Quantum Conscience or Conscient Quantum?

The second hard problem of modern science is the origin of consciousness or the problem of free will. This post focuses on the relation of this problem with quantum mechanics. As an example of the difficulty of the matter, I begin by including two famous quotes from renowned scientists:

·         J. B. S. Haldane, Possible Worlds (1927): The universe [of quantum theory] is, not only queerer than we suppose, but queerer than we can suppose.

·         James Jeans, The Mysterious Universe (1930): The universe begins to look more like a great thought than a great machine.

Can density be infinite?

First photo
of a black hole

Einstein’s general theory of relativity allows for the existence of objects with infinite density (singularities). There are two types:

1.      Black holes, accumulations of matter in a null volume, either at the center of a galaxy, or as the result of a supernova explosion.

2.      The universe, at its initial moment (the Big Bang).

A star like the sun is in equilibrium because the gravitational attraction, which tends to make it contract, is equal to the expansion caused by the nuclear reactions taking place inside the star. When a star much larger than the sun exhausts its nuclear fuel (first hydrogen, then helium, then other elements), as there are no longer nuclear reactions to stop the contraction, the star implodes. When the implosion rebounds, the star throws large quantities of matter into space: a supernova explosion, which for some time makes the star brighter than a whole galaxy. But there is always a remainder of matter, which gives rise to a new type of object.

Roger Penrose versus William Craig

Roger Penrose

I thank Plácido Doménech Espí for drawing my attention to this debate held in 2019 between Roger Penrose and William Craig, entitled The Universe: How did it get here & why are we part of it?

Roger Penrose rose to fame as a cosmologist in 1970 when he proved, with Stephen Hawking, a theorem stating that the application of Einstein’s theory of General Relativity to the entire universe requires the existence of at least one singular point in the universe (a point where all the geodesics of the universe meet). In other words, the Big Bang.

In 1989, Penrose became one of the most famous scientific popularizers with The emperor’s new mind, a book with deep philosophical implications. Among other things, he proposed the following question, inspired by Gödel’s theorem: how is it possible that we can prove that a theorem is true, if it cannot be proved mathematically from a reasonable set of axioms? According to Penrose, this would indicate that human intelligence is qualitatively different from computing machines.

In 2004 he published a book of extremely hard popularization, The Road to Reality, which is full of equations, where he proposes a unification of Einstein’s general relativity with quantum mechanics (a theory of quantum gravity). Then came his own cosmological theory, Conformal cyclical cosmology (CCC), according to which the universe did not begin with the Big Bang, which would only be the beginning of the current aeon, but there would be an infinite succession of previous eons, each beginning with a Big Bang and evolving to global heat death, when all that would remain in the entire universe would be photons. At that moment, (no one knows how) the entropy would suddenly drop to a minimum value again, to start a new cycle.

William Craig has proposed the kalam cosmological argument, which can be summarized thus:

1. Whatever begins to exist, has a cause of its existence.
2. The universe began to exist.
3. Therefore, the universe has a cause.

William Lane Craig

Craig argues that the Big Bang was the beginning of the existence of the universe, so there must be a cause for that existence: an uncaused Creator, existing without beginning, changeless, immaterial, timeless, spaceless, enormously powerful, and omniscient, to be the author of the abstract world. In other word: God.

In the debate, Penrose began by arguing that there are three components of reality: an abstract or Platonic world (mathematics); a physical world (the material world); and a mental world (the world of consciousness). In addition, he points out the existence of three mysteries, which refer to the relationships between these three worlds:

1. The unreasonable effectiveness of mathematics (Eugene Paul Wigner): Why does the abstract world describe so well the workings of the physical world?
2. The origin of consciousness: How can consciousness arise from the physical world?
3. The mind’s ability to understand the abstract world: Why can we understand mathematics and apply it to describe counterintuitive phenomena?

Craig agreed with Penrose’s analysis, and added this consideration:

The abstract world cannot be the cause of the other two worlds, the physical and the mental, because it has no causal power and cannot make decisions. It is not clear that the physical world is the cause of the mental world: Penrose himself admits that this is a mystery. Can the mental world be the cause of the physical and the abstract worlds? It appears it can: we have the experience that our minds can produce physical changes through human intentionality. Could there not be an omniscient mind who is the author of the physical and the abstract worlds? That would solve the problem of the origin of the three worlds.

To this, Penrose could only reply that he does not like this idea (he declares himself an atheist) and would rather think that the abstract world is primordial, although he does not know how the other two worlds could proceed from the abstract world.

