Showing posts with label opinion. Show all posts
Showing posts with label opinion. Show all posts
Friday, October 2, 2026
Wednesday, September 23, 2026
Saturday, September 19, 2026
integer factorization reconsidered - trial multiplication
In nature, there is always a path of least resistance. Similarly, in math, there is always an optimal algorithm for any situation.
Regarding the integer factorization problem, only one case is of particular interest for cryptography: the factorization of large semiprimes when the prime factors are nearly equal.
In this case, the most efficient method is to find the smallest integer n such that n^2 exceeds the semiprime. Any semiprime p*q will be less than some n^2 with p < n < q, and q << 2*n.
Suppose we want to factor 988027 and know it is semiprime. Its square root rounded to the nearest integer is 999. From trial multiplication, we find that 992 is the smallest integer that when squared is greater than 988027. And if we systematically check the numbers greater than 992 which end in 1, 3, 7, or 9, we quickly find that 997 is a factor of 988027.
The semiprimes used for cryptography are vastly larger, but the principle is the same. It makes more sense to use trial multiplication before trial division.
Trial multiplication is a method for solving the discrete logarithm problem. I see it as part of a one-two punch for the integer factorization problem.
Saturday, September 12, 2026
Von Neumann and the Collatz Conjecture
He famously said that: "Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin."
I wonder if he knew about the Collatz Conjecture when he said that.
On his Wikipedia page, I read:
***
At times he could be ignorant of the standard mathematical literature, finding it easier to rederive basic information he needed rather than chase references.
***
So it's possible, even likely, he did not know about it.
The Collatz Conjecture definitely involves a deterministic process, and I say it produces random numbers.
Here is my informal proof of that: given any number, there is no algorithm for determining how many iterations it will take the Collatz Conjecture process to reach 1. There is also no algorithm or equation you could use to find the maximum value of the iterations. Small changes in the initial value produce drastically different results, which is a hallmark of chaos theory.
In this way, the process is akin to rolling dice. The overall and final results can be calculated beforehand, but the specific and intermediate results are unknowable.
If something is deterministic but unpredictable, it is effectively random.
Saturday, August 22, 2026
suggested reading for those curious about joining the military
1. Storm of Steel - a German soldier's harrowing account of the horrors of WW1
2. The Things They Carried - what it was like to be drafted into the Vietnam War
3. About Face - the autobiography of one soldier's long and distinguished career in the Army
4. To Hell and Back - the eyewitness account of Audie Murphy, America's most decorated hero of WW2
5. The Forever War - a sci-fi parable by a Vietnam combat veteran.
6. Slaughterhouse Five - a mix of history, comedy, and sci-fi as told by a US POW during WW2
7. Bill the Galactic Hero - a sci-fi satire of the military by a WW2 veteran
8. Once an Eagle - a classic and epic novel by a combat veteran of WW2
9. Escape from Laos - the true story of one pilot's survival and daring escape from a POW camp
10. The Private History of a Campaign that Failed - Mark Twain's hilarious memoir of his brief time as a soldier in the Civil War.
Thursday, August 20, 2026
meanwhile in Africa
Here's what foreign aid pays for:
I exaggerate somewhat, but the main result of foreign aid is population growth. Perhaps someday Africa will industrialize to a similar level as Europe or North America. I doubt it. In any case, Africa is and will be dependent on food aid and food imports, as well as imports of fuel, fertilizer, and machinery.
The above screenshot is from the 7:42 mark of this video:
The Collective African Culture Is Broken
Elsewhere
The orphanage director I worked with in Tanzania tried unsuccessfully to get permission for a pregnant girl to return to school as she was less than a year from graduating.
Tuesday, August 18, 2026
Friday, August 7, 2026
suggested video games for homeschoolers and gifted/talented students
All these games are from the mid to late 90s but should be available used (cheap!) or on Steam. There are also similar games currently and from recent years.
Real-time strategy games and city-building games are best because they teach how to manage complex systems. It's like a faster version of chess. Some role-playing games involve creative problem solving.
Fighting and first-person shooter games tend to be popular and fun, but don't teach much. Racing and flying games are good for building hand-eye coordination. I never played sports games much, so I don't know what the pros and cons of those are.
