Time is a Fourth Dimension

Super fact 58 : In relativity, time is considered the fourth dimension, inseparable from the three spatial dimensions to form a four-dimensional continuum called spacetime. Adding time as a fourth dimension, not (x, y, z), but (x, y, z, t), results in spacetime measurements called spacetime intervals that all observers can agree on.

Before relativity the distance between two points was the same for all observers. The distance between points is calculated using the Pythagorean theorem: (d^{2}=x^{2}+y^{2}+z^{2}). You calculate the distance between two end points in a coordinate system using Pythagoras theorem because the points make right angled triangles along the x-axis, y-axis and z-axis. See the picture below.

The image shows the formula for Pythagoras theorem in two and three dimensions and Pythagoras theorem applied to the distance between two points.
Pythagoras theorem in two and three dimensions which also apply to the distance between two points. The points are indicated in red.

Let say you add another coordinate system (x’, y’, z’). The new coordinate system could be translated and rotated compared to the first one. The values of (x, y, z) and (x’, y’, z’) would be different and yet the distance between point-1 and point-2 would be the same. Well as long as you don’t change units, like using meters in one coordinate system and feet in the other. The distance between the points would be a so-called invariant. Now imagine that you forgot to include one coordinate in Pythagoras theorem, for example, y and y’ or x and x’, then your calculation for the distance would be different for the two coordinate systems. We need all coordinates, or all dimensions. See the picture below.

The picture shows two different coordinate systems. One is rotated and translated compared to the other. There are also two points and the distance between them is indicated. The formula for Pythagoras theorem is shown for both coordinate systems.
Pythagoras theorem is used to calculate the distance between two points from two different coordinate systems, with different coordinate values for the points. You still have the same distance for both coordinate systems. The points are indicated in red.

 In relativity the length of objects, as well as the time between events is relative and varies from observer to observer. In other words, distance and time varies from coordinate system to coordinate system. However, if you add time to the three space dimensions and calculate the distance between events using the Pythagorean theorem for intervals (between two events): or  (s^{2}= x^{2}+y^{2}+z^{2} – t^{2}) or (where the ‘t’ represents time in appropriate units), then the difference between different observers vanish. The interval is the same for all observers. It is a so-called invariant. The formula for the spacetime interval comes in a few different forms. One for distance like intervals (space distance bigger than time) (s^{2}= x^{2}+y^{2}+z^{2} – t^{2}), and one for time like intervals (time is bigger than the space distance) (s^{2}= t^{2} – (x^{2}+y^{2}+z^{2})). There is also one that includes the imaginary number (s^{2}= x^{2}+y^{2}+z^{2} + (it)^{2}). See below.

The image shows three formulas for the spacetime interval Euclidian: “(s^{2}=x^{2}+y^{2}+z^{2}+(it)^{2}”. For Time like intervals, the standard form: “(s^{2} = t^{2} – (x^{2}+y^{2}+z^{2}))”. For distance like intervals: “(s^{2} = ((x^{2}+y^{2}+z^{2}) – t^{2}))”.
The three formulas for the spacetime interval above all assume that the unit used for time is the time it takes light in vacuum to travel the distance unit used. If that is meters, it would be the time it takes light to travel one meter. The top formula is the Euclidian form of spacetime. It contains only the ‘+’ operator at the expense of adding the imaginary number (square root of -1) in front of the time coordinate. The second form is typically used with time like intervals and considered the standard form. The third form is used when the distance between two events is larger than the time distance, or distance like intervals.

The interval concept was developed, not by Einstein, but by Hermann Minkowski (a few years after special relativity) and is often referred to as Minkowski space. Time is like a space coordinate but the opposite signs in the equation make it different. Based on articles I found it appears that the opposite signs (minus vs. plus) means that you cannot move “backwards” in time as you can in a space dimension.

I admit that this is a very abstract super fact, but it basically means that if you add time as an extra coordinate to the three space coordinates x, y, z you get something, the spacetime interval, that everyone regardless of speed, orientation, etc., agrees on, despite relativistic length contraction and despite time dilation and non-simultaneity.

