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.
This post is not another super fact but a blog note about the blog and a request for opinions. My most recent post included three super facts combined into one post. The three super facts were:
There has been a steep decline in extreme poverty
There has been a steep decline in child mortality
War and violence have declined
The post became very long. It had more than 2,000 words and several graphs filled with additional text and data. In addition, I rushed the third super fact. The discussion of the third super fact was muddy, incomplete, and it lacked references. Therefore, I deleted the third super fact. I think that was the right thing to do, especially since I had planned a separate super fact entry for it anyway with the title “We are living in relatively peaceful times”. I will write that post for it soon.
However, I’ve realized that some of my other posts have problems as well. The second half of the post titled “Two events may be simultaneous for some but not for others” feature equations and complex reasoning that physics nerds may appreciate but not typical readers. I don’t think I need to delete that section but, in the future, I need separate such sections from the rest and make it clear that I don’t expect readers to read that, well unless they are physics or math nerds, etc.
Expand your mind. Smash your old beliefs with new surprising facts, so called super facts. But there’s no need to confuse or bore your mind. Shutterstock ID: 1685660680 by MattL_Images
So, I am wondering what you all think about this and if you have suggestions or opinions on how I can improve my super fact posts. Blog notes are very much welcome.
Superfact 3 : Economic Externalities Are Spoilers of Free Markets
Economic externalities are spoilers of free markets. So called externalities result in unfettered free markets being non-optimal and can render the correct government intervention more effective even from a purely economic perspective. This comes as a big surprise to the market fundamentalists who believe that an unfettered free market is always the best approach for the economy.
An economic externality or external cost is an indirect cost or benefit to an uninvolved third party that arises as an effect of economic activities. They are unpriced components of market transactions.
An example is the gasoline you buy. Burning the gasoline causes pollution that harms other people including those who do not own cars, future generations, and it harms the environment including animals. Society incurs a cost from that pollution that you don’t pay for at the pump. The gasoline producers and vendors do not pay for it either. Unless you add a tax or make other adjustments the act of polluting is free of charge, even though there is a real cost associated with it. It is a cost that is invisible to unfettered “free markets”. It is a market failure.
Note I am putting “free markets” in quotes because the free market does not exist all by itself. It exists within a framework of laws, a banking system, and entities such as limited liability corporations, etc.
Pollution is an example of a negative externality. Photo by Chris LeBoutillier on Pexels.com
Economic Externalities
The existence of economic externalities is entirely uncontroversial among economists, including laissez-faire (libertarian) economists such as Milton Friedman, Friedrich Hayek, and Ludwig von Mises, even though Ludwig von Mises said that they arise from lack of “clear personal property definition.” In fact, Milton Friedman, Nobel prize winner in economics, and a leading anti-tax champion, stated that pollution met the test for when government should act, but that when it did so, it should use market principles to the greatest extent possible — as with a pollution tax. The unfettered free market is not optimal.
This simplified supply and demand graph shows two different graphs in blue. One for the private/production cost per unit of a goods and a second that also includes the cost of the externality.
However, in my experience the existence of economic externalities is unwelcome news to less educated market fundamentalists, including many libertarian leaning politicians. I don’t have a Gallup poll to back this up, but I believe it is correct to say that economic externalities are controversial among a significant portion of the public despite being a universally accepted and a fundamental concept of economic science. Externalities are known to exist and that is not an easy pill to swallow for some.
The existence of externalities is sometimes a hard pill to swallow. Photo by Artem Podrez on Pexels.comThis simplified supply and demand graph also shows two different graphs in blue. Again, one for the private/production cost per unit of a goods and a second that also includes the cost of the externality. In this case the cost for production goes down as quantity increases but the cost of the externality goes up per unit perhaps because increasingly damaging production methods are used as the quantity increases.
In the simple supply-demand graphs above we see how the price of a product per unit (private cost / or production cost) varies with the increased quantities produced. In the first graph, as the production quantity increases the production cost per unit goes up perhaps because labor and other resources get increasingly rare. In the second graph, as the production quantity increases the production cost per unit goes down perhaps because production becomes more efficient with increased quantities.
In both cases demand goes down with quantity (the red demand curve/line) because fewer people want to buy more of the product as the quantity increases. In both cases the externality adds a cost. In this case the externality cost per unit goes up because increasingly damaging production methods are used as the quantity increases. There are many possible examples of these graphs, but the point is that the externality adds a cost that reduces quantity sold in a free market, assuming the cost of the externality is accounted for.
Economic Externalities In The Real Word
Unfortunately, in the real world, externalities are often not accounted for, and figuring out the real cost of an externality is a thorny issue. However, if we know the cost of the externality and have a way of accounting for it, perhaps via tax or a fee, then we would reach a new equilibrium, a new optimal price for the product that will include the social cost. I can add that in the 1920’s an economist Arthur Pigou argued that a tax, equal to the marginal damage or marginal external cost on negative externalities could be used to reduce their incidence to an efficient level.
Notice this tax is not for redistributing wealth or bringing revenue for the government but to reduce economic harm to society. There are other ways to address the problem, but this type of tax is called a Pigouvian tax.
How a Pigouvian tax can reduce economic harm to society. Photo by Pixabay on Pexels.com
Finally, I would like to give a few examples of negative and positive externalities. Negative externalities could be :
Pollution
Climate Change
Depletion of fish due to overfishing
Depletion of other resources
Overuse of antibiotics
Spam email
Some positive externalities are :
A beekeeper keeps the bees for their honey, but a side effect or externality is the pollination of surrounding crops by the bees.
Education (societal benefits beyond the individual).
Research and development.
