Live and Let Howl

It's not easy being a werewolf. Fortunately, there's only one full moon per month, and the change only lasts from sunset to sunrise. I don't remember much from those times. Maybe other werewolves are different. We don't gather often, at least I don't, and when we do meet, we usually talk about anything except what happens that time of the month. There's no set age for the first change, though most are in their 20s when it happens. Some people it seems are born into it while others get converted by a werewolf bite or scratch. If you want to become a werewolf, and you shouldn't, you need to be one of the lucky encounters that does not end in a fatality. On the bright side, the aging process basically stops, though we still get white hair eventually. Our health is generally excellent, no matter how many bad habits we pick up. Alas, since we spend most of our time in human form, we must work to eat. 

I chose to be a park ranger, as it makes it easier for me to isolate myself during the change. My territory covers several square miles of a famous national park. You've probably heard of it. It has geysers and gets millions of visitors per year. The good news is almost all of them leave before sunset, and I can use my ranger truck on the back roads to find a secluded spot for my wild nights. Also, there is plenty of game nearby. The circle of life can be delicious. The change is a kind of fever dream. Though my senses are aware, the volume on my ego is turned down. Instinct takes over for the most part. My preferred prey are bison, particularly the larger males as I enjoy the challenge of the fight, and I don't always win. Werewolves feel pain just as intensely as any other mammal, and though our healing is greatly accelerated, it still takes hours to recover from serious injuries.    

Far as I can tell, most werewolves die by suicide in their human form. Sometimes, it's suicide by cop or some other situation where they deliberately decide to bite off more than they can chew, so to say. It's never clear what pushes them over the edge. A lot of us end up in the military, hoping to find ourselves in a situation where our qualities are more useful. Those same qualities generally result in most of us getting kicked out of the military or killed in battle. I must say it was a great challenge to hide my lycanthropy when I was in the Army. I had learned when I was younger to keep track of the lunar cycle and to plan well in advance. It was a great stroke of luck the day I learned that I can sleep through the transformation if I heavily drug myself just before sunset, though it leads to a terrible sort of hangover the next morning. 

It's been about 20 years since the night of my first change. I had no idea it was coming, and so it ended up being an epic rampage. Luckily for me, there were no fatalities, but it made the paper before being dismissed as a case of a rabid bear. On a related note, I can say with confidence that many sasquatch sightings were actually of werewolves. The reason for the lack of bigfoot photos is that werewolves are nocturnal whereas wildlife photographers are not. Some bigfoot tracks are definitely from werewolves. I did an experiment on myself to check. A few hours before my change, I went to an abandoned warehouse and scattered flour on the floor around me before lying down. When I came back the next day, there were indeed tracks that looked bigfoot prints. I took photos to save for my journal. Maybe someday I will find someone to publish it. I doubt it would be believed, though there is a real subculture of werewolf hunters.   

Some of the werewolf hunters are very keen. They know that silver bullets don't work. Silver is too fragile a metal for bullets anyway. It's basically impossible to kill a werewolf, though it is possible to injure them enough so as to incapacitate them for several hours. Fortunately for us, when the morning comes, we revert to our human form, and so we are generally let go. I managed to dig up one account of a werewolf who had been captured and sold to circus freak show. The plan was to put him in a cage so an audience could witness his transformation. Well, they did get to witness it, and it was the last thing about a dozen of them ever saw. It's hard to say how strong a werewolf is, but we're at least as strong a silverback gorilla as far as I can tell. I once locked myself in a cage with iron bars to see for myself. As a back-up plan and to avoid the temptation, I swallowed the key. As it turned out, I did not end up needing the key to escape. 

As far as I can tell, there is no active campaign to increase our numbers, though I often wonder how the world would be different. Perhaps if everyone had an outlet for their violent impulses, the mass catharsis would usher in a more peaceful world. The novelty of lycanthropy wears off quickly. Most of us quickly conclude that it is impossible for us to live normal lives. Perhaps tribal shamans were the way ancient societies dealt with lycanthropy. I read an account in an anthropology book where the chief of some tribe said, "thank God we have only one shaman and not two". There is no cure for our sickness, if that's the right word for it. Even if there was a cure, I wouldn't want it. I've gotten used to my life as it is. 

For me, there is no curse in being an immortal carnivore. I suspect there is a small percent of the human population that would feel the same way. My motto these days is: live and let howl.  

Presented Without Comment - Emilia Decaudin, NY Democrat

 

Invader Zim Jack-o'-lantern

Technically, it's the logo of the Irken army. I messed up the eye sockets and ended up using cardboard strips as replacements. I've never been much of an artist, but I was pleased with my work. 

Happy Halloween!

Electric guitar Invader Zim theme: 

On the Future of Airships

Suppose the Hindenburg disaster had not happened, and that US freely exported helium. In that case, airship technology would have continued to advance along with other aircraft. Even in the 1930s, airships were faster and more fuel efficient than ocean liners. While they were slower than aircraft, they were more fuel efficient. The cruising speed of the Hindenburg was about 80 miles per hour. A cruise ship today sails at about 20 miles per hour. The passengers had much more room as well. Below are pictures of the lounge and restaurant from the Hindenburg:

Luxurious, especially when compared to today's first-class seats on a passenger jet.

The use of airships to transport cargo is also an intriguing possibility, as they require far less infrastructure than freight trains or cargo ships. Airships contain less metal, and so are cheaper and easier to build. They also would greatly reduce the cost of shipping cargo to remote locations, and that has caught the interest of Canada. 

There is a possibility that smaller air taxis and airbuses could be used reduce traffic in cities. 

The main problem with airplanes and helicopters is fuel efficiency and cost. Airships are superior in both categories. They have a much longer range than helicopters, can hover, and can stay aloft for much longer than helicopters or airplanes. A zeppelin held the record for fastest circumnavigation for a few years in the 1930s.

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LZ-127 Graf Zeppelin, in 1929, piloted by Hugo Eckener made the first circumnavigation by an airship. It was also the then fastest aerial circumnavigation, in 21 days.

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Much like analog computers, the possibilities of airships have not been fully explored. 

Here is a blimp pulling water skiers:

Joe Biden Repeatedly Disrespects Troops

 In case there was any doubt left about Biden's character, here he is insulting troops:

And here he is checking his watch during a memorial ceremony for troops killed in Afghanistan:

This clip of a grieving mother says it well:

So does this:

It seems many people are fed up with Biden:

I remember the news cycle being dominated for several days based on an unconfirmed story that Trump had insulted US troops. Biden does it on camera and it barely gets covered in US media. 

 

Why Joe Biden Sucks

 This is not an exhaustive list.

1. He is clearly senile. He is unable to speak coherently or even dress himself.

2. He is corrupt. Here he is bragging about getting a Ukrainian prosecutor fired. The prosecutor was investigating a company called Burisma which paid $3 million to his son Hunter Biden. 

3. Even before he went senile, he was dumb. His 1988 presidential campaigned ended after he got caught plagiarizing various politicians. 

4. He has a long history of saying stupid things in public. Behold the glory of his Corn Pop speech:

5. He has been caught on camera many times acting like a creep.

6. He is incompetent. He abandoned the airport in Kabul to the Taliban, which resulted in a hasty and disastrous evacuation. 

7. Six months after that, Russia invaded Ukraine. That war has cost the US $100 billion so far and shows no signs of ending soon. 

8. He's added $3.5 trillion to the national debt in less than three years in office. He's on track to add on more debt than any other president. 

