The goal of this blog is to create a long list of facts that are important, not trivia, and that are known to be true yet are either disputed by large segments of the public or highly surprising or misunderstood by many.
Superfact 22: Suppose you’re on a game show, and you’re given the choice between three doors: Behind one door is a car; behind the other two doors there are goats. You want to pick the car. You pick a door, and the host, who knows what’s behind the three doors, opens another door revealing a goat. Now the question is, is it to your advantage to switch door choice? The answer is yes. And that is the surprising Monty Hall Problem.
The Monty Hall gameshow Three Doors Problem. There is a car behind one door, and goats behind the other two. You pick a door. Monty Hall, the gameshow host, opens one of the other doors and it has a goat. Should you change your choice of door? Yes, you should. But why? – Monty Hall Problem Stock Illustration ID: 1881849649 by SATYA94.
It is quite common to argue that it does not matter. You don’t know what is behind the two remaining doors so it should be 50/50 right? In a test involving 228 people only 13% chose to switch. However, you should switch.
Monty Hall, the gameshow host of the Let’s Make a Deal television game show, knows where the car is, so he never chooses the door with the car. And by curating the remaining two doors for you, he raises the odds that switching is always a good bet. By switching your choice, you have a 2/3 chance of winning the car but if you stay with your original choice, you only have a 1/3 chance of winning the car.
So why is this a super-fact? First, we know it is true. It is mathematically proven and experimentally verified that switching door is the best choice. Secondly, this was widely contested and is still surprising to people. Finally, probabilistic thinking is the key to being rational and making good decisions. This fact is true, important and disputed and thus a super fact.
One way of viewing the situation is by noting that there is a 1/3 chance that the car is behind any door that the contestant picks and a 2/3 chance that the car is behind one of the other two doors.
The car has a 1/3 chance of being behind the contestant’s pick and a 2/3 chance of being behind the other two doors. Picture from Wikimedia commons public domain.
If Monty opens one of the two doors that the contestant did not pick there is still a 1/3 probability that the car is behind the door the contestant picked and a 2/3 chance that the car is behind one of the other two doors. However, one of the doors that the contestant did not pick is now known to feature a goat. Therefore, the probability that the car is behind the other door is 2/3.
The host opens a door. The odds for the two sets don’t change but the odds become 0 for the open door and 2/3 for the closed door. Picture from Wikimedia commons public domain.
The table below is probably (no pun intended) a better way of illustrating the situation. In the table door 1 is the door designated to be the contestant’s first choice. Monty opens one of the remaining doors that has a goat behind it.
Behind door 1
Behind door 2
Behind door 3
Result if staying at door 1
Result if switching to door offered.
Goat
Goat
Car
Wins goat
Wins Car
Goat
Car
Goat
Wins goat
Wins Car
Car
Goat
Goat
Wins Car
Wins goat
There are various other ways of explaining the situation including Steven Pinker’s approach. It is easy to test this is real life and repeated experiments and simulations shown that if you switch you have a 2/3 chance of winning.
As an example of the controversy this probability puzzle caused was Marily Savant’s column in Parade Magazine. As a side note, Marilyn Vos Savant is the person who has the highest recorded intelligence quotient (IQ) as stated in the Guinness Book of Records. In response to a question regarding the Monty Hall game show problem she wrote that you should switch. She received letters from 10,000 readers disputing this, including 1,000 with PhDs. In the long run she prevailed.
Superfact 19: An account impersonating you on Facebook does not mean you have been hacked. When someone using your name and photo starts sending friend requests to your friends on Facebook, they are most likely just copying your information. You have not been hacked.
I am considering this a super-fact because almost every time I see this the person being impersonated states “….I have been hacked”. Most likely they have not been hacked. They don’t need to change their password or take special precautions related to their account or password. It is not the problem.
Facebook is the world’s largest social network with over 3 billion users and few people understand this common Facebook problem, which is why I am calling it super-fact. All that happened is that someone downloaded their photo, copied some information, and started sending out friend requests to their friends. It is so easy to do that. Any 10-year-old can do it and there’s no hacking required. If you think about it for a minute, I am sure you all could do it.
However, it is not appropriate behavior and Facebook can delete your account and ban you if you resort to this behavior.
WP AI generated image
So, what can you do to reduce the chance of being impersonated? You can go to Settings & Privacy > Privacy Settings and set your profile to private by setting “Who can see your posts?” to friends only, but if you want visibility and don’t want to go that far you can set the “Who can see your friends list?” to “only me”. You can also set “Who can see posts you’re tagged in?” to “Friends” or “Only me”. You can “Limit Who can see your profile picture and cover photo?” to “Friends.”
Additional things you can do are regularly search your name on Facebook to check for fake profiles and avoid oversharing.
