Monthly Archives: April 2021

Euclid’s molecules

One of these days, we will get around to studying the history of music, and you will understand why Wagner was the high fructose corn syrup of his century. We still need to work on constructing a foundation for the study of music theory. That requires us to return to number theory, and Euclid.

In an earlier post, we discussed Euclid’s atoms, the prime numbers:

The main thrust of that article was to prove what some call Euclid’s theorem: there are infinitely many prime numbers. To be more precise: any finite list of primes excludes some prime number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

A prime number is defined as a natural number greater than one divisible only by itself and one. You might guess that prime numbers are very important in multiplication, and you would be right. Take the number 60, for example. Is it prime? No, it is composite, in multiple ways. 60 equals 2 times 30, 3 times 20, 4 times 15, 5 times 12, and 6 times 10.

In each of these factorizations, at least one of the factors is also composite, so it too may be factored as a product of smaller numbers. Keep factoring all the factors until you cannot factor any longer. Common sense tells us that the resulting irreducible numbers are prime numbers; otherwise we could continue the factoring process.

But will you and I always get the same list of factors? 60 = 2 x 30 = 2 x 10 x 3 = 2 x 2 x 5 x 3. However, it is also true that 60 = 6 x 10 = 2 x 3 x 2 x 5. The two lists of prime factors are not identical, unless – unless I am allowed to change the order. You can do that in multiplication, just as in addition. If we write the prime factors in order from smallest to largest, we must always get 2 x 2 x 3 x 5, or 2^2 x 3 x 5. (That first factor is 2 squared.)

Euclid’s Fundamental Theorem of Arithmetic states that every natural number can be factored as a product of prime numbers in only one way, assuming the factors are listed in order from smallest to largest. It is an incredibly important statement in number theory, that has major implications for musical scales.

But even though it seems obvious, as in our example, it is really not a triviality. In some of the more advanced number systems in higher mathematics, the Fundamental Theorem of Arithmetic is not true. Euclid’s genius lay in recognizing the importance of the proof, not to mention carrying out the proof.

Along the way, Euclid invented a technique known today as the Euclidean algorithm (a method) which has the reputation of being one of the most efficient algorithms in all of mathematics. It is so easy, however, a child could do it, because all it involves is long division of whole numbers.

For example, suppose we need to determine the greatest common divisor of 30 and 48 (the largest natural number dividing evenly into both 30 and 48). Euclid said: divide the smaller number into the larger – 30 into 48 – and keep track of the remainder. The number we seek is also the greatest common divisor of the remainder and the divisor.

In this case, 30 goes once into 48, with a remainder of 18. Now I seek the greatest common divisor of 18 and 30. I divide 18 into 30, which goes once with a remainder of 12. Next I seek the greatest common divisor of 12 and 18. I divide 12 into 18, which goes once with a remainder of 6. On we go – divide 6 into 12, which goes twice with a remainder of 0 – and that is the end. Euclid says that your last non-zero remainder, 6, is the number you sought: the greatest common divisor of 30 and 48. 6 divides both 30 and 48, and no larger number does both.

The Euclidean algorithm was pointless in this example, for anyone who knows the multiplication table. For much larger numbers, however, it is invaluable.

Next, Euclid challenges the person who might doubt the Fundamental Theorem of Arithmetic: find me the smallest natural number that can be factored in two irreconcilable ways, with different prime factors. That number must be composite, of course. Line up the two different rows of prime factors. All smaller factors of this number must have unique factorizations themselves. Euclid pulls out his famous algorithm to slowly match up, one pair at a time, the prime factors belonging to the two allegedly different factorizations. Voila! This number does not have two different factorizations after all. Silly goose!

Using this great theorem, we see that all the natural numbers are like molecules with unique chemical formulas. Just as water is always H2O, with two hydrogen atoms and one oxygen atom and never any other chemical elements, so too the number 60 can only be made up of two factors of 2, one factor of 3, and one factor of 5, and never any other prime factors.

