Is time infinite?

S.Augustin, by Louis Comfort Tiffany
Lightner Museum

Since ancient times, man has been interested in the enigma of time. Even though we all experience time, time is an enigma. As St. Augustine said in his Confessions (B.XI C.XIV): What is time? If no one asks me, I know; if I want to explain it to a questioner, I don’t know.

As I said in another post, the explanations devised to solve the enigma of time are of two types: those that consider it cyclical, with or without multiple repetitions, which would allow the passage of time to be represented geometrically by a circle, and those that consider it linear, which represent it by a straight line. In turn, this last case is divided into several: one can accept, or not, that time had a beginning; and one can accept, or not, that there will be a final moment of time. Combining these two alternatives, we have four different cases. So in total there are six possibilities, which we will analyze next in the light of modern cosmology:

Is space infinite?

Georg Cantor

According to Georg Cantor, one of the first to study the concept of infinity in depth, there is not just one concept of infinity, but three different ones. Let's see how he expresses it:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number, or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Georg Cantor, Gesammelte Abhandlungen, Springer, 1980. Translation taken from Rudy Rucker, Infinity and the Mind, Princeton University Press, 2004).

The origin of eukaryotes

John Maynard Smith

As I have said several times in this blog, the theory of evolution is now well established. However, it is far from explaining everything. Many mysteries still remain. I listed some of them in a previous post. A book by J. Maynard Smith and E. Szathmáry, The Major Transitions in Evolution (Oxford University Press, 1995), describes them in more detail.

One of these problems refers to the changes of level that have taken place in the history of life, which I made the central idea of ​​my book The Fifth Level of Evolution. As its title implies, during evolution, things have not happened in an orderly or stable manner. At various points, there were changes of state (similar to those in physics) where evolution passed a critical point that made it possible to reach higher levels and opened up huge new fields in the configuration space. These points are the following:

Paul Davies, popularizer of science

Paul Davies

Paul Davies came to the fore among scientists who devote time to popular science with his 1992 book The Mind of God, written in response to Stephen Hawking’s final words in his popular best-seller A Brief History of Time. In another post I talked about another of his popular books, The Eerie Silence. Here I am going to discuss two other books he has written.

The Last Three Minutes (1994): This book on popular science is a little behind the times, as it predates the standard cosmological model, but explains well the state of cosmology when the book was published, and many of the things it says are still valid. It says something very interesting: that the Big Bang theory by Lemaître (whom Davies does not name) should have been accepted long before its two surprisingly accurate predictions gave it a boost in the sixties, because there is another argument supporting it, that scientists of the 19th century should have noticed, but didn’t: If the universe were infinitely old, it would have died by now. It is evident that something that moves to a stop at a finite rate cannot have existed from all eternity. By the way, there is an error in this paragraph: Davies ignores the difference between what is eternal and everlasting, which was solved fifteen centuries ago by Boethius. And there is a major flaw when he says that the radius of the visible universe is 15 billion light-years, because he does not take into account the expansion of the universe. The correct radius is about 43 billion light-years.

Science Cannot Prove That God Does Not Exist

In several posts, I have pointed out that it is impossible for science to prove that God exists, just as it is impossible to prove that God does not exist. The reason is that the object of scientific inquiry is the material world, and God is not part of that world and is therefore beyond the reach of science.

In a previous post, I criticized a book that attempted to do the former, from the perspective of believers. In this post, I will criticize another book that attempts to do the latter, from the atheist perspective. It is M-E: The God Within, by Joseph R. Abrahamson.

Although the author claims to rely on the principles of logic and the scientific method, he makes significant errors that indicate his lack of in-depth knowledge of these disciplines. The argument he presents as proof that God does not exist, although not explicitly stated in the book, can be deduced from reading it and can be summarized as follows:

Phantoms in the Universe?

