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.
Super fact 54 : Satellites currently handle a very small percentage of global internet traffic, estimated at about 1%. The vast majority of internet traffic is carried by undersea cables.
I consider this a super fact because it is surprising, true and not trivia. It is an important fact since most of us use internet every day. It is a very common belief that satellites handle most of the global internet traffic, or at least a very large portion of it. I should say that a few years ago I thought so myself.
Stock Illustration ID: 1372134458 by Boris RabtsevichSubmarine underwater communication fiber optic cable on deep seabed. Asset id: 2175977719 by Dragon Claws
How Much Internet Traffic is Handled by Satellites
I should say that I did not find a lot of sites that answered this question, but all of the sites that I found gave similar answers such as, less than 1%, 1.5%, 1-2%, very little, etc.
I started out by asking ChatGPT this question “How much of internet communication does Satellites handle?” The answer I got was that Satellites handle a relatively small percentage of global internet traffic — typically less than 1–2% — with most of the world’s internet communication carried through undersea fiber optic cables and terrestrial infrastructure (like cell towers and wired broadband). Wikipedia states that satellites handle less than 5% – to an estimate of even 0.5%. I should add I do not rely on ChatGPT, SGE or Gemini, or Wikipedia for this blog but I take hints from them.
The reason satellite internet is used less is because satellite internet is significantly more expensive to use than traditional wired connections. In addition, satellites have higher latency (delay) compared to fiber optic cables, and less bandwidth (data capacity). Satellite internet is primarily used in remote areas where other forms of internet access are unavailable. Satellite internet is also used for military and government operations, as well as maritime and aviation connectivity. However, satellite internet is improving so this may change in the future. This is a comparison between satellite internet and optical fiber.
Photo by SpaceX on Pexels.comThis is a cross section of submarine fiber optic cable. Picture by Oona Räisänen (User:Mysid), Public domain, via Wikimedia Commons.
The layers in the picture of the submarine communications cable above are (from outside to inside): (1) Polyethylene (2) Mylar tape (3) Stranded steel wires (4) Aluminum water barrier (5) Polycarbonate (6) Copper or aluminum tube (7) Petroleum jelly (8) Optical fibers.
Super fact 53 : The Euler number denoted e, is an irrational number, which like the number pi is extremely important in mathematics. In addition, the relationship between the Euler number and pi; seemingly unrelated numbers, is quite amazing, especially if you throw the imaginary number: i = square root of -1 into the mix. Euler’s formula e^ix = cos(x) + isin(x), where x is degrees expressed in radians, is mind blowing to say the least. Radians means that 180 degrees is replaced by pi, and 90 degrees is replaced by pi/2, etc. A simpler special case, but equally amazing is Euler’s identity e^ix = -1, or e^ix + 1 =0. This is amazing math assuming you understand it.
As I said all this is amazing, mind blowing if you will, if you understand it, which is why I will try to explain it. Why I consider this a super fact is because when you first encounter the Euler number and the Euler formula, and you somewhat understand what it means, it is likely to be a mind-blowing experience. Those among you who have studied higher math, AP math classes in high school, or college level math are probably familiar with what I am about to describe, so your mind may not be blown. By the way you pronounce Euler like “Oiler”.
Euler’s formula in cyber space with grid 3d illustration, Asset id: 1636161301 by Giggle2000
Euler’s Number and Pi Two Irrational Numbers
Pi is the number you get when you divide the distance around a circle (the circumference) by the distance across the middle (the diameter). The Euler number is a bit more complicated to explain. I will do that next. Both pi and the Euler number are irrational numbers, which means that when written as a decimal, the number neither terminates nor repeats. As I mentioned, both pi and the Euler number are extremely important numbers in math. Perhaps the Euler should have its own day, just like pi has its own day (March 14). Maybe we should start celebrating Euler number day on February 7.
The first 20 decimals of pi and of the Euler number.
