Tag: Blogging

Infinities Come in Different Sizes

Super fact 68 : Infinities come in different sizes. Some infinities are larger than others. In fact, it is possible to create an infinite number of different-sized infinities. Some infinities are countable and others are uncountable.

How can infinity be of different sizes? Infinity is infinity after all. Infinity is an absolute, an absolute we cannot imagine. However, at the end of the 19th century a German mathematician by the name Georg Cantor demonstrated that there exists a variety of infinities, and some are larger than others. In fact, his theorem implies the existence of an infinity of infinities. For those who have not heard of this concept before it is surprising and yet it is true, and it is also kind of an important thing to know about mathematics. This is why I consider this a super fact.

Let me explain. Think about all natural numbers, 1, 2, 3, 4, 5, …, a billion, a quintillion, … You can keep counting forever. There are infinitely many natural numbers. Now take two natural numbers, the numbers 3 and 4. How many numbers are in between 3 and 4? Well, you have 3.5, 3.55555, 3.016893, and you have the number pi, 3.14159265358979323846, and infinitely many other numbers with infinitely many decimals. 3 and 4 are only two numbers but you have infinitely many decimal numbers, or so called real numbers, between 3 and 4. That is true for the two numbers 4 and 5 as well, and 5 and 6, and all natural numbers. Even though there are infinitely many natural numbers there are infinitely many more real numbers.

For the explanation of the mathematical proof see this article in Scientific American. This article explains why there are an infinite number of different-sized infinities.

A neon infinity metaverse symbol. 3D illustration | Infinities Come in Different Sizes
Infinity Asset id: 2118543950 by Sahara Prince

I should say that today Saturday November 8, 2025, is National STEM Day, or STEAM Day. Stem stands for Science, Technology, Engineering, and Mathematics. The extra ‘A’ in STEAM stands for Art. Therefore, I thought that posting something related was appropriate for today, in this case it is Mathematics. I have to admit I am posting it a little bit late in the day though.

To infinity … and beyond!

Madrid, Spain; 05-14-2024: Large figure of the famous character Buzz Lightyear from the movie Toy Story in an exhibition called Pixar World about the studio's films.
Buzz Lightyear “To infinity … and beyond”.  Shutterstock Asset id: 2464838811 by MSCT Pics

As mentioned, infinites can have different sizes. How about, for example, the set of all natural numbers and the set of even numbers. After all, it seems like the set of all even numbers should be half as big. As it turns out they are the same size. That’s because for all natural numbers 1, 2, 3, 4, 5 you can always find a buddy, 2, 4, 6, 8, 10 among the even numbers. This is called a bijection. However, you cannot do this with natural numbers versus real numbers. You cannot pair up a natural number with the real numbers because there are infinitely many for each single natural number.

The set of all real numbers is really a larger infinity than natural numbers, which by the way is the smallest infinity. The sets of natural numbers and, for example, even numbers are called countable infinities, and the set of real numbers are called uncountable infinities. In addition, there are infinitely many different sizes of infinities that are larger than both natural numbers and real numbers.

Another interesting, related issue is that Cantor tried to prove that there are no infinities with sizes that lie in between the natural numbers and the real numbers. This was called the continuum hypothesis. As it turned out this hypothesis is not possible to prove (you can prove that it cannot be proved) at the same time as it is not possible to disprove. It is related to Gödels incompleteness theorem but is not the same. However, it is another absolute limit to human knowledge, things we know that we can never know.


If you want to have your mind blown, watch this 8 minute YouTube video about infinities of different sizes and the continuum hypothesis.

Other Mathematics Related Super Facts

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More than half of Internet Traffic is Bots

Super fact 66 : Bots make up more than half of all internet traffic surpassing human activity for the first time in 2024. The 2025 Imperva Bad Bot Report found that bots accounted for 51% of all web traffic. Human activity accounted for 49% of all internet traffic, malicious “bad bots” accounted for 37%,  and 14% of traffic comes from “good bots,” such as search engine crawlers.