The Standard Cosmological Model has introduced in physics two new concepts that didn't exist before:

• Dark matter: It seems to be five times more abundant than ordinary matter, but we don't know what it is, what it's made of. We only know that it appears to be affected by gravity, and so far, its existence has been concluded in two different ways: a) By analyzing the rotational motion of galaxies, which seems to require that there is more mass in them than what we can see. b) By studying the cosmic microwave background radiation, which has served as the basis for adjusting the standard cosmological model.
• Dark energy: We have no idea what it is. Some speak of a fifth fundamental interaction (or force), the quintessence, which would join the four we know: gravitational, electromagnetic, strong, and weak. Others offer different explanations, none of which have received experimental confirmation. The hypothesis of its existence is supported by two observations: a) Analyzing the expansion rate of the universe, after the 1998 discovery that this rate is accelerating. b) By studying the cosmic microwave background radiation, which has served as the basis for adjusting the standard cosmological model.

Arguments against the theory of evolution

Drosophila melanogaster

Despite what I said in the last paragraph of my previous post, there are still well-intentioned people who oppose the theory of evolution (although this is very rare among biologists), and sometimes offer arguments to defend their way of thinking. I will consider some of those arguments here and offer my answers.

Answer: The claim that evolution has not been successfully reproduced artificially is mistaken. We have been doing this for thousands of years through artificial selection, which gave Darwin the idea of ​​natural selection. We have been doing it for decades in the laboratory in a controlled way, as this Wikipedia article explains: Experimental evolution. And this has been done not just with bacteria, which have a very short life cycle, but also with higher animals.

The theory of evolution, is it science?

In three previous posts (this was the latest), I wrote more or less the following words:

The scientific theory of evolution is strongly supported by data from other sciences, such as embryology, comparative anatomy, paleontology, biogeography, and molecular biology (DNA analysis).

Since, despite everything, there are still those who doubt the scientific nature of this theory, in this post I will expand on the previous paragraph, explaining in a little more detail the scientific data that favor evolution.

What is the theory of evolution?

Tree of Life

The theory of evolution, in its current form, asserts that the transformation of species (the evolution of life) depends on five factors:

1.      Spontaneous variations in the genome (mutations, genetic recombination, and other events that modify the genome).

2.      Spontaneous variations in the environment. This factor is often overlooked, as the environment is usually quite stable, although sudden changes sometimes occur that can have huge consequences.

3.      Inheritance, through which the variations that occur as a result of the first factor are passed on to offspring and are subject to the action of natural selection.

4.      Natural selection, which means that those individuals whose genome is best adapted to the environment will leave more offspring (at least statistically).

5.      The basic laws of the universe, which are currently represented by quantum theory and the theory of relativity.

Are we speciesist?

In chapter 6 of his book ¿Qué es la Antropología? (What is Antropology, 2020), Francisco de Paula Rodríguez Valls writes:

Human beings would be speciesist if they acted according to the logic of survival by using the power of his faculties in his own benefit. All the other species would do that, of course... Human beings are the only species that may not be speciesist by taking care of the entire planet. By putting their power at the service of the entire kingdom of life.

According to the Merriam-Webster dictionary, speciesism is prejudice or discrimination based on species, especially against animals. It can also refer to the assumption that humans are superior to other species.

This is a recently coined word, one of those neologisms associated with the ideology of political correctness, which insists that we shouldn’t upset anyone, neither with our actions, nor with our words, nor with our thoughts. Starting from a laudable anti-racist stance, they extended it to increasingly exaggerated and absurd situations (there are many examples), and in particular to all other animal species, based on the ideological premise that no species is superior to any other, which, as I have explained several times in this blog, is highly debatable.

Evolutionary convergence

Stephen Jay Gould

One of the most spectacular controversies to have arisen in biology at the end of the 20th century was that between two famous biologists: the American Stephen Jay Gould and the British Simon Conway Morris. The controversy began with the former's book, published in 1989, Wonderful Life: The Burgess Shale and the Nature of History, to which Conway Morris responded in 1997 with another book, The Crucible of Creation. As the subtitle of Gould's book indicates, both biologists based their work on the discoveries of the Cambrian fauna of the Burgess Shale (Canada), which I referred to in another post, and which was discovered and studied precisely by Conway Morris.