9. As a result of that debt, inflation is at the highest level in 40 years. 

10. He resumed aid to Hamas and unfroze Iranian assets. This was quickly followed by a massive terrorist attack against Israel. Biden is not respected in the Middle East. 

 

I regret voting for him in 2008 when he was Obama's running mate. Please, do not vote for this man.   

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As Robert Gates, former defense secretary in the Obama administration, once put it, Biden has “been wrong on nearly every major foreign policy and national security issue over the past four decades.” 

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source

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Speaking to a fellow Democrat about Joe Biden being the party’s nominee in 2020, Obama famously warned, “Don’t underestimate Joe’s ability to fuck things up.”

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source

Ideal Force Structure, Weapons, and Equipment for the US military

This list is based on what is actually necessary for the US to defend its people and territory. It also covers humanitarian and peacekeeping operations. In general, the US spends far too much on big ticket items like surface ships, submarines, manned combat aircraft, and armored vehicles. All of those have little utility in the wars the US is likely to fight. America's nuclear stockpile should also be greatly reduced. The 400 or so active land-based ICBMs are more than enough to be an effective deterrent. 

The service academies should also be closed. There is no evidence they produce better officers than other much cheaper programs like ROTC and OCS. Overseas military bases should be closed and auctioned off. It's not our responsibility to defend other countries, especially rich ones that have well-funded and capable militaries. It was a mistake to establish the Space Force. Let the Air Force handle the military satellites. 

Special forces should be on the chopping block too. Army Rangers are the only ones in that bunch who have ever been on the winning side of a war, and that one ended in 1945. The money would be better spent on drones, cyber operations, and foreign language training. 

The US Army in the 1930s had about 100,000 soldiers. That's about the size it should be now, though a large reserve of perhaps 300,000 is a good idea. I'd decrease the arsenal to the following weapons: M9 pistol, M4 rifle, M67 grenade, M203 grenade launcher, M249 machine gun, Javelin anti-tank missile, Stinger anti-aircraft missile, and M24 sniper rifle. Ideally, all troops should do familiarization fire with each of those weapons, though simulated rounds would be acceptable for the M203, Javelin, and Stinger. I'd prefer to see the Humvee fleet get gradually replaced with Toyota Hilux trucks, as they are cheaper, more reliable, and easier to maintain. 

As for vehicles, I'd keep a small force of HIMARS and tanks, perhaps 100 of each. A fleet of 50 or so Blackhawk helicopters would be reasonable as well. It'd be good for the Army to have a few rapid response battalions that could fly out in C-130s to trouble spots. 

For the Marines, I'd let them have two expeditionary units with all the bells and whistles. There isn't much of a reason to have more than that. Historically, USMC was the smallest branch, usually having less than 10,000 personnel total.

I'd let the Air Force keep their cargo and refueler aircraft, plus some rescue helicopters. I'd cap the number of their manned aircraft at 100. Their focus should be on drones and nuclear deterrence. 

The Navy would get to keep 10 submarines with two of them carrying ICBMs. I'd prefer to see them focus on cruise missile strikes. I'd likewise cap their manned aircraft at about 100. 

The Coast Guard I'd leave at its current size. They're not much of a drain on the system. 

The bulk of manned aircraft would be Blackhawks and C-130s. A few hundred Predator and Reaper drones would be enough for airstrikes. Cruise missiles are the best option for the minor wars the US is likely to engage in. 

It's very unlikely any of this will happen, but this is the right direction to head in. There's simply no good reason to keep spending what we have been for the results we've been getting and for the wars we are likely to fight. 

No More Proxy Wars and What the US Should Do Instead

The first proxy war the US engaged in was in the Russian civil war of 1917 to 1921. The US-supported side lost, and the communists established the USSR. Later, the US supported the nationalist faction in the Chinese civil war, which also ended in defeat for the US side in 1949. Likewise, the US-sponsored intervention in Cuba ended in defeat during the Bay of Pigs fiasco in 1961. There was another defeat in Vietnam in 1975 even after a decade of direct US intervention. More recently, the US-supported government fell to the Taliban in 2021 after 20 years of American military and other foreign aid. The only civil war in the 20th century where the US-supported side won was in Greece in 1949. The war in Ukraine continues, but the prognosis is not good for the US-supported Ukrainian government. 

The US military is good at gaining air superiority and winning conventional wars, such as in Desert Storm in 1991. It has also had success with humanitarian and peace-keeping operations. The Berlin Airlift was a great example of American prowess in a humanitarian operation. It is not good at defeating insurgencies, as the wars Vietnam and Afghanistan illustrate. While it has won wars against vastly inferior opponents like Panama and Grenada, it has also lost wars to significantly weaker forces like militias in Somalia and Lebanon. 

One thing events of the past few years has shown is that the US military needs to improve its ability to evacuate Americans and foreign partners from trouble spots. A few months ago, about 16,000 US citizens became trapped in Sudan because of a civil war there. Before that in August of 2021, a number of Americans and thousands of Afghan partners were abandoned in Afghanistan. A few days ago, hundreds of Americans were stranded in Israel and Gaza when US airlines stopped flights to Israel. 

Clearly, the US military needs more practice at these operations. Furthermore, the US government has an obligation to us the military to rescue Americans who are in danger overseas. At a minimum, US military and civilian leaders need to have a plan in place for evacuating Americans from any country. That plan should include a contingency for setting up airstrips in case there are no safe airports available. Convoys of trucks and buses could also be used in some cases to evacuate people to another country before flying them back to the US.  

Msukule, the Zombie of East African Folklore

 Here is my translation of the Swahili article about it on Wikipedia:

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An msukule is a person who a number of people believe has died by sorcery. In this community, it is often heard that someone has died and been buried, but actually it is said that this person has not died completely, but instead has been transported by supernatural means to another place, and that another person is forcing them to work at various tasks, especially very hard, tiring work. 

Explanation of this belief

Certainly it is difficult to take an able-bodied and aware person and force them to do whatever you want. Of course, for someone who agrees with you, and has no objections from friends, family, or relatives about what you want to do, there is no difficulty. However, it is different with witch-doctors. They routinely take the souls of people to the spirit world and force their bodies to do grueling work like farming, manufacturing, and tending livestock. 

The witch-doctors or sorcerers always take people who are healthy in mind and body and put their mind and soul to abide in the spirit realm.  

Therefore, the victim's remains alive both on the earth in body and in the spirit realm as mind and soul. This why if such a person is tending a store, he may call customers to come and buy, but for those with normal eyes, they usually can't see him. It is only those whose spiritual eyes are open or have been opened that can see what is going on. 

Basically, in the spirit world, no one has a body. Anyone who has a life-threatening medical condition is also in the spirit realm, indeed this is the origin of it. Unless they go to heaven or become a ghost, they stay in the spirit world. Therefore, if someone dies with their soul and body intact, they either go to heaven or become a ghost, according to their deeds while they were alive. 

Another thing: no one has the right to take anyone's life except God himself decides to or allows another to do so. That person would be someone in great distress because their soul had been removed. Witch-doctors do not normally kill people in order to make them zombies; they take healthy people and force their souls to reside in the spirit world. 

That is why it is impossible for a person to be in the spirit world while their soul and body are together. Witch-doctors use magical means to extract the soul and prevent it from returning to the body. 

This is why the body of a person restrained in such a manner retains all of its physical abilities and strength. The vital force always pulls it to return from the spirit world and keeps it locked in the body. 

You will see that someone who has died in the past will appear again, even if all the prayers were said for him, and whatever medical treatment was done for him, he will return because the magic that was binding his soul to the spirit world has gone and so he returns the realm of the living. 