Older video games like Super Mario or Pac-Man tend to be more about reaction time and winning through trial and error. Other than nostalgia, there's not much point in playing them.
1. Zelda: Ocarina of Time
This one has mild fantasy violence, but otherwise nothing objectionable. Beating this game requires patience and creativity as there are a wide variety of puzzles to solve.
2. Age of Empires 2
Any game from this series is solid, and it indirectly teaches about history. It combines city-building with strategy.
3. Railroad Tycoon 2
Again, any game from this series is good, and it also teaches about economics and the history of railroads.
4. Tropico
This is also a series of games. You govern an island nation where you can have free and fair elections or become a dictator through various means. There is little violence but some adult references (cigars, rum, gambling, cabaret). The game teaches history, politics, and economics. I highly recommend it.
5. StarCraft
This a great one for sci-fi fans. It has stronger violence than Age of Empires and is basically that game in space. Warhammer fans will love this one.
6. Caesar 3
This is a city building game that teaches a lot about ancient Rome. There's mild violence as you command legions to fight various barbarians. And you must build temples to various pagan gods or face their wrath.
7. Command and Conquer
This is a series of games starting in 1995. Red Alert 2 is my favorite as it has amusing cut scenes and campy humor. The violence is PG-13.
8. Oregon Trail
If you let your kid play one video game, let it be this. The 90s version is best. There is mild violence in the hunting minigame and references to death.
9. Destroy all Humans!
Another sci-fi gem and a great game for misanthropes. The violence is mild and there are some adult references. It has some of the best humor of any video game I've ever played.
10. Primal Rage
Who doesn't love dinosaurs? Well, this game is basically Mortal Kombat with dinosaurs. Or at least creatures similar to them. There's a lot of blood, but it sure is fun. Maybe save this one as a reward for good behavior. It's what my parents did.
Video games have a bad reputation, but some of them are educational in addition to being entertaining.
It's better to get your kid hooked on one of the above before they stumble upon a mindless, amoral cesspool like Grand Theft Auto (a fun game, but it does not develop the mind).
I should note that I played all the "bad" video games too and did not grow up to be a career criminal. Video games can desensitize someone to violence, but they do not make people violent.
Tuesday, August 4, 2026
knowledge as a social cue
An educated native speaker of English has a vocabulary of about 25,000 words even though only about 6,000 of them account for 95% of what they say. So what is the value of knowing the other 19,000 words? A large vocabulary is a reliable signal that someone has read a lot, because that is the usual way someone comes to know many words. People who read a lot are usually smart; thus, the use of rare words is a signal to other intelligent people that they are alike and should interact. The fact that we have dictionaries (and can instantly look up the definition of words online) does not negate the advantage of having a large vocabulary.
It's similar to the way people wear certain clothes in order to fit into a group. There's a reason why businessmen always wear suits. It's an advertisement about who they are and wish to associate with.
Indeed, the most common way people try to ingratiate themselves into a group is by changing their appearance and sometimes their speech. People who move to a different country or region often adopt the accent there in order to be accepted.
Knowledge also works as a social cue. Most knowledge, especially the kind from formal education, has little direct utility, especially today when almost everyone has the internet in their pocket. The amount of practical knowledge a typical adult needs is surprisingly small. Almost all the rest functions as way to show interests and status. For example, knowing how to change a tire is a lot more useful than being able to read Latin, yet knowing Latin is a clear indicator that someone is inquisitive, well-read, and probably intelligent. I suspect this is the reason the high IQ society Mensa uses a Latin word for its name.
Someone who is very knowledgeable and demonstrates it is showing (unintentionally or not) who they are and who they want to associate with. This is why people should be careful about what knowledge they share. If you talk about astronomy all the time, people will wonder why you aren't working at a planetarium or a member of a stargazer club. Sharing knowledge on different topics sends mixed signals, sort of like switching from one language to another. If you want to speak English, it does no good to go around speaking Spanish or any other language.
Still, being knowledgeable on many topics is generally respected. Scholars hundreds of years ago were respected precisely because it was known to take a lifetime of study to learn so much. The key to avoid being called a know-it-all is to say little. Sile et philosophus esto is Latin for "be silent and you will pass for a philosopher". In any case, know-it-all refers to someone who pretends to be more knowledgeable than they are. Someone who really does know a lot on many topics is a polymath.
