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Our future, our universe, and other weighty topics


Saturday, January 18, 2014

Humanity Prerequisites: A Table of 18 Anthropic Requirements

The Standard Model is regarded as a highly “unnatural” theory. Aside from having a large number of different particles and forces, many of which seem surplus to requirement, it is also very precariously balanced. If you change any of the 20+ numbers that have to be put into the theory even a little, you rapidly find yourself living in a universe without atoms. This spooky fine-tuning worries many physicists, leaving the universe looking as though it has been set up in just the right way for life to exist.
Harry Cliff, Particle Physicist, in a Scientific American article

If you have not read much on the topic of the anthropic principle and the issue of possible fine-tuning in the universe, it may be hard to follow the topic. Discussions typically involves subatomic physics, cosmology, biology, evolution and some other subjects that don't exactly make light reading. I think that the topic will be easier to understand if we condense it into one simple table that summarizes the most relevant facts. I have created such a table, which appears below.

The left column of the table lists various items that appear in nature. The right column lists requirements of those items. The table is in chronological order. It starts out with requirements that must be met in the very beginning, near the time of the Big Bang, if the universe is ever going to end up with people like us, inhabitants of a technical civilization living near a sunlike star. Towards the end of the table are items that appeared billions of years later in time. The final item in the table is “Civilizations near sunlike stars.” It is interesting that for the last item to come into existence, all of the previous items in the list must previously come into existence. I have added color coding which makes the various interlinked dependencies much easier to follow. 

Anthropic Principle
Click to Expand

I will now explain why each item has the requirements I have listed.

Row 1 (Higgs field): The Higgs field (related to the Higgs boson) is said to give mass to other particles. Scientists are puzzled by why the Higgs field has the strength it has, and they say that it seems to require fine-tuning to 15 decimal places. This is a problem called the hierarchy problem or the naturalness problem. It is discussed in this scientific paper entitled The Higgs: so simple yet so unnatural. As a Daily Galaxy article put it, “Using theory as it currently stands, the mass of the Higgs boson can only be explained as the result of a random fine-tuning of the physical constants of the universe at a level of accuracy of one in one quadrillion.”

Row 2 (up quarks and down quarks, electrons): The particles in the nuclei of atoms (protons and neutrons) are made up of smaller particles called up quarks and down quarks. A requirement of the large-scale existence of up quarks and down quarks (and also electrons) is what scientists call matter/antimatter asymmetry (a situation where matter is vastly more abundant than antimatter). This is a puzzle to scientists, because the standard model of physics seems to predict that matter and antimatter should have existed in equal amounts at the time of the Big Bang, which would have caused both types of particles to collide with each other and convert into energy, leaving almost nothing but energy in the universe. A requirement for electrons is the Higgs field, and on this page a physicist says that the electron would not have mass without the Higgs field. 

Row 3 (protons, neutrons): The simple requirement is that there be up quarks and down quarks, discussed in the previous paragraph.

Row 4 (hydrogen atoms): The requirement for a hydrogen atom is that you have one proton and one electron, and also the electromagnetic force, the force of attraction between a proton and an electron. Without that force, electrons would not have any tendency to orbit a nucleus.

Row 5 (galaxies): Galaxies are huge collections of stars. There are many requirements for the formation of galaxies after the Big Bang. The universe had to begin with a fine-tuned expansion rate, as a slighter higher rate would have caused an expansion too fast for galaxies to form, and a slightly slower rate would have caused all matter to collapse into superdense black holes. Scientists also say that numerous other things had to be just right (the other items listed in this row). One requirement is primordial density perturbations greater than .000001 and less than .0001, as explained here. One particularly severe requirement seems to involve dark energy, which is regarded pretty much the same as the cosmological constant. Cosmologists conclude that the level of dark energy seems to have been fine-tuned to something like 1 part in 1060 or one part in 10120. The issue, called the vacuum catastrophe, has been fretted over by many physicists. This paper refers to the “tremendous, unsolved naturalness problem” posed by the cosmological constant.
 