Time Expressed in Appropriate Units

I would also like to explain what I mean by (where the ‘t’ represents time in appropriate units), as I stated in the above. For physical formulas to work they need to be expressed in consistent units. For example, you can’t use kilometers for the coordinate x, and miles for coordinate y, not without adding a constant to adjust for it. For the formula (s^{2}=x^{2}+y^{2}+z^{2}-t^{2}) to work you need to express time in a unit that corresponds the time light travels in one meter if x, y and z are expressed in meters. If you express x, y, and z in meters and express time in seconds you must adjust the formula with the constant c = 299,792,458, the speed of light in meters per second, so you get (s^{2}=x^{2}+y^{2}+z^{2}-(ct)^{2}). See the picture below.

The image shows the formulas for the spacetime interval with the constant representing the speed of light in vacuum “(s^{2}=x^{2}+y^{2}+z^{2}+(ict)^{2}”, “s^{2}= (ct)^{2} – (x^{2}+y^{2}+z^{2})” and “(s^{2}=x^{2}+y^{2}+z^{2}-(ct)^{2}”.
If you measure the space coordinates in meters and the time in seconds you must adjust the units to match by inserting the speed of light in vacuum c = 299,792,458. The three forms of the space interval now have the constant c attached to the time coordinate.

Time Like Space Intervals

The formula for time like intervals is typically used for the situation where the time component is larger than the space component, which also means that it is possible to physically travel between the two events forming the space interval. As you can guess, that is a pretty normal situation. Let’s say you are watching TV and having a pizza. Your sofa is your coordinate system. You turn on the TV and 100 seconds later you move 2 meters to get a slice of pizza. Let’s calculate the spacetime distance between those two events.

The space component is easy, that’s 2 meters. However, if we express time in the time it takes light (in vacuum) to travel one meter we get 100 times 299,792,458. If you express time in seconds, you adjust it using the constant c = 299,792,458, and again you multiply 100 with 299,792,458, which is 29,979,245,800. So, the distance in time is almost 15 billion times larger. You really did not move far in space, but you moved very far in time. Now ask yourself. Are you spending your time well?

The Minus in Front of the Time Coordinate

There is one obvious difference between time and the space coordinates. In a coordinate system you can walk forward, along let’s say, the x-axis and then walk back the same way. You can walk back and forth as many times as you want, no problem, but you cannot do that with time. Time may be a space-time coordinate, but it is different from the other three coordinates in that way, and that’s where the opposite signs in the formula for the space-time interval comes in. This is beyond the scope of this super fact blog post, but you can read more about this here and here.

Other Relativity Related Superfacts

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Half the World’s Population Live within a 2 Percent Circle

Super fact 57 : Half the World’s Population live within a circle that covers 2% of the world’s surface, or 10% of earth’s land area. This circle is often referred to as the “Valeriepieris Circle” or Yuxi Circle, and it is centered on southeast Asia.

This circle, has a radius of a bit more than 2,000 miles, and encompasses densely populated areas of East and South Asia, including major population centers like China, India, and Indonesia. The original Valeriepieris Circle was created by a teacher named Ken Myers in 2013 and was larger (radius 2,500 miles) than the more optimized circle created in 2015. In 2015, Singaporean professor Danny Quah—with the aid of an intern named Ken Teoh created a significantly smaller circle (radius 2,050 miles) that included half the world’s population. 4.2 billion people live in the Valeriepieris Circle, which is 5.6 times as many people as in Europe and 12.4 times as many people as in the Unites States.

I consider this a super fact because it is true, it is an important fact, and it is a surprising fact to those of us who have not come across this information before. It is an important fact because it impacts how we view our world. The circle is located far away from Europe and North America, in a part of the world that is rising quickly economically. The people in this highly populated circle have different cultures, music, literature and religions from the US and Europe. They speak different languages, and they play different sports, well soccer (the real football) is international but not as common in the Valeriepieris Circle as in Europe or South America.

Those among us who live outside of this circle, for example, in the United States or Europe, probably need to pay more attention to this half of world. Especially, if you live in the United States, it is easy to believe that the world is about us. The existence of this circle demonstrates that this view is not a realistic view.