The small diagram below shows a view of some of the smaller natural numbers, with 1 at the lower left. Every time you proceed up to the right along a maroon line, you are multiplying by 2. When you move up to the right along a blue line, you are multiplying by 3; green 5; lavender 7.

These are some of Euclid’s infinitely many molecules.

Latest pandemic and vaccine resources

Before we start with the news, I ask you to please keep Steffen Ritter’s wife in your prayers for a speedy and complete healing, as she goes in for knee replacement surgery on Thursday. We are now something of a virtual family, and as Chuck Fire noted, the quality of the discussion here is higher than many other blogs – thanks to all of you! Wolfie is my friend all the way back from Disqus days. His service to his country and to his God have been exceptional, and I know we wish his family the best.

Fellow blogger Nitzakhon is getting back into the writing saddle at Liberty’s Torch. He put together the usual well-researched article on the newest wave of coronavirus in India. It is very alarming to read.

Nitzakhon provides English-language resources to support Mrs. Surak’s suspicions reading Chinese-language blogs: namely, that the current variant of coronavirus ravaging India may well be outright biological warfare that is RACE-SPECIFIC in its target. Moreover, Mrs. Surak reads that Chinese with Indian friends are reporting that symptoms of the newest variant include bleeding from facial orifices (eyes, nose, mouth), very much like the Ebola virus, suggesting deliberate VIRAL ENGINEERING.

China is rubbing salt in the wound by warning India to back off of its alliance with America. Can World War Three be far behind? Consider too that Joe Biden is unlikely to stop travel from India until many Americans are infected. Under the circumstances, as Nitzakhon rightly warns, we must take the pandemic very seriously indeed. It is not just a cold. But the “vaccines” are equally problematic.

Here is one resource, called “No Jab for Me”, on the deleterious effects of the current “vaccines” (hat tip Nitzakhon again):

This much longer resource is a thorough, global documentation of “vaccine” injuries and deaths, called “Informed Consent Matters”:

Here is a very important reminder that… “Federal law prohibits employers and others from requiring vaccination with a Covid-19 vaccine distributed under an EUA”

Finally, investigative reporter Sharyl Attkisson provides evidence suggesting a connection between the development of CoVID-19 and one Anthony Fauci:

Mrs. Surak says that she has read that some doctors are more concerned about the long-term neurological consequences to CoVID-19 than the early inflammatory response. People may “recover”, and remain disabled for a long time, perhaps forever.

Under the circumstances, I am more inclined to be cautious than I was previously. I am happy to teach my summer class from home, and I would rather not go back on campus after all in the fall. I would rather stay home another year, and see how things play out from the pandemic waves and the aftermath of the “vaccines”.

God, please give us strength. We have no help but You.

Oikophobia, Tucker Carlson, and the ADL

There is a new outrage every day, of course. ABC, CBS, CNN, MSNBC, NBC, NPR, NYT, PBS, WaPo, Facebook, Twitter, and the like could not survive without some fresh outrage, something to retweet: #WeStandTogetherAgainstIndependentThought. You know, the thing.

You know that xenophobia is (irrational) fear of the strange, the foreign. In a limited way, I subscribe to a bit of xenophilia: interest in the strange and foreign. My interests in Western music and philosophy led me to study world music and philosophy. The long road back to my ancestral religion of Judaism involved the study of world religions. And our lockdown has been made bearable with the seasoning of (kosher) food from several continents.

For too many of our cognitive elite, however, xenophilia has been accompanied by oikophobia: fear, even hatred, of one’s own home. The itinerant Swedish-German-French-American philosophy professor Benedict Beckeld wrote a popular essay on this topic in 2019: “‘Oikophobia’: Our Western Self-Hatred”

Here is an excerpt: “…we may say that in the beginning, a people relatively uncivilized and uncultured, but possessed of great mobility and untested strength, awakens and, as it were, goes to war in service of its deities. Initial successes against surrounding peoples lead to greater wealth and prestige, and a national identity is forged, accompanied by literary epics and other accoutrements of culture. Eventually, the people reaches its pinnacle of success, with so much wealth that a broad and permanent leisure class can be established, and this era of greatest political power will generally coincide, more or less, with the pinnacle of the nation’s cultural and scientific achievements. There is finally enough wealth and power for the leisure class, and in many cases for people lower on the social ladder as well, to become more occupied with achieving higher states of wealth and prestige vis-à-vis their countrymen than they are with the health of the community itself.

