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.
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.
They took down the flag as a sign of surrender to keep the Taliban from looting it and humiliating the US even more.
So I wonder how well my country, the US, will fare against Iran. Below is a clue.
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Mohammad Hossein Fahmideh (Persian: محمد حسین فهمیده;[1] 6 May 1967 – 30 October 1980) was an Iranian child soldier and an icon of the Iran–Iraq War. During the First Battle of Khorramshahr in 1980, he served with the Basij and fought invading Iraqi forces in and around the city of Khorramshahr. Fahmideh is credited with having halted the advance of an Iraqi tank column after he jumped underneath an Iraqi tank and detonated a full grenade belt, killing himself in the process. He is celebrated as a war hero in Iran.
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It will be a cold day in hell when Americans recruit, deploy, and celebrate the suicide combat deaths of child soldiers.
Iran lost about 2% of their population during their 10-year war with Iraq. That's a similar percent to what the US lost during its civil war. To this day, there are hundreds of monuments to that war in the US, even though the war ended over 160 years ago. And even today, the war inspires strong feelings.
They have a cemetery in Tehran with a "blood" fountain to honor their dead from the war with Iraq.
Sacrifice and martyrdom are powerful themes in Islam and especially Shia Islam, the main religion of Iran.
During WW2, Germany lost about 10% of its population and Japan about 5% of its population. That is what is required for unconditional surrender. Iran has 90 million people today. Are US leader willing to kill 5 or 9 million Iranians to compel their unconditional surrender? I think not.
Also, if the US does kill 5 million Iranians, doesn't that make them just as bad as the Iranian hardliners who want to wipe Israel off the map?
My advice to American leaders is to declare victory and stop bombing Iran. Otherwise, Iran will drag out this war to make us look like even bigger idiots than we have been already.
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At a March 2026 Christian worship service at the Pentagon — the first since the U.S. and Israel began military operations in Iran — Defense Secretary Pete Hegseth asked Pentagon officials to pray for “overwhelming violence” against enemies in Iran and elsewhere, invoking the “mighty and powerful name of Jesus Christ”
Hegseth recited a prayer he says was given by a chaplain to troops ahead of the U.S. raid on Venezuela and the kidnapping of then-President Nicolás Maduro in January. The prayer, drawn from passages in Psalm 18:37–42 and other biblical texts, includes verses such as:
“I pursued my enemies and overtook them. I did not turn back till they were consumed. I thrust them through so that they were not able to rise. They fell under my feet… And those who hated me, I destroyed. They cried for help, but there was none to save” .
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I like Psalm 18:37 too, but that's John Wick stuff, not strategy.
Maybe Hegseth is unfamiliar with the "blessed are the peacemakers" and "turn the other cheek" - some of the most powerful words Jesus ever spoke.
Jesus was not a warrior and never killed anyone. Aside from that freakout at the temple with the blasphemous moneychangers, he never did violence of any sort.
And what kind of warrior turns himself over to his enemies to be tortured and humiliated? I don't believe Jesus rose from the dead. I do believe there was a real man named Jesus who said and did most of things described in the New Testament. Like Socrates, Jesus wanted to make statement with his death.
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.
Today I noticed that if you use the Collatz Conjecture with a prime as a seed, the first odd result greater than 1 that is not a multiple of 5 (greater than 5) will be prime or semiprime. Here are examples with the primes between 1 and 100
2 1
3 10 5...
5 is prime.
5 16 8 4 2 1
7 22 11...
11 is prime.
11 22 34 17...
17 is prime.
13 40 20 10 5...
5 is prime.
17 52 26 13...
13 is prime.
19 58 29...
29 is prime.
23 70 35 106 53...
53 is prime.
29 88 44 22 11...
11 is prime.
31 94 47 142 71...
71 is prime.
37 112 56 28 14 7...
7 is prime.
41 124 62 31...
31 is prime.
43 130 65 196 98 49...
49 is semiprime.
47 142 71...
71 is prime.
53 160 80 40 10 5...
5 is prime.
59 178 89...
89 is prime.
61 184 92 46 23...
23 is prime.
67 202 101...
101 is prime.
71 214 107...
107 is prime.
73 220 110 55 166 83...
83 is prime.
79 238 119...
119 is semiprime.
83 250 125 376 188 94 47...
47 is prime.
89 268 134 67...
67 is prime.
97 292 146 73...
73 is prime.
skipping a bit
997 2992 1496 748 374 187...
187 is semiprime with factors of 11 and 17.
9973 29920 14960 7480 3740 1870 935 2806 1403...
1403 is semiprime with factors 23 and 61.
By combining this with the Goldbach Conjecture, we have a new primality test and a way of generating primes. Start with a large even number (100 digits or more) and divide by 2 until you get an odd number. Then use that odd number as a seed for the Collatz conjecture. The first odd result that isn't a multiple of 5 will be either prime or semiprime. I suspect that as for large seeds, the first odd result is more likely to be semiprime than prime.
In this way, it is possible to build up a library of large semiprimes, which eases the integer factorization problem.
What happens if the seed is semiprime?
187 562 281...
281 is prime.
1403 4210 2105 6316 3158 1579...
1579 is prime.
So if we start with a semiprime, we can get an actual prime in a few iterations.
For any given range, there will be somewhat more semiprimes than primes.
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.