This is a world map showing all the continents with the colors of the Valeriepieris Circle inverted. It should be noted that the circle is quite small compared to the whole world | Half the World’s Population Live within a 2 Percent Circle | The original 2013 map by Ken Myers, with the interior of the circle.
The original 2013 map by Ken Myers, with the interior of the circle. Half as many people live inside the circle as outside the circle. However, it is larger and less optimized compared to the circle from 2015 below. This circle is NASA, Public domain, via Wikimedia Commons
This is a special geometric projection of planet earth showing the Valeriepieris Circle at the center. The proportion of the circle (yellow circle) and the whole earth is proportional, and the circle is obviously much smaller | Half the World’s Population Live within a 2 Percent Circle | Danny Quah's 2015 circle, on a Lambert azimuthal equal-area projection.
Danny Quah’s 2015 circle, on a Lambert azimuthal equal-area projection. It should be noted that the fraction of the area of the circle to that of the globe is equal to its equivalent on Earth. Again, half as many people live inside the circle as outside the circle. From Wikipedia cmglee, jimht at shaw dot ca, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons.

Population of Southeast Asia

The countries that are part of the Valeriepieris Circle are, for example,

The map shows the countries in Southeast Asia as relatively large, especially, China and India. Almost the entire right-hand side of the map is filled with Southeast Asian countries making it easy to understand how just around 20 Southeast Asian countries can correspond to half the world’s population.
Each country’s size represents the size of the population in 2018. Each little square represents 500,000 people. All 15,266 squares show where the world’s 7,633 billion peopls lived in 2018 (now the world population is 8,244 billion people). Image from our World in Data. By Max Roser for OurWorldinData.org – the free online publication on the world’s largest problems and how to make progress against them.

Population Statistics

Most people know that in recent centuries the world population has grown almost exponentially but is now projected to level off sometime around the middle of this century. Europe is an interesting example. A thousand years ago Europe’s share of the world population was around 14.5%. Then came the scientific revolution and the industrial revolution and by 1900 it was 25%. As other countries around the world became industrialized Europe’s share of the world population shrunk, even though the population of Europe kept increasing, just slower. Now Europe’s share of the world population is 9%.

As countries become wealthier their population growth tends to slow down, not just in Europe, but around the world. The world’s population growth is illustrated by the image from Our World in Data below (starting 5,000 years ago, ending the year 2000) and the six minute YouTube video below from the American Museum of Natural History (starting 100,000 years ago and ending the year 2100). The YouTube video also shows the projected population decline beyond the year 2050.

Twelve maps depicting earth’s population distribution (population per square kilometer) at different twelve different times in history. The times are 3000BC, 2000BC, 1000BC, 1AD, 500AD, 1000AD, 1500AD, 1600AD, 1700AD, 1800AD, and 2000AD | Half the World’s Population Live within a 2 Percent Circle
Population per square kilometer. Source of the original visualization Klein Goldewijk, Beusen and Janssen (2010). Long term dynamic modeling of global population and built-up area in a spatially explicit way: HYDE 3.1. In the Holocene 20(4) 565-573. The original visualization was adapted by OurWorldinData.org

A somewhat related super fact is – Poverty and child mortality has been sharply reduced worldwide.

Next Super fact coming up is : Time is the fourth dimension

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The Bermuda Triangle the Big Non-Mystery

Super fact 56 : The Bermuda Triangle mystery is a myth. There is not a higher risk of disappearances in the Bermuda Triangle. To be specific, disappearances do not occur in the so-called Bermuda Triangle, or Devils Triangle, with any higher frequency than in other comparable regions of the ocean. The “mystery” of the Bermuda Triangle is largely a manufactured one, perpetuated by sensationalized accounts that often misrepresent the facts and downplay the role of natural hazards like storms.

