understanding algorithms

According to Trakhtenbrot, there is no mathematically precise definition of an algorithm. 

More about Trakhtenbrot here: Derpetology: Trakhtenbrot, an Unsung Hero of Computer Science

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Boris (Boaz) Abramovich Trakhtenbrot was a Russian-Israeli mathematician in logic, algorithms, theory of computation, and cybernetics.

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A flowchart is like an algorithm. The German animal name flowchart is my favorite.

Here is how I would define one: an algorithm is a finite set of computations with at least one loop. A simple example of this is long division. As an algorithm, it looks like this:

1. Multiply the divisor by a number so that it is close to but does not exceed the dividend. Start with 1 and increment to 9.

2. Subtract the result of step 1 from the dividend and use the remaining number as the new dividend.

3. Repeat steps 1 and 2 until the remaining number is smaller than the divisor.

4. Make a fraction of the remaining number and the divisor, convert it to a decimal, and add it to the rest of the quotient.

The details of the YouTube algorithm for suggesting videos are proprietary, but it works something like this: If people who watch video A also watch video B, video B is suggested after video A is watched. As a user watches more videos, the algorithm gets better at making suggestions because it has more information about what the user likes to watch. The goal of the algorithm is to maximize the amount of time the user spends watching videos. 

Algorithms are subject to the halting problem. That is, there is no way of knowing in advance whether an algorithm will get stuck in a loop or not for every possible input. 

Simple algorithms tend to be slower than more complex ones. Below are some visual aids. 

15 Sorting Algorithms in 6 Minutes

Intro to Algorithms: Crash Course Computer Science #13

There are problems that can't be solved with algorithms, but that doesn't mean the problem is unsolvable. Sometimes proving there is no general solution to a problem opens up a new field of math. Group Theory came into being because Galois used it to prove there is no general solution to a 5th order polynomial equation. 

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. 

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. 

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.

The War of the Worlds (1953)

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

7. Robocop

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

my favorite

Hannah Barbera's The Greatest Adventure - David and Goliath

2. Crash Course

Early Computing: Crash Course Computer Science #1

3. Veritasium

This equation will change how you see the world (the logistic map)

4. PBS Eons

Why Do Things Keep Evolving Into Crabs?

5. Ancient Recitations

Go Rin No Sho - The Book of Five Rings by Miyamoto Musashi (Complete Audiobook)

6. Mark Rober

Egg Drop From Space - YouTube

7. Hungarian Folktales

Hungarian Folk Tales: The Diligent Girl and the Lazy Girl (S03E11)

8. Greatest Audiobooks

THE TIME MACHINE by H.G. Wells - FULL AudioBook | Greatest AudioBooks V4

9. YouTube Movies

Full Metal Jacket

10. Traditional Music Channel

Balkan Gypsy Music

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 

my favorite economics videos

 George Ought to Help

The Jones Plantation

"Good Intentions" with Walter E. Williams

Viral Influencer Gloria Alvarez Fights Socialism

economics rap - Keynes vs Hayek

Fear the Boom and Bust: Keynes vs. Hayek - The Original Economics Rap Battle!

Fight of the Century: Keynes vs. Hayek - Economics Rap Battle Round Two

long version

Free To Choose 1980 - Vol. 01 The Power of the Market - Full Video

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. 

nature's way

 

Busy Beavers Build Dam Ahead of Winter | Yellowstone | BBC Earth

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. 

suggested homeschool schedule

I hope to have kids someday and ideally homeschool them with the help of a stay-at-home mom. It probably won't work out that way, but it's useful to consider the ideal case. Kids should help with cooking and cleaning. Actual school would last six hours with 30 minutes each for 12 periods:

1. copying dictionary (for handwriting, spelling, vocabulary, and reading comprehension)

2. reading the Bible (for moral instruction, cultural awareness, and reading comprehension)

3. math (emphasis on arithmetic up to algebra)

4. music (listening and playing/singing)

5.  art (appreciation and drawing/painting)

6. walk outside

7. Spanish or another foreign language

8. science (alternate biology, chemistry, physics, astronomy)

9. geography

10. history

11. news

12. poetry

0700 to 0800 - hygiene and breakfast

0800 to 1200 - school

1200 to 1300 - lunch

1300 to 1500 - school

1500 to 1600 - chores

1600 to 1700 - sports/strength training/cardio

1700 to 1800 - dinner

1800 to 1900 - TV and video games

1900 to 2000 - hygiene

2000 to 2200 - movie

2200 to 0600 - sleep

weekend and summer schedule

0900 to 1000 - hygiene and breakfast

1700 to 1800 - dinner 

2000 to 2200 - movie

education, immigration, or eugenics? - what brings in more smart people?

The scientific and technological achievements of the US are not because the US has the best educational system, but because it attracts smart people from all over the world. Nuclear weapons and the moon landings were made possible by foreign-born scientists who came to America for a better life (freedom and prosperity). 

In that case, the US should be spending less on education and more on recruiting talented foreigners. Good education can make smart people even smarter, but it can't turn average joes into geniuses. Unfortunately, the best evidence is that intelligence is mostly genetic. 

Eugenics gets a bad rap for many reasons, yet sperm bank customers consistently demand donors with high IQs. Paying high-IQ men to donate sperm would be an easy way to increase the number of smart people. Mensa already has a database of such people. 

There are many existing incentives that reward smart Americans such as scholarships, but these do not lead to smart people having more children. 

More smart people = a better life for everyone. If it's not possible to breed more of them, the ones we have need to be kept alive, happy, and working. 

There is evidence that certain unorthodox educational approaches can be helpful with low-performing groups. This Texas math teacher managed to boost test scores with rap:

Texas teacher brings rap music into the classroom : NPR

Well done, but the US Math Olympiad team remains heavily Asian. They don't train by singing songs about math.

American mathletes come in 4th place in International Mathematical Olympiad - YouTube

Here is what US math teachers are up against:

ADHD Study

And here is the best attempt to make math as interesting as Star Wars:

Math is Art

thucydides quote

 

overeducation

Some relevant facts:

1. Most people don't like school and don't learn much from it.

2. Education takes a lot of time and money, much of which is wasted. 

3. IQ is the best measure we have of intelligence, and it can be measured quickly and reliably. 

4. IQ changes little over time. Smart children become smart adults, etc.

5. The earlier someone starts learning a skill, the better they end up at it. 

The rational thing to do would be to measure the IQ of all children around age 6 and have separate educational tracks. My suggestion for the IQ-education cutoffs:

below 85 - special education with a focus on basic literacy

85 to 100 - educate to the 5th grade and encourage art, music, sports, and shop class 

101 to 115 - educate to 8th grade, encourage enrollment in trade schools and military

116 to 130 - educate to 12th grade, maybe skip a grade or two, encourage associate's degrees

above 130 - college and beyond with special enrichment in grade school 

The advantages of such a system: cheaper, faster, better results, happier students, parents, and teachers

The smarter the students are, the more socialization they get, but with those on their level. My experience was that pretty much everyone with an IQ above 70 spent 12 years in school and got the same diploma on graduation day. That's a travesty.

be all you can be

 

amish

 

mental math