Exponents
Before I explain what, the Euler number is, I need to explain what an exponent is. If you multiply a number by itself x number of times, then x is the exponent. If you multiply two by itself four times 2*2*2*2, called 2 raised to 4, then 4 is the exponent. By the way the answer is 2^4 = 16 (called 2 raised to 4 is 16). I hope the illustration below will explain it.
Overview of exponents.
And finally, before explaining what the Euler number is I should also mention what a factorial is. The factorial of a number is the product of all positive integers less than or equal to that number. The factorial of 5 is denoted 5! and is 1*2*3*4*5 = 120. Also, the factorial of 0 or 0! = 1 (per definition).
Definition of the Euler Number
One more thing I need to explain before I go ahead with the definition for the Euler number is what is meant by allowing a number n in a formula to go towards infinity (limit –> infinity). Let’s say you have a formula that contains the number n. If the value of the formula does not change much as n becomes very large than it might be approaching a specific number as n approaches infinity. You say that it approaches a limit. I am trying to illustrate this in the picture below.
As the number n gets bigger the formula stops getting bigger and instead approaches a limit. When n approaches infinity that will be a very specific number. Which number do you think it is?The definition of Euler’s number plus an infinite series sum that is also the same as Euler’s number.Definition of the Euler’s constant in two different ways, Asset id: 1227561829, by benjaminec.
Euler’s Number in Calculus
As I mentioned, Euler’s number shows up in mathematics in a lot of places. It is an extremely useful number with some amazing properties and that includes calculus. However, explaining functions and calculus may be going a bit too far, so I am just going to simply state that the derivate of e^x is just e^x and the indefinite integral, or the anti-derivative of e^x is e^x. In other words, differentiation / integration does not change this function. It also means that the slope of the curve is the same as the curve itself. Among all the infinite number of functions this is only true for e^x.
Differentiation and integration does not change the function e^x.
Trigonometric Functions
Next, I would like to launch into Euler’s formula. However, before I do that, I need to explain what trigonometric functions and imaginary numbers are. The trigonometric function sin(x) is the ratio of the length of the side opposite to a given angle to the length of the hypotenuse. In other words, if the hypotenuse is equal to 1, then sin(x) is the length of the opposite side to the given angle. The trigonometric function cos(x) is the ratio of the side of the triangle adjacent to the angle divided by the hypotenuse. In other words, if the hypotenuse is equal to 1, then cos(x) is the length of the adjacent side to the given angle.
Sin and cos are always between 1 and -1. ‘x’ is often expressed in degrees going from 0 to 360 (or 0 to 90 in a right-angled triangle). However, there is another way to express angles in triangles and that is radians. In this case the number pi corresponds to 180 degrees, pi/2 corresponds to 90 degrees, pi/4 corresponds to 45 degrees, etc. Euler’s formula uses trigonometric functions, but it only works if you use pi instead of degrees. Pi and Euler’s number have a special relationship. Sin and cos are illustrated in the picture below.
Illustration of the trigonometric functions sin(x) and cos(x).
Imaginary Numbers
The last thing I need to explain before demonstrating Euler’s formula is imaginary numbers. The square root of a number is another number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 * 2 = 4. The square root of 9 is 3, because 3 * 3 = 9. As long as you deal with real numbers, square roots must be positive numbers because you cannot multiply two numbers and get a negative number. -2 * -2 is 4, not -4.
However, that did not stop some mathematicians from making up a square root that was negative. This imaginary number is the square root of -1 and is referred to as i, yes just i, for imaginary. So, what’s the point of making up numbers that can’t exist? Well, it turned out to be quite useful and you can manipulate imaginary numbers to result in real numbers. For example, if you multiply the imaginary number i by itself i*i you get -1. If you multiply i by itself four times, in other words i^4, or i raised to 4, you get 1. Even more impressively, i raised to i, or i^i, is a real number. i^i = 0.207879… This is illustrated in the picture below.
