Higgenbotham's Dark Age Hovel

[Higgenbotham]

When you worked for a company that was thoroughly immersed in Stacking in the early 1980s my best analogy was to think of myself as being in an all male prison, except the inmates in there were more clever.

One thing that was still fashionable at that time was to take the new "recruits" around to top management and have a brief, friendly conversation of maybe 20 minutes. Most all of the top managements at companies presented themselves a pretty nice people at these meetings. This company was a little different as in the majority of the top management still presented themselves as pretty nice people, but interspersed within top management were a fair number of assholes.

One day I was scheduled to meet with a management person named Dave and another newish young recruit named Walt was going to join me. Walt was from Buffalo, New York, like many of the other young recruits from decaying Great Lakes Rust Belt hellholes that had lost their manufacturing base. Walt was what I called a Glad Hander. A Glad Hander ranks at the top echelons of Ass Kissers, like at the 95th percentile of Ass Kissers and above. You can't really blame a Glad Hander for wanting to permanently escape a Rust Belt hellhole, I guess.

So we're having a conversation with this management guy who in my opinion was showing himself to be a pathetic knob and a complete asshole. He was enumerating all the company priorities that he could list, when I asked him which of those were the most important. Cleverly, as in advanced prison clever, he replied that was like asking which leg of a 3-legged stool was most important, at which time Walt, on the edge of his seat, quickly blurted out, "They're all important!" Perfect!

I just recalled another great anecdote about Walt. On some regular basis, everyone had to eventually give a presentation to our group of about 30. It was something like 3 per month. Someone gave their presentation and the person did a pretty good job but it was evident this person was slightly nervous. After the presentations were finished, people would offer comments for improvement. As I recall, there were a couple constructive comments. Then Walt offered that some of the person's intonations or pitches rose slightly at the end of some sentences. The person then smiled and asked the group if it was OK to sit down now. A few people smiled and laughed and then someone said OK, yes, you can sit down now.

[Guest]

The third level knobs will be the ones that assure Sorites paradox.
They will never sit down since they never stood up for what should of been done.

[Higgenbotham]

The third level knobs will be the ones that assure Sorites paradox.
They will never sit down since they never stood up for what should of been done.

You've already figured out where I've been heading with the last 9 posts. There are a few more things to put in place first.

[Higgenbotham]

So far as I'm aware, high tech companies like the Magnificent 7 (or any other company for that matter) will never ask an interview question that involves calculus. Let's take a look at what it's reported that they do ask.

Amazon engineering interview math question

AI Overview

Solving Amazon's Poles Distance Interview Question with Math

Amazon engineering math interviews often test applied quantitative reasoning, probability, or mathematical logic rather than pure calculus. A popular example is the "Hanging Cable" logic puzzle, which evaluates a candidate’s ability to strip away complex formulas and use spatial reasoning to find a simple solution.

The Hanging Cable Puzzle

The Problem Statement:
Imagine two 50 meter poles are standing on the ground. A cable exactly 80 meters long is strung between the two poles. Because of the cable's length, it hangs down, and its lowest point reaches exactly 10 meters above the ground. How far apart are the two poles?

The Solution:
Instead of setting up complex hyperbolic catenary curve equations, test the limits of the problem. Picture bringing the two poles directly together (with a distance of 0 meters between them). Because the cable is 80 meters long, it will go 40 meters straight down to its lowest point, and then 40 meters straight back up to the tops of the poles. Since the poles are 50 meters high, the lowest point of the cable will be at 50 - 40 = 10 meters off the ground. Since this perfectly matches the conditions of the problem, the only possible distance between the poles is 0 meters.

This question in my estimation is right at The 97th Percentile. In other words, 3 percent of the population will quickly solve this in an Amazon interview and 97 percent won't. In the case of the engineers they interview, it will be higher than 3 percent because they don't represent the population average.

OK, why do they do this? It's because they have a company to run and they have to hire people to run it. To hire people, they have to establish a cutoff. A reasonable cutoff is at The 97th Percentile. So they cut it off at that level and work with what they get.

The way I look at the problem, the level of the problem is actually high school geometry. What you do given the diagram is approximate one side as a right triangle to get an approximate answer. So they are giving the hypotenuse of the triangle in the diagram as 40 (half of 80). They are also giving one leg as 40 also (50 minus 10). Therefore, because the formula for a right triangle is a squared plus b squared equals r squared, the length of the other leg must be 0 and thus the approximation is also shown to be exact.

If Amazon were to start asking interview questions based on calculus, the bar would be so high and the number of candidates who could clear it so infinitesimally small that they would not be able to run their company. That's why the world has to run at the level of this interview question and similar.

[Higgenbotham]

There was a similar interview question that I read a high tech company asked over 20 years ago when they were hiring for the Internet buildout. The question was if a bug is in the corner of a cubic room say 10 feet on each side (can't remember exactly) what is the minimum distance it needs to travel to get to the opposite corner. This is almost identical in difficulty to the Amazon interview question.

[Higgenbotham]

Since the Guest prompted me, I will cut to the chase and briefly discuss one of the core conclusions that arise from the previous 11 posts.