This is where oikophobia sets in. Diverse interests are created that view each other as greater enemies than they do foreign threats. Since the common civilizational enemy has been successfully repulsed, it can no longer serve as an effective target for and outlet of people’s sense of superiority, and human psychology generally requires an adversary for the purpose of self-identification, and so a new adversary is crafted: other people in the same civilization. Since this condition of leisure and empowerment, as well as a perception of external threats as non-existential, are the results of a society’s success, success is, ironically, a prerequisite for a society’s self-hatred.”

Such an elite sees nothing wrong in replacing its own population, perhaps as a means to atone for alleged sins of past generations – or as a means of increasing profit margins. This replacement was named le grand remplacement, the Great Replacement, by French author Renaud Camus.

Wikipedia has grafted the words “conspiracy theory” as an inseparable suffix onto the phrase “great replacement”. The discussion page for that Wikipedia article features protests by a few readers that the great replacement is not a theory of any sort, but provable fact, based on census counts. The editors reply that they are not interested in mere facts.

Tucker Carlson alluded to this replacement in a discussion on Fox with Mark Steyn.

To this, the Anti-Defamation League, under the leadership of Obama assistant Jonathan Greenblatt, expressed high dudgeon. Tucker’s words, opined Greenblatt, were dog whistles to white supremacists, dog whistles which only the hard left are attuned to hear.

Greenblatt should listen to the speeches of the late Barbara Jordan against illegal immigration, and then tell us whether she was also a white supremacist. He also should study the immigration policies of China, India, Japan, and Russia, and direct his ire at them.

The ADL was founded in 1913 in response to the lynching of a Jewish man in Atlanta. In more recent years, it has expended no energy on fighting the abundant anti-Semitism on the left, apparently interested more in promoting leftist policies. It is definitely not a pro-Jewish advocacy organization.

Conservative blogs gleefully covered the controversy, and opened the hellish gates of savage hatred present on the kook right in the comments section. I have read such ugliness in the past few days that make me fear what may be right around the corner even for patriotic Jews. Some of these commenters expressed gleeful delight at the memory of the Atlanta lynching, apparently hoping that we would witness a return to such barbarism today. Those same blogs, some of them claiming to be pro-Israel and pro-Jewish, did not cover at all the strong denunciation of the ADL’s statements by right-leaning Jewish organizations.

Many of us have felt for decades that we were not represented by the existing Jewish communal organizations. In the links at the bottom of the blog, I have started to identify what I call “righteous Jewish voices”. (It is a happy coincidence that “righteous” begins with “right”…) For example:

“1,500 rabbis accuse ADL of ‘grossly misplaced charges of anti-Semitism’ in attack”

Has any conservative blog even published this information?

The Conference of Jewish Affairs, headed by author and television commentator Rabbi Aryeh Spero, is giving the non-leftist Jew a spiritual home as well.

In recent days, I have read about a possible schism in the Methodist movement, if memory serves, over the issue of same-sex marriage. I am not aware of any interest in lynching Methodists, however.

My personal preference is that America’s activist Jews just shut up and focus on Torah observance, but I cannot enforce that. Sadly, social media has eroded public discourse and radicalized people who think their bubble of like-minded friends constitutes a representative sample of their country; they are enraged to find this is not the case.

Those who suffer from oikophobia are warmly invited to find another country that is more congenial to their preferences: perhaps Somalia, Afghanistan, or North Korea.

The endless culture war: late April, 2021

The left are relentless. Demoralization, destabilization, crisis, new normal.

“Christian university sues to block HUD order forcing male student placement in female dorms” Res ipsa loquitor.