The number of ships and aircraft reported missing in the Bermuda Triangle is not significantly greater, proportionally speaking, than in any other part of the ocean. The U.S. Coast Guard, along with NOAA, the U.S. Navy, Lloyds of London who pays out insurance for ships and aircraft lost/missing at sea, and other organizations do not recognize the Bermuda Triangle as a unique or mysterious geographic hazard. They emphasize that this is a highly traveled area where the losses are consistent with natural phenomena such as strong storms, the Gulf Stream, human error, and poor navigation, rather than any mysterious forces.

Considering all this, the number of disappearances and accidents is what you’d expect. The Bermuda Triangle isn’t any more mysterious than the Greenland square, the New Zeeland circle, or the Azores Octagon, that I just made up. I consider this a super fact because it is very likely true, and yet surprising to many people who are convinced that there really is a mystery. Furthermore, it is important because it is such a well-known myth.

The Bermuda triangle has one corner in Bermuda, one in Puerto Rico and one around Miami, Florida | The Bermuda Triangle the Big Non-Mystery
The Bermuda Triangle: It is approximately defined as a triangle Florida, Bermuda, and Puerto Rico. There is no exact definition. Alphaiosderivative work: -Majestic-, Public domain, via Wikimedia Commons.

Bermuda Triangle Mysteries

Just because the risk of disappearances of planes and ships is not higher in the Bermuda Triangle, does not mean that there aren’t mysterious disappearances and mysterious phenomenon occurring in the Bermuda Triangle. Some notable disappearances are USS Cyclops (1918), Flight 19 (1945), Star Tiger and Star Ariel (1948–1949), and the Witchcraft (1967). However, there are mysteries and mysterious phenomena occurring all around the world.

One of the mysterious phenomena occurring in the Bermuda Triangle is ocean swirls, and rogue waves, and methane burps might be another problem, but it is far from unique to the Bermuda triangle, and there are no magnetic anomalies in the Bermuda triangle as often alleged.

Ocean swirls frequently occur all over the world with some famous hotspots for ocean swirls by the coasts of Japan, Norway, Italy, Scotland, and Maine, USA. The ocean swirls in the Bermuda triangle might be due to movement of water between landmasses and/or the Gulf stream, but this is under investigation. There are no known giant or permanent ocean swirls in the Bermuda triangle.

A giant deep ocean swirl in the middle of the blue ocean.
Ocean swirl allegedly in the Bermuda Triangle Asset id: 1158148882 by PHOTO JUNCTION

As mentioned, another mysterious phenomenon is methane bubbling to the surface of the ocean. However, as can be seen in the maps in this National Geographic blog post the source of these methane burps of death aren’t typical to the Bermuda triangle. The methane hydrate field in the first map of the National Geographic blog post is mostly outside of the Bermuda triangle stretching from Cuba and up along the Florida coast. The second map, the world map, shows that these methane hydrate fields exist all around the world.

Our Honeymoon in Bermuda

Below are some old photos from our honeymoon in Bermuda in August of 1991.

Thomas Wikman Super Facts
The Bermuda Triangle the Big Non-Mystery
The Bermuda Triangle the Big Non-Mystery
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Quicksand

A lot of people have died on the silver screen from being trapped in quicksand. In the 1960s, almost 3% of films featured someone sinking in clay, mud or sand. However, this is extremely rare, if it has ever happened, and it is very difficult to find any documented cases of people drowning in quicksand even when they struggle. The reason is that you can never completely become submerged in quicksand because quicksand is much denser than water so you’ll easily float. If you relax you will float and sink no more than up your waist or lower chest. In addition, quicksand pits are rarely more than a few feet deep. Another misconception spread by the silver screen is that quicksand appear in the desert. However, quicksand usually appears near water.

Quicksand is thick and heavy, and it is extremely difficult to get out once you are stuck. The best way to get out of quicksand on your own is to slowly lean back so that the weight of your body is distributed over a wider area and then do back and forth movements as if you are swimming. It will take a long time though, so expect to take it very slowly and gently.

That does not mean that getting stuck in quicksand is not dangerous. There are documented cases where people have gotten stuck in quicksand and there was no one around to help them and they couldn’t get out on their own and eventually died from thirst, exposure, or attacking animals. Another dangerous situation is when the quicksand is located on a beach near the shore. There are cases where a person was stuck in quicksand, and the tide came in resulting in a drowning.