What made me look up this information is that I’ve recently seen a lot of idiotic and inflammatory comments, as well as inappropriate laughing emojis on social media pages and posts. The pages that seem to be targeted the most by this abuse seems to be pages related to things like climate change, clean energy, EV cars, evolution, vaccines, modern medicine, modern physics, geopolitics, information on political issues, etc. However, those topics might reflect my interests. Perhaps all topics are targeted by this growing strange abuse.

It looks like those among us who slept through the science classes in high school now think they are the real experts and have declared war on all science nerds. The question that arose in my mind is, are these keyboard warriors humans or are they bots? It is true that Artificial Intelligence does not (yet) demonstrate true independent intelligence, but that is true for many people as well. So, how do you know the difference? Anyway, that is the background to why I investigated this issue.

I looked it up and found that bot traffic has been increasing and is now the majority of all internet traffic according to, for example, the 2025 Imperva Bad Bot Report. You can read more here. Facebook is not an exception. 40% of all posts are machine generated. These bots/fake accounts spread a lot of misinformation, inflammatory comments, and some are scams.

Many people are also spreading false information and some of them are scammers, but the fact that machines do it as well add to the problem. It is also very common for bots and fake accounts to leave reactions on Facebook posts, which might be what I saw, but I am not sure. What is certain is that I have come across a lot of false information on Facebook, as well as scams and deep fakes, and Meta/Facebook is obviously not able to clean it out. There are also bots that are remotely controlled ransomware, computer viruses, spyware, and other malware.

A picture of giant computer screen with a red warning triangle containing an exclamation mark. Underneath the triangle is the text “System Hacked” | More than half of Internet Traffic is Bots
Warning of a system hacked. Virus, cyber attack, malware concept. Asset id: 1916985977 by Sashkin

Why I consider this a super fact is because it appears to me that people underestimate the influence of malicious bots. If you had asked me before I looked this up how common bot traffic was, I might have said a few percent. After all streaming, youTube, gaming, etc., require a lot of bandwidth. Considering all the fake stuff and nonsense that is spreading partially with the help of bots, this is dangerous. We know the bots make up more than half of all internet traffic, and bot traffic is growing faster than human traffic, it is important information, and I think it is surprising information to a lot of people, thus making it a super fact.

Fake Nonsense on Facebook

This section is not directly tied to the super fact above, but it concerns a related topic and is based on my personal experience with the social media platform that I have used the most, Facebook. Instagram seems to be even worse, but I am not using it as much. Why I am bringing this up is because increased bot traffic and the increased presence of fake accounts and deep fakes on social media can make this a lot worse. Combined with our gullibility and lack of critical thinking as well as the failure of social media platforms to keep after this, we are facing a serious threat.

Gullible Planet

It is well known that there are a lot of nonsense posts on Facebook (and elsewhere). The fact that we so easily fall for it and don’t check with reliable sources is a big problem. When I see something fake, I often post corrections, for example, using sites like snopes. Sometimes people are grateful, sometimes they get angry, and I’ve even been blocked and lost friends just by posting a snopes link. A lot of the fake stuff is posted by people, but a lot of posts, comments and reactions are posted by bots, and this is becoming more common. With increased malicious bot traffic, AI and deep fakes, we must improve our critical thinking skills.

Below are some examples of fake stuff I’ve come across on Facebook

Did you read that viral article on Facebook claiming that they found 20 feet humanoid skeletons in Turkey? The article stated that archeologists think that they might be fossilized Nephilim, the giants mentioned in the Old Testament. If so, did you doubt the accuracy of the article? If you did, you did good. It was based on an article in a satirical website called World News Daily Report. However, judging from the comment section, including the comments of some of my friends, most people didn’t doubt the article’s accuracy.

How about the story from a purported science magazine that scientists had just discovered that the Easter Island statues/heads have bodies/torsos below the ground. The article stated that this was a revolution in archeology that forced a reevaluation of history. The commentors were amazed over this discovery and some pointed out that not realizing this sooner was a big failure on the part of archeologists and scientists. Well, that the Easter Island statues/heads have bodies/torsos below the ground has been known all along.

How about the story about the lunch lady named Aileen G. Ainuse who poisoned the water supply at Sunnydale High School in Goobersville, Indiana, killing over 300 students and staff. It was accompanied by a scary photo of a starving lady. The readers were shocked and appalled, but not many bothered to verify the story, for example, with the help of snopes. The story was false.

