a dance for Peter Muller
(Forbes photo)

Finance like we've never seen before - Peter Muller's PDT Partners hedge fund: [bold added]

During 2015, when many hedge fund managers–from mighty activists like Bill Ackman to noted short-sellers like David Einhorn–lost money, Muller spun the market’s volatility into gold. The largest fund of his three-year-old PDT Partners firm, which oversees $4.5 billion, was up 21.5% net of fees in the first 11 months of 2015.

Peter Muller, polymath:

At Princeton he studied math and played in a jazz band...In 1992 he joined Morgan Stanley in New York as a proprietary trader to see if he could use math and computers to trade himself....Nobody outside the bank knew it, but for a long time Muller was Morgan Stanley’s supersecret weapon, making big contributions to its earnings each year, hidden in the firm’s income statement under “principal transactions.”...Crossword puzzles became an escapist obsession; he even created them for the New York Times....He went on sabbatical, rediscovering his love of music partly by busking in New York subway stations and sojourning in far-off places like Bhutan.

Peter Muller's ceiling won't be set by Wall Street competition, but by the limit of his own desire.

The Best Number

Six writers of varied backgrounds opine on "What’s the best number?"

Their answers--13, 17, 42, 747, 200 billion, and infinity (∞)--are by turns whimsical and thoughtful.

On Sunday, the first day of the week, it may seem fitting to celebrate ONE, the beginning of the natural numbers, and the rank that everyone is striving to be in the good old U.S. of A.

I'm partial to THREE, however. It's the day of the month when I was born and connotes stability (a three-legged stool, a tricycle versus a bicycle). Besides, three is the limit of the number of things I can retain in memory.

As we visit our place of worship today, three is also a reminder that the world and beyond are more complicated than the monotheistic one.

O blessed glorious Trinity,
Bones to philosophy, but milk to faith,
Which, as wise serpents, diversely
Most slipperiness, yet most entanglings hath,
As you distinguish'd, undistinct,
By power, love, knowledge be,
Give me a such self different instinct,
Of these let all me elemented be,
Of power, to love, to know you unnumbered three.
                    ---John Donne