Russels Paradox

Super fact 111 : Russel’s Paradox is a logical contradiction discovered in 1901 that showed that the mathematical discipline of “Set Theory” was fundamentally flawed. Mathematicians had naively assumed that any definable property can be used to form a collection (or set) of items, but that is not true. An example of the Paradox is “A male barber shaves all men who do not shave themselves and only men who do not shave themselves. Does he shave himself?” Both “yes” and “no” are impossible answers. That is an example of an impossible set. Set theory needed an exclusion of such impossible sets.

Bearded client visiting barber shop. Barber scissors and straight razor, barber shop, suit. Vintage barber shop, shaving. Portrait bearded man. Mustache men. Brutal guy, scissors, straight razor. | Russels Paradox
Bearded client visiting barber shop. Shutterstock asset id: asset id: 1821348236 by Body Stock.

Russell’s paradox is a famous logical contradiction discovered by the philosopher and mathematician Bertrand Russell in 1901. To solve the contradiction, you need to remove the assumption that any property can form a set. In other words, not every set is possible. Basically, self-reference cannot be allowed.

To take the example above “A male barber who shaves all men who do not shave themselves and only men who do not shave themselves.” Is something that cannot exist. If the barber shaves himself then he is shaving someone who shaves himself, which was not allowed. If the barber does not shave himself, then he is not shaving all the men who do not shave themselves. Either way, it does not work. Such a barber cannot exist. In general, you cannot define a set anyway you like.

I consider this a super fact because it shows that contractions can be hidden even in mathematical disciplines, and it is important because you certainly don’t want contradictions hidden in a mathematical or scientific discipline. Contradictions lead to more contradictions and lots of problems.

It is a black and white photo of the mathematician Bertrand Russel.
Bertrand Russell portrait. Honourable Bertrand Russell.jpg: Photographer not identifiedderivative work: Conquistador, Public domain, via Wikimedia Commons

A Crazy Barber Story Involving Our Children

This happened soon after the September 11 attacks in 2001. In addition to planes crashing into buildings, there were attempts at biological warfare by spreading anthrax through the postal service. This is something we paid special attention to at my work because we were making postal sorting machines. It is also the reason I do not like people who write addresses in cursive.

Anyway, my wife called me at work, and she was very upset because our daughter’s hair was falling out. She touched her hair and it just fell off. She did not know what could be causing her hair to suddenly fall out, but she thought that it might have been biological warfare. I told her to call our doctor who had the good sense of suggesting that perhaps the kids had been playing barbershop. As it turned out they had. Our son confessed to cutting off our daughter’s hair. He had realized that this was bad, so he tried to put her hair back as well as he could. Afterwards, she was walking around with loose hair on top and that’s when my wife found her.

Was our son the barber who cut everyone’s hair and only those who did not cut their own hair? No because that barber can’t exist. Some sets can’t exist and you need to include that in the definition of what a set is, or in this case what kind of groups of barbers you can have.
Our son is cutting his sisters hair. The picture is generated with the help of ChatGPT.



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The Unfolding Solar Energy Revolution

The goal of this blog is to create a list of what I call super facts. Super facts are important true facts that nevertheless are surprising to many, misunderstood, or disputed among the non-experts. They are special facts that we all can learn something important from. However, I also make posts that are not super facts but feature other interesting information, such as this book review and book recommendation. I should say that this book is not written by a scientist but an environmentalist, and he did not provide references for his hundreds of factual claims. However, I fact checked at least 20 claims and found only one that was not entirely correct, so I think his facts are for the part correct. The book is:

Here Comes the Sun: A Last Chance for the Climate and a Fresh Chance for Civilization by Bill McKibben

Below I am listing the four versions of this book. I bought the hardback version.