Row 6 (carbon atoms): This row refers to the abundant existence of carbon atoms, something which ends up having lots of requirements. Besides the previously mentioned requirements for the hydrogen atom (protons, electrons, and the electromagnetic force), there are the additional requirements of the neutron and the strong nuclear force (the two of them allow you to have a carbon nucleus that holds together, despite the mutual repulsion between the protons). There is also the requirement that you have a law of nature called the Pauli Exclusion Principle, something that is quite necessary for both solid matter and complex carbon bonds. Then there is an additional requirement for something called nuclear resonances, which assures that carbon is produced in abundant quantities by stars through a process called the triple alpha process. Without this additional requirement, there would not be enough carbon (which wasn't produced in the Big Bang). This point has been widely discussed by scientists such as Hoyle, and in this scientific paper stating that a 0.4% change in one parameter would have left us without a universe abundant in both carbon and oxygen. An additional requirement that I had no space to list in my table is the requirement that the neutron mass be higher than the proton mass.

Row 7 (oxygen atoms): Oxygen atoms have all the same requirements of carbon atoms, including the same special requirement involving nuclear resonances, necessary for oxygen to be produced by stars in abundant amounts. The scientific paper here argues that there would not be much oxygen without the weak nuclear force, so I have also listed that as a requirement. 

Row 8 (Heavier atoms): By heavier atoms I mean all atoms than have more than about 25 protons (which includes copper, lead, silver, gold, zinc, tin, and probably also iron). These types of atoms have most of the same requirements of carbon atoms and oxygen atoms, except that to have these atoms in abundance you don't need nuclear resonances but instead the stellar explosions called supernovae explosions (explosions of stars that produce heavy elements such as lead and iron). These supernovae explosions require a tiny particle called the neutrino and a force called the weak nuclear force.

Row 9 (Sunlike stars): I may define sunlike stars as those that are white, yellow, or orange (or some combination of those colors). Sunlike stars require galaxies (since if galaxies had not formed, there would be no stars). Sunlike stars also require a very delicate fine-tuning of some of the most fundamental constants of nature. The physicist Paul Davies says on page 73 of The Accidental Universe: “If gravity were very slightly weaker, or electromagnetism very slightly stronger (or the electron slightly less massive relative to the proton), all stars would be red dwarfs. A correspondingly tiny change the other way, and they would all be blue giants.” Blue giants are too-short lived for life to evolve near them, and red dwarf stars are not believed to be as favorable for life's evolution as sunlike stars. 

Row 10 (water): Water requires oxygen atoms and hydrogen atoms, as we can tell from its formula H20. Because of its remarkable features that make it unique among liquids, there are probably additional requirements for water, but I haven't listed them.

Row 11 (stable planets): One requirement for stable planets is gravitation, the force that holds planets and stars together. But there is another very interesting requirement: that the electric charge of the proton exactly match the electric charge of the electron, to many decimal places. Electromagnetism (the fundamental force involving electric charges) is roughly 1036 times stronger than gravitation, the weakest of the fundamental forces by far. Consequently a very slight mismatch between the charge of the electron and the proton would cause electromagnetism (roughly a trillion trillion trillion times stronger than gravitation) to completely overwhelm the gravity holding the planet together. In his book The Symbiotic Universe, astronomer George Greenstein (a professor emeritus at Amherst College) says this about the equality of the proton and electron charges: "Relatively small things like stones, people, and the like would fly apart if the two charges differed by as little as one part in 100 billion. Large structures like the Earth and the Sun require for their existence a yet more perfect balance of one part in a billion billion." In fact, experiments do indicate that the charge of the proton and the electron match to eighteen decimal places. 

proton electron charge
A curious coincidence

Row 12 (nucleotides): Nucleotides are molecules that are the building blocks of RNA and DNA, molecules essential for life. Nucleotides require three types of atoms mentioned above (carbon, oxygen, and hydrogen atoms), as well as phosphorus atoms. They also require physics to be arranged in a way that allows for atoms to combine to make molecules consisting of multiple atoms.

Row 13 (genetic code): The genetic code is a semantic framework used by DNA and RNA, one in which particular combination of nucleotides stand for particular amino acids. The genetic code could roughly be called the software used by DNA and RNA. The origin of this code is one of science's great mysteries. We do not know how this code (required for all biological evolution) appeared from mere chemicals. This is the “code from chemicals” problem described in this blog post.

Row 14 (RNA): RNA is one of the two main molecules used by all living things, and it is believed to have preceded the more well-known and more complicated molecule DNA. It requires nucleotides (from which RNA is built), as well as the genetic code and water (as a substrate).

Row 15 (DNA): DNA requires nucleotides (from which it is built), as well as the genetic code and water. I also list RNA as a requirement since it is believed that RNA was a necessary predecessor of DNA.