Someone who has been turned into a zombie cannot be seen by normal eyes. Only those properly educated, such as servants of God, seers, and prophets, can see zombies. 

Evaluation

These explanations have no basis in science. However this belief continues to be found among many Africans, even Muslims and Christians, though some sects see belief in zombies as a form of paganism. 

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It's been 14 years since I spoke Swahili daily, so I'm sure I made some mistakes. On a related note, the word "zombie" comes from a Kikongo (another African language) word "nzumbi".  It's probably related to the word nzambi which means god. 

I translated mchawi as witch-doctor since this is a term English-speakers are familiar with. It originally referred to charlatans in England who claimed to cure diseases brought on by the devil. 

I first learned about msukule as a Peace Corps volunteer in Tanzania. Here is the story:

I was hanging out at a bar and a friend said I looked really tired. He then speculated that I had been turned into an msukule. This led to asking him what an msukule was. 

Outlaw of the Jungle

In a distant land, there were never any people, and so the animals developed differently. The country, called the Animal Kingdom, was divided into two nations: the Carnivore Dictatorship and the Herbivore Republic. Each side chose leaders once a year. The carnivores had a trial by combat while the herbivores took a vote. Both nations found their systems suitable and had adhered to them for a long time. 

The carnivores were fewer in both number and kind, and so they competed more fiercely. Their kingdom was divided into several houses: lion, tiger, bear, wolf, eagle, and crocodile. The House of Tiger included cheetahs and leopards, but they were rarely the head of their house much less the kingdom. In a similar way, alligators and pythons were part of House Crocodile. 

Meanwhile, in the Herbivore Republic, there were the houses of elephant, buffalo, deer, and ape. The House of Elephant counted the rhinos and the hippos in its ranks. Likewise with the other great houses, the largest of which was House Ape, which included the largest gorilla down to the smallest monkey. The rats felt equally at home in both groups, which made them the swing voters of the Animal Kingdom, though neither nation ever understood why the House of Rat would switch back and forth.    

The time came for the carnivores to choose a new leader, and the contest was decided through trial by combat. House Eagle, generally never having much of a chance, abstained as usual. House Python defeated House Crocodile to win the Reptile League while House Tiger beat House Lion. In an upset win, House Wolf prevailed over House Bear, who blamed their defeat on having just come out of hibernation. In the final rounds, House Python was victorious over House Wolf which then lost to House Tiger. 

As the tigers and their kin were celebrating, a messenger from House Rat came before them and announced they wished to challenge House Tiger. The tiger champion laughed and told the rat messenger that the rat challenger should come straight away. Just as soon as had the tiger champion said that, a horde of rats burst forth from every direction, covered the tiger and began biting him everywhere. The tiger begged for mercy and the rats relented. 

"Now that we have won the contest", said the rat messenger, "you must bow down before me, for I am the Emperor of Rats". 

"But that's not fair", the tiger champion protested. "You rats ganged up on me."

"Ah, but we were only following the law of the jungle, just as you. And that law is merely 'might makes right'."

There was a hue and cry from the other carnivores who had come to see what the commotion was a bout. Though the rats were great in number, their emperor knew they could not win against all of them by force.

"There's only one fair way to settle this", said the rat emperor, "we will take our dispute to the Herbivore Republic and let them decide who is right."

The tigers and other carnivores agree this was fair, so the tiger champion and his leopard bodyguard left with the rat emperor and his army for the Herbivore Republic.

"I don't trust these rats", whispered the tiger to the leopard. "At night, we'll take turns sleeping so that neither of us is caught off guard." 

Likewise, the rat cautioned his troops to be on guard, for the tiger and leopard could quickly kill many of them in a surprise attack. There were many tense nights during the journey to the territory of the Herbivore Republic, but the uneasy truce held. 

Near the border, they were questioned by one of the elephants guarding nearby. After explaining their dispute, the elephant guard told them to wait so that he could fetch the elders of the Herbivore Republic. After a few hours of waiting, the wisest herbivores appeared: the gorilla and the orangutan. 

"The elephant told us of your case, and we discussed it during our walk here", began the gorilla. 

"But we thought each of you should have one more chance to persuade us before we make our final decision", said the orangutan. "Tiger, you may go first."

"Thank you, your excellency", spoke the tiger most obsequiously. "I had just won a fair tournament against the other carnivores, as is our custom, when this upstart rat barged in and demanded we duel. Naturally, and quite generously, I obliged him, only to have my trust betrayed when he called up thousands of his fellows to overwhelm me. This is quite unheard of among our kind as trial by combat is universally understood to be a one-on-one contest. As I am the rightful winner of that contest, I should be ruler of the carnivores."

"Well said, tiger", agreed the orangutan, "well rat, what have you to say to that?"

"Fellow mammals, surely we all recognize that here there is but one supreme law, which is the law of the jungle. In nature, do not the ants gang up on their prey? They must in order to survive. Even among the carnivores, there is the wolf pack and other predators who use teamwork to hunt. There is no way a single rat could possibly defeat a tiger, which is why the eagle refuses to participate in the great carnivore tournament. You herbivores are well known to be wise and I trust you to reach the right judgement in this case."

The gorilla and the orangutan began to rub their chins thoughtfully, as though they were lost in thought. Just then, a group of strange creatures burst upon the scene. They walked on two legs and were mostly hairless. Some carried burning sticks while others carried long sticks with sharp stones on the end. There were many of them and they looked fierce. one of them casually tossed the tusk of an elephant into the midst of the group of animals. At last, one of them spoke.

"Greetings. We are called humans and we have been listening to you for a long time. We did not know animals could speak as we do, for you are the first of that sort we've ever met. We rule over all the earth because we are the smartest and have the best weapons. Our spears and fire are much better than your claws or fangs. There is no way you can defeat us, especially when we have weapons and fight in a group, as we are ready to do now. We will kill a few of you from time to time because we need to eat, just as you carnivores have been doing. Be warned, though, that if you kill any of us, you will surely die. The Animal Kingdom is hereby abolished. Now go and stay away from us unless we call you."

At this, the men raised their spears and began beating drums. The terrified animals scattered and ran. As the tiger ran for his life, he roared "truly man is the outlaw of the jungle!"  

Nahal Toosi Makes an Oopsy

In an article titled "Here’s how the Israel-Hamas conflict affects Ukraine, China, Iran — and everyone else" published yesterday, the author accidentally hyperlinked to a Google doc. A screenshot is below:

The hyperlink address is still visible, but when you click on it, you get this:

Here is a screenshot showing the Google doc hyperlink in the article (see the grey box in the bottom left):

Captain Stormfield Visits Valhalla

Everyone in San Francisco said Captain Stormfield was crazy when he announced he planned to ride a hot air balloon and hitch a ride on Halley's Comet. There was no laughing when neither he nor the balloon were ever seen again after the night of Stormfield's great experimental flight. For in truth, Stormfield had not told everyone everything about his design, and with the help of some esoteric devices (Tesla had attempted to explain how they worked, but Stormfield didn't understand and Tesla never wrote about it, like many of his other ideas), had reached the comet and was now resting comfortably on its surface. When his provisions ran out, much to his delight, he found that the entire comet was edible, nutritious, and delicious. Although it would be another 72 years before the comet would pass earth again, Stormfield felt confident that he had enough time to devise a solution. To his surprise, as he ate of the comet, he was de-aging. His white hair regained its former color and grew thicker, he had more energy, and all his old wrinkles and wounds vanished. Stormfield sealed some in snuff box for use in case of an emergency.    