Another article stated that the fact that there were no stars in the black sky in a photo allegedly taken on the moon was proof that the photo was fake and that the astronauts were never on the moon. First of all, it was day, the sun was out. When the sun is out it is very difficult to see the stars because the sun’s light is a million times brighter than the light from the stars and in addition the bright sunlight reflected off the surface of the moon dims the stars. In addition, the cameras used had short shutter speeds for picking up the bright light, not faint stars. Seeing stars in a daytime photo taken on the moon is not something you should expect. Several commentors pointed this out but most other commentors didn’t pay attention and were fooled.

I’ve also seen the opposite, people refusing to believe a true story because they fundamentally misunderstand something. Below is a youTube video showing an animation composed of actual satellite photos by NASA. Many commentors seeing this video insisted that it was a hoax because the back side of the moon is dark. But it is not. When the side of the moon that is turned towards us (the near side) is dark (a new moon) the back side reflects the sun’s light (like a full moon). The backside (far side) of the moon also looks different from the side turned towards us. In the video below the sun is behind the camera and shines on earth as well as the backside of the moon.

A final example is a deep fake Ad featuring Meryl Streep and Dr. Sanjay Gupta promoting an Alzheimer’s cure. I saw it on Facebook several times over a period of several weeks. It looked very real to me, but something felt off, so I fact checked. It turned out that Meryl Streep and Sanjay Gupta had nothing to do with the video. They were AI generated likenesses promoting a scam product. The video used all the typical polemic tricks such as “a cure that the billion dollar companies don’t want you to know about”, “buy now before they take our website down”…. We need to get better at protecting ourselves and believing 20 feet skeletons on Facebook are real is not the way to do it.

To see the other Super Facts click here

There Are Scientific Facts

Super fact 62 : Facts exist in science; a scientific “fact” is an observation of a natural phenomenon that has been repeatedly confirmed by independent observers and is accepted as true for all practical purposes.

Outside of mathematics and logic nothing is ever the final truth, not in science, and not anywhere else. However, there are facts that have been so well confirmed and are so basic that there is no reason to doubt them. Earth is not flat like a pancake, and the sun is a star, are two examples of astronomical facts. Most dogs have four legs is another fact. The speed of light in vacuum is the same for all observers is a fact in physics that is surprising if you didn’t know it before. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. It is possible that we are all living in a virtual reality, like in the movie The Matrix, and that Earth is really flat like a pancake after all, because all of reality is a dream. However, for all practical purposes, it is not the case.

This blog, super facts, deal with facts that are surprising, strange, or disputed by non-experts, and yet true because they have been verified, for example, in the case of scientific facts, by repeatable careful observation. Anyone is free to object if you think I am wrong about a fact.

My next super fact is going to be “Evolution is a fact”. Evolution is also a scientific theory, but it means something different from when you say evolution is a fact. Moreover, a Scientific Theory is not a guess, as commonly but incorrectly assumed. I am bringing this up because many people who are typically unaware of the evidence behind a fact will use arguments such as “science does not know everything”, “it is just a theory”, etc., in efforts to dismiss a well-supported claim.

I should say that this post is inspired by a Facebook post by “The Credible Hulk”, a Facebook page managed by a group of anonymous scientists opposing misinformation around vaccines, global warming, evolution and GMOs. I did not save the post, but it went something like this:

One of the commentors said : “Calling evolution a “fact” defeats your argument. The Theory of Evolution is by definition a theory not a fact. It’s the currently agreed upon hypothesis but not a fact”

What the commentor did not realize is that “Theory” in the context of science does not mean what he thought it did. I am using past tense because he got “schooled”. To his credit he did not respond with insults and neither did the Credible Hulk, which does not seem to be standard on Facebook. However, his comment illustrates something that drives scientists like those who created “The Credible Hulk” nuts, and that is the widespread lack of understanding of the difference between a guess, a hypothesis, a scientific fact, theory as used in common language and used when talking about a scientific theory.

