Jonathan Bartlett

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Antiracism In Math Promotes Racism and Bad Math

_{If you are scratching your head over how math might be racist, you are not alone}_{Jonathan Bartlett
February 26, 2021}

Recently, a conglomeration of California education associations got together to work on a series of resources for mathematics teachers. The goal? Eliminate racism in mathematics classes by promoting Equitable Math. If you are struggling to imagine how mathematics could be racist, you are not alone. I am certain there exist racist teachers, and probably teachers who exhibit racist expectations of their students. I would support any reasonable action to get rid of or reform such teachers. But that is not the primary goal of these resources. The website, equitablemath.org, instead believes that the very way that mathematics is commonly taught is not just racist, but is specifically white supremacist. While I consider myself to be somewhat of a mathematics reformer (see this …

The Myth of “No Code” Software (Part III)

_{The complexities of human language present problems for natural language programming}_{Jonathan Bartlett
February 22, 2021}

Many visions of the future include humans programming through “natural language” — where humans merely state what they want and computers “figure out” how to write code that does what is requested. While there have been many demos that have led people to believe that this will be possible, the truth is, the idea has so many problems with it, it is hard to know where to begin. Let’s begin with the successes of natural language programming. Wolfram|Alpha is probably the best-known natural language programming system. You type in a command in natural English, and Wolfram|Alpha converts that command into native Mathematica code and runs it. In 2010, Stephen Wolfram announced that Wolfram|Alpha signified that natural language programming really was going …

The Myth of “No Code” Software (Part II)

_{Why (and where) no-code doesn't work}_{Jonathan Bartlett
February 10, 2021}

In my previous article, I noted that what programmers do is translate ambiguous specifications into very exact specifications, taking into account all of the specific subtleties that the implementation requires. However, I recognize that those not familiar with custom software may not recognize the problem. This article describes in additional detail the kinds of considerations that cause no-code solutions to be problematic. The essence of the problem is this: there are an infinite number of possible ways your business could possibly work, but only one way that it actually works. The work of the programmer is to make sure the software matches the specific way that your business works. Let’s take something simple like calculating shipping. It might be easy enough to say, …

The Myth of “No Code” Software (Part I)

_{"No code" software has its place, but not as a replacement for programmers}_{Jonathan Bartlett
February 8, 2021}

For at least the past twenty-five years of software development, people have been claiming that, using this tool or that tool, we will be able to build software with “no code,” and that our tools will build code for us. The claims have varied with whatever the current technology is. In the 1990s, the idea was that we could have a system which allowed building software entirely with drag-and-drop interfaces. Tools such as Visual Basic, Delphi, PowerBuilder, and even Microsoft Access made people think that this was an achievable dream. It turned out not to be deliverable on its promises. We’ll get more into the “why” later on. Today we have a new set of tools and a new set of dreams. We have claims that GPT-3-based systems will be able to write code for …

Who Is Allowed in the Smoke-Filled Rooms of Investment?

_{How the stock market is manipulated, using the GameStop episode as an example}_{Jonathan Bartlett
January 30, 2021}

Full disclosure: I continue to maintain positions in some of the stocks mentioned in this article. But, as you will see, my goal here is neither to promote stock or dissuade from it, but rather to ask a deeper question about who is allowed to do what about a stock. For those who are unaware, the last two weeks in the stock market have gone crazy. GameStop (GME), a company that continues to lose money, skyrocketed from $18/share to, as of the time I’m writing, just about $450 per share. That’s right the stock soared over 20 times in value over the period of a few weeks. Several other stocks have also skyrocketed, including AMC Entertainment (AMC) and Koss Corporation (KOSS). Koss, for instance, went from $3/share to over $140/share. So what triggered this inflation of value? A …

Bitcoin: What’s Good, What’s Bad and What’s the Future?