The second part of the discussion dealt with the fine-tuning problem. Craig indicated that there are three solutions to the problem:

1. Universal constants must have the value they have.
2. Our existence in such a fine-tuned universe may be due to chance in a multiverse.
3. Our universe has been designed by a Creator.

Penrose began by denying that fine-tuning is a fact, although he ultimately declared himself agnostic about this question. He proposed his CCC theory as an explanation of the origin of our universe. Craig pointed out that this theory is just another multiverse theory, in time rather than in space, (most multiverses are supposed to exist in space). Penrose, for whom this idea seemed to be new, embraced it happily and asserted that his theory has been experimentally confirmed, an assertion most current cosmologists would not accept.

My conclusion from this debate: Penrose was mostly on the defensive, and he was unable to offer one convincing argument in favor of his atheism.

The same post in Spanish

Thematic Thread on Science, Faith and Atheism: Previous Next

Manuel Alfonseca

The limits of mathematics

Kurt Gödel

In the last decades of the nineteenth century, Friedrich Ludwig Gottlob Frege, a professor in the university of Vienna, undertook an ambitious goal: formalizing the arithmetic in a set of axioms and deduction rules, in such a way that every true theorem would be deductible from the axioms by a finite number of applications of the deduction rules. The result was a monumental book, Grundgesetze der Arithmetike (1893-1903), which introduced, among other things, a basic formalization of set theory and a cumbersome notation, quickly replaced by Peano’s, which we are using now.

Unfortunately for Frege, when the second volume of his book was about to be published, he received a letter from Bertrand Russell, proving that his formulation of set theory entails an inconsistency. In Frege’s set theory, some sets are not member of themselves (as the set of all integers, which is not an integer), while other sets are members of themselves (as the set of all infinite sets, which is an infinite set). Russell then defined this set: the set of all sets that are not members of themselves. It is easy to see that this set leads to a paradox: if it is a member of itself, it cannot be a member of itself, and vice versa. Russell’s paradox wreaked havoc with Frege’s work, who had to add a hasty appendix to his book and then abandoned his research on the fundamentals of mathematics.

What is a good scientific popularization?

Isaac Asimov

This news was published on November 20, 2007 in the Spanish major newspaper ABC:

Jugene, the most powerful and ecological civilian computer in the world, is German. [In the] Rhinelandic town of Jülich [was installed] Jugene (Jülicher Blue Gene), whose 167,000 million basic operations (teraflops) per second make it the world's first computer for civilian use...

Actually, the most powerful computers at the time could run at a few hundred teraflops. This news exaggerated the speed of the computer by nine orders of magnitude. This error has not been corrected. It’s still in the web.

Heard on a Radio broadcast on May 30, 2008: Fishermen complain about the rising price of diesel. Five years ago it cost them 320% less. In other words, five years ago they were paid to fill the tank.

Let's look at another example of a wrong headline published on 2/18/2020. The headline says: New green technology generates electricity "out of thin air." The text clarifies that it is generated from the humidity of the air acting on a protein.

These errors, so frequent in the media (I could contribute many more), have led me to formulate the following golden rule of scientific popularization:

Any statement you assert must be correct and contrastable.

Everything one says must be carefully checked to ensure that it is not a mistake, hasty or misrepresented news, or in the worst case, fake news.

Another typical error of scientific popularization in the media is showing as already done news that are really nothing but predictions about the future. This usually happens in headlines, which are usually reduced to the minimum, while keeping maximum impact. For instance, in a recent news published on 2/12/2020, the headline is: Mars was also beaten and for a long time. The text, however, is much less conclusive. What the headline gives as certain, becomes just possible: The red planet could have formed in a longer time scale than previously thought.

Statistics are prone to many manipulations, sometimes with unexpected consequences:

In 1995, one study showed that the contraceptive pill increases the risk of thrombus embolism by 100%. The press published it with great headlines. Thousands of women stopped taking the pill. It is estimated that, as a result, 10,000 more abortions took place, only in Great Britain.

What had really happened? What did that study discover?

Risk of thrombo-embolism in women who do not take the pill: 1 in 14,000. Risk of thrombus embolism in women taking the pill: 2 in 14,000.

In this case, the news was not incorrect. What was wrong was the way of making it public. It’s true, the risk increased by 100% (from 0.00007 to 0.00014). But expressed in that way, it could cause a panic, and it did.

I have given more examples in two old posts in this blog: this one and this one.

