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 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.
This post is not another super fact but a blog note about the blog and a request for opinions. My most recent post included three super facts combined into one post. The three super facts were:
There has been a steep decline in extreme poverty
There has been a steep decline in child mortality
War and violence have declined
The post became very long. It had more than 2,000 words and several graphs filled with additional text and data. In addition, I rushed the third super fact. The discussion of the third super fact was muddy, incomplete, and it lacked references. Therefore, I deleted the third super fact. I think that was the right thing to do, especially since I had planned a separate super fact entry for it anyway with the title “We are living in relatively peaceful times”. I will write that post for it soon.
However, I’ve realized that some of my other posts have problems as well. The second half of the post titled “Two events may be simultaneous for some but not for others” feature equations and complex reasoning that physics nerds may appreciate but not typical readers. I don’t think I need to delete that section but, in the future, I need separate such sections from the rest and make it clear that I don’t expect readers to read that, well unless they are physics or math nerds, etc.
Expand your mind. Smash your old beliefs with new surprising facts, so called super facts. But there’s no need to confuse or bore your mind. Shutterstock ID: 1685660680 by MattL_Images
So, I am wondering what you all think about this and if you have suggestions or opinions on how I can improve my super fact posts. Blog notes are very much welcome.
Superfact 4 : The Speed of Light In Vacuum Is a Universal Constant
The speed of light in vacuum isa universal constant. The speed of light in vacuum is the same for all observers regardless of their speed and the direction in which they are going. It is always c = 299,792,458 meters per second. If you try to catch up to a light beam and try to travel close to the speed of the light beam, you will not be able to catch up. The speed of the light beam will still be c = 299,792,458 meters per second compared to you no matter how fast you go. This is possible because time and space don’t behave like we expect.
Superfacts
This is the fifth post of my super-factful blog and my fourth super-fact. As I mentioned previously, the goal of this blog is to create a long list of facts that are important and known to be true and yet are either disputed by large segments of the public or highly surprising or misunderstood by many.
These facts are not trivia, they are accepted as true by the experts in the relevant fields, the evidence that the fact is true is impressive, and they are important to the way we view the world and to what we believe, and despite being known to be true they are hard pills to swallow for many. They are not scientific theories or complicated insights but facts that can be stated simply. In a paragraph or less. They may need more explanation than you can fit in one paragraph, but they can be stated, with a brief explanation in just one paragraph.
The Fourth Superfact
My fourth super-fact is that the speed of light in vacuum compared to yourself is the same regardless of your motion. A beam from a flashlight you are pointing forward is traveling at a specific speed c = 299,792,458 meters per second forward, no matter what you are comparing to. It is important to understand that speed is relative. If you drive 95 miles per hour on a Texas highway you are driving 95 miles per hour compared to the pavement, but you are traveling more than 2,000 miles per hour compared to the moon.
However, a light beam will be traveling at the speed of c = 299,792,458 meters per second (186,000 miles per second) compared to the pavement and also compared to the moon, the sun, the galaxy, the fastest spaceship possible and another light beam. The speed of light in vacuum is not relative. For light in vacuum there is only one speed compared to everything.
Someone passing you at the speed of 99.99% of the speed of light in vacuum will measure his flashlight beam to have the speed c = 299,792,458 meters per second and he will measure your flashlight beam to have the speed c = 299,792,458 meters per second and so will you. It is as if c + c = c. 1 + 1 = 1 not 2, didn’t you know? This is logically possible because time and space is different for different observers.
This is quite shocking if you haven’t come across it before and there are a lot of people (not professional physicists) who refuse to believe it. So, in my opinion it is a super fact. In summary:
No matter how fast you travel, or in what direction, or where you are, you will measure the speed of light in vacuum compared to yourself to be c = 299,792,458 meters per second or approximately 186,000 miles per second or 671 million miles per hour. That goes for all light beams passing by you regardless of origin.
In this picture Amy is traveling past Alan in a rocket. Both have a laser. Both measure the speed of both laser beams to be c = 299,792,458 meters per second.
In the picture above let’s say Amy is flying past Alan at half the speed of light. If you believe Alan when he says that both laser beams are traveling at the speed of c = 186,000 miles per second, then you would expect Amy to measure her laser beam to travel at a speed that is half of that c/2 = 93,000 miles per hour, but she doesn’t. She measures her laser light beam to travel at the speed of c = 186,000 miles per second just like Alan. This seems contradictory.
The solution that the special theory of relativity offers for this paradox is that time and space are relative and Amy and Alan measure time and space differently (more on that in another post).
Time is going to be different for me than for you. From shutterstock Illustration ID: 1055076638 by andrey_l
I should add that the realization that the speed of light in vacuum is a constant regardless of the speed or direction of the observer or the light source was a result of many experiments, which began with the Michelson-Morley experiments at Case Western Reserve University, Cleveland, Ohio in the years 1881-1887.