Row 16 (Proteins, cells): Proteins are made by DNA and RNA using the genetic code. Requirements include water and amino acids (which I didn't list in the table for space reasons).

Row 17 (Photosynthesis): Photosynthesis is the process by which plants convert sunlight to chemical energy. Recent studies suggest that photosynthesis uses exotic quantum effects.

Row 18 (Civilizations near sunlike stars): Now we come to the last and most important row, which mentions civilizations such as our civilization. There are many requirements for such a civilization. All of the items on the 17 previous rows on the table are indirect or direct requirements of civilizations near sunlike stars. The well-understood direct requirements of such civilizations are heavier atoms (needed so that the civilization can have the metals needed for technology), sunlike stars, stable planets, proteins, cells, and photosynthesis (the last one being necessary even if the beings in a civilization ate nothing but meat, because they would still rely on a food chain that would require photosynthesis).


The table I have created illustrates the great number of intertwining requirements needed for the universe to be consistent with the eventual appearance of civilizations such as ours. A huge amount of fine-tuning is required to meet these requirements, most notably in rows 1, 5, 9, and 11, each of which require “1 in a trillion” type coincidences with a very low likelihood of randomly occurring, We also have the very mysterious requirements of rows 13 and row 18, both of which almost seem to require “blood from stone” type of requirements (row 13 involving the origin of the genetic code from chemicals, and row 18 involving the origin of human-like consciousness from mere matter).

Our existence seems to require an almost miraculous conspiracy of conveniences, coincidences and fine-tuning within nature. As Stephen Hawking and Leonard Mlodinow said in their book The Grand Design (page 161), The laws of nature form a system that is extremely fine-tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it.”

Postscript (2/14/14): The table of anthropic requirements above is not at all a complete list of all of the requirements for creatures like us to exist. For example, I didn't list a major additional requirement for atoms: a dependency on Heisenberg's Uncertainty Principle. As discussed here,  were it not for this law of nature, electrons would fall into the nucleus of an atom, preventing any type of atom from existing.

Wednesday, January 15, 2014

Scientists Ponder: What Scientific Idea Should be Retired?

Edge.org is a web site that every year posts a thought-provoking question to a group of scientists and other thinkers. Each set of answers usually ends up getting published in book form, and this series of books has made some very interesting reading. This year's question is: what scientific idea is ready for retirement?

There are some big thinkers who respond to this question, but some of the answers involve some lame reasoning.

The first answer given is by cosmologist Andrei Linde, who gives “Uniformity and uniqueness of the universe” as the scientific idea he thinks should be retired. Linde cites cases in which our universe seems to be tailor-made for life, and notes that if the mass of the electron were slightly different, or protons were not almost the same mass as neutrons, or the energy of empty space were not just right, we wouldn't be here. Linde then suggests that we should therefore adopt the concept of a multiverse, a vast ensemble of universes:

If the universe were given to us in one copy..we would need to speculate about the divine cause making the universe custom built for humans. Meanwhile, in the multiverse consisting of many different parts with different properties, the correlation between our properties and the properties of the part of the world where we can live makes perfect sense.

But this reasoning by Linde is not correct. If there are a million billion trillion quadrillion universes, then the match or correlation between our universe and a habitable universe would not make any more sense (and would not be even .0000000001 percent more likely) than it would be if there is only one universe. This in because in both cases the chance of our universe being a habitable universe is exactly the same. Multiplying the number of universes does not change the probability of any one of those universes being successful. It may change the likelihood of at least one of those universes being successful, but it would have no effect at all on the likelihood of any one of those universes being successful. Similarly, selling a million lottery tickets with 7 random digits may increase the chance that some ticket buyer may win, but it does nothing to increase the chance that any one of those tickets will be a winner. To put it in terms of probability mathematics, increasing the number of trials does not increase the chance of any one trial being successful. So if our universe requires an almost miraculous conspiracy of lucky breaks to be habitable, you do nothing to make that seem less miraculous by supposing a vast number of universes. The habitability of our universe (not to be confused with some universe) is a zillion to one shot before the multiverse assumption, and it's just as much of a zillion to one shot after the multiverse assumption.