  • Hardback –  Publisher : W. W. Norton & Company (August 19, 2025), ISBN-10 : 1324106239, ISBN-13 : 978-1324106234, 224 pages, item weight : 12 ounces, dimensions : 5.8 x 0.9 x 8.6 inches. It costs $15.91on US Amazon. Click here to order it from Amazon.com.
  • Paperback –  Publisher : W. W. Norton & Company (August 11, 2026), ISBN-10 : 1324130628, ISBN-13 : 978-1324130628, 240 pages, item weight : 13 ounces, dimensions : 1 x 5.5 x 8.25 inches. It costs $19.99 on US Amazon. Click here to order it from Amazon.com.
  • Kindle –  Publisher : W. W. Norton & Company (August 19, 2025), ASIN : B0DXQGBM4Z, 220 pages, it costs $9.40 on US Amazon. Click here to order it from Amazon.com.
  • Audiobook – Publisher : Highbridge Audio (August 19, 2025), ASIN : B0F95QL1C2, Listening length : 7 hours and 36 minutes. $0.00 with membership. Click here to order it from Amazon.com.
The front cover of Here Comes the Sun: A Last Chance for the Climate and a Fresh Chance for Civilization by Bill McKibben. | The Unfolding Solar Energy Revolution
The front cover of Here Comes the Sun: A Last Chance for the Climate and a Fresh Chance for Civilization by Bill McKibben. Click on the image to go to the Amazon page for the hardback version of the book.

Amazon’s Description of the Book

From the acclaimed environmentalist, a call to harness the power of the sun and rewrite our scientific, economic, and political future.

Our climate, and our democracy, are melting down. But Bill McKibben, one of the first to sound the alarm about the climate crisis, insists the moment is also full of possibility. Energy from the sun and wind is suddenly the cheapest power on the planet and growing faster than any energy source in history―if we can keep accelerating the pace, we have a chance.

Here Comes the Sun tells the story of the sudden spike in power from the sun and wind―and the desperate fight of the fossil fuel industry and their politicians to hold this new power at bay. From the everyday citizens who installed solar panels equal to a third of Pakistan’s electric grid in a year to the world’s sixth-largest economy―California―nearly halving its use of natural gas in the last two years, Bill McKibben traces the arrival of plentiful, inexpensive solar energy. And he shows how solar power is more than just a path out of the climate crisis: it is a chance to reorder the world on saner and more humane grounds. You can’t hoard solar energy or hold it in reserves―it’s available to all.

There’s no guarantee we can make this change in time, but there is a hope―in McKibben’s eyes, our best hope for a new civilization: one that looks up to the sun, every day, as the star that fuels our world.

This is my five-star review for Here Comes the Sun

The Spectacular Success of Renewables

Here comes the sun tells the story of the spectacular success of renewables around the world, especially the success of solar power and wind power, with a special emphasis on solar power. The success of renewables was one reason that the IPCC will likely retire the RCP8.5 emissions scenario. The RCP8.5 emissions scenario, which was the extremely bad emissions scenario, was never very likely to begin with, but the fact that the world, including China, is turning away from coal and fossil fuels made this scenario implausible as they stated. I am not sure whether Bill McKibben could have predicted this when he wrote this book, but I think this recent event makes this book very relevant now in 2026.

The book describes a very interesting situation for our world and contains interesting personal anecdotes and is written in a positive and optimistic way. However, I was delighted that the book was full of interesting facts, for example, in 2024 92.5% of all new electricity bought online around the world came from renewables. Other facts are, Chinese emissions are dropping. He tells us that forty percent of the world’s ship traffic consists of moving coal and gas back and forth across the ocean to be burned. He states that the entire continent of Africa has barely produced 3% of the greenhouse gases warming the atmosphere, whilst they are likely to bear the brunt of the effects of global warming.

Other interesting facts are; Chinese citizens can expect to live on average 2.2 years longer than they would have a decade ago, due to the sharp drop in pollution (thanks to renewables and EVs). Dealing with cleantech waste is a small problem compared to fossil fuels, and we have enough minerals, especially considering recycling. He tells us about various physics facts related to the sun, how our health is effected by the sun, the history of the day “Sunday”, sun worship in the ancient world, and other sun related facts.

He reviews the history of fossil fuels and renewables, particularly solar power, and the how the fossil fuel industry and certain politicians are fighting against renewables with disinformation and bad faith arguments. He explains the problems with fossil fuels and the dangers they pose, which is not just limited to climate change. He also explains a little bit about why we know that fossil fuels are causing global warming / climate change, why we need to keep pushing for renewables despite their success. He states that because fossil fuels themselves are easy to concentrate, they often yield authoritarian outcomes.

