Tag: education

Common Sense Calculus

I’m not going to lie. I think I would have grasped calculus a lot more easily, and perhaps even remembered it better, if it had been taught to me by starting with the actual meaning of the symbols instead of with all the jargon and symbols unconnected to the underlying concepts, as it used to be taught to 15-year-old American boys instead of not being taught to university graduates.

The preliminary terror, which chokes off most fifth-­form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning—in common-sense terms—of the two principal symbols that are used in calculating.

These dreadful symbols are:

(1) d which merely means “ a little bit of.” Thus dx means a little bit of x; or du means a little bit of u. Ordinary mathematicians think it more polite to say “ an element of,” instead of “ a little bit of.” Just as you please. But you will find that these little bits (or elements) may be considered to be indefinitely small.

(2) f which is merely a long S, and may be called (if you like) “ the sum of.” Thus fdx means the sum of all the little bits of x or fdt means the sum of all the little bits of t. Ordinary mathematicians call this symbol “the integral of.”

Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dxs, which is the same thing as the whole of x. The word “integral” simply means “the whole.” If you think of the duration of time for one hour, you may (if you like) think of it as cut up into 3,600 little bits called seconds. The whole of the 3,600 little bits added up together make one hour.

When you see an expression that begins with this terrifying symbol, you will henceforth know that it is put there merely to give you instructions that you are now to perform the operation (if you can) of totalling up all the little bits that are indicated by the symbols that follow.

That’s all.

If anyone is interested in Castalia re-releasing this early 20th century introduction to Calculus, let me know. Although I have to say, I think we’d lose the parentheticals, which are unnecessary and don’t help at all.

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Learning From History

Dominic Cummings is attempting to help people better understand the repeated failures of the governing elites, or at least, the elites that appears to be governing. He started this back in 2023.

One of the most fundamental things I’ve learned in 24 years involvement is that almost nobody has any interest in general principles underlying success and failure, nor interest in execution/management, and although political people read a lot of history books it’s hard to see any learning.

This is a core feature of why the world is as it is. It’s why I found a lot of interest in Silicon Valley about ‘why did Leave win the referendum’ and ‘how exactly does No10 and the deep state work’ but in London practically no interest beyond the surface phenomena. This is so extreme I’ve found more interest from people in San Francisco in ‘how exactly does X work’ than I have from the actual minister in London nominally ‘in charge’ of X.

So this is mainly for a) people outside politics interested in how it really works and b) people (almost all young) interested in the general problem of ‘the hard thing about doing really hard things’ (cf. Ben Horowitz’s excellent book on this in the entrepreneur context). I predict I will have ~100X more interest from entrepreneurs and researchers than from people ‘working in politics’. (And 1,000X more interest from some deep state officials than MPs who aren’t even interested in how the media really works even though they’re obsessed with the media.) But I also learned that odd people in politics are interested in these things and the <1% who are interested have an interesting knack of finding each other and working on things. These people are disproportionately young. (This is partly what happened in Vote Leave.)

If you disbelieve me, reflect on one simple fact that I’ve hammered repeatedly: the entire Westminster debate has, with the sort of ruthless focus it cannot muster to achieve anything positive, totally ignored the loathed, despised, lowest status issue in Westminster — how the government actually buys critical goods and services and the capacity of our industrial production. And it has maintained this ruthless focus through the worst pandemic in a century that left over a hundred thousand unnecessarily choking to death then through the biggest war in Europe since 1945. There has literally been more interest in Russel Brand among political-media-academia elites than this central aspect of how our state and society work and why we’re worse at it than we were in the pre-computer age.

We are living through exactly what we read about in periods like summer 1914 — a structural blindness of dominant political-media-academic elites about core features of the system they participate in all day. We read history books about summer 1914 and ask ‘how could the entire Cabinet week after week not probe exactly what our military commitments to Belgium were, what exactly the plans were, and expose that there was no actual plan or institution to cope with the crisis’. We’re in a worse situation than they were.