In his study, Stephen Jay Gould focuses in particular on the surprising and abrupt diversification that took place 550 million years ago and left its mark on the Burgess Shale fauna to argue that evolution is dominated by the effects of chance, so that, if we rewound the history of life and repeated the evolutionary process, the results would not resemble anything we have now. As a corollary, if there is animal life on other worlds, around other stars, it won’t resemble anything on Earth. And if there is intelligent life outside Earth, their physical appearance will not resemble ours.

Water and the origin of life

All living beings, from microbes to humans, live in water or contain water. All chemical reactions that take place inside cells are carried out in water.

Liquid water is an extraordinary compound, with strange properties. It has one of the highest specific heats of all substances. This means that when heat is added to or removed from a body of water, the temperature varies more slowly than in any other liquid. This is important for living beings, as water acts as an environmental stabilizer. Also, it is the non-metallic liquid with the highest thermal conductivity, so local temperature variations are balanced very quickly.

Most liquids contract when they solidify, but water is an exception. It has its maximum density at a temperature of 4°C. The density of ice is lower, 0.92 times lower, so ice floats on water. So, when the temperature drops, water freezes from top to bottom, while other liquids solidify from bottom to top. This also has important biological consequences. In polar seas and in fresh waters of cold regions, when the temperature drops below the freezing point, the surface layer of ice insulates the water below from the cold, so that it never freezes and the beings that live there can remain alive and active, despite the harsh environmental conditions.

The chemical composition of life in other worlds

Is it a coincidence that life on Earth is based on carbon? Is this the only element capable of becoming the basis for life? Could there exist, somewhere in the Universe, a type of life different from ours, whose chemical composition is not based on carbon? On what atom or group of atoms could a chemistry of comparable complexity to organic chemistry be built, in theory?

There are 91 different chemical elements on Earth. Others have been generated artificially in the laboratory, and it is suspected that they can be produced in small quantities inside a giant star that becomes a supernova, but their life is short, because they are very radioactive and disintegrate quickly, transforming into more stable elements. Therefore, the search can be reduced to the 91 natural elements. We will select from these those that meet the following two conditions, essential to be able to be the chemical basis of life:

1. They must be capable of establishing more than two covalent bonds with other atoms.
2. They must be stable. That is, they must have at least one non-radioactive isotope.

Rational and scientific inklings about God’s existence

In the previous post I mentioned that science does not provide proof of the existence of God, but it does give inklings. In a book I wrote, which was published in Spanish in 2013 with the title ¿Es compatible Dios con la ciencia? Evolución y Cosmología (Is God Compatible with Science? Evolution and Cosmology) I described a list of those inklings. Here I will summarize a few of them. The first three are scientific, the others are not.

1.      The universe is a physical object. During the 19th century, atheist philosophers denied that the universe is a concept applicable to a concrete object that exists outside our mind. The universe is usually defined as the set of everything that exists. According to those philosophers, such a set does not exist, since the concept of the universe is an invention of the human mind, which does not correspond to any physical object. Therefore, it would not be necessary to look for its origin (its cause) outside our mind. This argument was disproved in the 20th century: Einstein’s theory of general relativity leads to a cosmological equation that applies to the universe, which implies that the cosmos has real existence, that it is a physical object.

Scientific proofs of God’s existence?

Two French engineers, Michel-Yves Bolloré and Olivier Bonnassies, have published a best-seller entitled Dieu - la science - les preuves: L'aube d'une revolution (God - Science - The Proofs: The Dawn of a Revolution), where they claim that science has proven the existence of God. The book is interesting, because it contains many anecdotes and quotes from scientists, and some little-known facts. However, I do not agree with their approach, which is apparent in the title of the book.

Can science prove the existence of God? As I have said in this blog more than once, the answer to this question must be negative. The object of science is the study of the material world. But God is not in the material world, He is not part of it. Therefore, he cannot be an object of study by science. This means that science will never succeed in proving the existence of God, nor will it succeed in proving his nonexistence.