There are situations in which the dangers associated with being submerged in quicksand are real, and that is what is called “grain entrapment” or “grain engulfment”. Several people are killed each year when they become submerged in grain and cannot escape. This happens in grain elevators and silos. So don’t jump into grain silos.

I should say that I do not consider this a super fact because it is not very important information, sort of trivia, and I also don’t think there is enough reliable information out there about this. However, I think it is interesting information that relates to me a little bit (see next section). To remind you, this is what I consider a super fact.

A super fact is:

  • An important fact that can be simply stated.
  • It is very surprising, shocking, widely disputed, misunderstood, or mind-blowing.
  • Yet it is true with a very high degree of certainty.
Outdoor photo of a cute young woman wearing a safari outfit sinking deep into the ground as like it was jungle quicksand, the ground turned into sandy milkshake mud, with a quicksand sign at the edge.
Woman sinking in quicksand Shutterstock Asset id: 2576940253 by Shutterstock AI

My Quicksand Experience

When I was about 6-7 years old, I had my own experience with quicksand or at least a mudpuddle that acted very much like quicksand. I should say that back then neighbors were friends, and your lawn was everyone’s lawn, and the kids in the neighborhood played with each other. The kids roamed the neighborhood and the forest. We threw stones at imaginary witches, screamed at moose, broke into barns to jump in the hay, ate dirt and cheerfully watched the schoolhouse burn down. There were no cellphones, doomscrolling, political keyboard warriors, online predators or overprotective parents. Kids were happy back then, but life was less safe.

I was with a group of kids, including a couple of kids a bit older than I was. We came upon a funny-looking mudpuddle, about two feet wide, and I decided to step in to check it out. I don’t remember why. Maybe I wanted to impress. Maybe I was curious. It only took a few seconds for me to sink in to right above my knees and then it was impossible to get out. The mud/quicksand held my legs in an iron grip. The fact that I stopped sinking around my knees might have been because my feet had hit solid ground. My friends tried to pull me up but could not get me up.

The older kids told me not to struggle and one of them ran to get my parents. They came running as fast as they could. My dad gripped me around the waist and slowly, bit by bit, he was able to pull me up. The rubber boots I was wearing stayed in the mud/quicksand. They might still be there like a fossil to be found by future inhabitants of our planet. Was it some sort of strange mud, or quicksand? I don’t know, but I remember being afraid. It taught me one lesson. Don’t step in funny looking mud puddles. In fact, maybe you shouldn’t step in mud at all unless you have to.

To see a list of the Super Facts click here

The Enormous Kuiper belt

Super fact 55 : The enormous Kuiper belt.

The Kuiper Belt is a vast torus/donut shaped region of space beyond Neptune, filled with icy, rocky bodies, including dwarf planets like Pluto. It shares a lot of similarities with the Asteroid belt, but it is much larger, and further out. The Kuiper belt is 20 times wider than the Asteroid belt, 1,000 larger by volume, and 20 to 200 times more massive than the Asteroid belt. It extends from roughly 30 to 50 astronomical units (AU) from the Sun.

I can add that one Astronomical Unit (AU) is the distance from the sun to Earth.

In the middle of the picture is the sun and around it is Mercury, Venus, Earth and Mars. Then there is a grey circular band representing the asteroid belt. Further out is Jupiter, Saturn, Uranus, Neptune and Pluto and a large circular band representing the Kuiper belt | The Enormous Kuiper belt
I drew this illustration of the solar system and the Kuiper belt. It is not entirely to scale, and in reality, Mercury and Venus are not attached to the sun.

The Kuiper belt is like a giant Asteroid belt located further out, beyond Neptune. The Kuiper Object Pluto, formerly known as the Planet Pluto, is the most admired, the cutest and most beloved of all planets, and it was the first Kuiper object discovered in 1930. However, we did not know of the existence of the Kuiper belt at the time. The Kuiper belt was discovered in 1992 and predicted to possibly exist by Astronomer Gerard Kuiper in 1951. The discovery of the Kuiper belt was one of the reasons Pluto was demoted from its planet status in 2006. There are other dwarf planets in the Kuiper belt similar Pluto, including Makemake, Haumea, and Eris. However, there could be hundreds. Ceres is a dwarf planet located in the Asteroid belt. To read more about the Kuiper belt and verify the facts above, click here, or here, or here.