It’s a disaster and an opportunity. And studying this chronology can help you see how to create opportunities from disasters. In 2015 I thought the structure of the system was a disaster but the referendum was an opportunity and I tried to apply some of the things I’d learned. This proved unexpectedly successful. And, in keeping with the point above about people struggling to learn, the same happened in 2019 even though powerful forces really wanted it not to happen.

What’s needed is a shift in governing institutions roughly as profound as the shift from the ancien regime pre-1789 to what we think of as the modern western state — a shift in the types of people, their training, their tools, institutions, and the fundamental principles and incentives by which they operate. We are still governed by the Cabinet Room almost indistinguishable from what it looked like when it was overwhelmed in summer 1914: a dozen or so people with poor education and training on top of highly centralised dysfunctional institutions largely blind to the incredible system complexity yet responsible for crises that can affect billions. 

His Bismarck project is a fascinating one. I’m giving some serious contemplation into engaging in it, assuming that he’s actually continued with it over the last two years, and it might make for an interesting collective effort in the old Voxiversity sense. Share your thoughts on this if it might be of any interest to you.

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An Existential Crisis

It’s a little hard to take seriously the warnings of those who proclaim an “existential crisis” due to declining fertility rates when they won’t even address the primary cause of those declining rates and are not aware of the primary cause in declining fertility. Even when the crisis is real.

The U.S. is facing a worsening fertility crisis, according to analysts.

While the nation’s fertility rate has been declining for decades, it dropped to a new record low in 2025. Experts told the Daily Caller News Foundation that deregulation, improving fertility care and bringing down costs related to raising children could help boost the declining birth rate.

The U.S. general fertility rate was 53.1 births per 1,000 women aged 15 to 44 in 2025, down from 53.8 in 2024, according to National Center for Health Statistics data published in April.

“While there are many factors contributing to the declining birth rate, three reasons stand out to me: First, there is the influence of smart phones and social media,” Heritage Foundation Senior Policy Analyst Emma Water told the DCNF. “Since the introduction of the iPhone, [every] country has seen a marked decline in births that doesn’t look like it is reversing any time soon, including the U.S. … we are seeing more men and women replace meaningful time with others with scrolling, screen addictions, or a sense that there is too much to be done.”

“Second, we cannot discount the role of abortion, birth control, and reproductive technologies,” Waters said. “While we can have a meaningful conversation about the morality of each separately, the statistics don’t lie: The last year that the birth rate was above replacement was 1972, and since the Supreme Court decision in Roe v. Wade erroneously created a constitutional right to abortion in 1973, the birth rate has never recovered.”

Waters added that a drop in U.S. marriage rates is one of the “primary drivers of declining birth rates.”

The U.S. marriage rate dropped to a 140-year low in 2019 and has yet to fully bounce back, The New York Times reported. Less than half of American households were married couples in 2025, marking a significant decrease from 50 years earlier, according to U.S. Census Bureau estimates.

Prioritizing infertility treatment and early diagnosis could help boost the U.S. fertility rate, according to Waters.

First, prioritizing infertility treatment will only make matters worse. Average female fertility has been dropping steadily since 1900 due to the frozen gene and the inability of natural selection to continue keeping the human genome free of deleterious mutations, so using technology to help the genetically deficient to reproduce is digging the hole deeper. This is a very serious scientific problem that concerns genetic degradation and most of the solutions appear to range from ghastly and politically impossible to unthinkable and inhuman.

Second, the problem with fertility rates is about female choices, not genetic degradation. The problem is that women like Emma Water are college-educated and Senior Policy Analysts at the Heritage Foundation instead of getting married at 20 and having 4-6 children.

This is not a mystery and this is not in doubt. The correlation between post-8th-grade female education and declining fertility is extremely high, and while correlation is not necessarily causation, a high degree of correlation does tend to point toward correct causality. And this causation is sufficiently well-known that overpopulation advocates specifically push for female education in order to reduce birth rates.

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Rethinking University

Now even women are beginning to realize that a college degree is a terrible investment of time and money that accomplishes little more than put a young person into lifelong debt. And this is in the UK, where the degrees are less expensive and the debt can be eliminated after 30 years.