Based on how often he had to answer the call of nature, Stormfield was able to estimate about how long he'd been on the comet. The days stretched into weeks and then months. Stormfield hoped with all his heart it would not extend into years, though he was certain he would survive the journey and return to earth. He had the foresight to bring a telescope with him, and when he wasn't writing in his journal, he was scanning the heavens for any sign of hope. To his surprise and relief, a blue point of light appeared, and daily it grew larger. Stormfield was ecstatic to sea an earth-like planet so far out in the cosmos and after such a long night on the comet. Once while peering at the distant planet, he saw a much smaller object that grew larger with a much greater frequency. Could it be a craft sent out to rescue him? He could only hope that was the case. In preparation, he gouged out a large X on the surface of the comet with his own stricken ship in the center. He knew it was unlikely that his would-be rescuers could read or understand English, but hopefully they could recognize the difference between natural and artificial shapes. 

Indeed, as the object grew closer, it was plain enough that it was a spacecraft, just as Stormfield had suspected. It had a large window at the front, various lights along its fish-shaped body, and the flames and smoke pouring out the rear looked much like a flying rocket during a Fourth of July Fireworks show. He concluded that if he had a telescope that allowed him to see them, surely they had something much more advanced that allowed them to see him. By this point, the sun the planet orbited was close enough so that its brightness was similar to earth's sun. Stormfield retrieved a signal mirror and began flashing it at the craft. After a few minutes of that, he checked his telescope and saw that the ship was flashing back at him. Soon enough, the alien vessel was large enough to be seen with the naked eye. There has a flash from the ship, and a harpoon-like device shot out and embedded near the center of Stormfield's X. Towards the of the harpoon was a kind of harness which he concluded was meant for him to wear. He put on the harness and fastened it tight. Then he used his mirror to signal the ship. 

Later, he concluded that the ship must have been matching course and speed with the comet, else the harpoon would not have stayed stuck in its surface. As soon as the craft stopped its engine, the comet tore away from the harpoon and Stormfield was left floating in space. Fortunately, the special suit Tesla had made for just such andevent worked perfectly. It resembled a Siebe apparatus outwardly, though Tesla had made numerous improvements. What a shame it was that Tesla never documented the suit's design. Slowly, Stormfield was winched toward the ship. At last, he approached some sort of hatch that had what looked like a ship's wheel. Stormfield turned it left a few turns and the hatch opened. What an interesting coincidence it was that the righty-tighty, lefty-loosey rule would work in the far reaches of outer space. He closed the hatch behind him and tightened the wheel to seal the chamber. On the other side of the chamber was a similar hatch, but he sensed he shouldn't open it. He had just been in the vacuum of space and while the comet's atmosphere was enough such that he could remove his suit for a few hours at a time, he knew that wasn't the case once he had been launched into space. 

He saw a red light illuminated near the inner door of the chamber and next to it was an unlit light whose bulb was made with green-tinted glass. After a few minutes, the red light went out and the green light turned on. Stormfield went the inner door and opened it. On the other side were several men who looked Scandinavian, one had red hair, another had blonde hair, and the third had blue eyes. Stormfield concluded they must be from earth, and not sure what other language to use, took out a pen and paper and wrote some Latin on it. Then he read it out loud as he pointed to the words, which were "in vino veritas". One of the men laughed, spoke to his comrades in another language, and they laughed too. A few moments later, one of them returned with a goatskin full of mead, which Stormfield guzzled contentedly. He had correctly deduced that these must be men of learning, and so it was likely that it least one of them knew some Latin.  

The cleats on Stormfields boots had kept him anchored to the comet, but he was not sure what was holding him to the floor aboard the ship. The red-haired one motioned him to follow and Stormfield was led to the cockpit. The red-haired one was apparently the pilot, and after he adjusted some knobs and buttons, the ship turned so that the planet Stormfield had gazed at so intently was now in view. The blonde one then motioned Stormfield to look into the eyepiece of the ship's telescope, and after playing a few knobs, he brought the view into focus and was able to magnify it tremendously. He saw farms, ports, cities, roads, canals and every other form of physical civilization. At the maximum setting, he could see individual people as though they were toy soldiers on a table right in front of him.

Stormfield was taken down to the planet and slowly learned the language and culture of its people. They called their world Valhalla, after the paradise of the Viking religion. It turned out they were the descendants of a Viking expedition that had been lost thousands of years ago. They themselves weren't sure quite how it happened, but as far as their scientists could tell, their longship had drifted into some sort of portal which catapulted them trillions of miles through space, and by a fantastic stroke of luck, they landed safely on an earth-like planet. A few other Viking ships suffered the same fate, and that built up their population enough so that their society became self-sustaining. With no other rivals and a common language, religion, and culture, their civilization flourished and advanced to tremendous levels. Their scientific knowledge far exceeded that of the earth-born, as they referred to Stormfield's people. When Stormfield asked if they would not prefer to return to earth, their chief scientist replied that the time was not right, but Stormfield would have the honor of being their ambassador, the first they had ever sent to earth.

As proof of his voyage, Stormfield was given a book which contained all sorts of advanced math and science written in their language, which had diverged little from Old Norse. He knew that if he showed this book to any expert in the history or language of the Vikings, they would surely conclude that no man from earth could have written it. Futhermore, being fluent and literate in this language, Stormfield could explain its contents to scientists, historians, and mathematicians. With much fanfare, Stormfield was ushered off to latch onto the comet as it passed by. He was given an improved space suit with a special harpoon gun that would allow him to reach and board the comet. With all their advanced technology, even the denizens of Valhalla had yet to perfect long-distance space travel. He was also given a potion that would allow him to sleep for several decades. When it wore off, he would be mere days away from passing Earth, where upon he could use the grappling gun to attach to the earth. 

Stormfield waved farewell, took aim, and fired the harpoon gun into the comet. Instantly, he was hoisted off the ground, and after a few minutes, winched toward the surface. He trudged back to the wreckage of his balloon ship, found a comfortable place to lie down, and took the hibernation pill. He awoke as though from a short nap, went back outside and saw the earth once more in all its glory. He aimed for a point near San Francisco and fired the gun. In the blink of an eye, he was hurtling through space once more. By an extraordinary coincidence, he made landfall on Alcatraz Island. He had practiced a bit on Valhalla with using the harpoon gun to travel shorter distances, and so made another much smaller leap across the bay to the shore. 

Now that he was home, safe and sound, he removed his helmet and suit. Almost instantly, he felt sick. There had been too many shocks to his system. In a panic, he staggered toward a passerby and begged for help. The stranger watched in horror as Stormfield dessicated and disintegrated in a matter of seconds. The passerby explained what he saw and showed the remains to the authorities. Alas, he was declared insane and sent away. The remains of Stormfield, including the suit, the book, and the tin of comet meat was gathered up by the police. After a few professors looked at it with little interest, the remains were auctioned off, and ended up in the hands of a Chinatown antique dealer. The dealer wasn't sure what the artifacts were either, but he was certain they were important, and therefore priceless. In this way, the artifacts stayed hidden for many years. 

A Periodic Table for Molecules: Using Artificial Intelligence for Chemical Analysis

ChatGPT works by finding patterns in large data sets, that is to say, the texts of books, websites, etc. The same principle could be applied to chemistry, whereby with a large enough data set, an AI program could propose molecules with the desired properties that have yet to be discovered or synthesized.

Just as the periodic table enabled scientists to predict the existence and properties of elements before they were discovered, using AI to analyze a large chemistry database would allow chemists to find desired molecules with greater efficiency. 