Another scientist who offers a flawed answer to the Edge.org question is physicist Alan Guth, who answers the question of “What scientific idea is ready for retirement?” by saying: “The Universe Began in a State of Extraordinarily Low Entropy.” In fact, there are still absolutely compelling reasons for believing that the universe did begin in a state of extraordinarily low entropy. According to the second law of thermodynamics, entropy is always increasing. So if we just rewind things back to the time of the Big Bang, we are left with a state of incredibly little entropy. The diagram below illustrates the point:



Why would Guth want to propose that the universe did not begin in an incredibly low entropy state? Because the low entropy of the early universe is a major reason for doubting the cosmic inflation theory that Guth originated (a point that cosmologist Roger Penrose has made). It turns out that the cosmic inflation makes the “incredibly low early entropy” problem much worse, and requires that the universe must begin in an even more special state (entropy-wise) than it would have begun in without cosmic inflation. As physicist Sean Carroll says, "To get inflation to start requires even lower-entropy initial conditions than those implied by the conventional Big Bang model." So naturally Guth wants to bolster his pet theory by getting rid of ultra-low entropy at the Big Bang, somewhat in the same way that a believer in Earth's uniqueness might want to get rid of evidence for extrasolar planets.

But what does Guth propose as a way to get rid of this ultra-low entropy at the universe's beginning? He suggests some theoretical work he describes like this: “This work, by Sean Carroll, Chien-Yao Tseng, and me, is still in the realm of speculation, and has not yet been vetted by the scientific community."

That candid statement shows on what very weak speculative ground Guth is standing on in this matter. Let's stick with the facts, and continue believing that the universe did begin in an astonishingly low entropy state.

Another flawed answer to the Edge.org question is given by Bruce Hood, who answers the question of “What scientific idea is ready for retirement?” by giving this answer: “The self.” Hood gives us some materialist reductionist nonsense that is designed to make you think that you don't have a you. Sorry Bruce, but having read my Descartes long ago, I can paraphrase him by simply saying: “I think, therefore you're wrong.” To anyone who has a self, there is nothing less necessary than disproving an argument against the self (only a computer might need to make such an argument).

Similar comments can be made about the strange, strained reasoning of physicist Nigel Goldenfeld, who suggests “Individuality” as the scientific idea that should be retired, and who assures us that “you can't attribute an event in time to a single earlier cause.”

Another weak answer to the Edge.org question is given by physicist Steve Giddings, who suggests “spacetime” as the scientific idea that should be retired. Giddings points out that general relativity and quantum mechanics need to be reconciled, and that the idea of spacetime may not survive once that happens. Yes, but that may take centuries; and meanwhile we need the notion of spacetime.

Worse than Giddings' answer is the answer given by W. Daniel Hillis, a physicist who suggests “Cause and effect” as the scientific idea that should be retired. He says, “We will come to appreciate that causes and effects do not exist in nature, that they are just convenient creations of our own minds.” Nonsense. If I jump off a high cliff, my jumping will be the cause, and my death will be the effect.


Don't come near this if you're a Hillis fan

Another silly answer is given by Jerry Coyne, who suggests “Free Will” as the scientific idea that should be retired. He claims there is “no evidence for a mind separate from the physical brain,” something that would be doubted by many people studying near-death experiences. Coyne then claims “recent experiments support the idea that our 'decisions' often precede our consciousness of having made them.” These experiments (involving a difference of only an instant) have been well-debunked by detractors (anyone interested can read this article). The supposed evidence for a “decision before the decision” is very dubious, since we don't have the technology to read a mind, and can't tell exactly when a person has made a decision by reading his brain activity. 

Another dubious answer is given by philosopher Daniel C. Dennett, who answers "the hard problem of consciousness" as his scientific idea that should be retired. This is the problem of how matter (something so different from consciousness) could give rise to consciousness. I suspect that Dennett wants to get rid of the problem because he has no answer to it, and it is troubling to his worldview. He gives no real reason why the problem should be retired. Dennett's imperfect judgement may be shown by his very misleading statement elsewhere: "We have pretty much figured out how life got started, the big bang, black holes, gravity, and electricity."  At least two of these (the big bang and the origin of life) are still very major mysteries, the big bang in particular being completely unexplained.

The home page of Edge.org currently trumpets itself as “a forum for the world's most brilliant minds,” although you would never know it from some of these answers to this year's Edge.org question.