The actions above will greatly reduce the chance that someone will impersonate you but if it happens anyway, you can report the offender by going to the fake profile and click on the three dots (…) on their cover photo, select “Find support” or “report profile” and choose “Pretending to Be Someone” and follow the instructions to report the account. Encourage your friends to do the same.
Superfact 16: Wind power is providing more than a quarter of Texas Power. In 2023, wind represented 28.6 percent of Texas energy generation. In 2022, wind power accounted for about 25 percent of Texas’ energy generation.
I am referring to this fact as a super fact because, it is true, important, and yet it’s a fact that is difficult to believe for many people. That wind power, allegedly a marginal energy source, is successful in fossil fuel loving Texas is hard to believe. I have come across what appears to be well informed people who were certain it was nonsense. However, as you can see from the Texas government links above, it is true, something they could not dispute.
The reason for the success of wind power in Texas is economics, which is another fact that may be surprising to some. Fossil fuels are a major source of income for us in Texas, but everyone also wants to save money. Texas has its own electric grid, it’s deregulated, and organized along free market principles.
When companies sell their energy (to ERCOT) it works like a continuous auction. The one with the lowest price is picked first and allowed to contribute with whatever they are able to and also, of course, considering what the grid-powerlines can carry safely. Naturally, the price of wind in Texas includes federal subsidies, which make it even cheaper.
However, all energy sources are subsidized, and fossil fuels have a long history of government subsidies. Below is the average unsubsidized levelized cost of energy according to Lazard. Levelized means that construction costs, land rent, and other costs not directly caused by electricity generation are taken into consideration. Notice how cheap wind is (blue line). This is for the United States not just Texas. I don’t have any numbers, but I’ve heard that for Texas solar is the cheapest .
Average unsubsidized levelized cost of energy. Notice that the light blue line indicates that wind power is pretty cheap. Mir-445511, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons.
Affordability
Windpower is not only relatively cheap. Wind power is one of the most efficient and sustainable energy sources available. The energy required to manufacture, install, and maintain wind turbines is small compared to the energy they produce over their lifespan. This is known as their energy return on investment (EROI), which is quite favorable for wind energy.
The Institute of Environmental Management and Assessment (IEMA) states that the average wind farm will pay back the energy that was used in its manufacture within 3-5 months of operation. This article in the journal Renewable Energy found that the average windfarm produces 20-25 times more energy during its operational life than was used to construct and install its turbines. It included data from 119 turbines across 50 sites going back 30 years.
It is important to be aware that there are many false claims floating around about wind power. The sound from wind power stations does not cause cancer, it does not use any other energy sources while operating; it solely harnesses the kinetic energy from the wind to generate electricity, meaning it only relies on wind to function as its primary energy source. Windpower is not a major cause if bird deaths. To read more about false claims about wind power click here.
There are positive and negative aspects of wind power, like any other source of energy. One issue with wind power (and solar) is that it is an intermittent source of energy. When the wind is not blowing you need other sources of energy (until there is sufficient energy storage). This is less of a problem when you have a mix of energy sources as Texas does.
Superfact 12: The United States is both a Republic and a Democracy
I believe that most people do not find that statement surprising in the least. When I became a citizen of the United States, through naturalization (I am originally from Sweden), I had to learn about the US government, and I was told by the US government officials that the United States is both a Republic and a Democracy.
However, I’ve come across a lot of people who state something like “The United States is a Republic and therefore not a Democracy” as if being a Republic and a Democracy are mutually exclusive. Well, as this article explains it is not. To be very specific, the United States is a “federal constitutional representative democracy.” Because the United States is indeed both a Republic and a Democracy and yet many would dispute that fact, I consider this to be a super-fact.
This is an article from the United States Citizenship and Immigration Services on the topic that confirms that the United States is a Republic and a Democracy. This is an article from NPR on the topic. This is what the Wikipedia entry on the United States says under the headline “Government and politics” “It is a liberal representative democracy “in which majority rule is tempered by minority rights protected by law.””
The United States is a representative democracy. Photo by Brett Sayles on Pexels.com
It should be noted that United States is not a Direct Democracy, like ancient Greece, but it features some aspects of it in referendums. Just like most democracies around the world. Another thing to note is that the Economists Intelligence Unit downgraded the United States from a full democracy to a flawed democracy in 2016. But it is still a democracy.
Is the United States a democracy?
If you ask google / AI this question “Is the United States a democracy?”. The answer you get is:
The United States is a representative democracy. This means that our government is elected by citizens. Here, citizens vote for their government officials. These officials represent the citizens’ ideas and concerns in government.
When I asked ChatGPT the same question (Is the United States a democracy?) I got this answer:
Yes, the United States is considered a democracy, but more specifically, it is a representative democracy or democratic republic. In a pure democracy, citizens directly vote on all laws and policies. In a representative democracy, like in the U.S., citizens elect officials (such as members of Congress, the president, and local representatives) who make decisions and pass laws on their behalf.