At first scientists thought that there was an ether, which acted as a medium for light. They assumed that earth would be moving through this ether. What they tried to establish was earth’s velocity through the ether, but all measurements resulted in light always having the same speed, in all directions, all the time, in summer and in winter, no matter in which direction earth was going. At first, they tried to explain this by saying that the ether compressed the experimental equipment and distorted clocks exactly so that it seemed like the speed of light in vacuum always came out the same.
Others said that earth was dragging the ether with it, but that explanation turned out not to hold water. With the special theory of relativity in 1905 those speculations were laid to rest. It was the way time and space were constructed and connected.
The first Michelson-Interferometer from 1881. It was used to measure the speed difference of two light beams (well a split light beam) with a very high accuracy (for the time). The light traveled with the same speed in all directions and no matter what earth’s position and speed was in its orbit around the sun. This picture is taken from Wikipedia and is in the public domain of the United States.
The speed c = 299,792,458 meters per second is a universal speed limit created by time and space
I should point out that there is nothing magical about the speed of light in a vacuum. Light traveling through matter, like glass or water, does not travel at this speed c, but slower. That is why I keep saying the “speed of light in vacuum” instead of “the speed of light”.
It is also not entirely correct to say that the speed of light in vacuum is a universal constant, because it isn’t only about the speed light. It is just that light that travels unimpeded through vacuum reaches the universal speed limit created by time and space, or the space-time continuum (that’s another post). The light is prevented from traveling infinitely fast by this speed limit, and light is not the only thing behaving this way. All massless particles / radiation is prevented from reaching infinite speed by this universal speed limit and they will also travel with exactly the same speed c = 299,792,458 meters per second compared to all observers, just like light in vacuum.
So how is time and space arranged to cause this universal speed limit? Well, that is a surprising super fact post for another day (I will link to it once I have made the post). I can add that the discovery that light in vacuum is a universal constant changed basically everything in physics. We had to change the equations and the physics regarding not just time and space but energy, momentum, mass, force, electromagnetics, space geometry, particle physics, and much more. The energy and mass equivalency is a direct result of this E = mc2.
Examples:
Below are some examples of what this discovery led to. Again, don’t worry about the details or how it works. I might explain these effects in future super fact posts and link to them.
Time for travelers moving fast compared to you is running slower.
Length intervals for travelers moving fast compared to you are contracted.
Simultaneous events may not be simultaneous for another observer.
The order of events may be reversed for different observers.
If you accelerate to a speed that is 99.999% of the speed of light you still haven’t gotten any closer to the speed of light from your perspective. Light in vacuum will still speed off from you at c = 186,000 miles per second. You think you’ll keep accelerating but that the light keeps accelerating just as much ahead of you. You cannot catch up. What other observers see is you accelerating less and less and never catch up even though you get closer.
Forces, the mass of objects, momentum, energy and many other physical quantities will reach infinity as you approach the speed of light in vacuum assuming you are not a massless particle.
Mass is energy and vice versa E = mc2
Magnetic fields pop out as a relativistic side-effect of moving charges.
Mass is energy and vice versa, a direct result of the way time and space are related. Stock Photo ID: 2163111377 by Aree_S
Can We Travel Faster Than The Speed Of Light?
So, it seems like we cannot travel faster than the speed of light in vacuum. It seems like the universal speed limit is a hard limit, unlike the speed limits on Texas highways. That is maybe true, at least locally where we are.
However, you could get around it, by what is kind of cheating, by stretching and bending space to the extreme by using, for example, enormous amounts of negative energy. That’s happening to our Universe over a scale of tens of billions of lightyears. I should add that a lightyear is the distance light in vacuum travel in one year. Stretching and bending space is not part of the special theory of relativity. That is Einstein’s General Theory of Relativity.
Some things cannot be known. There are things in mathematics and about our physical world that we know can never be known. For example, we can’t simultaneously know both the exact speed and the exact position of small particles (Heisenberg uncertainty principle). This is not because of a limitation of our instruments. It is a fundamental property of the Universe. But there are more examples of unattainable knowledge. In mathematics there are true statements that can never be proven.
“This”Some Things Cannot be Known” is the third post on my super-factful blog. As mentioned, the goal of this blog is to create a long list of facts that are important and known to be true, yet either disputed by large segments of the public or highly surprising or misunderstood by many. They are facts that are so unnecessarily controversial or astounding that I refer to them as super-facts.
This post is about a fact that may be highly surprising to many. Science knows a lot. People without a solid education in science are often surprised when they find out about some of the amazing things we actually do know.
