Brilliant Tutorials in Mathematics and Computer Programming

The name is the attractor. I certainly want to be brilliant, if only in my own estimation though not the world’s. About 272 days ago, we both signed up and paid $161.88 each. She is still mad at me because she paid for something that does not work. I pointed out that they say that they are hiring and proofreading high school math is exactly her kind of job. So, that ball is in her court. I still work the problems, even when the problems have problems. 

I usually work at night and sometimes I have to skip one (even two) sessions, but I earn battery charges that carry me over. 

So far, I have completed series in elementary algebra, geometry, and calculus in addition to Probability & Chance, Functions, and Vectors, and large sections of logic, data analysis, and some others. A few, I began and chose not to pursue. The lessons on Digital Circuits and Circuits are waiting for me to make time to haul out the breadboarding kits. (I want to see their answers.) 

The reviews are nice exercises at bedtime. I do most of the work in my head. Some got complicated and required pen and paper and some of those are long tutorials, which, if I quit, I lose my place and have to start over. (About the third pass, I have memorized the first several answers.) It’s bedtime reading. I do enjoy the learning.

Find sin(a+b). 

I worked this through over three nights and was able to conceptually integrate the lesson and the proof of the formula. 

The Pythagorean Theorem has over 300 published proofs (one of the them by Pres. James Garfield). The proof in Euclid’s Elements is one of the most complex and demanding and least intuitively obvious presentations of this well known truth. So, too, with this demonstration of the measure of the sines of two adjacent angles. Nonetheless, after several repetitions, I found it elegant.

But not everything works that well. I ran into bugs in their tutorials for polar coordinates and for modulo arithmetic. As I told Laurel when she discovered other errors, all that is required is to document everything with screenshots, write out a descriptive narrative to show your work, and send it to them. 

51 mod 3 = 0 and also 51 mod 17 = 0.
And 51 mod 2 = 1.
But not here.

The Polar Coordinates maths are inverted.

The iPhone can be a barrier. I stopped working in Python, computer science, and AI because it is easier on the keyboard and I seldom sit here before going to sleep. So, I do what I can in bed and let the rest slide until I can have some daytime hours free for fun and games. I did finish the packet on Algorithmic Thinking. 

For another overview, see Wikipedia here https://en.wikipedia.org/wiki/Brilliant_(website)

More pros and cons on Quora here https://www.quora.com/What-is-your-review-of-Brilliant-org

PREVIOUSLY ON NECESSARY FACTS

Elisha S. Loomis and the Pythagorean Proposition 

How the Martians Discovered Algebra 

The Man Who Loved Only Numbers 

G. H. Hardy’s ‘Apology’ 

Birth of a Theorem by Cédric Villani 

A Simple Truth 

Grigory Perelman’s Perfect Rigor by by Masha Gessen 

On Second Thought

 

PREVIOUSLY ON NECESSARY FACTS

Open Secrets

NYC, Covid-19, and Conservative Business Interests 

All Volitional Beings Deserve Rights 

How to Start Your Own Country 

200,000 Pageviews

On or about July 17, 2017, this blog tallied its 200,000^th page view. Launched on 2 January 2011, about 100 people per day read the posts, often as a result of Internet searches for topical information. Everyone can be a publisher, and perhaps too many people are. But I believe that we are experiencing a renaissance, a silver age, if not a golden age, in which the sharing of information – facts and opinions alike — creates a flourishing. Our lives are better.

In a previous post, I wrote about Jerry Emanuelson’s algebraic proof of Ricardo’s Law of Comparative Advantage. Emanuelson has other interests. He previously created and marketed a high school level kit for experimenting with superconductors. The Internet gave him an easy and extensive exposure.

Science hobbyists of our generation knew well the Edmund Scientific Catalog. Edmund also wrote about the scientific method. He taught it as a 14-step engagement in discovery. Norman W. Edmund lived long enough (1916-2012) to bring his work to the Internet (see here http://scientificmethod.com/index2.html ). It proved much more efficient than the U.S. Post Office.