Rather than having this discussion over at my upcoming “Evolution is a fact” post, I am making a separate post about it. I consider “There are Scientific Facts” a super fact because it is true, and yet the confusion around it and what a Scientific Theory pertains is massive, and it is an important topic.

What is Science?

Science is the process of learning about the world through systematic observation and experimentation to gain knowledge about how things work. It involves observing phenomena, forming testable ideas (hypotheses), systematic studies, conducting experiments, and collecting evidence and facts that support or refute those ideas, ultimately leading to a deeper understanding of general truths and natural laws. If an idea/hypothesis correctly predicts and explains facts, it becomes a theory, which is something that is very different from a guess.

The process of making observations, formulating testable hypotheses, conducting experiments, analyzing data, and drawing conclusions to understand phenomena and solve problems is referred to as the scientific method, and there are different types of scientific methods. Some involve experiments, other involve analysis historical artifacts or existing data. Objectivity, reproducibility, falsifiability, and predictive power or problem solving are essential.

Banner research vector illustration concept with keywords and icons for Analysis, Data, Survey, Development, Fact, Knowledge, and Data Entry
Aspects of scientific research include analysis, data collection, sometimes surveys, development, establishing facts, creating knowledge, and data entry so that others can repeat it and verify results. Shutterstock Asset id: 1100776715 by Trueffelpix

What is a Scientific Theory?

When people hear the phrase “evolution is a theory,” many mistakenly assume it means evolution is just a guess or speculation. In science, however, a theory is far more than a guess. A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. In other words, it is a well-tested, comprehensive explanation of natural phenomena, supported by an extensive body of evidence.

3D Isometric Flat Vector Conceptual Illustration of Scientific Method and Knowledge Acquiring. Icons organized in a circle, observation, question, hypothesis, experiment, conclusion, and result | There Are Scientific Facts
Conceptual Illustration of Scientific Method and Knowledge Acquiring. Notice, not all scientific methods necessarily include experiments. Some include surveys, or testing of ancient artifacts, etc. Shutterstock Asset id: 2139402875 by TarikVision

The evidence for evolution is both vast and compelling. It is not just the massive fossil record, it is in DNA, anatomy, there’s geographic evidence, and evidence from dozens of other scientific fields, not to mention that evolution is directly observable. There is a Theory of Evolution, that is the well supported explanation for evolution, or evolution by natural selection. There is also “Evolution is a fact” referring to, for example, the fact that we can directly observe it. It is true for all practical purposes, and that does not mean that evolution stops being a scientific theory as well as a fact.

Afterword

Even though science is constantly evolving and our knowledge is evolving and sometimes our understanding and scientific theories on a topic needs to be updated, scientific facts exist. Some scientific facts are extremely unlikely to change. For example, Jupiter has multiple moons, galaxies exist, global warming is real and is caused by us, and evolution is a fact. Before you decide to dismiss such a fact make sure you know what “theory” means in science, and most importantly educate yourself on the relevant evidence. There might be a whole lot more than you imagined, and you may discover that the evidence you thought was contrary is not evidence.

You often hear “science does not know everything”. That’s true. If science knew everything it would stop. However, the collective knowledge created by science is enormous and as individuals we know next to nothing. So be humble and learn from scientific evidence presented by reliable sources.

To see the other Super Facts click here

Superfluid Liquids are Like Magic

Super fact 60 : Superfluids such as liquid Helium cooled below -455.58 Fahrenheit exhibit some very strange characteristics such as it flows right through many solids, it climbs walls, it has near zero viscosity, it exhibits circulating flows that never stop despite no energy being added. It is a Macroscopic Quantum Phenomenon.

When gases are cooled far enough, they will turn into liquids and eventually typically to solids. For example, Oxygen becomes a liquid when its temperature drops to -297 Fahrenheit, which is -183 Celsius, or 90 degrees Kelvin. Kelvin is 0 at absolute zero, the coldest possible temperature, and in addition it uses Celsius for the scale. So, 90 degrees Kelvin is 90 degrees Celsius above absolute zero or 162 degrees Fahrenheit above absolute zero. When Oxygen becomes a liquid, it turns into a pale blue liquid. Oxygen becomes a solid at 54 Kelvin, or −218.8 Celsius, and −361.8 Fahrenheit (at normal pressure). It becomes sky blue ice.

