As you know, we are surrounded by extraterrestrial aliens. The Drake equation proves that the intelligent life must arise almost everywhere. However, we haven't seen any extraterrestrial friends yet. The question "where are they?" is known as the Fermi paradox.

Clearly, they must be hiding. Why?

Well, as you know, the fossil fuels are a global problem. All extraterrestrial civilizations realize that it is a problem they must wrestle with. Moreover, they need the optimum kind of energy. Most of them choose solar panels and they surround their whole star by solar panels, to capture all the emitted energy.

Still, the large artificial sphere surrounding the star - a Dyson sphere - is eventually heated to a new temperature. Its thermal radiation emits the same total energy (from the whole surface) as the star. You can see that the total power emitted per unit time

TThe fourth power of temperature comes from the well-known black body laws and the squared radius is the surface area. Note that the temperature goes like the inverse square root of the radius.^{4}R^{2}= const.

For example, the surface of the Sun has temperature around 5,000 K and it is 2 light seconds from the center. However, the Earth is around 500 light seconds from the Sun, about 250 times further than the surface. The corresponding temperature is therefore sqrt(250) = 15+epsilon times lower than the Sun's surface temperature. Numerically, 5000 K/15 = 300+epsilon K, close to the observed average temperature on the Earth. (You would have to deal with the albedo and the absorption by the atmosphere to get more accurate results.)

Let me use the figure 0 °C = 273.15 K for the temperature at the Earth's distance from the Sun to simplify the numbers. ;-)

What is the temperature of the Dyson spheres?

Now, the best civilizations realize that 300 K is still too warm. They only want to lose their energy at much lower temperatures, close to the LHC temperature of 1.9 K, relevant for the superconducting materials, in order to save the energy for cooling. So they build the Dyson spheres 10,000 astronomical units away from their Sun, a few light months. The temperature of the black body radiation emitted by this large sphere is sqrt(10,000) = 100 times lower than the temperature on Earth, around 2.7 K.

Can we see some evidence of these large Dyson spheres that the omnipresent extraterrestrial civilizations use to effectively capture their stellar energy? To prove the existence of the extraterrestrial civilization, we would have to detect thermal radiation at temperature 2.7 K. Can we do it? :-)

Now, as Cosmic Variance reports, Fermilab is paying for a project trying to find the extraterrestrial aliens via the thermal radiation of their Dyson spheres. But they're not ingenious enough to realize that the right Dyson spheres have a radius of 10,000 astronomical units (or smaller for less powerful stars) so that the temperature is 2.7 K instead of hundreds of Kelvin degrees.

The correct ingenious explanation is that, of course, we see the extraterrestrial aliens everywhere through the thermal radiation at 2.7 K. It has been called "cosmic microwave background" by the scientists who wanted to hide that they had discovered the aliens so they invented the so-called Big Bang. ;-) Of course, the only Big Bang occurred when these scientists' heads were hit by an alien spaceship. :-) As you can see, this comment explains the cosmic microwave background radiation. It explains dark matter, too: 80% of the stars host advanced intelligent life and are surrounded by the Dyson spheres so we don't see them. Instead, we see their microwave radiation.

*The density of energetically advanced extraterrestrial civilizations in different directions of the skies, visualized as the deviation from the cosmic average.*

As these civilizations are getting more powerful, they need more space, so they pay an energy tax to accelerate away from the other civilizations. This also explains the acceleration of the expansion of the Universe, previously incorrectly attributed to the "cosmological constant". If you think for a while, the extraterrestrial aliens explain everything. :-)

**Now seriously**

Freeman Dyson's independence and unusual theories are cool and I admire him for lots of reasons but frankly speaking, I am sometimes surprised that he doesn't believe the catastrophic global warming theory because the latter theory is rather similar to some of his unlikely theories.