Imaginary numbers illustrated
Eulers Formula
Without giving the proof, or any detailed explanations, below is Euler’s identity and Euler’s Formula (e^ix = cos(x) + isin(x)). Notice the mix of Euler’s number, pi, the trigonometric functions using radians (based on pi), and the imaginary number. Well, likely mind-blown, if you have not seen it already and you understood this post up to here.
Euler’s identity and Euler’s formula.Euler’s formula illustrated in the complex plane. Asset id: 2345669209 by Sasha701
If you want to see how you prove Euler’s Formula check out this youTube video.
If you want to learn more about the importance of Euler’s number in sommon and useful mathematics, check out this youTube video.
Super fact 52 : Climate change, including increased heat, extended drought, and a thirsty atmosphere, has been a key driver in increasing the risk and extent of wildfires in the United States, particularly the western United States during the last two decades. The number of Wildfire acres burned in the United States has significantly increased even though the number of wildfires has not. Another important factor is forest management.
Wildfire acres burned in the United States. Number of acres of wildfire burned in a given year in the United States. This is shown from 1983 onwards, when consistent reporting began. Data source : National Interagency Fire Center (NIFC). Presented by OurWorldinData/natural disasters.
To some people this does not come as a surprise. However, due to the complexity of the issue combined with political spin, this is a surprise to me, or even something they refuse to believe. I’ve come across many people who are surprised to hear that there really is a connection between climate change and wildfires in regions of the world which are getting dryer and hotter due to climate change. There are also others who are surprised to hear about the complex picture and the importance of good forest management. In any case, since it is a surprising fact to many, and an important fact, I consider it a super fact.
In general, you can’t look at wildfire statistics and draw conclusions without considering the context. Below are some considerations.
Wildfires are not started by climate change or poor forest management. They are started by lighting, falling powerlines, campfires that are not properly put out, and sometimes by arson. That doesn’t mean that climate change and poor forest management does not increase the risk and extent of wildfires.
Research organizations such as NOAA recognize that wildfire is a natural part of the western US ecosystem. However, climate change is significantly exacerbating the problem by creating conditions more conducive to intense and widespread wildfires.
Suppression of fire in certain ecosystems may in fact increase the likelihood that a wildfire will occur.
In the past, forests evolved with frequent, low-intensity fires that helped clear out underbrush. They can have ecological benefits. Therefore, the number of wildfires may not have increased over the last 100 years.
Local conditions and forest management have evolved through time complicating the wildfire statistics around the world.
Highly skilled hotshot firemen crew working in a challenging remote area with flames reaching the treetops. Shutter stock asset id: 2258645599 by Gorodenkoff
Fix Our Forest Act
Climate change is a huge problem that is going to take decades to tackle and the whole world needs to be involved in that effort. However, we can quickly address wildfires here in the US, especially the American West by addressing the other half of the problem, forest management. There is currently a bill in congress called the Fix Our Forest Act that does that. It streamlines and enhances forest management based on the science. In the house of representatives, it has the number H.R.471 and in the Senate it is S.1642.
I was recently in Washington DC to do volunteer lobbying for these bills. You can read about it here.
Super fact 51 : In 1968 5,033 Americans died from a drug overdose. In 1978 5,506 Americans died from a drug overdose. In 1999 16,801 Americans died from a drug overdose. In 2022 107,941 Americans died from a drug overdose. 82,000 of those deaths involved opioids (about 76%). The number of people who died from an opioid overdose in 2022 was 10 times the number in 1999. More than half of all opioid deaths in the world were Americans despite being only 4.2% of the world population. The hardest hit demographic is white males.
Note the data in the super fact above is taken from Wikipedia, which in turn took it from CDC. However, the data across multiple sources look roughly the same (CDC / CDC, NIDA/NIH, Our world in Data, Wikipedia). I think this is a super fact. I should add that the statistics seem to have improved a little bit in 2023 and 2024.