As I explained in another post, perhaps Pope Pius XII was tempted to think that science had proved creation, although it is suspected that Georges Lemaître, discoverer of the Hubble-Lemaître law and the Big Bang theory, dissuaded him, for the Pope, in a speech shortly after their interview, said this: science, while progressing by leaps and bounds, will never be able to answer the ultimate questions, such as the origin of everything.

Changes in the Scientific Paradigm

Thomas Kuhn

As Thomas Kuhn pointed out, from time to time there are shifts in the scientific paradigm that cause sharp deviations in the direction of research. These shifts can occur in any of the sciences. Here are some important historical examples:

Puerperal fever was for centuries the leading cause of death in women giving birth. In 1795, the Scottish obstetrician Alexander Gordon claimed that the disease was transmitted by doctors and midwives. In 1842, the English physician Thomas Watson, known for his description of the aortic pulse, recommended that doctors wash their hands with diluted lye before attending a birth. And in 1847, the Austrian physician Ignaz Semmelweis advised the same, based on data showing that the incidence of puerperal fever was higher in hospitals than in births taking place at home, and higher among women in labor attended by doctors than by midwives. Semmelweis' proposals were violently rejected by contemporary physicians, who were outraged by the idea of ​​being blamed for infections caused by themselves, to the point that Semmelweis was committed to an asylum where he only survived two weeks. His death is believed to have been the result of a beating by the asylum guards when Semmelweis, who was 47 years old, tried to escape. His proposals were confirmed by the discovery of the germ theory of infectious diseases by Louis Pasteur, according to which diseases are caused by microorganisms, and not by miasmas transmitted by air, as previously believed. This caused an abrupt change in the scientific paradigm applied to medicine.

Is homo economicus rational?

Nicolás Bernoulli

In 1713, Nicolás Bernoulli formulated the St. Petersburg paradox, which can be summarized as follows:

Let us consider the following game: a coin is tossed. If it comes up heads, you receive $2. If it comes up tails, it is tossed again. If it comes up heads, you receive $4. If it comes up tails, it is tossed again. And so on. With each toss, the prize is multiplied by 2. How much would you be willing to pay to participate in the game?

The probability of winning $2 is 0.5; the probability of winning $4 is 0.25; the probability of winning $2^k is 2^-k. The expected value is obtained by multiplying each value by its probability and adding them all together. So the expected value of the profit that could be obtained by playing that game is:

The Chinese and artificial intelligence

Wolfgang von Goethe

The media has been reporting on a recent breakthrough in LLMs (large language models), the hottest applications in the field of artificial intelligence, which in the last two years have given rise to great hype, suspicions of stagnation and accusations of excessive energy and water costs.

This latest breakthrough has been achieved by a Chinese company, DeepSeek, which has jumped to the front line because it successfully competes with the big companies in the field, OpenAI (which built ChatGPT and GPT4) and Google (with GEMINI), but at a lower cost.

There are now many tools of this type, but the two mentioned in the previous paragraph (GEMINI and GPT4) provided the best performance, although they were the most expensive. Their code is secret, owned by the two companies (Google and OpenAI) and users cannot modify it. Alongside them, now there are others with open source, which can be adapted to each user, but with lesser performance.

Anything can be assigned a probability?

In the previous post I mentioned the book Radical Uncertainty: Decision Making Beyond the Numbers by Mervyn King and John Kay. The book, written by two prestigious British economists, attacks the bad use of statistics and probability calculus in fields where they are not always applicable, such as history, economics and the law. Let’s look at a few examples:

• What do we mean when we say that Liverpool F.C. has a 90% chance of winning the next match? One possible interpretation is that if the match were to be played a hundred times, with the same players and the same weather conditions and the same referee, Liverpool would win 90 times, and draw or lose the other ten. But the match will be played just once. Does it make sense to talk about probabilities? No, because there are no supporting data on frequency. What is meant is that the person speaking believes that Liverpool will win. Nothing more. It is a subjective probability. Milton Friedman wrote: We can treat people as if they assigned numerical probabilities to every conceivable event. (Price Theory, 1962).