The artificial origin of the cosmic microwave background above may look intriguing or literally ingenious: as a crackpot, your humble correspondent could literally make a hole into the world. ;-) But if you think about the "theory", there exists not a single rational yet nontrivial argument supporting the hypothesis about the extraterrestrial aliens in the text above (or elsewhere, for that matter).

The numbers - such as the temperature - only agree because I have arranged other numbers so that the results agree. And if you calculate other numbers, such as the predicted intensity of the thermal radiation, be sure that you will obtain a much lower number of photons than what we observe, even if you assume that most stars are surrounded by Dyson spheres. You will also predict wrong properties of the dark matter (the Dyson spheres) and many other things.

**How many civilizations are there?**

Recall that the Drake equation was proposed by Frank Drake (UCSC) in 1960 to calculate the number of extraterrestrial civilizations. This number is presented as the product of many factors such as the number of stars, the average number of planets per star, the fraction of planets that are good enough for some life, the probability for life to become intelligent, and so forth. See also the more sophisticated 2005 edition of the Drake equation.

Clearly, as long as this identity is rationally justifiable and accurate, it tells us exactly nothing. We just replace one completely unknown quantity by many almost completely unknown quantities. It is clear that we don't have solid data or arguments about most of them so the factorization can't help us to determine the number of extraterrestrial civilization. The correctly calculated uncertainty that we have about both sides of the equation is obviously identical. We haven't incorporated any nontrivial, independently derived and verified physical law(s) into the construction of the equation, so it is obvious that the equation cannot tell us anything besides tautologies.

If common sense is not enough to make a sensible estimate of the number of extraterrestrial civilizations, I find it obvious that this equation can't do the job, either.

The most reliable method to determine the number of advanced, intelligent, extraterrestrial civilizations that we have at this moment are the observations. We haven't seen any. It follows that according to the best evidence we can have, the number of intelligent civilizations in this Universe is rather low. We may even be the only ones in the Milky Way and perhaps in the observable Universe.

Many people are bothered by this likely conclusion. I am not bothered at all.

First of all, I completely subscribe to late Michael Crichton's comments about this issue explained in his 2003 talk at Caltech, Aliens Cause Global Warming. The Drake equation was the first example of a pseudoscientific, meaningless relationship that was used to irrationally distort the people's opinions. This equation was later recycled into the equally meaningless (and less original) I=PAT equation and many others.

Psychological illusions of the Drake equation

In the Drake equation, you are led to believe that all the dimensionless factors on the right hand side (such as the probability for pre-existing life to evolve into higher forms) are rather close to one. Well, most of them may be close to one. But there are so many of these factors that it is very plausible that some of them are much smaller than one. If just one of these factors equals 10^{-20} or two of them equal 10^{-10} or so, you can already see that the Sun is the only intelligent star in the Universe.

If you construct the equation out of 20 factors and each of them is around 0.1, you will reach the same conclusion.

And it is damn possible. There are just too many weak links in the argument that life is inevitable. The first simple proteins or DNA molecules - or their survival - simply may be very unlikely and depend on rare reactions or a fine ratio of various elements in the environment. I am not claiming that all of these "evolutionary steps" require miracles.

But I am surely claiming that the belief that all of them - 20 out of 20 - are pretty much inevitable is just an unsubstantiated prejudice. It is on the very same footing as religions that claim that the man must be the only decent creation of God and that the creation was a true miracle. There is no scientific evidence for either - the uniqueness of human beings or their membership in a huge set of clever beings in this Universe.

Some people think that by believing a scenario that is "opposite" to the conventional and popular religions, they must get closer to the truth. But it's just not the case. Neither of these ideologies is justified by scientific evidence.

The Drake equation leads some gullible people to believe that all the factors on the right hand side must have comparable values because they "look" similar and each of them is represented by one letter. And because the value for some of them may be argued to be close to one, the gullible people believe that all of them must be close to one, and the resulting number of civilizations is therefore high, too. But that's wrong. The factors are very different and only a full proof of a high value of each of them could make the factorization useful. Otherwise we're just dividing the (constant) ignorance into many baskets.