“Joe Biden Planning $1 Trillion More Spending for Child Care, Universal Pre-School, and Free Community Colleges” The community colleges may teach the arithmetic the students failed to learn in first grade, because they were too busy being taught critical race theory, global warming, and social justice. I suspect they will kick the can to graduate school, after they make STEM more “equitable”.

“Norfolk Police officer fired after anonymous donation to Kyle Rittenhouse defense fund” No privacy.

“Oklahoma State Senators Introduce Bill To Ban Critical Race Theory From Public Schools And Universities” This is likely to provoke a boycott of the state if it passes, because of the triggering content reminiscent of Rev. Martin Luther King, Jr., who progressives now consider to be a tool of white supremacy. From the article:

Teachers, administrators, and other staff would also be prohibited from teaching the following concepts:

  1. one race or sex is inherently superior to another race or sex,
  2. an individual, by virtue of his or her race or sex, is inherently racist, sexist or oppressive, whether consciously or unconsciously,
  3. an individual should be discriminated against or receive adverse treatment solely or partly because of his or her race or sex,
  4. members of one race or sex cannot and should not attempt to treat others without respect to race or sex,
  5. an individual’s moral character is necessarily determined by his or her race or sex,
  6. an individual, by virtue of his or her race or sex, bears responsibility for actions committed in the past by other members of the same race or sex,
  7. any individual should feel discomfort, guilt, anguish or any other form of psychological distress on account of his or her race or sex, or
  8. meritocracy or traits such as a hard work ethic are racist or sexist or were created by members of a particular race to oppress members of another race.

“Tennessee professor rejects ‘racist’ label in flyers distributed by colleagues” His “crime”, for which he was libeled, was being the faculty sponsor of a student chapter of Turning Point USA, a very mild conservative group. The school won’t defend him. I foresee a lawsuit.

“Virginia moving to eliminate all accelerated math courses before 11th grade as part of equity-focused plan” If everyone can’t be a genius, then no one will be. Harrison Bergeron, please pick up the discourtesy phone.

“Dems are out to destroy a Chauvin defense witness’s life and reputation” The former chief medical examiner of Maryland testified as a defense witness for Chauvin. Now the Maryland Attorney General will review all of this examiner’s decisions throughout his career. You must not tell the public that George Floyd had almost four times the lethal level of fentanyl in his blood, even if he did.

“Senate defeats legislation to ban discrimination against Asian-Americans in higher education” On a party-line vote. Remind me again which is the party for civil rights for minorities?

“Isaac Newton latest historical figure swept up in ‘decolonisation’ drive” Newton will be unpersoned, so to speak, but the cultural appropriation of his work will continue.

Thank you for bearing with me as I increase the number of posts here. These are mere news articles, of course, symptoms of an underlying sickness. We will discuss our response another day.

Pandemic and vaccine news: late April, 2021

As India is dealing with an enormous surge of coronavirus cases and deaths, some involving a “triple variant” (third-generation mutation), here are some of the top developments.

A very well written essay, with plenty of links and videos: “18 Reasons I Won’t Be Getting a Covid Vaccine”


Gynecologic and obstetric consequences of the vaccine are being minimized: “Unvaccinated Women Report Miscarriages After Interactions with Vaccinated People”

“French drug assessment center demands removal of all four widely used COVID vaccines”

This means Alzheimer’s disease and mad cow disease as potential consequences of the “vaccines”. “COVID-19 RNA Based Vaccines and the Risk of Prion Disease”

The Chinese dissidents whose blogs my wife follows believe that Xi and the CCP are unleashing a new wave of bioweapon viruses currently; that they have the goal of killing a large number of non-Chinese; that they are indifferent to the costs of a pandemic to their own people. These bloggers believe, further, that Putin is far more alarmed about China than he is about America, and presumably he believes that only Trump has the strength to stop China, not Biden.

Mrs. Surak says that Xi and the CCP must be stopped before they kill a large fraction of the human race. It looks like Peter Navarro and Steve Bannon and Dr. Li-Meng Yan have been right all along.