_{Bitcoins are currently bouncing in the range of $30,000 to $40,000 each}_{Jonathan Bartlett
January 19, 2021}

Bitcoin has been having quite the wild ride over the last several months, and especially the last several weeks. During 2020, the price of a single bitcoin dipped below $5,000, then soared past $20,000 in December. It is currently bouncing in the range of $30,000 to $40,000.So what is the attraction of the digital currency Bitcoin? Why is the value of a bitcoin so high and what are people doing with it? To begin with, keep in mind that a “single bitcoin” is a bit of a misnomer. While a single bitcoin is indeed expensive, coins can be split. The smallest unit in Bitcoin is known as a satoshi, which is 0.00000001 bitcoin. While the quoted price is always given for full coins, one doesn’t have to have the cash for a full coin in order to use the system. So why did bitcoins soar …

Can We Add New Numbers to Mathematics?

_{We can work with hyperreal numbers using conventional methods. It could start in high school}_{Jonathan Bartlett
January 18, 2021}

Sometimes mathematics is moved forward by the discovery of new formulas and solutions to problems. However, sometimes mathematics grows by adding new kinds of numbers to the number system. In the early days of mathematics, it was thought that whole numbers were the only kind that existed. Sure, there were fractions, but fractions are merely ratios of whole numbers. It was thought that every possible number could be written in terms of whole numbers. These numbers were called rational numbers because they could be written as a ratio. There is a story about a Greek philosopher, Hippasus who discovered, roughly 2500 years ago, that certain numbers (specifically the square root of two) could not be written in terms of ratios at all. In other words, it was an irrational number. The …

Gödel’s Incompleteness Theorems: The Cause—and Cure—of Wokeness?

_{Why do so many people today think there are only arguments, not facts?}_{Jonathan Bartlett
December 31, 2020}

In modern “woke” ideology, there are no facts, only arguments which express cultural power— based on the acceptance of those arguments by current society. In such ideologies, it is not important whether or not the arguments are logically consistent or if they are true in any real sense. What is important is whether or not they achieve the desired results in politics and society. This is not a criticism. It is a description of their methodology (for a review of the academic literature on the subject, see the book Cynical Theories by Helen Pluckrose and James Lindsay. Many people wonder how we got here. Why do so many scholars actively reject logic as a method of finding the truth, and reject truth-finding altogether as a valid enterprise? Here, I am going to present a …

Is Technology Always Progress? Let’s Talk About That

_{Tradition itself is a type of technology}_{Jonathan Bartlett
December 30, 2020}

We often make a sharp distinction between “traditional” and “modern.” We view tradition with distrust, assuming that we are simply latching ourselves onto arbitrary decisions from yesteryear. Technology, on the other hand, is viewed as progressive. Rather than entrenching us in the past, technology is supposed to propel us into the future. Technology is the way that we structure our environment in order to maximize our productivity and happiness. We use technology to automate away the bad and boring parts of work, and emphasize the fun parts more predominate. We use technology to boost our productivity to make sure that everyone has everything that they need. What most people miss is that tradition itself is a type of technology. Tradition deserves our respect, attention, …

How Toxic Bias Infiltrates Computer Code

_{A look at the dark underbelly of modern algorithms}_{Jonathan Bartlett
December 14, 2020}

The newly released documentary Coded Bias from Shalini Kantayya takes the viewer on a tour of the way modern algorithms can undermine justice and society and are actively subverting justice at the present moment. Coded Bias highlights many under-discussed issues regarding data and its usage by governments and corporations. While its prescriptions for government usage of data are well considered, the issue of corporate use of data involves many additional issues that the film skirts entirely. As the film points out, we are presented these algorithms as if they were a form of intelligence. But they are actually just math—and this math can be used to, intentionally or unintentionally, encode biases. In fact, as Bradley Center fellows Robert J. Marks and George Montañez …

How Bayes’ Math Rule Can Counter Unreasonable Skepticism

_{Mathematics is much more interesting if we know a bit about the players and their positions}_{Jonathan Bartlett
December 1, 2020}

