The problem of Achilles and the tortoise

Zeno of Elea

Zeno of Elea, a follower of Parmenides, is mainly remembered for his paradoxes which try to prove that movement does not exist, especially the paradox of Achilles and the tortoise, which asserted that it would be impossible for Achilles to catch the tortoise in a race, if he had accepted a starting handicap.

We know that Achilles runs faster than the tortoise (otherwise he could not catch it and the paradox would make no sense). As he has taken a handicap, when Achilles starts to run the tortoise will already be at a certain distance, at point A. When Achilles reaches point A, the tortoise will have advanced to point B. When Achilles reaches B, the tortoise is already in C, and so on, ad infinitum.

The time Achilles needs to catch the tortoise will be the sum of the times it takes him to reach points A, B, C... The total time is, therefore, the sum of an infinite series of numbers. The problem is that Zeno thinks that the sum of an infinite series of numbers must be infinite, so Achilles will never catch the tortoise (this is the conclusion of his reasoning). This, however, is not true: there are many infinite series whose sum is finite. One of them is precisely the series that computes the time needed by Achilles to catch the tortoise, according to Zeno’s reasoning.

Alternatives to the Big Bang

The Big Bang theory has a problem, which can be explained by the following set of questions:

• The farthest we can see is the cosmic microwave background radiation, which originated about 380,000 years after the Big Bang. We cannot see directly what happened before, because it is hidden behind that radiation.
• It is true that we cannot see, but we can deduce what happened in those first 380,000 years by applying the standard physical theory, i.e. general relativity. It is also possible to check those deductions, for they offer predictions, such as the average composition of the cosmos, which fit well with the experimental data.
• The problem is, general relativity does not take us to time zero, the Big Bang itself. This theory can be applied only from 5×10^-44 seconds after the Big Bang (the Planck time), as quantum effects were predominant before that time, and we do not have a physical theory that unifies quantum mechanics with general relativity.

Did the universe have a beginning?

Georges Lemaître

This question has fascinated scientists since 1931, when the Belgian astronomer, physicist and priest Georges Lemaître formulated the theory of the primordial atom, which since 1950 was known as the Big Bang theory. According to this cosmological theory, as the universe is expanding, if we move back in time we must come to a point (13,800 million years ago, the cosmologists tell us) when it would have gone through a singularity, with a volume tending to zero, while pressure and density would tend to infinity. Could this have been the beginning of the universe?

In 1951 Pope Pius XII, in a speech to the Pontifical Academy of Sciences, said the following words:

A mind illuminated and enriched by modern scientific knowledge, calmly evaluating this problem, is led to break the circle of a matter entirely independent and autochthonous, either uncreated, or because it has arisen by itself, and to rise to a creative Spirit... It seems really that present science, by jumping back over millions of centuries, has succeeded in being witness to that primordial “Fiat lux”, when out of nowhere burst forth, together with matter, a sea of light and radiation, while the particles of the chemical elements split and were reunited into millions of galaxies

More about immortality

Ray Kurzweil

Ray Kurzweil calls himself futurist, meaning that he knows how to predict the future of technology. Actually, what he does is adjusting his predictions as time passes, when he sees that they won’t be fulfilled, as I explained in a post on the horizon effect, which dealt with his predictions about artificial intelligence.

Lately, Kurzweil’s predictions have expanded their scope to medicine. One of his obsessions is that we are about to become immortal. At first he thought this would happen when we will be able to download our consciousness into the memory of a computer, and continue living inside it after our biological death. A few years ago, he predicted that this would take place before 2035.

No longer so confident in this prediction (2035 is around the corner), he now expect us to be immortal shortly before 2050, when he will be 102 years old, so that, by delaying the fulfillment of his prophecies, he begins to risk not to be able to see them.

In a widely publicized interview with Computerworld, Kurzweil now expects us to become immortal through the development of a family of nano-robots that will be injected into our blood and act as a new, much better than our original immune system, detecting and attacking all possible pathogens and cancer cells before they can affect us. Without diseases, we would be immortal. Let's look at a paragraph about that interview:

Imaged prepared by Waquar Ahmad

Futurist Ray Kurzweil said that anyone alive come 2040 or 2050 could be close to immortal. The quickening advance of nanotechnology means that the human condition will shift into more of a collaboration of man and machine, as nanobots flow through human blood streams and eventually even replace biological blood, he added. That may sound like something out of a sci-fi movie, but Kurzweil, a member of the Inventor's Hall of Fame and a recipient of the National Medal of Technology, says that research well underway today is leading to a time when a combination of nanotechnology and biotechnology will wipe out cancer…

That figure, 86% hits, is provided by Kurzweil himself, and in my opinion is far from being real, as Kurzweil usually does not score failures, just delays the date of his predictions. The headline of the story (Nanotech could make humans immortal by 2040, futurist says) would be more suitable if it had been replaced by the following: Ray Kurzweil delays by 10 years the date when we will attain immortality.

Normal and cancer cells

One must be very optimistic to think that in 30 years we will be able to design a better immune system than the one we acquired during a 1000 million years evolution, after a never ending arms race between multicellular beings on the one side, and pathogenic microorganisms and cancer cells on the other. Also remember that these organisms are quite capable to adapt to new situations very quickly, so they would probably find ways to escape from our nano-robots, whose software would have to be constantly changed to adapt to them. I think it probable that we will never be able to defeat them completely.

Finally, overcoming disease is not enough to achieve immortality, we must also stop aging. Otherwise, as I said in last month’s post, we would live for 100 or 110 years, and then die. Too many advances, to be achieved in just about 30 years.

The same post in Spanish
Thematic thread on Immortality: Preceding Next

Manuel Alfonseca