In the past renewables were an expensive alternative and fossil fuels cheap, but that situation has been reversed. He explains why EVs are in general cleaner and better for the environment than cars with internal combustion engines. He explains how we get around the intermittence issue with wind and solar and that batteries are getting much cheaper and environmentally friendlier, and why a lot of negative information you hear about batteries is not true anymore. Salt batteries is an example of an emerging technology.

My only concern with the book is that Bill McKibben is not a scientist. He is an activist. Because of that it is extra important that he provides references to reputable sources for all his claims. Typically, scientists provide references to their claims even though you in general can trust scientists more than activists. However, Bill McKibben provided no references to any of his several hundred facts and claims, except for some general and vague information in the back about where he got his information from.

I should say that I fact checked about two dozen of his claims and found only one that was not entirely accurate, so overall I trust this book. The book is easy, lighthearted and positive reading. It is not a heavy science book, the book was well organized, and he is a good author. Therefore, I highly recommend this book.

The back cover of Here Comes the Sun: A Last Chance for the Climate and a Fresh Chance for Civilization by Bill McKibben.
The back cover of Here Comes the Sun: A Last Chance for the Climate and a Fresh Chance for Civilization by Bill McKibben. Click on the image to go to the Amazon page for the paperback version of the book.

A related super fact is “The Unfolding Clean Energy Revolution”




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EVs are Replacing the Internal Combustion Engine

Superfact 107: Electric vehicles are rapidly replacing the internal combustion engine (ICE cars) and are becoming commonplace around the world. It is analogous to how cars once replaced the horse and buggy.

In Norway close to 100% of all new cars sold in 2025 were electric vehicles. Around the world a substantial percentage of new cars sold in 2025 were electric vehicles. This phenomenon is not as visible here in the US, where I live, but if you travel, you’ll notice.

The graphs below show that the share of new cars that were sold in 2025 that were EVs was substantial, but more importantly there is a sharp upward slope of the curve(s). The share of new cars sold in 2025 that were electric was in respective region or country: Norway 97%, Denmark 71%, China 53%, European Union 27%, World 25%, the United States 10%. The graphs are taken from this page on the Our World in Data web page. I encourage you to play around with the interactive graphs. You can read more about new cars sales in Norway here.

EVs are Replacing the Internal Combustion Engine

It should be noted that electric cars include fully battery-electric and plug-in hybrids. With battery-electric cars is meant cars or other vehicles that are powered entirely by an electric motor and battery, instead of an internal combustion engine. With plug-in hybrid is meant cars or other vehicles that have a rechargeable battery and electric motor, and an internal combustion engine. The battery in plug-in hybrids is smaller and has a shorter range than battery-electric cars, so over longer distances, the car starts running on gasoline once the battery has run out.

This is a fact that is important, and that likely comes as a surprise to people living in countries that are lagging in this transition, such as the United States. Therefore, I consider it a super fact.

The Share of EVs

The sharp increase in the sale of electric cars is a recent phenomenon and therefore there are still a lot of ICE cars on the roads. Therefore, there is a significant difference between the share of electric vehicles on the road and the share of new cars sales being EVs. The share of electric cars on the roads in 2024 was in the United States 2.7%, in the world 4.5%, in China 11%, in Sweden 13% and in Norway 32%. See the graph below.

The graph shows the share of cars currently in use that are electric for the world, the United States, China, Sweden and Norway.
Share of cars currently in use that are electric, 2010 to 2024. Data source: International Energy Agency Global EV Outlook 2025.   OurWorldinData.org/energy | CC BY

The graph below illustrates the sales of fully battery-electric cars versus plug-in hybrids.

EVs are Replacing the Internal Combustion Engine

The bar graph below is an alternative illustration showing the share of  new cars sold that are electric in 2024 for the world and 8 countries.

The bar graph shows the share of new cars sold that are electric in 2024 for the world and 8 countries. The numbers are India 2.1%, the United States 10%, Germany 19%, European Union 21%, United Kingdom 28%, China 48%. Sweden 58%, Norway 92%, and the World 22%
Share of new cars sold that are electric, 2024. Electric cars include fully battery-electric and plug-in hybrids. Data source: International Energy Agency  Global EV Outlook 2025.  OurWorldinData.org | CC BY

This article states that there are now more new electric cars sold in the EU than ICEs. However, it should be noted that they include hybrids (non-plug-in) in this number.

Are EVs cleaner than ICE cars ?