I’ve posted about good super facts in this blog several times:
However, unfortunately there are also bad super facts, like this one.
The Severe Drug Overdose Epidemic in the US is a Super Fact
We recently went to the funeral for the young son (in his 20’s) of good friends of ours. He died from a drug overdose. The same thing happened to another friend of ours not too long ago. Despite all the talk about drugs, the war of drugs, and the “just say no campaign”, in the 1980’s I don’t remember this happening to people I knew when I was young, so I looked up the statistics. I knew we had an opioid epidemic with Fentanyl being the greatest culprit followed by Heroin. I just didn’t realize how severe it was and how American it was. This is important and shocking and the sources behind the data are reliable, which is why I consider this a super fact.
The United States Has by Far the Highest Death Rate from Opioids
If you play around with this graph from Our World in Data you will notice that the United States has a very high rate of deaths from drug overdoses, especially opioids, much higher than any other country. For example, take my home country Sweden, where 283 people died from opioid in 2021 (398 all drugs, data from IHME). Compare that with the United States, where 55,452 died from opioid in 2021 (70,893 all drugs, data from IHME). Adjust that for the population in each country you get a rate of 16.3 deaths per 100,000 inhabitants for the US and 2.7 deaths per 100,000 inhabitants for the Sweden. Sweden and the US are both open wealthy democracies in which certain opioids are legal for medical purposes but otherwise illegal. The graph below has slightly different numbers but notice that the year (2024) is different.
Data source : Institute for Health Metrics and Evaluation (IHME), Global Burden of Disease (2024). The graph is taken from Our World in Data .
Some illustrative Graphics on Drug Deaths
The graphs below illustrate both the sharp rise in drug related deaths, especially opioids, as well as how hard hit the United States is compared to the rest of the world.
The population of the United States is 340 million.The population of South America is 438 millionThe population of Europe is 744 million.The population of Asia is 4,800 million.This graph shows the contribution to US deaths from specific drugs including synthetic opioids (Fentanyl), Heroin, prescription opioids, and cocaine. Notice that the vertical axis shows the death rate per 100,000 people and not the total number of deaths. Data source : US Centers for Disease Control and Prevention WONDER. Note: Opioids include prescription pain relief drugs, synthetic opioids, excluding methadone and other opioids such as heroin. The graph is taken from Our World in Data.
Super fact 50 : There are hundreds of types of beer but in general they fall into two main categories, ales and lagers, and these two categories are not differentiated based on color. The ales are not necessarily dark and lagers light. There are light colored ales and dark, even black ales. There are light colored lagers and dark and almost black lagers (Schwarzbier). The difference between ales and lagers is the type of yeast used and the fermentation temperature. Ales are typically made with top-fermenting yeast at warmer temperatures. This result is a wider range of flavors and aromas, often with fruity or spicy notes. Lagers, on the other hand, are made with bottom-fermenting yeast at cooler temperatures making them crisper and more subtle. Ales have been around for 6,000 years. The lager is a more recent invention.
I consider this a super fact, first, because even though beer is a well-known drink that a lot of us drink almost every day, a lot of people don’t know what the two basic kinds of beer are. They don’t know what an ale is or what a lager is. Even beer fans and many people who drink beer every day are often clueless about this, the most basic fact about beer. A lot of people say that they like light/blond beer or they like dark beer. In my native country Sweden, which I admit is not a true beer country, I often hear people say that they prefer “ljus öl” (light/blond beer) rather than “mörk öl” (dark beer), or the other way around, which is like saying that you like blond / light colored food rather than dark colored food. It doesn’t make sense.
This is a so called Schwarzbier that I drank some time ago. Das Schwarze a German Schwarzbier from Dinkelacker-Schwabenbräu, ABV 4.9%. Some roasted notes, sweet caramel, light flavor, a bit fizzy, somewhat thin but good enough. This is a Lager but notice a how dark it is, basically black. I did not put black dye in it. It is how they really look despite being Lagers.