This picture features the photo of Pluto taken by NASA’s New Horizons spacecraft in 2015 plus some text. The text says : This is Pluto! In 2006, the International Astronomical Union declared that Pluto is no longer a planet. Despite that, it keeps revolving around the Sun the same way it has been doing for billions of years. Pluto doesn't care what others think about it! Be Like Pluto!
Pluto and its moon Charon from NASA/JHUAPL/SwRI. NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute, Public domain, via Wikimedia Commons. NASA’s New Horizons spacecraft captured this high-resolution enhanced color view of Pluto in 2015.

I selected this to be a super fact because the existence of the Kuiper belt drastically changed our view of our Solar system, so it is important, we know it exists, so it is a true fact, and despite its enormous size the Kuiper belt is much less known than the Asteroid belt, and its existence often comes as a surprise to people.

The Kuiper Belt Resides in Darkness

You may wonder why the Kuiper belt was discovered so late whilst the Asteroid belt has been known since the beginning of the 19th century (Ceres 1801, Pallas 1802, Vesta 1807, etc.) The reason is that the Kuiper belt resides in darkness. The Asteroid belt is 2.2AU to 3.2AU from the sun whereas the Kuiper belt is between 30 to 50AU from the sun.

Let’s say you take an object that is 2.5AU from the sun and place it at a distance that is 40AU from the sun. Due to the spreading of the light the object will now receive 16 X 16 = 256 times less sunlight. This is called Geometric dilution. In addition, this light needs to be reflected back to earth for us to see the object, and once again the light will  spread resulting in 256 X 256 = 65,536 times less light reaching our telescopes. The Kuiper belt is huge, but it resides in darkness. Despite this fact, we have now discovered and catalogued more than 2,000 Kuiper belt objects. However, it is estimated that there are hundreds of thousands of Kuiper belt objects wider than 100 kilometers.

What is a Dwarf Planet?

A planet as well as dwarf planet is a celestial body that orbits the Sun and is nearly round due to its own gravity. Basically, it must be large enough to have compressed itself to a near spherical shape. To be classified as a planet and not a dwarf planet it must also have cleared its orbit of debris. So, a dwarf planet is therefore a celestial body that orbits the Sun, is nearly round due to its own gravity, but has not cleared the neighborhood around its orbit. Obviously, a planet in the Asteroid belt or the Kuiper belt is a dwarf planet. Just to make this complicated Astronomers have found giant exoplanets that have not cleared their orbit of debris . I wonder, are these exo-planets giant dwarf planets?

Oort Cloud

Astronomer and Author David Lee Summers (blog here) reminded me of the Oort cloud, which could be interesting to bring up in this context. The Oort Cloud is a vast spherical cloud of icy bodies, which is hypothesized to surround the solar system, extending from about 2,000 to 200,000 AU. It is thus thousands of times further out and wide than the Kuiper belt. I say hypothesized because the objects are so small, there’s really no direct observation of them and there’s some variation in numbers for its distance and extent, meaning it’s still not well defined yet. Still, its outer edge is believed to be the boundary between where the sun’s gravity dominates and the galaxy’s gravity dominates.

The Oort cloud is generally considered to be the outer edge of the solar system and believed to be the origin of most long period comets. The Oort cloud is thought to encompass two regions: a disc-shaped inner Oort cloud aligned with the solar ecliptic (also called its Hills cloud) and a spherical outer Oort cloud enclosing the entire Solar System.

The picture is of the Oort cloud with an inset picture of the Kuiper belt at the top. The inset picture is an enlargement of the dot in the middle corresponding to the Kuiper belt.
NASA This SVG image was created by Medium69.Cette image SVG a été créée par Medium69.Please credit this : William Crochot, Public domain, via Wikimedia Commons.

Other Astronomy Related Super Facts

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