I was 18, full of hope and expectation, with three years ahead of me studying English Literature and the authors I loved, from Chaucer and Shakespeare to Virginia Woolf.Seven years on, though, and life looks very different.
Yes, I had a great time. I read a lot of books, made lifelong friends and played masses of sport. But was any of it truly worth it? Financially, professionally, socially and even in terms of ‘real’ education – would I have been better off turning around, dumping my gown on the floor of my halls, heading back down the M1 and buckling down to a proper job?
Let’s take the money first. By the time I’d finished my undergraduate degree in 2022 – followed by a one-year Masters in English Literature at Bristol University then a journalism qualification – I’d borrowed nearly £60,000, despite doing part-time jobs throughout.
Two years on from finishing my further education, and now that I’m earning a fairly typical graduate salary, thanks to the appalling interest rate my student loan balance stands at £76,227.49. In the past five months, I’ve contributed £335 towards the loan, yet the total amount has risen by £627.49.
I’m essentially paying a ‘graduate tax’ of nine per cent of my gross income for the course of my working life. I may never pay the loan back – 44 per cent of graduates won’t, according to the Government’s own figures – and it’s only scant comfort that the debt will be wiped after 30 years.
Durham is generally seen as one of Britain’s better universities, perhaps second only to Oxbridge. So if I feel like this, what about the 2.86 million other students currently enrolled in other universities across the country?

Only ten percent of men used to attend university back in the time when a university degree actually meant something, and that was largely because only the true cognitive elite attended. There is absolutely no reason for most men and virtually all women to pursue a university degree, as doing so virtually guarantees a suboptimal life track compared to not wasting 4-5 years out of the workforce, gaining no experience, being ideologically indoctrinated by wicked retards, and ending up saddled with lifelong debt.

UPDATE: Here is a comprehensive return-on-investment calculator for virtually every institution of post-high school learning in the USA, but keep in mind that the return-on-investment doesn’t include debt, so the debt calculations need to be compared to the hypothetical ROI.

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Feature, Not Bug

A young woman is taking legal action against her high school, alleging she was awarded honors at graduation even though she’s illiterate. – Thomas Sowell

The problem is that a class action lawsuit of this kind that encompassed even a small fraction of those for whom this is true would create sufficient liability to end public schooling in America.

Yeah, so, that’s not at all a problem.

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Vol. 9 Sport & Adventure

As previously promised, we’ve made it possible to order the two-volume set of Volumes 9 and 10 in order to complete your set of the Castalia Junior Classics 2020 edition if you happened to purchase the previous eight volumes over time. Original backers should note that they do not need to buy this set because both volumes are included with your backing of the original crowdfund.

We do not intend to make the full 10-volume set available for purchase until the annual Thanksgiving Sale next month because we do not wish to have anyone to pay the full retail price for a set and then be unpleasantly surprised when the sale price is offered a few weeks later. 

We will not be doing anything on the first leather edition until the new year. Also in the new year, we will make second leather edition sets available by sale and a new subscription starting January 1. We have not determined a price yet, but it will be similar to the price for the original backers of the first set. We do not have any extra complete first edition sets available.

To see the Volume 9 cover, more details about the book, and two example pages with illustrations, please visit Castalia Library.

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The Schools Aren’t Magic

Immigrants are proving literally uneducable(PDF) by the schools in the countries they have invaded:

In spite of the many criticisms to which PISA can and should be legitimately subjected, it is difficult to deny that this large and highly successful OECD project is a blessing for research in Comparative Education, as it provides strictly comparable data on inputs, processes and results for most educational systems in the world. The outcomes of analyzing these enormous data sets are rather disappointing for those who had expected from it quick and solid adjudications among rival theories. First the PISA reports, and then the many reanalyses carried out on the PISA data, have found only very weak relations between students’ outcomes and characteristics of educational systems which are usually thought of
paramount importance (Carabaña, 2008).