Risk versus Uncertainty

I have read the book Radical Uncertainty: Decision Making Beyond the Numbers by Mervyn King & John Kay. As the title suggests, it talks about radical uncertainty. What is uncertainty? Its definition is simple: any uncertain knowledge. But there are two types of uncertainty:

·         Risk: Measurable or resolvable uncertainty. Probability calculations can be applied. Example: the outcome of a roulette or lottery game. Problems of this type can be called puzzles. Phenomena of this type are stationary (their properties do not change over time).

·         Radical uncertainty: Uncertainty that is not measurable. It arises when there is obscurity, ignorance, vagueness, ambiguity, ill-defined problems, lack of information. It cannot be described by probability calculations. Problems of this type can be called mysteries. Phenomena of this type are usually not stationary.

Probability of the existence of extraterrestrial life

In a previous post I talked about the probability of the existence of extraterrestrial intelligence and mentioned the difficulty of its calculation, as we don’t know of any planet where they exist, apart from Earth, and to calculate the probability of an event one must know the number of favorable cases and the number of possible cases. For extraterrestrial life, we ​​don’t know either.

In another post I detailed the conditions that should be necessary if life similar to ours were to be possible on a planet similar to Earth. These conditions are many, which reduces the probability that we will find life on some extrasolar planet located in our vicinity. In fact, among the almost 10,000 planets detected so far (of which just over half have been confirmed), 65 are at a distance from their star that could be favorable for life (the Goldilocks zone), but only three of them orbit around stars similar to the Sun (of the stellar class G).

500 posts in PopulScience

This is the 500th post I have published on the Spanish version of this blog, just after 11 years since the creation of, on January 15, 2014. The English blog, PopulScience, where I almost always publish the same posts, translated into English, came about later. I did not publish the first article until August 12, 2014, so it was half a year late. However, over the years, it has gradually recovered the lost ground, to the point that right now there are 498 posts, only two less than the Spanish blog.

Why is this? It is very simple: in the United States the summer holidays are shorter and end in mid-August, while in Spain the whole month of August is a non-working month. When I take a vacation from the blog, I stop publishing posts in the Spanish version for most of July and all of August, and start the new course at the beginning of September. On the English blog, however, I start in mid-August, and so every year I catch up on two or three posts. After eleven years, I have almost made up for the half-year delay that the English blog was behind. This summer, God willing, the two blogs will be on a par.

Giant Viruses

John Maynard Smith

In 1966, H.J. Muller defined living beings as follows: Any being capable of multiplying with inheritance and variation. With this definition, which prioritizes reproduction and evolution as the definition of life, viruses should be considered as living beings. Other biologists, such as John Maynard Smith, thought that this criterion was too broad. It would mean that nucleic acids are alive, since they are capable of reproducing with inheritance and variation. That is why they propose adding another criterion: A living being is capable of reproducing and metabolizing. This would exclude nucleic acids, and therefore viruses, which are nucleic acids enclosed in a protein capsule, and viroids, which are isolated nucleic acids.

The tree of life, the family tree of all species of living beings, seems to indicate that all beings formed by one or more cells descend from a single individual, the first living being, which is called LUCA (Last Universal Common Ancestor). As I said in another post, some think that perhaps LUCA was not a single individual, but a network of individuals. But where do viruses come from?

Universe or multiverse?

In the posts in this blog I have often said that theories about the multiverse (there are many) are not science, but speculations, because it is impossible to design an experiment that demonstrates the existence or non-existence of these multiverses.

In an article published in May 2023 in the journal Springer Nature, entitled Is Everyone Probably Elsewhere?, the authors claim that it would at least be possible to distinguish between the following two hypotheses:

1. Our universe is unique, it does not belong to any multiverse.
2. Our universe belongs to some multiverse. Of course, we would have no idea what type of multiverse it would belong to.

Physics, Mathematics and Mathematical Physics

Eugene Wigner

Eugene Paul Wigner was a Hungarian physicist who received the Nobel Prize in Physics in 1963 for his contribution to the theory of the atomic nucleus and elementary particles. In a famous article published in 1960, Wigner said:

It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. (“The unreasonable effectiveness of mathematics in the natural sciences”. Communications on Pure and Applied Mathematics 13: 1-14).