We know that states exist because they have a monopoly on violence. Like someone can't point a nuke at Washington and tell it not to tax them. So, in very simple terms, people pay taxes and Washington uses that money to increase their monopoly on violence. Until they can't. Nukes were the ultimate monopoly on violence because it took such a rare level of skill, what I called the Gold Tier of mathematical and scientific skill that only perhaps 500 people in the world possessed in 1945, to design and build them. We don't need to talk about Iran.

A couple months ago, I was talking to a guy about my age who graduated from Princeton. He's told me he wasn't a great student but he knows a lot of people and loves to talk. I brought up the Covid-19 virus escaping or being released from the Wuhan Lab. I said it was obvious it was an engineered virus that escaped from the Wuhan Lab - why did the media lie about it with the bat story and say it was naturally occurring? His immediate response was, "To protect Fauci." I then veered the conversation off in another direction from where I've been going with this.

I wouldn't doubt his answer is part of it, but I think there is something else going on that is more subtle. Let's say that early on when Covid was such a big story that the fact the virus had escaped from the Wuhan Lab had become part of the discussion. The discussion at that time could have quickly evolved into, "How difficult is it really to engineer and release a lethal virus?" The answer would have been it's not really that difficult at all. As in, 1 or 2 of those half a million people with Bronze Tier math skills could probably do it in their garage. And if they did and a few others did, whoops, there goes the state's monopoly on violence. The reason, in addition "To protect Fauci." could have also been "To protect the state's monopoly on violence."

[Higgenbotham]

The state monopoly on violence and engineered viruses

AI Overview

The state monopoly on violence, defined by sociologist Max Weber, is the principle that a government is the only entity authorized to use or authorize physical force within a given territory. Engineered viruses challenge this foundation, as synthetic biology empowers non-state actors or rogue groups to inflict mass harm.

The intersection of these concepts creates a major modern security dilemma. Here is how they interact:

1. The Core Definition
In political science, a state’s legitimacy rests on its ability to protect citizens from internal and external threats, which requires it to successfully claim a monopoly over the use of force. This centralization stops society from devolving into constant, decentralized conflict.

2. The Decentralization of Threat
The advancement of biotechnology (such as synthetic genomics) makes it easier and cheaper to manipulate microbes, meaning destructive power that once required entire state programs can increasingly fall into the hands of a few. Because of this, scholars warn that synthetic biology could erode the state’s monopoly on violence, allowing lone actors to deploy weapons of mass destruction.

3. Asymmetric Warfare and Attribution
Engineered viruses represent an asymmetrical threat. Because bio-agents are living and can spread invisibly, it can be extremely difficult for governments to definitively prove who created or released them. A major challenge for the state is tracing these bio-threats back to their origin to hold malicious actors accountable.

4. The Regulatory Response
To maintain their authority and protect public safety, states aggressively expand their regulatory and surveillance capabilities. Through bodies like the Defense Advanced Research Projects Agency (DARPA), governments are developing screening, computational tracking, and detection tools to preemptively identify engineered organisms.

Ultimately, engineered viruses complicate how the state maintains order and enforces its legitimacy. To counter this, governments continuously rely on preemptive monitoring and international treaties to prevent dangerous pathogens from slipping outside official, state-sanctioned control.

[Higgenbotham]

The state monopoly on violence and nuclear weapons

AI Overview

The state monopoly on violence, a concept popularized by sociologist Max Weber, defines a sovereign state as the sole entity within a territory with the legitimate right to use physical force. Nuclear weapons represent the absolute pinnacle of this monopoly, elevating a state's power from territorial control to ultimate global existential deterrence.

The Theory of the Monopoly

Legitimacy: The state's power to use force is theoretically granted by its citizens through a "social contract" in exchange for the protection of their rights, lives, and property.

Control of Force: All other entities—such as police departments or private citizens—are only permitted to use force if explicitly authorized and regulated by the state (e.g., in self-defense or law enforcement).

Max Weber's Definition: Sociologist Max Weber famously defined the modern state by its specific means: the monopoly of the legitimate use of physical force within a given territory.

Nuclear Weapons as the Ultimate Monopolizer

Extreme Expression of Power: The possession of nuclear weapons is the most extreme manifestation of a state's sovereign power, allowing it to project invincibility and deter aggression from foreign adversaries.

The "Nuclear Peace": Nuclear monopolies or mutual ownership radically alter the state's relationship with violence. Theorists of "mutually assured destruction" argue that nuclear capabilities prevent large-scale existential wars between major powers, though they can sometimes result in increased indirect or proxy conflicts.

Monopoly vs. Proliferation: When only one or a few states possess nuclear weapons, it creates a severe power imbalance. This is why international non-proliferation treaties (like the Treaty on the Non-Proliferation of Nuclear Weapons) exist to control which authorities are granted this ultimate level of destructive power.

Intersectionality and Criticism

Critiques of the State: Critics from various political spectrums, including libertarianism and anarchism, argue that this monopoly inherently results in coercion, imperial violence, and unchecked taxation.