The Beilstein database has information on millions of chemical compounds. Imagine what could be discovered if an AI program searched through it all. That is possible while it is impossible for any group of scientists to accomplish the same feat. 

It is true that computers have been used in similar ways for years, but to the best of my knowledge, never on the scale that I am proposing. 

The first stage would be to correlate data such as molecular weight, IUPAC name, known uses, etc. For example, the user could ask the program to return a chemical that contains a certain functional group (methyl for instance) that can be used for some purpose or has some property. The program would then return the names of existing chemicals of that nature as well as an educated guess on the IUPAC name of a compound with the desired properties. It's sort of like the way you can ask ChatGPT to write a story or poem about a given topic. 

It would be harder, but not impossible to train the same system using molecular diagrams, but that becomes an image recognition problem, albeit of a simpler variety. With a neural net and a sufficient set of training data, it would be possible for a program to correctly identify chemical compounds from their respective structural formulas. The next step would be to have they AI generate structural formulas based on input such as desired properties or applications. 

In the ideal case, a user could ask the program to give the structural formula of a molecule that cures cancer or AIDS, and the output would be something that's never been tried before. Perhaps it would even work. I don't know how much pharmaceutical information is in the Beilstein database, but whatever is lacking would be easy enough to add. 

The World Health Organization has a list of 1200 recommendations for 591 drugs and 103 therapeutic equivalents. Oh, how wonderful it would be if that list was analyzed by AI, though it would be best if the structural and empirical formulas were included with the list. Information gleaned from it could be used to search the Beilstein database and to generate novel structural formulas. 

There would plenty of other things to discover, which would include better and cheaper plastics, lubricants, solvents, coolants, refrigerants, catalysts and many more of all kinds. 

I will conclude this article with a shout-out to Elizabeth Fulhame, who invented the concept of catalysis. In the preface to one of her books published in 1810, she wrote: 

"But censure is perhaps inevitable: for some are so ignorant, that they grow sullen and silent, and are chilled with horror at the sight of anything that nears the semblance of learning, in whatever shape it may appear; and should be the spectre appear in the shape of a woman, the pangs which they suffer are truly dismal."

If any such chemical analysis program is invented, I suggest it be named Fulhame. 

A Practical Guide to World Domination

The largest empires and nations in history, as well as the ones that lasted the longest, had a few things in common. The three key elements are: a common language, a common, currency, and religious toleration. A common language and currency fosters trade and cultural exchange, which tends to bring about religious tolerance. 

Some states and empires have succeeded for a time in establishing a common religion, but religious toleration has been more typical. Both the Roman and Mongol empires had religious toleration. The same is true of the Russian, British, and French empires. Napoleon toyed with the idea of making Islam the official religion of his empire. 

Generally, whichever country has the strongest economy will do the most international trade, and so its currency will to some degree or another become the global currency. Economic strength is in part derived from both the amount of territory controlled and a country's population. If Bangladesh or Nigeria controlled a territory as large as China, they would be global powers. In a similar way, If Australia or Canada had populations the size of India, they too would be global powers. 

By global power, I mean one of the top five or 10 most influential countries in the world. In order to move from global power to hegemon, more is needed. The US became a world power through uniting a large area and population under the same language, and to a lesser extent, a common religion, though religious toleration was codified by law in the US Constitution. 

What about Brazil? Why is it not a global power? Although it has a large territory and population, its language, Portuguese, is not as widely spoken as English, nor is Portuguese a global language with respect to science or business like English is. Brazil also has a relatively small economy with respect to its population. 

While Arabic is the common language of 20 or so countries and binds the over 50 Muslim majority countries, those countries do not form a cohesive bloc like the European Union. The overall output of the Islamic world is small compared to its size and population. Furthermore, it is heavily dependent on oil and natural gas rather than being diversified with manufacturing. 

Only a few countries in the world now have a chance at becoming the hegemon, that is, the country that can get what it wants in nearly any dispute. The US is the country in the best position to do that. Many falsely believe the US has been the sole superpower since 1991, but a mere glance at world news shows this is not the case. 

If the goal is global supremacy, here is the recipe: 

1) Strengthen the US economy and trade more with other countries. This will strengthen the US dollar and thus make it attractive for others to use it. The best way to strengthen the US economy would be to cut spending, taxes, and regulations. It is also essential to build more oil refineries and nuclear power plants. In brief, cheap oil = world peace.

2) The promotion of trade will promote the English language as a side-effect. For the cost of one nuclear submarine, thousands of foreigners could be educated annually in English on US soil. An exchange program like this would be a sort of reverse Peace Corps. The Friendship of Peoples University in Russia is a perfect example of this and is one of the best moves the Soviets ever made. 

3) The US has been pretty good at promoting religious toleration. The largest Hindu temple outside of Asia recently opened in New Jersey. It contains carvings of Abraham Lincoln and Martin Luther King alongside Hindu luminaries. 

Here are some of the things the US should NOT be doing if the goal is retain and expand its power:

1) ignoring illegal immigration

2) subsidizing electric vehicles, wind power, and solar energy

3) weakening the dollar through deficit spending and increasing the money supply

4) getting involved in foreign wars and alliances

5) continuing policies that foster below-replacement fertility

6) weakening English language education standards 

7) maintaining a large overseas military presence

8) propping up Social Security, the greatest Ponzi scheme in history

I could go on, but those are the main issues. 

On a side note, territorial conquest is only useful if the territory conquered can be held permanently and is contiguous with the existing territory. The US, UK, Russia and others have territorial enclaves, yet these do nothing but pose risks. The US base in Guantanamo, Cuba has done nothing but strain relations, and Britain was dragged into a war with Argentina to keep the Falklands. Germany and Italy ended up losing their African colonies after just a few decades, and France did hardly any better in Indochina.

It's interesting that the Spanish, French, British, Russian, Mongol, Chinese (Qing), and Ottoman empires all lost most of their territory about 30 years after reaching their peaks. The Roman Empire was the only one that outlasted its peak by more than a century. 

True world domination does not come through imperialism, and that is the lesson so many have failed to learn.   

The 25 Most Important Languages for Publishing

According to the Wikipedia page on Robert Luttwak, his books have been published in the following languages besides English (16 of which use the Latin alphabet):

1. Arabic 

2. Chinese simplified 

3. Chinese traditional 

4. Czech 

5. Danish 

6. Dutch 

7. Estonian 

8. Finnish

9. French 

10. German 

11. Greek 

12. Hebrew

13. Bahasa Indonesia 

14. Italian 

15. Japanese 

16. Korean

17. Mongolian 

18. Norwegian 

19. Polish

20. Portuguese 

21. Romanian 

22. Russian 

23. Spanish 

24. Swedish 

25. Turkish 

Hungarian and Thai translations are forthcoming. 

Hearst Castle Library, San Simeon

 It's not a big library, but it certainly has a beautiful interior. 

Turqoise Creek in Glacier National Park

 The copper in the rocks causes the water to become at blue-green color. 

Atoms for Profit

Professor Murphy was quite proud of his work, which involved reverse-engineering a captured Soviet nuclear reactor from one of their fast attack submarines. Perhaps 

"captured" is too dramatic a word. In truth, a billionaire named Suleiman Agha Khan had discreetly purchased the submarine which the new Russian government was too poor to maintain. The luck of the Irish must have been at work, as Murphy just so happened to have the right connections to be acquainted with Khan. The reactor required superheated steam circulation when it was not running at full power. The sub was designed to spend most of its time in port, and when the need arose, it could dash out quickly to intercept slower American ships and submarines. It was a truly impressive piece of engineering, but like so many things the Soviets built, it was undermined by their economic mismanagement.    