Innovations
Scientific discoveries
Vaccination
When a beekeeper keeps bees for their honey, a side effect is the pollination of surrounding crops by the bees. This is an example of a positive externality. Photo by Pixabay on Pexels.com
Some things cannot be known. There are things in mathematics and about our physical world that we know can never be known. For example, we can’t simultaneously know both the exact speed and the exact position of small particles (Heisenberg uncertainty principle). This is not because of a limitation of our instruments. It is a fundamental property of the Universe. But there are more examples of unattainable knowledge. In mathematics there are true statements that can never be proven.
“This”Some Things Cannot be Known” is the third post on my super-factful blog. As mentioned, the goal of this blog is to create a long list of facts that are important and known to be true, yet either disputed by large segments of the public or highly surprising or misunderstood by many. They are facts that are so unnecessarily controversial or astounding that I refer to them as super-facts.
This post is about a fact that may be highly surprising to many. Science knows a lot. People without a solid education in science are often surprised when they find out about some of the amazing things we actually do know.
For example, just by studying the light from a distant star, we can determine what elements it is composed of. The star may be composed of 71% hydrogen, 27% helium, 1% Lithium, and 1% other elements, and we can know that just from its light. We can also determine its temperature, the distance to the star, how it is moving compared to us, where it will be 2.5 million years from now, roughly its age and longevity, and more. 150 years ago, we could not have dreamed of this capability.
We can know so much about a star from its light. Shutter Stock Illustration ID: 566774353 by Nostalgia for Infinity.
However, there are also many things we don’t know, and what may come as a big surprise, we know that there are things we can never know, no matter how advanced science becomes. Infinite experimentation, super intelligence, a quintillion super geniuses, infinite time, we simply cannot acquire some knowledge. The universe itself forbids some knowledge. It also means that the statement “nothing is impossible” is false.
At least my natural reaction to such a claim is, “come on you can’t say that with certainty”, and I expect many others will feel the same. However, the reason some knowledge will never be attainable is that physical laws as well as mathematics and logic forbid some knowledge. Some things are not meant to be known. I will give four examples in the four sections below: the event horizon, the Heisenberg uncertainty principle, beyond the observable Universe, and Gödels incompleteness theorem.
The Event Horizon of a Black Hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light, can escape it. The boundary of no escape is called the event horizon. If you pass the event horizon you cannot come back out no matter how much energy, you expand. Nothing can escape, no matter, no radiation, not light or other electromagnetic radiation, and no information. Nothing at all can escape. The curvature of time and space itself forbids it.
I should add that right at the event horizon, there is so called Hawking radiation, but without complicating things it is not the same thing as escaping a black hole. You can guess from physical laws what might be inside, but you can never observe and report what is inside to planet Earth.
Black Hole Stock Photo ID: 2024419973 by Elena11
I would also like to add some basic information about black holes. Some black holes are formed when large stars die and collapse. These black holes are estimated to have a mass of five to several tens of solar masses. However, there are also super massive black holes that reside in the center of galaxies.
The super massive black hole at the center of our galaxy, the Milky Way, is called Sagittarius A* and is estimated to have a mass of four million times the mass of our sun. The largest known supermassive black hole TON 618 is 66 billion times more massive than our sun. There are an estimated 100 million black holes in our own galaxy, the Milky Way. One interesting fact is that celestial objects can orbit a black hole, just like planets orbit the sun, but as you get too close you will rush, at the speed of light, into the depths of the black hole.
The Heisenberg uncertainty principle
The Heisenberg uncertainty principle states that it’s not possible to know the position and momentum of an object with perfect accuracy at the same time. Another way of saying that is that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy. The formula is: dX * dP >= h/4pi , or uncertainty in position (dX) times uncertainty in momentum (dP) is larger than half of Planck’s constant. There is also an energy and time precision limit : dT * dE >= h/4pi.
These equations basically means that there are no perfectly exact measurements or knowledge. Everything is a bit fuzzy. Planck’s constant is very small, so Heisenberg uncertainty principle does not matter for everyday objects, but it matters when sizes are very small (positions, energies, etc.) Note, Heisenberg uncertainty principle is not because of a limitation of our equipment, but a limit set by a law of physics. It is a limitation set by the Universe if you will.
Heisenberg uncertainty principle Shutter Stock Vector ID: 2380436193 by Sasha701
Beyond the observable Universe
The observable universe is a ball-shaped region of the universe consisting of all matter that currently can be observed from Earth or its space-based telescopes. The radius of the observable universe is 46.6 billion light-years. The size of the observable universe is growing. Unfortunately, at those distances, space itself is stretching/expanding faster than the speed of light. Since no signal or information can travel faster than the speed of light we are losing, not gaining, celestial objects from the observable universe.
In the past we’ve lost many galaxies this way. Since the expansion is accelerating, we will keep losing more galaxies beyond the boundary of the universe and some galaxies were always lost (with respect to observation). I can add that the universe may be infinite.
A view of a galaxy full of stars. Photo by Pixabay on Pexels.com
If we are wrong about the fact that the expansion of the universe is accelerating, then perhaps we can observe more galaxies in the future. But if not, then there are galaxies that we have never observed, galaxies that we can never observe, and there are galaxies that will become unobservable in the future. Depending on the size of the universe we may never be able to observe more than an infinitesimally small portion of the universe. Again, the universe is stopping us from knowing something.
Gödels incompleteness theorem(s)
The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. In other words, to find a complete and consistent set of axioms for all mathematics is impossible. There are forever hidden truths in mathematics. For the case of natural numbers this means that there will always be statements about natural numbers that are true, but that are unprovable. I can add that there is also a second incompleteness theorem that states that a formal system cannot prove that the system itself is consistent. Basically, there are limits to mathematics set by logic. And some things cannot be known.
I have a book on Gödels incompleteness theorem, which I have not read, but I will read it before I make a post about it. Photo by Andrea Piacquadio on Pexels.com
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