Yesterday, we discussed the importance of Bayes’ rule in statistical reasoning. We used the example of a person who goes for a battery of screening tests and comes up positive for HIV. Let’s say she is surprised (and alarmed) because she is not at any known risk for HIV. But, it turns out, the risk of false positives for the test is several times greater than the incidence of HIV in the population. In that case, it is reasonable for her to suspect—on a statistics science basis, not just wishful thinking—that the test is a false positive. The formula we used is part of Bayesian reasoning, originally developed by an eighteen-century British clergyman and mathematician Thomas Bayes (1702–1761), but now widely used to assess probabilities. When Bayes first proposed his …

Can an 18th Century Statistician Help Us Think More Clearly?

_{Distinguishing between types of probability can help us worry less and do more}_{Jonathan Bartlett
November 30, 2020}

Thomas Bayes (1702–1761) (pictured), a statistician and clergyman, developed a theory of decision-making which was only discussed after his death and only became important in the 20th century. It is now a significant topic in philosophy, in the form of Bayesian epistemology. Understanding Bayes’ Rule may be essential to making good decisions. Let’s say that you are a generally healthy person and have no symptoms of any illness and no specific risk factors for any illness. Acting on a friend’s suggestion, you get screened for a variety of diseases, just to be sure. Of the diseases you test for, the HIV test comes back positive. You read on the package that the test is 99.6% accurate. Are you more likely to have the disease or not? This question might seem simple, …

To Fix Math Education, See It as a Program That Needs an Update

_{As a computer programmer, I’ve seen this problem in my work: The basic idea is still sound but “fixes” have made it too complex}_{Jonathan Bartlett
November 26, 2020}

In this series we are looking at ways that math education can be reformed. In contrast to some other math reform efforts, we are not trying to fundamentally rewrite what math education is doing but to simply admit that we can do better and see where that takes us. (See Part 1, Part 2, and Part 3.) Here in Part 4, let’s look at specific content issues that, I will argue, we could improve when we do a curriculum revision. Mathematics is an old subject. We have inherited quite a bit of mathematical thought. We must educate future generations so as to make sure that this hard-won knowledge is not lost. But one of the biggest impediments to our task is simply the way in which mathematics is presented. Here is an illustration that may help: In computer programming we sometimes talk …

Helping Students See How Math Benefits Them in the Long Run

_{To keep them motivated, we need to answer the “Why bother?” question honestly and directly}_{Jonathan Bartlett
November 25, 2020}

In this series we are looking at ways that math education can be reformed. In contrast to some other math reform efforts, we are not trying to fundamentally rewrite what math education is doing but to simply admit that we can do better and see where that takes us. (See Part 1 and Part 2.) Here in Part 3, we will concentrate on making the curriculum more “conscious” of what students are supposed to be learning in mathematics. One of the primary complaints students have about higher mathematics is that they don’t see where they are going to use the information later in their jobs. There are a number of ways of answering this question but first I want to emphasize the importance of having an answer to give. While we might wish students would just trust the system, the fact is that …

Straight Talk About Fitting the Math Curriculum to the Student

_{We need to avoid pushing too much too soon, lest students come to see themselves as “bad at math” when they are just not ready for it}_{Jonathan Bartlett
November 24, 2020}

In this series we are looking at ways that math education can be reformed (Part 1 here). In contrast to some other math reform efforts, we are not trying to fundamentally rewrite what math education is doing but to simply admit that we can do better and see where that takes us. This article, Part 2, will concentrate on improving math education by better identifying where students are when we encounter them. Mathematics curriculum is generally developed with a goal of “fitting it all in.” That is, educators assume that people learn at a relatively fixed pace. They then pace the lessons so as to fit all of them into the curriculum in the right amount of time. However, this approach has almost no relationship with how students actually develop in mathematical ability. Starting …

How Can We Really Fix the Way Math Is Taught?

