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).

Time travel in science fiction

H.G. Wells

A few years ago, I published in this blog a series of posts about the scientific aspect of time travel, the paradoxes it could cause if it were possible (which almost certainly it is not) and proposed solutions to these paradoxes, such as the quantum multiverse, one of the most absurd theories physicists have ever concocted. In another post I talked about the scientific errors in Michael Crichton’s sci-fi novel Timeline, which tries to avoid the paradoxes in this way, but does it poorly.

Here I am going to speak about time travel from a literary point of view, as a subgenre of science fiction. In this context, it’s irrelevant that time travel may or may not be possible. We are interested in the question, because this is one of the most frequent topics in this type of literature.

Information paradoxes

Woody Allen

As I have mentioned before, time travel, if it were possible, would cause many paradoxes. In a previous post I mentioned the paradox of unsourced information, which can be summarized thus:

A time traveler who lives in time 3 knows that a person A said or did something at time 2, prior to time 3. 

The traveler goes back from time 3 to time 1, prior to time 2, where he meets A. 

While they are together, the traveler suggests person A the idea of ​​doing or saying what he knows that person will do or say in the future, which has not yet taken place. 

Whose idea was it originally? Not the traveler’s, because he learned it from the history of person A at time 3. Not from person A, because the traveler suggested the idea to person A at time 1. 

The information in question has come out of nowhere, without anyone having thought it out.

The following diagram explains it.

The paradox of unsourced information

Ted Chiang

In a previous post in this blog I discussed the paradoxes that would take place if time travel were possible. One of them was this:

• The existence of objects without a cause, illustrated by the science fiction story Find the sculptor by Sam Mimes, which can be summarized thus: on his first trip, the inventor of the time machine jumps 100 years into the future, where he finds a statue that has been erected in his honor. He takes the statue, travels with it 100 years into the past (i.e., to the starting point of his journey), and places it in the same place where he found it, where it will remain for 100 years without anyone touching it. But who made the statue? Nobody. It is an object without a cause, that only exists during those hundred years.

What does mathematics say about time travel?

On September 21st, an article on time travel by Germain Tobar and Fabio Costa was published in the scientific magazine Classical and Quantum Gravity. This article has been given considerable coverage by the mass media. The article argues that time travel would be possible if certain mathematical restrictions were fulfilled that would eliminate the paradoxes. In a previous post in this blog I explain those paradoxes and their different types.

In relation to this we must distinguish two different things:

1. What the article actually says: it only mentions the grandfather paradox (the time traveler who returns to the past to kill his grandfather as a child, which would make his own existence impossible), and specifies a mathematical equation that supposedly prevents it, without making the traveler's freedom of action totally impossible. The equation is this:

Will time travel be possible?

Hibernation in 2001, a Space Odyssey

The obvious answer to this question, such as it is formulated, is yes, of course it’s possible! We all travel in time at the rate of 24 hours a day.

Naturally, this is not what comes to mind when this question is asked. What is usually meant is this: will we be able someday to make sudden jumps in time, either forward (to the future) or backward (to the past)?

There are several schemes for traveling to the future. If they aren’t possible just now, one day they could become so. For example, perhaps human beings will be frozen and remain in suspended animation, to wake up and resume their ordinary lives a hundred years later. Or they could take passage on a spacecraft, make a trip at relativistic speed, and return to their starting point a century later, whilst for the travelers the elapsed time would have been just one year. In both cases, from the point of view of the persons in question, this would have been a trip forward in time, but in reality no sudden leap would have happened, for time would have kept going on for the hibernated body, though the mind would not be aware, and also for the relativistic traveler, although in this case time would have been accelerated.

But when we speak of time travel, we do not refer to these cases, which are possible in principle. We mean disappearing from the present and appearing in the past or in the future. Will we be able to do this someday?