Helium stays a gas until very extreme temperatures. Helium becomes a liquid at 4.2 kelvin or -269 Celsius, or -452.11 Fahrenheit. If the temperature is reduced further by almost half to 2.17 Kelvin, or -270.98 Celsius, or -455.8 Fahrenheit, then Helium suddenly becomes a superfluid, exhibiting macroscopic quantum phenomena. It is so different from normal liquid Helium that it is called Helium II. Its heat conductivity (speed of heat/cold transfer) suddenly increases by one million, and the temperature will become the same throughout the liquid instantly. Even a big pool of liquid helium would almost instantly get the same temperature throughout, and the atoms will start behaving in unison. Regular bubbles can no longer exist (atom sized electron bubbles can exist though).

The liquid starts behaving in bizarre ways. If you place an open metal container of Helium II in a closed room the Helium II would climb out of the container and escape, and a thin film of Helium II would climb the walls and the ceiling. If the floor was made of metal or glazed tile the Helium II would remain on the floor. If the floor was made of unglazed tile or stone, it would leak right through the floor as if the floor was a sieve. If you get a whirlpool or fountain going it will keep going forever without any energy loss. In addition, it would also exhibit many quantum effects that are out of scope for this post.

Superfluid Liquids are Like Magic
Unlike ordinary liquids, helium II will creep along surfaces in order to reach an equal level; after a short while, the levels in the two containers will equalize. The Rollin film also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape. From : Hampel, Clifford A. (1968). The Encyclopedia of the Chemical Elements. New York: Van Nostrand Reinhold. pp. 256–268 (referenced by Wikipedia). Design: Aarchiba; SVG rendering: Júlio Reis, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0&gt;, via Wikimedia Commons

I consider this a super fact because this is a strange, surprising and not a well-known phenomenon. It is a quantum effect that you can observe with your own eyes. It is important because the discovery of superfluidity and its twin effect superconductivity are very important for science and might lead to revolutionizing energy transport in the future. It is no doubt that the phenomenon is real  (true), and it has been documented by numerous experiments and papers. It is described in thousands of textbooks, and I’ve observed the phenomenon with my own eyes (that is next).

Our Experiment with Superfluid Helium

During my first class in Quantum Physics, we performed experiments with liquid Helium. We started out by cooling helium using liquid nitrogen (colder than -196 Celsius or -321 Fahrenheit). Then using vacuum pumps, we kept cooling the Helium until it became liquid. We continued cooling it and we could see lots of bubbles and boiling as we kept going, and then it boiled extra much, and then very quickly the bubbles vanished, and the content of the entire glass container settled down and then stood perfectly still.

As 2.17 Kelvin was reached the viscosity (flow resistance) was instantly lowered with about one million times, and non-microscopic bubbles could no longer exist. The heat conductivity (the speed with which temperature spreads) increased by one million times. It means that the heat of a drop falling in one end of a swimming pool of Helium II would spread throughout the swimming pool in a second. Except, we only had a glass container in which sameness reigned throughout the liquid.

We continued doing experiments such as watching the Helium II climb walls inside the experimental setup, and of course the famous fountain. Insert a little metallic straw and watch a Helium fountain start to flow, by itself. Without any energy or pressure added, it just kept going by itself because no energy was lost either.

I can add that it was more of a demonstration than an experiment that we actively participated in because playing with extreme temperatures high or low is dangerous. If you’ve read this blog for a while you might remember when I put a Cesium-137 sample (800 times more radioactive than Plutonium-239) in my jeans pocket instead of back into its lead brick container and walked around with it a whole day. Or that time when I replaced a fuse for a 380 volt three phase powered laser with my finger because I was curious what would happen if I put my finger in there, and I was shocked, and it hurt. Students shouldn’t play with dangerous stuff.

Below is a one minute and forty four second YouTube video of a Superfluid / Helium II experiment showing an eternal fountain.

Below is a four minute explanation of a superfluid / Helium II experiment.

I can add that Helium II (super cold helium) is not the only superfluid but the easiest one to achieve.

Other Physics Related Superfacts

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