_{First, we must understand why we teach math in the first place}_{Jonathan Bartlett
November 23, 2020}

Many people recognize that there are problems with modern mathematics curricula. However, the solutions proposed by current would-be math reformers are, I fear, worse than the cure. Some reformers want to stop having kids memorize their arithmetic facts, some want kids to just use computers to solve their problems, others think that the way we teach mathematics is racist, and still others seem to want to just greatly reduce the quantity of math education altogether. In this first part of a four-part series of short posts, I want to look at the most basic question: Why do we teach math? Earlier this month, an article by Yoree Koh in the Wall Street Journal took a look at the “Movement to Modernize Math Class”: “‘Freakonomics’ co-author Steven Levitt and other reformers …

What Real Advantage Do Self-Driving Cars Provide?

_{It’s time for a hard-headed look at the costs and benefits of the pursuit of fully self-driving cars}_{Jonathan Bartlett
November 18, 2020}

More and more people are realizing that autonomous (self-driving) vehicles are not a road to automotive prosperity. To recap, Level 5 self-driving is what most people think of when they hear the term “self-driving.” You type in an address and the car takes you where you want to go while you sleep in the back. That car is not going to hit the road anytime soon. Level 4 self-driving is similar but only works within well-defined areas or situations. In practice, Level 4 essentially relies on either intelligent infrastructure or a territory that is so predictable and well-mapped that it obviates the need for intelligent infrastructure. Huge amounts have been invested in self-driving vehicles. The Information estimated that $16 billion dollars have been invested in research on …

Twitter Twitted Over Clumsy Political Censorship

_{Getting the algorithm to censor users can backfire and sometimes the results are funny}_{Jonathan Bartlett
November 9, 2020}

I once wrote an online forum system called Areopagus. It had a simple “bad words” (profanities, etc.) filter. It looked for common bad words and common variations of those words and automatically prevented any post containing those words or their variations from being posted. This is called “mechanical censorship” and, on its own, it is nothing new. Some users came up with cleverer variations of the bad words than the filter was set for and then moderators had to spot and remove the posts. During the recent presidential election campaign, Twitter has taken mechanical censorship to new levels. Instead of censoring ways of speaking, Twitter has decided to censor specific ideas and thoughts. Automatic censorship of ideas is a problematic use of technology in itself but Twitter …

Daimler, Waymo, and GM Make Big Gains in Level 4 Self-Driving

_{GM has been given a permit to test five driverless cars on streets in San Francisco later this year}_{Jonathan Bartlett
November 2, 2020}

The Society for Automotive Engineering (SAE) has identified five levels of self-driving which describe how much a particular vehicle is able to handle its own driving tasks. Level 1 means that the vehicle handles either the speed or the steering, but not both, and it requires supervision. While ordinary cruise control technically falls into this level, most people associate cruise control with adaptive cruise control, which slows down or speeds up with traffic. A Level 2 car can control the speed and the steering but the driver must still maintain full vigilance. At Level 3, the driver need not maintain total vigilance but must still be able to take control upon request. Level 4 is “full self-driving” but limited to specific locations and/or conditions. For instance, an …

Self-Driving Cars: Waymo Beats Tesla By Picking the Right Target

_{Trying to get the human out of the loop, as Musk proposes, becomes increasingly costly as the complexity increases}_{Jonathan Bartlett
October 26, 2020}

Full self-driving has been a contentious topic in the last few years. In 2016, Elon Musk started claiming that his cars had all the hardware needed to do full self-driving, and that the software would be there by 2019. You would be able to summon a car from across the United States and it would drive across the country, recharging as needed, to pick you up, no driver needed. He has specifically indicated that he means Level 5 autonomy, which means that no driver is needed at all. The driver can sleep, watch a movie, or just hang out in the back seat. In fact, in 2016, he indicated that drivers were merely there for regulatory purposes. Musk’s claims about full self-driving have continued apace. He led people to believe that they could eventually put their car on a “robotaxi …