The most popular articles from this blog so far are:

What (if anything) did Dorothy Learn? (4626)

Contradictions in the Constitution (2400)

Alongside Night to Run in Austin (1799)

Bob Swanson and Genentech (713)

William Sheldon: Psychologist, Numismatist, Thief (655)

Debt: the Seed of Civilization (556)

Crimes Against Logic: Exposing Bogus Arguments (409)

There is no John Galt and that’s Worse (356)

Supplies and Demands (340)

Romantic Realism (339)

Those numbers come from the Stats under the All time button on my control panel. However, I also have other numbers under View Count in the Posts:

Forgery and Fraud in Numismatics 1187

Debt: the Seed of Civilization 1183

Harriman’s Logical Leap Almost Makes it 884

(see, also, David Harriman’s Logical Leap 408)

Junk Criminology as Pseudo-Science 877

Nerd Nation: Natalie Portman, Danika McKeller, and Felicia Day 831

Unlimited Constitutional Government 797

ELI the ICE Man: Science and Technology 788

Hacking Computer Security: BSides Austin 2013 747

Art & Copy 729

Megacities 726

… that goddam Ayn Rand book 717

To Make Money 658

The Problem of Induction: Karl Popper and His Enemies 643

Employee Theft 639

The Fallibility of Fingerprinting 634

Sándor Kőrösi Csoma 626

Murray Rothbard: Fraud or Faker? 592

Shifting the Paradigm of Private Security 569

Venture Capital 566

Where All Children are Above Average 556

Karl Marx and the Dustbin of History 553

Gregory M. Browne’s Necessary Factual Truths 529

Republicans for Voldemort 528

Ayn Rand versus Conservatives 527

Firefly: Fact and Value Aboard “Serenity” 517

De Magnete by William Gilbert 466

George Boole’s Laws of Thought 459

Money as Press and Speech 439

Money as Living History 433

Against Gulching 396

Ma Kiley: Railroad Telegrapher 367

Short Snorters 354

The Virtues of Aviation Culture 339

A Successful Imitation of Alan Turing 335

The search terms that bring people here include Çatal Hüyük, (catal huyuk), supply and demand, supply and demand curve, contradictions in the Constitution, Merry Newtomas, and Employee Theft Facts. Although I write about Newtonmas every year, none of them makes the top of the lists.

Mirror sites

http://necessaryfacts.blogspot.de/

http://necessaryfacts.blogspot.fr/

http://necessaryfacts.blogspot.se/

http://necessaryfacts.blogspot.si/

http://necessaryfacts.blogspot.jp/

Among others…

PREVIOUSLY ON NECESSARY FACTS

Most Popular Page Views  (11 January 2017) 

Most Popular Necessary Facts (8January 2012)

100,000 Page Views

Crimes Against Logic: Exposing Bogus Arguments

The author calls this “a troubleshooting guide” similar to the owner’s manual of a car or computer. “It is aimed at everyday users and consumers of reasoning…” It certainly meets that measure. The main thrust is on failures of right reason such as inconsistency, equivocation, and begging the question. The author also reveals false claims, principally phony statistics.

Before moving into financial consulting and electioneering for the open market in his homeland of New Zealand, Jamie Whyte completed master’s and doctor’s degrees in  philosophy at Cambridge University (Wikipedia here).  You can find some of his essays archived at the Cobden Centre here. The Centre is named for the successful manufacturer and proponent of laissez-faire in early 19^th century Britain, Richard Cobden.  His writings are archived at the Online Library of Liberty here.

In formal terms, Jamie Whyte is an objectivist, a strict rational-empiricist whose logically consistent statements explain experiential facts. This book is his attack on some of the people who fail to meet either standard.

 

Crimes Against Logic: Exposing the Bogus Arguments
of Politicians, Priests, Journalists, and Other Serial Offenders
by Jamie Whyte. (McGraw-Hill 2004, 157 pages.)
Google Books has an extract of the first chapter
on why you do not have a right to your opinion, here. 