Much like the blonde woman who only wants her pizza to be cut to four slices because she couldn't eat as many as eight of them, and much like Zeno who was dividing the trajectory of an arrow into infinitely many pieces to prove that the arrow was always at rest, some people seem to think that if they divide an unknown number into many factors - or if they split a big mistake in an argument into many smaller errors :-) - the original ignorance or the mistake disappears. But it doesn't change at all.

Again, we don't know how many intelligent civilizations are there in this Galaxy (or the Universe) and the most solid currently available method to determine the answer, namely the observations, indicate that the number is low. There exists no paradox and no inconsistency of this conclusion with the known laws of physics and the term "Fermi paradox" is a misnomer.

Frankly speaking, I am equally unimpressed with the ideas such as the Dyson spheres. The project to surround the whole star by solar panels is surely about bad economics and management. But I think it is a case of bad fundamental physics, too. And I don't think that the discovery of a new thermal radiation in the Universe would prove the existence of an extraterrestrial civilization. It could also be a red-shifted thermal radiation of a different origin or e.g. the Hawking radiation from some black holes.

**Criticism of Dyson spheres**

It is clear that these spheres don't saturate any fundamental physical bound: they're ordinary pieces of low-energy, low-brow matter, after all. They're no black holes - objects that maximize the entropy in a volume and minimize the scrambling time, among many other things. And for low-energy, low-brow physics, it is the applications in everyday life - and economics - that decides which projects would be followed by a hypothetical extraterrestrial civilization.

And indeed, I don't think that the solar panels are the ultimate achievement of the technology that would dominate the millions of years in the future of mankind. In fact, I find this idea to be downright ludicrous. For example, artificial thermonuclear fusion is possible - and we may be just years (or decades) from a commercial realization of this technology. And better civilizations could get their energy from a catalyzed proton decay or microscopic black holes that radiate and violate the baryon number conservation. The energy obtained from the Sun is just "too slow", especially if you put the solar panels too far. The Sun is too ordinary and too slow.

So I also think that even if an intelligent civilization decided that it wants to use the solar panel paradigm and surround the whole star, it would try to put the solar panels closer to the star, not further, because it would need a smaller amount of the material and the energy per unit area of these solar panels would be higher. So I disagree that sensible civilizations would build this sphere 10,000 AU or 1 AU away from the star. It would be much closer. After all, what we usually want is concentrated energy.

By the way, the spherical shape of the sphere seems unlikely to me, too. Even if one assumes that the civilization would choose solar panels that are very distant from the star, the optimization problem that its wise economists would be solving would probably not result in a spherical shape. It would be irregular because parts of the structure would be easier to be built closer while others would be naturally constructed further from the star. There are many other points that seem completely arbitrary.

Let me conclude with this comment: the idea that such shields should be spherical was accepted because Freeman Dyson and others didn't want to do too much work and they picked the spherical solution that looked simple. In reality, the extraterrestrial engineers, managers, and politicians would be analyzing a very complicated engineering, logistical, and economical problem - it is not cheap to surround the Solar System by stuff - and they would almost certainly reach a completely different conclusion than the "simple" one.

The Dyson sphere, much like the idea of a dangerous greenhouse effect, is about the irrational overhyping of one completely random conceivable effect or plan or threat that is sociologically promoted to the most important paradigm in a whole quasi-scientific discipline - even though there are probably dozens or hundreds of (mostly unknown) effects that are more important and thousands of more reasonable explanations what may be going on.

We should only say that a discipline is "all about one effect" (exobiology about Dyson spheres, climate science about the greenhouse effect) if we actually have some evidence for such an assumption. And if the discipline is full of seemingly complex phenomena that we simply can't predict and verify well, or if the observations even disagree with our existing hypotheses, we shouldn't assume that we know what the essential phenomena are.