The U.S. system is also based on the principles of constitutional democracy, where the rule of law, individual rights, and the separation of powers (between the executive, legislative, and judicial branches) are foundational. The Constitution guarantees these principles, which are designed to protect minority rights while allowing majority rule through democratic elections.
In summary, the U.S. combines democratic elements with a framework that ensures checks and balances to prevent abuses of power.
The United States Capitol Building in Washington DC. Photo by Patrick Morris on Pexels.com
Partisan politics aside, the consensus seems to be that the United States is both a Republic and a Democracy.
Superfact 9 : We are living in relatively peaceful times
Despite all the wars going on, the world was filled with a lot more war and violence in the past. Despite the grim news reports we are living in relatively peaceful times.
If I asked you, what are the two biggest wars going on the world today (as of September 2024), you would probably say that it is the Russia / Ukraine war and the Israel / Gaza war. Well, unless you are really well informed, it would come as a surprise that there are more devastating wars going on in the world. For example, there is currently a big civil war going on in Sudan that began in April 2023.
According to the latest issue of the Economist perhaps 150,000 people have been slaughtered in this civil war, and 10 million people have fled their homes, and a famine is emerging that could kill 2.5 million people by the end of the year. This war is likely to destabilize neighboring countries and is sponsored by Russia and Middle Eastern states. It’s likely the biggest crisis in the world but most likely you’ve never heard of it.
In the recent Tigray war in Ethiopia between 162,000 and 600,000 people were killed according to Wikipedia. The Tigray war is mostly over, but the point I am trying to make is that you probably have never heard of it. You cannot use the impressions given by the amount of media attention a conflict gets to decide on how severe it is. You’ve got to check the statistics and compare, and the statistics might be quite unintuitive if you have relied on media attention as a metric.
What was the most devastating war in the 19th century?
So, to the next question. What was the most devastating war in the 19th century? If you say the American civil war, you are not correct (estimated 650,000+ deaths). A somewhat better answer is the Napoleonic wars (and estimated 4 million deaths). But none of the answers are correct. The Taiping rebellion in China was the worst. Estimates of the conflict’s death toll range between 20 and 30 million people. Some estimates say 100 million, which would make it the most devastating war in human history.
But did you hear about it? Again, you’ve got to check the statistics, and not rely on your impressions. I am saying this because the claim that deaths from wars and violence have declined over the last few decades is a quite unintuitive claim and yet it is true. That’s why it is a super fact.
Taiping Rebels at Shanghai China in 1853-54. ‘Small Swords’ refers to daggers used by warriors or martial artists in close combat. 19th century print. Stock Illustration ID: 237232531 by Everett Collection.
As this article in the Our World In Data states “While every war is a tragedy, the data suggests that fewer people died in conflicts in recent decades than in most of the 20th century. Countries have also built more peaceful relations between and within them.”. It should be noted that even though killing has never been as efficient as it is in the present, in the past a lot of civilians died from famine and disease resulting from the wars.
For example, the Spanish flu following World War I killed between 25 to 50 million people. I should say those numbers are typically not included in the deaths from World War I. The number of deaths from World War I are estimated at 20 million. 10 million combatants and 10 million civilians.
Death rate from wars since 1946. The uptick in 2022 is largely due to the Ethiopian Tigray war with 162,000–600,000 killed and the invasion of Ukraine, which US and BBC estimates at more than 200,000 deaths (but estimates from most other sources are less).
One problem with this kind of statistics is that the estimates vary, especially with respect to civilian causalities. In addition, very big wars lasting a few years create very bumpy graphs with large spikes making it harder to identify trends.
However, by listing estimated war deaths of the biggest wars, genocides and democides since the 1800’s you can see that deaths from this type of violence have overall been reduced over the last few decades. A note, democides are mass killings of civilians but are not necessarily directed at an ethnic group (democide include genocide).
The links below are mostly from Encyclopedia Britannica, but also from Wikipedia, the Census bureau, and a couple of other sources.
As I said, the numbers are estimates and not hard data, especially with respect to civilian casualties. However, you can see a trend going from several conflicts with numbers in the tens of millions before 1950, then numbers in millions until 2000/2007 and then during the last couple of decades the numbers have been less than a million. This does not cover homicide rates but even in that case we can see a reduction even though it is less distinct.
In this graph we can see that homicide rate worldwide has been reduced somewhat since the mid 1990’s. This graph is also taken from the Our World in Data website and they in turn used various databases from UN, WHO, etc.
Also remember that in the past there were a lot less people on earth, so relatively speaking a million deaths was a lot bigger number back then. In summary, despite all the wars going on, our world is less violent than it used to be.
Super Facts 