The first crime that Whyte investigates is the claim that you have a right to your opinion. No such right exists. Whyte points out that this assertion is founded on an ambiguity. You do have a political right to an opinion. However, that is not to be confused with the epistemic right to an opinion. The epistemic right to an opinion, says Whyte, is similar to the right to boast. Just as you first must achieve something worthy of boasting, so, too, is the “right” to an opinion earned by correctly identifying facts and then explaining them rationally. When someone retreats by claiming that they have a “right” their opinion, they are actually admitting that they are wrong, or at the very least, they can present no reasons and facts to support their assertions.

In the chapter “Prejudice in Fancy Dress” Whyte demolishes Pascal’s Wager and several other examples including Faith and Mystery. The subhead “But Still” examines calls for the acceptance of ignorance. This is actually a variant of the non-existent right to an opinion. Yes, the facts are on your side. Yes, your argument is logical. But still I prefer my prejudices.

The chapter “Shut Up!” scrutinizes several ways that those losing an argument seek to cut off debate by silencing their opponent. Well-known facts are boring. That a claim can be countered with a boring fact in no way mitigates the strength of the contrary assertion. That a boring fact has been marshaled is especially strong, as it points to a clear violation by the party demanding that the other shut up. 

Under the subhead “Shut Up, You Sound Like Hitler” Whyte calls mass murder “something of a lottery.”  He tells of being in a Lenin Bar in Auckland, “decorated with red stars and black and white images of the great Communist leader.”  Hitler bars, he notes, seem to be in short supply. 

In the chapter on “Empty Words” Whyte goes into some depth on the use and abuse of sneer quotes. His example focuses on post-modernist philosopher Imré Lakatos. When you say that my “facts” are in dispute, it is clear from the quotes that you do not believe my claims to be facts. Whyte says that in discussing the work of physicist A. A. Michelson, Lakotos’s excessive use of sneer quotes reveals that he believes knowledge to be impossible because facts are non-existent. This is not unique to one philosopher. Whyte calls the abuse of quotes a hallmark of post-modernist academic writing.

Implied Generalizations slip into discussions – and usually slip by unchallenged. Whyte offers a bald example. When a Christian says that homosexuality should be illegal because it is condemned in the Bible, that is an implied generalization because the Bible condemns many things, including the use of cotton-polyester blends. Backing off from making illegal the use of mixed fabrics (also working on the Sabbath and eating shellfish) then leads to an inconsistency. Whyte also offers a mundane example in Tony Blair’s active campaigning against fox hunting while insisting that other forms of hunting (including fishing) would never be proscribed by his government. Why not?  The implied generalization is that cruel sports are wrong. The resultant inconsistency is that some are acceptable after all.

The chapter “Begging the Question” is subtle and deep. Most of this book was fun to read and I had little difficulty relating to the material. Whyte is a good writer. His topic is compelling. His examples are from everyday experience. However, I read “Begging the Question” three times through and made close notes all along. It paid off well. Whyte sets up a debate in which libertarian Jack calls for an end to regulations. Socialist Jill claims that this would lead to mass poverty. In fact, Jill is begging the question. Jack’s position is that property rights are absolute. Rather than accepting the premise, Jill needs to address it by first showing that property rights are not absolute. Whyte then offers a longer discussion on tolerance. When a Christian fundamentalist asserts that abortion is murder, the response is not, “If you believe that, then do not have an abortion, but neither should you interfere with the rights of others to have them.”  Substitute the word “murder” for “abortion” and you can see that the plea for tolerance only begs the question: Is abortion murder or not? 

You will find discussions of false statistics, weasel words, hurrah words, morality fever, coincidences, and more. It is easily true that no one likes to be contradicted, but that is one way that we discover the truth. As Whyte points out, when you are crossing the street in the false belief that there are no cars coming, you don’t mind being contradicted. Intransigent devotion to the truth is always in your best interest.

  

(An earlier version appeared under Books on the Rebirth of Reason discussion site for September 3, 2008,  here.)  

PREVIOUSLY ON NECESSARY FACTS

George Boole's Laws of Thought

Gregory M. Browne's Necessary Factual Truths

Knowledge Maps

Harriman's Logical Leap Almost Makes It

Why Evidence is Not Enough