But there were some good answers to the question of what scientific idea should be retired. Among the more intelligent answers (provided by various thinkers) were the following:

There Is No Reality in the Quantum World
M Theory/String Theory is the Only Game in Town
Only “Scientists” Can Do Science
Natural Selection is the Only Engine of Evolution
String Theory
Unlimited and Eternal Growth
Unbridled Scientific and Technological Optimism
Science Makes Philosophy Obsolete
The Atheism Prerequisite
The Mind Is Just the Brain

I agree that these ideas are ripe for retirement.

Monday, January 13, 2014

Will You Experience Godlike Virtual Psychokinesis?

Imagine walking through a world in which you can control things with your mind. If you come to a closed door, you need merely think to yourself: open. Then the door will open. If you are attacked by someone charging you with a knife, you need merely think to yourself: burn. Then the assailant trying to kill you will catch on fire. Or if you are walking along and need a car, you need merely think to yourself: car, and a car will appear.

You may actually experience such a world in your lifetime, but it won't be real life. It will be virtual reality. But it may be so realistic it will seem just like real life, except for your godlike powers. In such a world you may have an ability to make some things happen just by thinking of them. In this virtual world you may feel like a god who can alter reality just by willing something.

Such a thing may be possible because virtual reality technology may be merged with mind-reading technology. The term “mind-reading technology” is somewhat misleading. It would probably be better to call such a technology “thought correlation technology.” The way it works is that the brain is scanned for some distinctive electrical pattern that corresponds to a particular thought. For example, scientists might get a hundred people to think of a dog, and try to look for a distinctive electrical pattern observed when people are thinking that thought. The scientists might then get a hundred people to think of a book, and try to look for a distinctive electrical pattern observed when people are thinking that thought. With sufficient practice, scientists might then be able to look at the electrical activity in someone's brain at a particular moment, and then guess whether the person was thinking of a dog or a book. 

Scientists have already made significant progress at such a task, as indicated by this link Mind-Reading Technology Speeds Ahead.  

If a great deal of progress is made in such technology, the creators of virtual reality worlds might be able to integrate mind-reading technology into their systems. The result might be a virtual reality system that requires two pieces of equipment. You would put on virtual reality glasses over your eyes. You would then put on some type of electrode cap over your head. The electrode cap would handle the mind-reading.

You would then enter a virtual world, in which you would be like the psychokinetic lead character in the movie Carrie, who can control matter just by willing it to move or burn. We can use the term virtual psychokinesis for such a system, in which you could alter a video game world just by thinking of things.

virtual reality

The ideal implementation of such a virtual reality system would be one in which you could think almost any thought, and it would materialize within the virtual reality world. For example, you might randomly think of Marilyn Monroe, and then, poof, you would see Marilyn Monroe within the video world, as a moving, talking 3D character. But the technology for a system that sophisticated is probably many centuries away. For one thing, we are unlikely to have anything like a general mind-reading system capable of recognizing almost any thought. The best we can hope for is a far cruder technology that simply consists of a few hundred cases (or a few thousand cases) in which we know what brain activity looks like when someone is thinking of a particular thing. For another thing, even if we could recognize almost any thought, it would be too hard to program a virtual world in which almost any thing could be brought into existence by your thoughts.

But developers could still create an exciting virtual reality system that recognized only a small number of thoughts. A user might be advised of a certain limited number of thoughts that the system can accept. For example, an instruction booklet might say, “If you want to destroy an attacker, think of fire or think of the opponent being instantly frozen.” Or the booklet might say, “If you need transportation in the virtual world, think of a car or think of a horse.”

Some might think that introducing such a feature might make the virtual world seem less realistic, but it might not be worse than some things in current video games. For example, let's take the popular video game Red Dead Redemption, in which you become a cowboy in the old West. In that game every time you want to switch from a lasso to a gun, you have to click a button, go to a menu, and choose one of the two items from the menu. That almost spoils the fun by reminding you: this is just a video game. If you had a virtual reality system in which you do things just by thinking about them, you wouldn't have this problem. There wouldn't be any pop-up interface to remind you: this isn't real life.

Let's imagine how you might feel in such a virtual world, in which you can make things happen just by thinking particular thoughts. You might feel like some kind of deity. You might say to yourself: I am the one lord of this domain. I can destroy my opponents merely by thinking of how they should be destroyed. I can make matter change its appearance merely by willing that it change its appearance in some way. Like a deity, I can bring into existence new objects merely by thinking that they should exist. This truly is godhood. I can perform stunning miracles solely through the awesome power of my mighty mind.