Global Implications: Anti-war and intersectional theorists argue that nuclear arsenals are the ultimate signifiers of state domination, and hold the potential to inflict catastrophic harm on civilian populations without their consent. The push for global nuclear disarmament continues to challenge the moral legitimacy of any state possessing the power to instantly destroy entire societies.

[Higgenbotham]

Now let's talk about the Math ability of the wealthiest tech moguls. The ones of interest to me are Bill Gates, Jeff Bezos and Elon Musk. This is because they have been the wealthiest people in the world for longer stretches of time than any others. Gates held the top spot for 18 years, followed by Bezos for 3 years and Musk for 4 years. Plus, Gates and Bezos have been refreshingly honest about their math abilities.

First, Gates gets a Bronze Tier award because he got an 800 on the SAT math back when an 800 meant something more than it does now. Let's try to see how far he went from there.

Realizing early on that I had a head for math was a critical step in my story. In his terrific book How Not to Be Wrong, mathematician Jordan Ellenberg observes that “knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.” Those X-ray specs helped me identify the order underlying the chaos, and reinforced my sense that the correct answer was always out there–I just needed to find it. That insight came at one of the most formative times of a kid’s life, when the brain is transforming into a more specialized and efficient tool. Facility with numbers gave me confidence, and even a sense of security.

There’s quite a lot about his years as a student at Harvard, especially about the freshman-year Math 55 class he took, which was taught by John Mather. This brought back a lot of memories for me of my experiences there a couple years later. Gates arrived as a freshman in the fall of 1973, which was two years before me. Something we had in common was not being the best students in Math 55, but somewhere in the middle. Our reactions to that however were very different, since Gates was extremely competitive:

In our Math 55 study sessions, even as we were helping each other, we were also subtly keeping score. That was true in our broader circle of math nerds as well. Everyone knew how everyone else was doing, for instance, that Lloyd in Wigg B aced a Math 21a test or that Peter–or was it someone else?–found an error in Mather’s notes. We all grasped who among us was quicker that day, sharper, the person who “got it” first and then could lead the rest of us to the answer. Every day you strived to be on top. By the end of the first semester, I realized that my ranking in the hierarchy wasn’t what I had hoped…

By most measures I was doing well. I earned a B+ in the first semester which was an achievement in that class. In my stark view however it was less of a measure of what I knew than how much I didn’t. The gap between B+ and A was the difference between being the top person in the class and being a fake…

I was recognizing that while I had an excellent math brain, I didn’t have the gift of insight that sets apart the best mathematicians. I had talent but not the ability to make fundamental discoveries.

https://www.math.columbia.edu/~woit/wordpress/?p=14370

Virtually everyone who takes Math 55 at Harvard scored an 800 on the SAT math. Probably, though, it's a more elite group of 800 scores than the typical 800 score. Also, a lot of the people who start the first semester of Math 55 don't finish out the semester. Accounts vary as to the percentage that drop the courses, but it's somewhere around half. Gates describes being in the middle of the remaining pack and only finishing the first semester of the two semester series. I think it's fair to say that Gates might be somewhere close to the Silver Tier of mathematical ability, about halfway between the Bronze Tier defined by the typical 800 score on the SAT math and the the Gold Tier of elite Manhattan Project principal scientists.

Next up is Jeff Bezos.

"There's nothing wrong with asking for SAT scores," Bezos says. Several of his employees blew away his 1,450, in fact. SATs are one minor metric in an elaborate assessment of job candidates. "If you start out with A's, you get to keep A's," he says. "If you start hiring B's, B's hire B's."

https://www.washingtonpost.com/archive/ ... 686e43415/

Jeff Bezos decided not to become a theoretical physicist during his time at Princeton University when he encountered a particularly difficult partial differential equation. Despite being a strong student, he and his roommate struggled for three hours to solve this problem without success.

They then sought help from their friend Yasantha Rajakarunanayake, considered the "smartest guy at Princeton," who solved it in seconds by recognizing it as analogous to a problem he had solved three years earlier.

This moment of realizing he could not excel as a theoretical physicist was pivotal for Bezos. He later said, "That was the very moment when I realized I was never going to be a great theoretical physicist." This experience contributed to his decision to shift his focus from physics to entrepreneurship, which eventually led him to found Amazon.

This story is well-documented from an interview Bezos gave at The Economic Club of Washington in 2018, where he humorously recounted this episode and its significance in his career path.

https://www.instagram.com/reel/DTZwnmyE2fR/

There's no breakdown on the 1450. Bezos probably doesn't reach the Bronze Tier of mathematical ability, but close. If he'd scored an 800 on the math it probably would have been noted somewhere.

Finally, Elon Musk.

Google search shows that the Globe and Mail (Canadian newspaper) reported that,

"Elon Musk, a Canadian: How Tesla's man was shaped by ...
The Globe and Mail
https://www.theglobeandmail.com › business › article-el...
Sep 10, 2023 — On his second round of the SAT tests, he got a 670 out of 800 on his verbal exam and a 730 on math.

This was supposedly documented on page 45 of a biography of Musk by Walter Isaacson. If true, Musk is a good distance below the Bronze Tier of mathematical ability.