I am in the process of learning Franch, and I’ve discovered that this confusion is even baked into the French language. Well as you might guess France is not a true beer country. If you use Google Translate and you type in “Lager” in the English edit box the answer you get in French is “Bière blonde”, even though French and Belgian beer that are labeled Blonde frequently are Ales not Lagers. I’ve read a lot of French language sites mentioning beer, and unless the author has some beer expertise, they make the same mistake as Google Translate. Blonde / light beer is not Lager, and dark beer is not necessarily Ale.
I had a discussion about this with one of my French teachers and despite me having talked a lot about beer in class and having previously shown him that I knew something about the topic, he had a very hard time accepting the truth. After a Google search he finally accepted the truth, but he was very surprised, perhaps even shocked.
The confusion is immense, it is worldwide, and the truth is surprising to some people. I should mention that Americans for the most part get this right. In general Americans know that Lager isn’t necessarily blonde and vice versa. They know that IPAs, which are not Lagers but Ales, typically are light colored. Perhaps because of the prominent craft beer industry in the US. I should also mention that there are also hybrid beer styles and beer styles that are hard to classify as lager or ale. More about that later.
This is Ba Ba Black Lager, an American Schwarzbier. I had sushi with this Schwarzbier.
Secondly, lagers, especially pale bland mass-produced lagers have become so common that when people taste an ale, especially if it is a little bit different, like fruity, tart, have chocolate or coffee flavors, etc., they don’t even consider it a real beer. In their minds real beer is a bland tasting lager. Never mind that we have had Ales for 6,000 years, and that Ales dominated beer drinking up to relatively modern times. Nowadays 90% of beer consumption worldwide is lagers (87% in the US), but throughout most of human history nearly 100% of beer consumption worldwide was ales.
This is an IPA called Cold War. IPAs are NOT Lagers. However, notice how light the color is. IPAs are popular in the US, which I think is one reason Americans are better educated on the difference between lagers and ales to countries that are not part of the European beer countries (Germany, Britain, Ireland, Belgium, the Czech Republic, etc.)
What is an Ale?
As mentioned, an Ale is a style of beer, brewed using a warm fermentation method. Ales are typically made with top-fermenting yeast at warmer temperatures. This result is a wider range of flavors and aromas, often with fruity or spicy notes. The word ale is an English word which in medieval England meant a drink brewed without hops (it is not what it means today). Some popular ales include IPA, Pale Ale, Stouts, Porter, Scotch Ale, and Barley Wine. Below is a more complete list of Ales. The list is from the beer advocate. Despite the 120 styles listed the list is not complete. It should be noted that I’ve added a few that were missing.
India Pale Ales : American IPA, Belgian IPA, Black IPA, Brut IPA, Cold IPA, English IPA, Imperial IPA, Milkshake IPA, New England IPA.
Pale Ales : American Amber / Red Ale, American Blonde Ale, American Pale Ale, Belgian Blonde Ale, Belgian Pale Ale, Bière de Garde, English Bitter, English Pale Ale, English, Pale Mild Ale, Extra Special / Strong Bitter (ESB), Grisette, Irish Red Ale, Kölsch, Saison.
Wild/Sour Beers : Berliner Weisse, Brett Beer, Faro, Flanders Oud Bruin, Flanders Red Ale, Fruit Lambic, Fruited Kettle Sour, Gose, Gueuze, Lambic, Wild Ale.
Wheat beers : American Dark Wheat Beer, American Pale Wheat Beer, Dunkelweizen, Grodziskie, Hefeweizen, Kristallweizen, Witbier.
Stouts : American Imperial Stout, American Stout, English Stout, Foreign / Export Stout, Irish Dry Stout, Oatmeal Stout, Russian Imperial Stout, Sweet / Milk Stout.
Porters : American Porter, Baltic Porter, English Porter, Imperial Porter, Robust Porter, Smoked Porter.