For example, just by studying the light from a distant star, we can determine what elements it is composed of. The star may be composed of 71% hydrogen, 27% helium, 1% Lithium, and 1% other elements, and we can know that just from its light. We can also determine its temperature, the distance to the star, how it is moving compared to us, where it will be 2.5 million years from now, roughly its age and longevity, and more. 150 years ago, we could not have dreamed of this capability.
We can know so much about a star from its light. Shutter Stock Illustration ID: 566774353 by Nostalgia for Infinity.
However, there are also many things we don’t know, and what may come as a big surprise, we know that there are things we can never know, no matter how advanced science becomes. Infinite experimentation, super intelligence, a quintillion super geniuses, infinite time, we simply cannot acquire some knowledge. The universe itself forbids some knowledge. It also means that the statement “nothing is impossible” is false.
At least my natural reaction to such a claim is, “come on you can’t say that with certainty”, and I expect many others will feel the same. However, the reason some knowledge will never be attainable is that physical laws as well as mathematics and logic forbid some knowledge. Some things are not meant to be known. I will give four examples in the four sections below: the event horizon, the Heisenberg uncertainty principle, beyond the observable Universe, and Gödels incompleteness theorem.
The Event Horizon of a Black Hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light, can escape it. The boundary of no escape is called the event horizon. If you pass the event horizon you cannot come back out no matter how much energy, you expand. Nothing can escape, no matter, no radiation, not light or other electromagnetic radiation, and no information. Nothing at all can escape. The curvature of time and space itself forbids it.
I should add that right at the event horizon, there is so called Hawking radiation, but without complicating things it is not the same thing as escaping a black hole. You can guess from physical laws what might be inside, but you can never observe and report what is inside to planet Earth.
Black Hole Stock Photo ID: 2024419973 by Elena11
I would also like to add some basic information about black holes. Some black holes are formed when large stars die and collapse. These black holes are estimated to have a mass of five to several tens of solar masses. However, there are also super massive black holes that reside in the center of galaxies.
The super massive black hole at the center of our galaxy, the Milky Way, is called Sagittarius A* and is estimated to have a mass of four million times the mass of our sun. The largest known supermassive black hole TON 618 is 66 billion times more massive than our sun. There are an estimated 100 million black holes in our own galaxy, the Milky Way. One interesting fact is that celestial objects can orbit a black hole, just like planets orbit the sun, but as you get too close you will rush, at the speed of light, into the depths of the black hole.
The Heisenberg uncertainty principle
The Heisenberg uncertainty principle states that it’s not possible to know the position and momentum of an object with perfect accuracy at the same time. Another way of saying that is that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy. The formula is: dX * dP >= h/4pi , or uncertainty in position (dX) times uncertainty in momentum (dP) is larger than half of Planck’s constant. There is also an energy and time precision limit : dT * dE >= h/4pi.
These equations basically means that there are no perfectly exact measurements or knowledge. Everything is a bit fuzzy. Planck’s constant is very small, so Heisenberg uncertainty principle does not matter for everyday objects, but it matters when sizes are very small (positions, energies, etc.) Note, Heisenberg uncertainty principle is not because of a limitation of our equipment, but a limit set by a law of physics. It is a limitation set by the Universe if you will.
Heisenberg uncertainty principle Shutter Stock Vector ID: 2380436193 by Sasha701
Beyond the observable Universe
The observable universe is a ball-shaped region of the universe consisting of all matter that currently can be observed from Earth or its space-based telescopes. The radius of the observable universe is 46.6 billion light-years. The size of the observable universe is growing. Unfortunately, at those distances, space itself is stretching/expanding faster than the speed of light. Since no signal or information can travel faster than the speed of light we are losing, not gaining, celestial objects from the observable universe.
In the past we’ve lost many galaxies this way. Since the expansion is accelerating, we will keep losing more galaxies beyond the boundary of the universe and some galaxies were always lost (with respect to observation). I can add that the universe may be infinite.
A view of a galaxy full of stars. Photo by Pixabay on Pexels.com
If we are wrong about the fact that the expansion of the universe is accelerating, then perhaps we can observe more galaxies in the future. But if not, then there are galaxies that we have never observed, galaxies that we can never observe, and there are galaxies that will become unobservable in the future. Depending on the size of the universe we may never be able to observe more than an infinitesimally small portion of the universe. Again, the universe is stopping us from knowing something.
Gödels incompleteness theorem(s)
The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. In other words, to find a complete and consistent set of axioms for all mathematics is impossible. There are forever hidden truths in mathematics. For the case of natural numbers this means that there will always be statements about natural numbers that are true, but that are unprovable. I can add that there is also a second incompleteness theorem that states that a formal system cannot prove that the system itself is consistent. Basically, there are limits to mathematics set by logic. And some things cannot be known.
I have a book on Gödels incompleteness theorem, which I have not read, but I will read it before I make a post about it. Photo by Andrea Piacquadio on Pexels.com
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