I say be a renaissance man if you can. The world can always benefit from another genius.
I should add that jokes are the most useful thing to memorize if you want to make friends and get people to like you.
Saturday, August 1, 2026
How many books should you read?
The short answer is the more, the better. But as in all other things, there are diminishing returns to reading.
It's better to read many short books than one long one. Nonfiction is more informative and often more enjoyable.
Here is a short reading list that provides a good education:
1. Bullfinch's Mythology
2. The Cartoon History of the Universe
3. Man's Search for Meaning
4. Animal Farm
5. Slaughterhouse 5
6. The Art of War
7. Ecclesiastes
8. Proverbs
9. Alice in Wonderland
10. The Hobbit
Anyone who reads all of those will have a pretty good grasp of life, the universe, and everything.
Should you go to college? Should you study engineering?
I think it is a bad idea to borrow a lot of money for college, though most who study law or medicine pay back their loans with no problem.
I was not enthusiastic about college. I went because I got a full scholarship and couldn't think of anything better to do. I don't regret going to college, but it made me realize that I did not want to spend any more time in school, though that ended up happening anyway.
My scholarship required that I study science, engineering, or technology. I picked chemical engineering because I liked chemistry in high school and the starting salaries were good. At the time, I wasn't sure if I wanted to get a PhD, so I thought engineering was a practical choice that would let me go to work right away if I wanted. As it turned out, after four years of studying engineering, I wanted to do something completely different for a while. So I joined the Peace Corps because I wanted to travel, learn another language, and have an adventure. That was probably the best decision I ever made.
In order to be a successful engineer, you have to be focused and driven. You have to care a lot about getting the design or process right. If you find the work boring, as I did, engineering will not work out for you as a career. Engineers usually work in teams, so they have to be sociable. If you're an introvert, avoid engineering unless you're really interested in the technology involved.
If I had to live my life over again knowing everything I know now, my life would be about 90% the same. That's a sign I don't have too many regrets and made mostly the right decisions.
suggested movies for homeschoolers and gifted/talented students
Many are available for free on YouTube.
7. Robocop
Some are family friendly, others not so much. Sex, violence, and profanity are parts of adulthood. Movies are a safe way to introduce them. Forbidden fruits are excellent incentives for good behavior.
1. The Lion, The Witch, and The Wardrobe (1979)
2. Jaws
3. Star Wars (original trilogy)
4. The Thing (1982)
5. Saving Private Ryan
6. The Blues Brothers
8. The Terminator
9. The Matrix
10. Patton
11. Tora! Tora! Tora!
12. Braveheart
13. Jurassic Park
14. Monty Python and the Holy Grail
15. Army of Darkness
16. Dragonheart
17. The Nightmare Before Christmas
18. Godzilla (1954)
19. Starship Troopers
20. Gladiator
21. Ghostbusters (1986)
22. Jumanji
YouTube videos for homeschoolers and gifted/talented students
1. Hanna-Barbera Bible stories
3. Veritasium
5. Ancient Recitations
6. Mark Rober
my favorite
2. Crash Course
4. PBS Eons
7. Hungarian Folktales
8. Greatest Audiobooks
9. YouTube Movies
10. Traditional Music Channel
suggested books for homeschoolers and gifted/talented students
These are all books I've read and enjoyed. They are also on the shorter side and are easy to read.
1. Escape from Laos
2. Hunter by J A Hunter
3. Slaughterhouse 5
4. The Art of War
5. Lies My Teacher Told Me
6. The Wind in the Willows
7. The Age of Reason
8. Animal Farm
9. Sixth Column
10. The Hobbit
11. Any book from the All About series, but particularly All About Strange Beasts of the Past
12. Calvin and Hobbes books
13. Dilbert books
14. The Far Side books
15. The Cartoon History of the Universe - by far the most interesting and educational comic book ever
16. Philosophy Made Simple
17. Bathroom Reader books
18. Alice in Wonderland
19. A Princess of Mars
20. Kipling's Just-So Stories
21. Badass by Ben Thompson
22. Bulfinch's Mythology
23. A Brief History of Time
24. Dune
25. Storm of Steel
26. Cows, Pigs, Wars, and Witches
27. The True Believer
28. Man's Search for Meaning
Thursday, July 30, 2026
what is the minimum education an American adult needs?