It is from these tenuous links that multilevel regressions extract cross-country coefficients that, when statistically significant, are quite hard to interpret even by the best willed officials and scholars. I will here address the question of the effects that schools in the destination countries have on the academic results of immigrant’s children. Immigration countries have generally better schools and better results than countries of emigration. It is therefore easy to imagine how the desire to improve the schooling conditions of their children might be one important pulling factor for emigrants. However, against all expectations of subjects and observers, immigrant students score in the PISA tests rather like students in their countries of origin than like native students in the countries of destination.

In spite of the allegedly better schools of the host countries, the learning of the newcomers remains at the level of their origin countries not only in the first generation, but also in the second and even later on.

This is because the differences across humanity are not merely “skin-deep”. The contents of one’s character do matter, but so too do the contents of one’s culture, and even more importantly, one’s genes. An 80-IQ Somali immigrant who attends a good public school in Minneapolis is still going to be an 80-IQ Somali after being given a piece of paper that declares he is educated. So too will his son, and his grandson, and his great-grandson.

This should be entirely obvious, as the British colonists did not gradually turn into American Indians after four generations in the New World. And the descendants of the African slaves imported into the Americas are still observably distinct in appearance, behavior, and educational outcome after many generations of education in the USA.

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Time to Move On

Ok, we tried women’s suffrage and discovered that their primary political concern is killing their own babies. Can we finally call this experiment failed and move on?

Indeed. The only question at this point is if the women’s suffrage experiment will be abandoned a) to prevent societal collapse or b) as a consequence of societal collapse.

Either way, it’s not going to survive. Neither will democracy, or to be more precise, the present illusion of “representative democracy”, for that matter.

The statistical evidence is absolutely clear and undeniable. Sustainable human society is not compatible with the average young woman receiving more than nine years of education. Ironically, it may only be the inferior state of public schooling that has prevented US fertility rates from declining even more dramatically than they have.

The laws of social dynamics may not be as clear-cut as the laws of thermodynamics, and the effects of ignoring them may not be as immediate, but we now have decades of evidence demonstrating how ignoring them will prove every bit as catastrophic over time.

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Less School, More Children

Any modern society that wishes to survive needs to reduce the number of years that young women spend in school. Russia has already figured this out and I have little doubt that China will soon follow suit.

A senior Russian demographer has proposed cutting the number of years children must attend school in order to promote earlier parenthood and reverse a national trend towards lower fertility, TASS reports. Sergey Rybalchenko, head of the Public Chamber’s Demography Commission, has argued that bold steps are necessary to prevent Russia’s population from shrinking.

In recent years, the country has seen negative natural population growth, falling from 149 million in 1993 to 146 million in 2025 despite an influx of immigrants and the unification of the country with Crimea in 2014 and four former Ukrainian regions in 2022.

The country’s population is poised to decrease to 138.8 million people in 2046, according to the base-case scenario developed by the federal statistics agency Rosstat.

“A shorter education period would enable young people to reach adulthood and plan to have children for two years earlier,” Rybalchenko told TASS, explaining the initiative.

Getting married and having children at a higher age is linked to a longer period of social maturation, the demographer pointed out. Young people only start to think about children by the age of 27, as they spend 17 years getting an education and dedicate an additional three years to social adaptation after finishing university, he explained.

A large scale study covering 1950 to 2023 clearly showed that to reach an average Total Fertility Rate of 3.0, the average number of years schooled for young women should be 10. And anything beyond 12 is a disaster; the most societally destructive thing that the USA has done since passing the 1965 Naturalization Act is to increase the number of women in higher education.

As I have stated repeatedly before, feminism is one of the few ideologies that are more lethal and destructive than either communism or national socialism. And whichever major power recognizes this and embraces post-feminism will have a significant advantage over its rivals.

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Outsmarted

It’s difficult to get too carried away by the euphoria of being auto-enlightened by one’s intelligence in the aftermath of getting played by a Ridgeback putting on an award-worthy performance of a starving puppy whom everyone somehow forgot to feed. The sheer pathos of her stunning portrayal of a sad, hungry little dog who had just been patiently waiting without complaint for HOURS after her normal dinnertime had passed would have brought tears to even Cruella De Vil’s eyes.

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