Dark Ales : Dubbel, Roggenbier, Scottish Ale, Winter Warmer.
Brown Ales : Altbier, American Brown Ale, Belgian Dark Ale, English Brown Ale, English Dark Mild Ale.
Strong Ales : American Barleywine, American Strong Ale, Belgian Dark Strong Ale, Belgian Pale Strong Ale, English Barleywine, English Strong Ale, Imperial Red Ale, Old Ale, Quadrupel (Quad), Scotch Ale / Wee Heavy, Tripel, Wheatwine.
Specialty Beers: Ancient Herbed Ale, Sahti.
Trappist Westvleteren from Brouwerij Westvleteren (Sint-Sixtusabdij van Westvleteren) a Belgian Quadruple might be the most renowned beer in the world. I’ve had it many times and it is heavenly. However, it is very difficult to get in the US. A Quadruple is a type of Ale.Plutonium-239 from the Manhattan Project Brewing Company in Dallas, Texas. It is a strong-tasting Porter with coconut flavors. (chocolate, coconut and coffee). There is no clear definition on the difference between porter and stout, other than porters are in general milder and not as strong as stouts. From that perspective Plutonium-239 is really a stout.
Wild Ales and Sour Beers often have fruity flavors. This can be achieved by adding fruits or berries to them but often fruit flavors emerge naturally from the fermentation process, which, at least if you use wild yeast, produce esters (fruit flavors). Wheat beers often have banana or pear notes and just as for Wild Ales these flavors emerge naturally from the fermentation process (esters again). Some of the IPAs also have distinct fruit flavors, especially the New England style IPAs, but in this case the fruit flavors come from the hops.
Jester King in Texas brews a Wild Ale called Atrial Rubicite. It is a Wild Ale infused with raspberries. The fermentation process uses “wild yeast” to create a tart and fruity base but raspberries are added to enhance the fruit flavor resulting in a thick full raspberry flavor which most people describe as heavenly.
What is a Lager?
As mentioned, lagers are made with bottom-fermenting yeast at cooler temperatures making them crisper and more subtle. The word lager (German) means to storage or storeroom and used to refer to beers stored at cold temperatures. Sometime in the 15th century cold fermentation yeast emerged, and people started using it to do fermentation at cold temperatures. As time went by this form of fermentation became more popular. It was brought to the US in 1840 and between 1860 and 1870 it became the most popular fermentation process in Bohemia. As mentioned, today 90% of beer consumption worldwide is lagers.
Below is a more complete list of Lagers. The list is from the beer advocate.
Pale Lagers: American Adjunct Lager, American Lager, Czech / Bohemian Pilsner, Czech Pale Lager, European / Dortmunder Export Lager, European Pale Lager, European Strong Lager, Festbier / Wiesnbier, German Pilsner, Helles, Imperial Pilsner, India Pale Lager (IPL), Kellerbier / Zwickelbier, Light Lager, Malt Liquor.
Dark Lagers : American Amber / Red Lager, Czech Amber Lager, Czech Dark Lager, European Dark Lager, Märzen, Munich Dunkel, Rauchbier, Schwarzbier, Vienna Lager.
Specialty Lagers : Japanese Rice Lager, Chile Beer
Paulaner is a so called Festbier (or Octoberfest), which is type of Lager made especially for Octoberfest in Germany.
Finally, there are also specialty beers that are hybrids, or neither or that can be both.
Hybrid (Ale/Lager): Bière de Champagne / Bière Brut, Braggot, California Common / Steam Beer, Cream Ale.
Neither lager or ale, or can be both : Fruit and Field Beer, Low-Alcohol Beer, Rye Beer, Smoked Beer, Herb and Spice Beer, Kvass, Gruit, Happoshu, Pumpkin Beer.
That’s 120 styles of beer. I’ve had 110 beer styles. How many have you had?
Super Facts 