Jonathan Bartlett

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The Needless Complexity of Modern Calculus

_{How 18th century mathematicians complicated calculus to avoid the criticisms of a bishop}_{Jonathan Bartlett
March 8, 2021}

Would you be surprised if I told you that the essentials of calculus are actually very straightforward and simple?

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…

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…

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…

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…

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…

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…

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…

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…

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…