It was the Suvorov, an Alfa-class vessel built during the mid 1970s. The submarine's reactor was at once smaller, more powerful, and safer the usual water-cooled reactors. The key to the cooling system was the use of lead and bismuth as the cooling fluid. The heat of the reactor caused the metal lead and bismuth to melt and remain in liquid form. The heat from the liquid metal was then passed onto water, which when turned into steam, would pass through a turbine to create both mechanical energy to turn the sub's propeller and electricity for all the other devices onboard.  

The molten lead and bismuth acted as a radiation shield, which reduced the need for bulky and heavy materials like concrete and steel. In the event of a reactor leak, the molten metal would quickly solidify and seal the breach. Murphy's plan was to mass produce these reactors and connect them to the grid all across the US. Not only would this provide all the electricity the US would need for at least a century, but the price of electricity would drop so low that it would become essentially free, or "too cheap to meter", as the older advocates of nuclear power used to say. The tricky part to all this was getting through all the regulatory and funding hurdles. 

The technology and the economics of the project were all solid; what was lacking was political and public support. Murphy decided to attack the problem on multiple fronts. In 1959, the US launched the NS Savannah, a civilian ship with nuclear propulsion. It was meant to tout the benefits of nuclear energy as part of President Eisenhower's Atoms for Peace initiative. The ship toured US water serving as an ambassador for nuclear power until it was deactivated in 1971. The first phase of Murphy's plan involved reactivating the ship, but by replacing its reactor with a lead-bismuth one. This was more expensive than building a new ship from scratch, but Murphy counted on the intangible psychological benefits of the ship's reputation to make the effort worthwhile.   

On the entertainment front, Murphy convinced Khan to fund various movies and TV shows to normalize nuclear energy. Films like The China Syndrome and The Simpsons had done a good job of demonizing nuclear energy and something equally compelling was needed to heal its reputation. The TV show Murphy pitched was like an office sitcom, but with the funniest and most attractive characters being nuclear technicians and engineers. Murphy's other idea was a science fiction movie where a nuclear-powered ray gun was used to fight off an alien invasion. Khan greased the right palms, writer wrote and scripts were doctored. Chomsky talked about manufacturing consent, but what will works is manufacturing desire. There is no propaganda more compelling than a story told well. 

While that was going on, Murphy was working to sell his reactor to various countries, particularly island nations that were otherwise dependent on expensive imports of coal, natural gas, and fuel oil. Then of course, there was China and India to consider. Both those countries struggled with air pollution and high demand for electricity. They were also both dependent on imported oil. Khan had contacts in India, so he went first to lay the groundwork. Once India had bought a reactor, it was easy enough for Murphy to start selling them to China. The Chinese of course were eager to tout their achievement, which led to more demand elsewhere. Murphy was counting on the bandwagon effect to take hold. Once while watching the evening news, he saw a report which showed the estimated number of nuclear reactors in several countries. This what he had been counting on. No country wants to be in second place, whether it's Olympic gold medals or tall buildings.

Soon enough, there was a growing clamor for the US to catch up with other countries and close the "reactor gap", as it was described by pundits and politicians. Congress held a series of hearings on how to solve the crisis, and Murphy had been invited. He was ecstatic, the finish line for his long project was now in sight. All that was necessary was to show up, look nice, and not say anything stupid. Murphy, on the advice of Khan got a new suit and did some practice hearings with ex-campaign advisers and other politicos. The day of the hearing came, and it was smooth sailing until a certain notoriously contentious senator got a turn to ask questions. Senator Palomino was both the oldest senator and universally regarded as the dumbest. He was sure to say something pugnacious and incoherent.   

"Mr. Murphy, I grew up on a farm and my daddy taught me to never buy anything you can't fix yourself. This new-fangled reactor of yours would seem to violate that principle. Do you think you are smarter than our wonderful hard-working farmers?"

"Well, Senator, it's a good thing your daddy wasn't in charge of the Manhattan Project, or we'd all be speaking German right now."

There was a generous amount of laughter quickly followed by frustrated gavel banging. Murphy decided it was time to seal the deal with a rhetorical flourish.

"The source of our country's greatness has always been our ingenuity. If we can put a man on the moon, there is no reason we should settle to be second best when it comes to nuclear energy."

He didn't plan it as an applause line, but it became one. A few months later, Murphy and Khan were lounging on a Florida beach. Sure, they could have gone to a private island, but Murphy was beginning to enjoy his celebrity status. He had been invited to opening ceremonies of several new reactors since appearing before Congress. 

GOP Struggles to Find Losing Strategy

DALLAS - "It's like, nothing we do is working" lamented Senior GOP Defeat Strategist Joanna Gambolputty. "No matter how hard we try to lose elections, people keep voting for us for some reason. It's really weird." Gambolputty added that no effort has been spared to alienate conservative and libertarian voters. "So far, we've double-crossed them over and over on things like war, guns, taxes, and spending but voters still turn out for us. We really hoped our support for the draconian pandemic restrictions would be the last nail in the coffin, but incredibly, many Republican voters support them." 

According to Gambolputty, desperate GOP leaders have pushed for launching more wars. "I tried to tell them that, absurd as it may seem, many GOP voters actually support endless war. The really insane part is the support is the strongest among those who never volunteered for the military. Figure that one out, because I can't." Gambolputty elaborated that the party's time-tested strategy of nominating terrible candidates no longer seems to be working. "We used to have solid, dependable losers like Mitt Romney and John McCain. But then this Trump guy comes along and out of nowhere, just starts winning. We were all like, 'hey buddy, stop doing that', but he just kept getting more popular despite our best efforts. If not for the pandemic, Trump would have been re-elected in a landslide and the GOP would have control of both houses of Congress, the Supreme Court, and most of the governorships and state legislatures. There's no way we could have recovered from a win like that."

Gambolputty and her team of failure experts have been working around the clock to find a new losing formula. "So far, our best idea is to have Mitt Romney propose a special tax on Chik-Fil-A customers and then use the money to fund drag queen story hours. Also, all gun owners will be required to eat at Chik-Fil-A at least once a week to ensure sufficient revenue and also to encourage them to voluntarily disarm. And then, to annoy libertarians, we'll establish a new government agency specifically tasked to enforce proper mask wear and social distancing. This new Control And Re-Education Network will have broad powers of warrantless search, seizure, arrest, and public scolding. Enforcement mechanisms will include fines, imprisonment, and pineapple pizza." 

Important Math Concepts To Know: Pareto Principle, Benford's Law, Survivorship Bias

The Pareto Principle is sometimes called the 80/20 rule, which means that 80% of the effects come from 20% of the causes. While the exact numbers vary in different situations, in general, some of the causes give most of the effects. For example, 20 ailments are the reason for over half of hospital visits.

Benford's Law states that 40% of statistics start with the number one, and that larger numbers are less likely to be the leading significant digit. This is a simple way of determining whether a group of statistics from the same source is credible. If the group of statistics do not mostly start with small numbers, it could mean there was some flaw in the study, such as the sample size being too small or not random enough. It could also mean the data does not follow a normal distribution, which is rare, but possible. 

Survivorship Bias refers to the fact that inverse data is often more useful than the actual data collected. During WW2, records were kept of damaged aircraft. Since aircraft with damaged wings often returned safely, this meant that aircraft damaged in other places did not. This led to engineers adding armor to the engines and cockpits of aircraft. 