And then, when your virtual reality session ended, you would take off your goggles, and go back to your meek little existence as a subservient corporate serf.

Sunday, January 12, 2014

The Multiverse Defendant: A Science Fiction Story

In the year 2051 the body of Ellen Taylor was found dead in her apartment, lying in a pool of blood. Two homicide detectives arrived on the scene, accompanied by their latest mobile robot, a TRM-49 unit specialized for doing work on homicides. The robot quickly took blood samples, and within 60 minutes had detected that the crime scene had blood for two different persons: the murdered woman and another person. The robot interfaced with the National Health Database to obtain a match for the second person's blood. The second person was identified as one Robert Fielding.

Homicide detectives then tried to determine the whereabouts of Robert Fielding using the citywide camera surveillance system, which had cameras on every city block. The detectives used the facial recognition system that had been introduced in the year 2040. The system told them that Robert Fielding had walked with Ellen Taylor on the streets for several days prior to the crime, and that Robert had accompanied Ellen Taylor to her apartment on the night of the murder.
 

 
The security camera system at Ellen's apartment apparently showed something similar: a man looking just like Robert Fielding entering the apartment building with Ellen. That camera system showed a man looking just like Robert Fielding running out of the apartment on the night of the murder, with blood stains on his clothes.

The police arrested Robert Fielding, and charged him with the murder of Ellen Taylor. A few months later the case came to trial. Robert Fielding pleaded not guilty.

The prosecution first presented the blood evidence. They produced a DNA expert who argued that the chance of someone else accidentally having blood matching Robert Fielding's was 1 in 1,000,000,000.

The prosecution then presented the photographic evidence. They zoomed in on the photographs, and called as witnesses facial feature analysis experts. The experts argued that the chance of someone else other than Fielding matching the face in the videos was about 1 in 500,000.

Then the prosecution called as a witness Karen Christie, a friend of Ellen who said that as Ellen was dying, she called Karen using her hologram phone and told her, “Robert Fielding stabbed me because I wouldn't have sex with him.”

Robert Fielding's lawyer did not question any of these witnesses, and called no witnesses himself. Robert Fielding was not called as a witness to defend himself.

When it came time for the closing summaries, the prosecution gave a triumphant summary, arguing that the case against Robert Fielding was the most open-and-shut murder case the court had ever seen.

Then it was the defense's turn for the closing summary. Dale Stafford, Fielding's lawyer, stood up and addressed the jury.

“This is a case about reasonable doubt,” said Stafford. “If you have reasonable doubt that my client killed this woman, you must acquit him. But you must have reasonable doubt, for a reason I will now explain.”

“Some scientists say that our universe may be only one of many universes that exist,” said Stafford. “They call this collection of universes the multiverse. Now let's imagine they're right. Let's imagine there are millions and billions and trillions and quadrillions of universes.”

“If such a thing is true, then many things that are incredibly unlikely must happen,” continued Stafford. “Even if something has only one chance in a billion trillion quadrillion of happening, we should imagine that it has happened not just once, but multiple times, assuming that there are a nearly infinite number of universes in the multiverse.”

“So let's imagine a very unlikely coincidence,” explained Stafford. “Imagine there's a country where there are two men named Robert Fielding. They both look the same, and they both have the same DNA. The chance of this happening may be one in a billion trillion quadrillion. But, in fact, such an unlikely coincidence would be likely to occur, given a sufficiently large number of universes in the multiverse.”

“So since it is perhaps likely that there could be some other Robert Fielding with a face and DNA matching my client's face and DNA,” finished Stafford, “and since that other Robert Fielding may have killed Ellen Taylor, you must have reasonable doubt that my client is guilty.”

The jury took fifty minutes to deliberate, and returned with a verdict of guilty. Robert Fielding was taken away to begin a life in prison.

After the trial as Stafford was leaving the court building, the defeated lawyer ran into one of the jurors in the elevator.

“Didn't I show there was a decent chance that some person would be wrongly accused because of some fantastically unlikely coincidence?” asked Stafford.

“Perhaps,” said the juror. “The problem was, you didn't do anything to show that this person, your client, was that some person.”

Note: this is a story of some philosophical relevance, being related to the issue of whether multiverse explanations are suitable for explaining coincidences and apparent fine-tuning in our universe.