I've been an adult living in America for 23 years. Here are the essential skills I use often:
-literacy (rarely above the 8th grade level)
-basic computer skills
-driving
-handwriting (not as important as it used to be)
-arithmetic and algebra
-hygiene
-laundry
-cooking
-basic knot tying
-money management
So that's the bare minimum. I think the average person could learn all of that in a few years or less.
The following skills are good to have, but not essential:
-swimming
-first aid
-driving a stick shift
-map reading
-a foreign language
-hand-to-hand combat
Here are some things I spent much time studying which rarely or never came up:
anthropology, astrology, biology, calculus, chemistry, dinosaurs, economics, entomology, etymology, French, Greek, history, Japanese, Latin, linguistics, literature, marksmanship, music, philosophy, physics, poetry, Shakespeare, Spanish, statistics, thermodynamics, trigonometry
I'm glad I studied all those things and more, but they are mostly irrelevant to my daily life.
Modern American education is mostly about keeping kids busy until they're old enough to work. This is a serious mistake. About 50% of students should stop going to school after the 5th grade and about 80% should stop after the 8th grade. Only the top 20% belong in high school, and only the top 10% belong in college.
Every kindergartener should be given an IQ test at the end of the year and put on the appropriate track. I don't expect that to happen, but it should. Americans really need to rethink their view of egalitarianism.
What should all these emancipated students be doing instead? I suggest things like sports, art, music, drama, computers, woodworking, auto repair, etc.
Monday, July 20, 2026
useful questions
1. What would you do if success was guaranteed?
I'd be a writer or maybe a scientist.
2. What would you do if you had unlimited money and no obligations?
Probably most of the same things I do now. I'd live a simple, peaceful life. I'd read, write, walk, swim, make AI art, tinker, travel, date, and spend time with family and friends.
The only big difference is that I'd buy a plot of land and put a mobile home on it.
3. What would you do if you were immortal and had eternal youth?
I'd go to Mars to help build a settlement there. Maybe every few decades, I'd head back to earth for a vacation.
Speaking of space colonization, it's a terrible idea for many reasons. The money and effort would be better used making sure civilization survives on earth for thousands of years to come. 99% of species go extinct within 15 million years.
the dilemma
Often, actions that are politically feasible won't help, and actions that would help are too unpopular to be politically feasible.
So in order to get anywhere, politicians have practice strategic hypocrisy: promise a popular policy and then implement the unpopular one. It's like putting pet medicine in a piece of cheese to get a dog to swallow it.
As a public service, below are some of my suggestions on how to sell necessary but unpopular policies.
Measure: repeal the minimum wage
Slogan: Maximizing Employment Act
Measure: school vouchers
Slogan: Helping Our Teachers Act
Measure: abolish the income tax
Slogan: Fairness for Working Families Act
The magic words are: children, families, working, freedom, teachers, defense, security, fair, smart, care
Measure: cut military spending 90%
Slogan: Smart Defense and Security Act
Sunday, July 19, 2026
suggested schedule and activities for gifted and talented children
In the US, this refers to children with IQs 130 or higher. They are in the top 2% for intelligence and do best with self-directed learning.
Places to take them: above all, libraries. After that, museums, zoos, aquariums, planetariums, and escape rooms. Regular weekend trips should be enough. If they can volunteer at these places or partner with a mentor there, they should.
If they're in public school, they should try to skip grades and graduate early. Schools are designed around an IQ range of 85 to 115.
Set a limit of about an hour of reading per day. One movie per day is acceptable. An hour of TV and video game time per day is reasonable. That covers about four hours.
Ideally, they should have some project they are working on that takes up most of their time during the day. This can include gardening, painting, drawing, writing, playing music, building models, solving puzzles, science experiments, or playing chess. Fours per day during the week should be enough.
Intellectual children often lack physical fitness. Running, swimming, weightlifting, and martial arts can counteract this. Scouting and 4H are great places for such children to socialize. If nothing else, long walks and bike rides build endurance and resilience.
It's very easy to get such children to do chores if you pay them. They should start working part-time as soon as they can.
They should conceal their intelligence, follow their passions, and take the path of least resistance.
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