The math of these concepts is fairly simple and easy to apply. Unfortunately, often it is not. Now that you know about them, try applying it. 

Similarities of the Wars in Israel and Ukraine

Israel got $3 billion in US military aid in 2022 and has been receiving a similar amount annually for decades. Ukraine has gotten over $100 billion since Russia invaded in early 2022. The objective of both countries is to defend their borders and people against overwhelming odds. 

An Israeli military theorist named Martin Van Creveld said that when a strong nation fights a weak one, if they win, they look like monsters and they lose, they look like morons. Israel is stronger than Palestine, but Palestine's ally is Iran, and they are stronger than Israel. The Israelis can defeat the Palestinians, but they cannot defeat the Iranians. In a similar way, Ukraine could have defeated the Donbas separatists, but they cannot defeat Russia. 

The problem with proxy wars is that sooner or later, it becomes necessary for sponsor of the losing side to start fighting directly. The USSR did it in Afghanistan, the US did it in Vietnam and Afghanistan, and China did it in Korea. When one side starts fighting directly, it is likely that it will eventually lose. 

In the end, there will be no lasting peace between Israel and Palestine until Iran is either persuaded or compelled to make peace with Israel. Similarly, there will be no peace in Ukraine until its sponsor, the US, faces pressure to make peace. 

The analysis of proxy conflicts is different when the opposing sides are of unequal strength, and that strength is a blend of material and psychological factors. 

The two principles to keep in mind for long term strategic advantage are:

1) accepting small losses to avoid greater ones

2) using the enemy's strength against him

In the case of Israel, exchanging prisoners for hostages is an example of the first principle. For Ukraine, if the US increased domestic oil production, that would hurt Russia and Iran, so it is an example of the second principle.

All the money that the US has spent on arming Israel and Ukraine would have been better used to fund domestic energy production in the form of nuclear reactors and oil refineries. Alas, the political influence of the global "green" energy movement and US military-industrial complex has stifled that. 

Experts Say Tanks in Tiananmen Square May Be Chinese

WASHINGTON DC- "We have multiple lines of evidence converging on the same conclusion" said Joanna Gambolputty, a senior defense analyst at the RANT Corporation. "We have satellite photos of soldiers wearing Chinese army uniforms entering tanks with Chinese markings on Chinese army bases. These tanks were then tracked as they traveled across Chinese territory to the Chinese city of Beijing, which is located in China. Clearly, these tanks could be Chinese" added Gambolputty. 

Gambolputty first gained prominence with her landmark zoology paper entitled "The Geography of Ursine Defecation: A Shocking Conclusion" first published in The American Journal of Hyporhinotology. "I was really going out on a limb with that one, but it paid off. I was even bold enough to suggest that further research was NOT needed" said Gambolputty. 

Meanwhile, Defense Department officials have struggled to determine what the tanks might do next once they reach Beijing. "Regardless of what happens next, this is a wake-up call for Congress to appropriate enough funds for us to close the tank gap with China" said General Haywood Jablome of the 1st Armored Division. "If they send out tanks to act as riot police, they must have many more than we do."

Democrats Push to Lower Retirement Age to 18

WASHINGTON DC - "Universal Basic Income doesn't go far enough. It's high time we freed the American people from the tyranny of work", said Rep. Cortez (D-NY). In response, Senate Majority Leader Mitch McConnell said "this proposal is as absurd as it is irresponsible, and threatens to destroy America's already weakened economy. I therefore propose lowering the retirement age to 21, and not a single day less." Economists and other experts have cautioned that such a move may not be sustainable.

According to Nobel Prize-winning economist Paul Krugman "look, I know I've been reliably carrying water for Team Blue for 30 years, but I can't keep it up much longer. This idea isn't just plain stupid; it's stupid with sprinkles and whipped cream. My god, what have I done with my life? Just because I hate Republicans doesn't mean I want retards in charge!" However, other experts disagree, noting that the proposal would reduce inequality, unemployment, and pollution, as well as increase diversity among retirees. "It's all very simple," explained Michael Moore. "Robots will do most of the work, and the rest will be done by criminals in Government Utility Labor Administration Groups." Elon Musk has promised to build a fleet of robots to fill all menial jobs in exchange for a title of nobility. When informed that this is unconstitutional, Musk said "What?! Damn their oily hides! I already bought a golden, jewel-encrusted scepter. What am I supposed to do with it now? Pawn it? This outrage will not be soon forgotten." Musk then slammed the hatch of his submarine and left for his underwater volcano lair.     

Grand Tetons Near Yellowstone

 

Roman Bath at Hearst Castle, San Simeon

 I picked a good day to visit. I practically had the place to myself. 

Golden Canyon, Death Valley

It reminded me of Tatooine from Star Wars. There were no Jawas to be found, however. Hoo-tee-nee!

 

How to Understand Euler's Identity

Euler's Identity is e^i*pi = -1, where e is about 2.718, i is the square root of -1, and pi is about 3.14. 

The identity is an alternative form of Euler's Formula which is e^(i*x) = cos(x) + i*sin(x).

In the above equation, if we let x = pi, we get:

e^(i*pi) = cos(pi) + i*sin(pi)

Since the cos(pi) = -1 and sin(pi) = 0, we get:

e^(i*pi) = -1

Strange as it may seem, this identity is useful for solving equations about real quantities, particularly in electrical engineering. A phasor is an example of the use of i to describe real quantities, for example. 

This identity can also be used to solve differential equations of the form ax^2y'' + bxy' + cy = 0. These are called Euler equations. 

This is about as far as 99% of college students get with math, so I feel this is a good stopping point for my math series. 

How to Understand Pascal's Triangle

 Most students who take algebra learn about FOIL, which stands for First, Outer, Inner, Last. It tells the order of multiplication for a binomial like (a + b).

(a + b)^2 = (a + b)(a +b) = a^2 + ab + ba + b^2 = a^2 + 2ab +b^2

It's easy enough for (a + b)^2, but what about (a + b)^3 or a greater exponent?

A mathematician named Pascal noticed a pattern when expanding binomials. The coefficients can be arranged into a triangle, like so:

                                                                            1

                                                                       1   2   1

                                                                     1   3   3   1

                                                                   1   4   6   4   1

Do you see the pattern? Take a few minutes to work out the next row. Hint: the first and last numbers will be 1 and the rest follow a rule from the row above. 

The next row is 1 5 10 10 5 1, and those are the coefficients for the expansion of (a + b)^5. The 1s and 4s in the previous row make 5 in two places and the two 4s and the 6 make 10 in two places. Filling out this chart is much easier than trying to work this out with FOIL. Let's do that anyway just to double check.

(a + b)^5 = (a + b)(a + b)^4 =

(a + b)(a + b)^2(a + b)^2 =

(a + b)(a^2 + 2ab + b^2)(a^2 + 2ab + b^2) =

(a + b)(a^2 + 2ab + b^2)^2 =

(a + b)(a^4 + 2a^3b + a^2b^2 + 2a^3b + 4a^2b^2 + 2ab^3 + a^2b^2 + 2ab^3 + b^4) =

(a + b)(a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4)  =

(a^5 + 4a^4b + 6a^3b^2 + 4a^2b^3 + ab^4 + a^4b + 4a^3b^2 + 6a^2b^3 + 4ab^4 + b^5) =

a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5

Whew! That's a lot of algebra. It's much easier just to use Pascal's Triangle. 