This is a list of 24 famous popularizers:

Michael Faraday

Galileo Galilei, Michael Faraday, Jean Martin Charcot, Camille Flammarion, Santiago Ramón y Cajal, Josep Comas and Solà, Gregorio Marañón, George Gamow, Willy Ley, Isaac Asimov, Arthur C. Clarke, Konrad Lorenz, Stephen Jay Gould, Martin Gardner, Félix Rodríguez de la Fuente, Douglas Hofstadter, Ian Stewart, Raymond Smullyan, Steven Weinberg, Richard Feynman, Carl Sagan, Stephen Hawking, Roger Penrose and Paul Davies.

Santiago Ramón y Cajal

Most of them were scientists, distributed among the following fields: 3 mathematicians; 12 physicists, chemists and astronomers; 3 biologists; 4 doctors in medicine; and an engineer. The exception is Martin Gardner, who graduated in philosophy, although he later specialized in philosophy of mathematics. Some of them worked on several disciplines, or kept up to date with them, at least from the informative point of view.

Many of the popularizers mentioned above also addressed the other way of popularizing science: by means of fiction. Some of the names indicated are also famous as authors of science fiction novels, or just fiction, with some scientific stroke: Asimov, Clarke, Gamow, Sagan, Davies, Ramón y Cajal, and Marañón wrote novels, some of which are considered among the best in the genre.

Are popularizers born or made? Surely both things at once. The best definition of a popularizer was given by Willy Ley, when one of his teachers asked the students to write a composition developing the following question: which profession do I want to practice when I’ll be grown up, and why? Willy Ley replied: I want to be an explorer. The teacher did not like the answer, and said there was nothing left to explore. Obviously, the teacher was wrong.

The same post in Spanish
Thematic Thread on Popularization of Science: Previous Next

Manuel Alfonseca
Happy summer holidays. See you by mid-August

Irreversible processes

Those physicists who consider the arrow of time as an illusion have a problem: not all physics is compatible with a reversible time, as the equations and theories mentioned in an earlier article of this blog seem to indicate. The second principle of thermodynamics is known since the mid-nineteenth century (1850), when Clausius introduced the concept of entropy and it was proved that the value of this physical magnitude always increases, if it is measured in an isolated system that does not exchange matter or energy with its outside. Since the universe is an isolated system, we have at least one physical quantity that makes it possible to unequivocally signal the direction of time flow.

Aware of this problem, physicists in favor of the reversibility of time have answered in different ways: it has been said that the second principle of thermodynamics is a fictitious, subjective law that does not conform to reality; a mental illusion; an approximation; a consequence of the initial conditions of the universe. It has been hypothesized that, if the universe were cyclic, the arrow of time would be reversed during the contraction stage. (This theory has been abandoned). To escape the problem, Stephen Hawking proposed a universe without initial conditions in his book A Brief History of Time. It is curious, this desire to defend at any price the reversibility of time, when it was precisely Hawking who proposed the existence of an arrow of time in black holes, which rather than being permanent, would disintegrate.

In 1928, a year after inventing the term the arrow of time, Arthur Eddington challenged the physicists who defend the reversibility of time with the following devastating words: If your theory is found to be against the second law of Thermodynamics... there is nothing for it but to collapse in deepest humiliation (The Nature of the Physcal World, 1928).

Cyclic Time and Linear Time

Stephen Hawking

In an article published in 1999, in volume 879 of the Annals of the New York Academy of Sciences, Pier Luigi Luisi speaks about the two traditional models of time that have been considered by traditional philosophy and the mythologies of various historical civilizations. They must not be confused with the two philosophical models originated in the twentieth century, the time A and time B of which I spoke in another post of this blog.

• Cyclical time, predominant in Asian civilizations and the Greco-Roman world until the Christian world view took root there. The origin of this model is evident, for many natural phenomena are cyclical: sunrise and sunset; the phases of the moon; the annual movements of the stars, synchronized with the seasons and with many biological phenomena...
• Linear time, prevailing in the three religions who consider themselves descendants of Abraham: Judaism, Christianity and Islam. Linear time can be compared with the course of the life of a living being, which begins at birth, goes on with changes during a certain period, and ends with death.

The scientific work of Stephen Hawking

The scientific work of Stephen Hawking has been quite productive, although the media, influenced by his sad personal situation, tend to exaggerate its importance, putting him sometimes at the level of Einstein. His most renowned works are the following:

• The singularity theorems, published in 1970 in collaboration with Roger Penrose, proved that the application of the equations of Einstein’s General Relativity to the entire universe requires at least one singular point in that universe (a point where all the geodesics in the universe converge). As a consequence of this theorem, in the book The Large Scale Structure of Space-Time (1973, written with George Ellis), Hawking unequivocally embraced the theory that the universe began at a point of infinite density (the Big Bang).