Yes, they are, for the most part. EV Cars emit less pollution than Internal Combustion Engine Cars, even considering manufacturing, disposal and EV Cars being charged by dirty grids. Basically, this is because burning oil to move a vehicle creates significantly more heat than motion.

It all depends on how dirty the grid is. This map shows the average EV as a gasoline MPG equivalent for the different grid networks in the United States in 2020. As you can see an average EV corresponds to a 76 mpg gas car in Texas (with the ERCOT) grid, which is much cleaner than almost any gasoline car. Also, the ERCOT grid has become cleaner since 2020. The average for the United States is 91 mpg. There are a couple of grids for which owning an EV may not be cleaner. I created another super fact post that explains the details called: super fact (29) EV Cars Indeed Emit Less Carbon Pollution. You can read more here.

There are concerns about the mining of minerals for EV cars, such as cobalt and lithium, which has an environmental impact. However, this environmental impact should be compared to the environmental impact caused by the drilling and transport of oil (and the burning of gas/oil). In general, the environmental impact of EVs is considered much less. In addition, EV batteries last a long time, and 95% to 98% of the valuable materials in EV batteries (lithium, cobalt, nickel, and copper.) can be recycled/recovered. You can read about other EV myths here. However, this is probably a topic for a future super-fact.


Craigavad a scientist and fellow blogger, wrote a very well balanced and insightful article on the issue of the carbon cost of electric vehicles. I encourage you to read it : “The Carbon Cost of Electric Cars: are they worth it?”




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My Post We Can See What Stars Are Made of Selected for Freshly Pressed

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The Sun is White but the Sky steals its Blue

Superfact 105: The Sun is white, but the Sky steals its Blue is a poetic way of saying that the sun’s light is scattered by the atmosphere giving the Sun a yellowish tint as well as giving us our blue sky. From space the sun looks completely white.

A bright white sun is setting over Earth. | The Sun is White but the Sky steals its Blue
Sunset from the International Space Station by NASA

Viewed from space the sun is entirely white. White light consists of a mix of all the colors of the rainbow. However, viewed from earth the sun has a yellow tint, which gets more pronounced, it even dips into orange, as the sun nears sunset. That does not happen in space as can be seen below in the one minute sunset timelapse video taken from the International Space Station.

Sunset Timelapse from the International Space Station

On earth the sunset looks more like something in the picture below.

The sun is setting over distant mountains. There are some clouds, a forest, and field in the foreground. The sun has a yellow tint; the clouds are slightly yellow-orange and sky above is blue. | The Sun is White but the Sky steals its Blue
The sky dusk has a dramatic background featuring a summer season golden sunset landscape. The light is at the horizon is an orange and yellow color with blue sky above. Shutterstock asset id: 2670235703 by Nature Peaceful

The sun is a so called yellow dwarf star, or a G-type main-sequence star. The term yellow dwarf is a bit of a misnomer, because they range in color from white, for more luminous G-types like the Sun, to only very slightly yellowish for less massive and less luminous G-type main-sequence stars. The sun emits all the colors of the rainbow simultaneously, but the most dominant color is green. However, this looks white to us.

When sunlight enters Earth’s atmosphere, tiny air molecules scatter shorter, blue wavelengths of light in all directions. This scattering is what makes the sky look blue. This is called Rayleigh scattering. Because much of the blue light is removed, the remaining wavelengths of light that reach your eyes combine to make the sun appear yellow. This is a super fact because it is a basic but surprising fact, and we know it is true.

Rayleigh Scattering

The blue color of the sky is caused by Rayleigh scattering of sunlight by the gases in the Earth’s atmosphere. The image below shows the degree to which Rayleigh scattering occurs at different wavelengths / frequencies of light. Blue has the shortest wavelength (highest frequency) for visible light and red the longest (lowest frequency). The curve shows that blue light scatters more than red light. It should be noted that UV light (not shown) scatter even more. The scattering curve shown is calculated for sunlight passing vertically through the atmosphere.

The graph shows the amount of scattering going from shorter wavelengths (higher frequences) on the left, to longer wavelengths (lower frequences) on the right. Blue has shorter wavelengths and red has longer wavelengths. The graph shows that blue scatter the most.
Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light. Robert A. Rohde derivative work:KES47 (talk) (converted to SVG)., CC BY-SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/, via Wikimedia Commons.



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