The problem of the cosmological constant

Albert Einstein

The value of the cosmological constant Λ in Einstein's equation has gone through many vicissitudes and alternatives:

The end of the universe

Will the cosmos expand indefinitely, or will its expansion stop one day? What could stop it? It is clear only gravity could do it. The expansion of the universe, which makes galaxies separate, goes against the gravitational attraction, which tries to hold all bodies together.

If we look at Einstein's cosmic equation of general relativity, the question of whether gravity will succeed in stopping the expansion of the universe depends on the relative values and signs of the three terms in the equation. Depending on them, three things can happen:

COVID-19 vaccines

The four main vaccines against COVID-19 can be classified into the following groups:

a)      Astra Zeneca and Janssen: Adenoviruses genetically modified to produce a protein, a part of the coronavirus causing COVID-19. This protein should give rise to the manufacture of antibodies to fight it, which would also attack the virus if it is present. These vaccines can cause blood clots that can even lead to death.

b)      Pfizer and Moderna: A messenger RNA molecule that synthesizes a coronavirus protein. These vaccines can cause heart ailments, according to studies conducted in Israel and other countries.

The limits of technology

Exponential curve

Transhumanists claim that technology is about to reach singularity: exponential growth towards infinity that will allow us to achieve goals such as immortality, strong artificial intelligence, the hybridization of machines and human beings, and much more. They thus make the same mistake made by the members of the club of Rome when in 1975 they predicted that the world's population would grow exponentially and reach catastrophic values ​​by 2020. It is the same mistake made by Malthus at the end of the 18th century, for the growth curves of natural systems are never exponential, but rather follow the logistic curve, as I have pointed out more than once in this blog.

To this criticism, transhumanists (such as Ray Kurzweil) argue that the human species is capable of linking two or more logistic curves, so that, even if real processes follow this curve rather than an exponential, growth would continue and the singularity could be reached, maybe a little later, but it will come anyway.

Those who say this are dreaming, and show they don’t know ​​mathematics. I show here two linked logistic curves, and compare them to exponential growth. It will be seen that the beginning of the two curves is quite similar, up to the point of abscissa 8.5. However, from that point, the differences are disproportionate. At the point of abscissa 10, the exponential curve reaches the value 3, while the logistics has not yet reached the value 1. At the point of abscissa 30, while the logistic curve reaches the value 2, the exponential would be at about 1446 million. So, claiming that several linked logistic curves equal one exponential, is mathematical folly.

Kurzweil also says that research in quantum computing should very soon send us into a new linked logistic curve. This shows that he does not know, or does not want to be aware, that quantum computing, if achieved, will make it possible to speed up the resolution of certain types of problems (NP-complete problems), but won’t let us solve new problems, such as I pointed out in another post. Although it is true that solving this challenge could send us up to a new logistic curve linked to the previous one, this advance won’t be as momentous as the media and some scientists would have us believe.

It is evident from the comparison made that, to approach exponential growth, it would be necessary to concatenate an enormous number of linked logistic curves, a number tending to infinity, which would require a time tending to infinity. But is it possible to link a very large number of logistic growths, or would we find a limit, if we tried?

Arnold J. Toynbee

Arnold J. Toynbee, in his monumental 12-volume Study of History, pointed out that human civilizations go through a stage of growth, during which they are subjected to several successive challenges that they usually manage to overcome, although as a rule each challenge solved causes new problems, and thus opens the way to the next challenge. Furthermore, he argues that the number of challenges that a civilization can successfully solve is usually not large: after defeating three or four, each of which may cost one to several centuries, it usually fails in the next one and collapses. Toynbee points out that Western civilization went into political collapse in the early 20th century, with the two world wars. In this he agrees with the diagnosis of Oswald Spengler, who reached the same conclusion in the interwar period.

It is true that the scientific-technological history of our civilization may not exactly coincide with its political history. However, I don’t think its decline is very far, as I have been predicting here. So, announcing that in the next hundred years we’ll reach singularity (as transhumanists do) is not doing science, but dreaming. At most, these musings could be the subject of science fiction novels, but nothing more.

Certainly, the limits of technology are practical, not theoretical, and further advancements could allow them to be transgressed. But the hopes of transhumanists in this regard are so exaggerated that they will probably never be achieved.

The same post in Spanish

Thematic Thread of Science in General: Previous Next

Manuel Alfonseca