The Origin of the Cope-Marsh Paleontology Feud

 

I saw this near the Paluxy dinosaur tracks site in Texas. It made me laugh. Nearby is the original statue of the dinosaur that became the Sinclair mascot. 

How to Understand the Bell Curve, Standard Deviation, and Normal Distributions

The bell curve is the graphical form of a normal distribution. It looks like a bell as seen from the side, hence its name. Sometimes it is called a Gaussian distribution because the mathematician Friedrich Gauss invented it. Most natural quantities follow a normal distribution, hence the name. Human height for a random sample follows a normal distribution, for example. So does IQ.

The standard deviation for IQ is 15 points. 68% of people are within plus or minus 15 points of the average IQ, which is 100. 95% of people are within plus or minus two standard deviations or 30 points of the average IQ. 99.7% of people are within plus or minus three standard deviations or 45 points of the average IQ.

In manufacturing, the phrase Six Sigma refers to a defect rate less than 0.3%. In other words, 99.7% of the product is good. So if a car manufacturer makes 1,000 cars per day and only 3 fail the quality inspection, that process meets the Six Sigma standard. Sigma is the name of the Greek letter often used to represent standard deviation, so Six Sigma means plus or minus three standard deviations. 

While there are other distributions, if they data does not fit the profile of a bell curve, it might mean that there was a flaw in the data collection. Perhaps the sample size was too small or not random enough. 

How to Understand Binary, Tree Diagrams, and Truth Tables

There are different ways of thinking about the number 2 in math, and some ways are more useful than others depending on the question.

For example, in computers, electricity is either flowing through a transistor or not, so there are only 2 possible states, usually written as 0 (off) and 1 (on). If you look at the power switch of most electronic devices, you will see a symbol that has a 1 inside of a 0. Here is an example of that:

Binary math works off of base 2 instead of base 10, also called decimal. In base 10, 341 is the same as

3*10^2 + 4*10^1 + 1*10^0. The same number in binary is written as 101010101, and it means:

1*2^8 + 0*2^7 + 1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 1*2^2 + 0*2^1 + 1*2^0.

Another way of thinking about the number 2 is with something called a tree diagram. How many possibilities are there for flipping a coin 3 times? 

There are 2 possibilities for the first toss, and then from each of those two possibilities, and so on. In other words, with every coin toss, the total number of outcomes doubles. So for tossing a coin 3 times, there are 2^3 or 8 possible outcomes. This diagram also works for figuring out the odds of a woman giving birth to at least 2 girls if she gives birth to 3 children total. 

In logic, when we have a statement with two or more parts, if one part of the statement is false, the whole statement is false. This can be shown with a truth table. Let p and q be statements and let T and F stand for true and false respectively. 

p        q        p and q        p or q

T        T        T                 T

F        T        F                 T

T        F        F                 T

F        F        F                 F

There are logical operators besides "and" and "or", but these are the basics.  It's important to note that in logic, it is impossible for a statement and its opposite to be true at the same time. For example, it is impossible in a given time in place for it to be both raining and not raining. "And" statements can only be true if each part is true. For more information, read up on Boolean algebra. 

Blue Whale Skeleton in Santa Cruz, CA

It's about 98 feet long. It washed up dead on a beach nearby many years ago. It now graces the grounds of the Santa Cruz aquarium and oceanographic center. It's interesting that whales have finger bones but no fingers. Below is a photo of a live blue whale I saw during a whale watching trip near Monterey.

How to Use Calculus to Solve Optimization Problems (First Derivative Test)

For any continuous function, whenever it is at a maximum or a minimum, the slope of the tangent line will be zero. That means the first derivative of the function at that point is equal to zero. 

Suppose we have 150 feet worth of fencing and we want to use it to build a rectangular enclosure. What is the maximum area we can enclose?

Take a few minutes to try this on your own. Draw a picture. Hint: the four sides of the enclosure must add up to 150. 

Call one side of the enclosure x. The side opposite it will also be x. The other 2 sides will be (150 - 2x)/2 long. Let's add all 4 sides together to double check:

x + x + (150 - 2x)/2 + (150 - 2x)/2 = 2x + 150 - 2x = 150

The area of the enclosure will be y = x*(150 - 2x)/2. We can simplify that to:

y = 75x - x^2

We take the first derivative to get:

y' = 75 - 2x

Then we set y' = 0. 

0 = 75 - 2x

2x = 75

x = 37.5

(150 - 2x)/2 = (150 - 75)/2 = 37.5

The maximum area is enclosed by a square with a side length of 37.5 feet. In general, a square is the geometric figure with 4 sides that encloses the most area with the least perimeter. 

How Many 5-Card Hands of Poker Are There?

There are 52 cards in a regular poker deck. If 5 cards are dealt at random, how many possibilities are there?

Questions like this require the formula for combinations. In a combination, we don't care about the order of the elements. In poker, if you are dealt the ace of spades, the king of hearts, the 10 of diamonds, the 2 of clubs, and 3 of clubs, that's the same as being dealt the 3 of clubs, the 2 of clubs, the 10 of diamonds, the king of hearts and the ace of spades. 

When the order is important, we must use the formula for permutations. 

Both formulas have something called factorials. 3! (read as 3 factorial) means 3*2*1, so 3! = 6. 

If we want to know the number of ways of picking r elements from a set of n elements, we use:

n!/(r!(n-r)!)

For the case of drawing 5 cards from a deck of 52:

52!/(5!(52-5)!) = 52!/(5!(47!)) = 2,598,960

This means that 2,598,960 people could play poker at the same time and all have a different hand. The catch is that it would require 49,980 decks of cards. 

How to Solve a Mixing Problem

Suppose a dishonest bartender decides to water down the liquor to make it last longer. He knows the customers will notice if he dilutes liquor below 30% alcohol by volume. If he has a half full 750 ml bottle of 40% ABV liquor, how much water can he add?

Let x = # of ml of water added

Half of 750 ml is 375 ml, and 40% of it is alcohol. 

The amount of alcohol in the liquor already (0.4)*750/2 = 150 ml. The other 225 ml is water. 

150/(375 + x) = 0.3

150 = (0.3)(375 + x)

500 = 375 + x

125 = x

x = 125 ml of water

If we add that 125 ml to the 375 ml we started with, we get 500 ml total, which will fit in a 750 ml bottle. 

How to Calculate the Mass of a Pipe

I saw this question on Florida state geometry test. Few of my students got it right. 

In the question, the students were given the inner and outer diameter of the pipe as well as its mass and length. Like this:

Find the mass of a 50 cm long pipe with an inner diameter of 2 cm and an outer diameter of 3 cm. The density of the metal in the pipe is 7 g/cm^3. 

Take a few minutes to work this out on your own. Draw a picture. Hint: The volume of the pipe is the same as the volume of one cylinder minus the volume of another cylinder. Let's call the volume of the big cylinder V and the volume of the little cylinder v.

If we calculate the volume of a cylinder whose diameter is the same as the outer diameter of the pipe and then subtract the volume of a cylinder whose diameter is the same as the inner diameter of the pipe, we get the volume of the pipe itself. The formula for the volume of a cylinder is V= pi*(R^2)*h. We need to remember that a radius is half a diameter. 

V - v = pi*((3/2)^2)*50 - pi*((2/2)^2)*50

V - v = pi*50*((3/2)^2 - (1)^2)) = 196.349 cm^3

Since density is mass divided by volume, multiplying volume with density gives us mass. 

(196.349 cm^3)*(7 g/cm^3) = 1374 g

Everything is easy when you know what to do. I was in engineering school the first time I saw a problem like this.