**I = PAT**

Now, let me talk about an environmental sibling of the Drake equation, the I = PAT equation. It is a kindergarten stupidity developed in the 1970s by three prominent eco-socialist crackpots, Barry Commoner, Paul R. Ehrlich, and John Holdren. (All of them are still alive and two of them are still prominent in the far-left and even Academic circles.) You can see that their way of calculating such quantities wasn't original: it was copied from the 1960 Drake equation.

What does the equation say? It says that the human impact on the environment, I, is the product of three quantities. Now, it is important to decide whether you want to hear the correct (but inconsequential) version of the equation or the consequential (but incorrect) version of the equation. They're very different but the confusion of these two versions of these equations is the main reason why some people found this stupidity so useful for their ideology.

The correct version of the equation divides the total impact I - whatever it is exactly supposed to be - to individual people. So the total impact per capita is I/P where P is the population. Now, it is clear that the impact of different people is different. You may imagine or assume (a point to be discussed later) that the richer people's environmental footprint is larger: in some very simple model, the footprint (per year) is proportional to the consumption (in dollars per year).

So instead of dividing the impact I (per year) to the people, we divide it to the consumed dollars (per year). The number of consumed dollars (per year) may be written as the product PA where P is the population and A is the average consumption. Finally, we use the letter T for the coefficient, i.e. the impact per dollar consumed (per year). I=PAT becomes a tautology because T=I/PA is really a definition of T.

However, such a tautology wouldn't be terribly useful for the eco-socialist crackpots. What's more useful are the (wrong) assumptions needed to argue that the equation is useful and the misinterpretations of the letters. Why is it useful for them? Well, they say that the variable I measures something wrong. It is the most important measure of "wrongness" in their whole ideology. To reduce I, they must reduce either P or A or T or several of them. They want less people, poorer people, and more "silent" people in order to protect the environment.

When this equation is used in this practical way, A is interpreted as the "affluence" and T as "technology": that's where the letters come from. Affluence and technology is bad, they say!

Have they proven that population, affluence, and technology are bad?

But of course, such a conclusion doesn't follow from the tautological equation above. Recall that T in the correct equation was not technology in any sense. T was the environmental impact per unit dollar of consumption (per year). That's something different than "technology" and these things are actually often a decreasing, not increasing, function of one another.

The assumptions leading to the "derivation" of the I=PAT equation were contrived, too. The money were incorporated in a very unnatural way. It is not true that the environmental impact increases with consumption in dollars - which is what would make it natural to write this law as a proportionality law. Instead, there exists something like the environmental Kuznets curve. The impact increases for very poor people - because extremely poor people have a small impact, indeed.

But if the people become wealthy enough and they no longer have to work much for their bare survival, the environmental impact decreases again because they start to care about their healthy environment and the poor innocent animals and plants. The relationship between the average/expected impact and consumption is highly nonlinear (and context-dependent) and it is, in fact, not even a uniformly increasing function. Because of all these reasons, the coefficient "T" is nothing else than "I/PA", how it was defined, and it doesn't have any simple interpretation.

As long as misleading interpretations of the equation are avoided, it simply says that I/PA = I/PA.

There is no simple way to see whether "T" increases or decreases if a policy is adopted. There is no rational reason to assume that "T" is constant in a given situation because it's far too complicated a quantity. The value of "T" is not a universal, calculable constant in any sense. You can't independently adjust P, A, T. The I=PAT equation is a meaningless tautology that obviously cannot have any practical implications for the people who haven't lost their mind. The eco-socialists are nasty folks who want to treat the individuals as equal, gray, destructive pieces of protein whose all quantities follow proportionality laws. But the reality is fortunately very different.

We should stop using equations with (many) highly uncertain, unmeasurable, and uninterpretable factors whose only goal is to confuse the gullible people among us by dividing a big mistake into many smaller mistakes and by creating many new opportunities for deception and confusion.

And that's the memo.

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