William M. Briggs

Statistician to the Stars!

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Is God is a Mathematician? Guest Post by Bob Kurland


Coincidentally, Bob Kurland sent this guest post on the day of miracles, a good follow up to yesterday’s post.

Feynman: “Do you know calculus?” Wouk: I admitted that I didn’t. Feynman: “You had better learn it…It’s the language God talks.” Herman Wouk, conversation with Richard Feynman in The Language God Talks, p.5.

In his very fine book, Is God a Mathematician?, Mario Livio gives a good history of mathematics and its foundational applications to science. He also discusses whether mathematics is a Platonic ideal or is a construction of the human mind—i.e. is mathematics “discovered” or “invented”? But he does not address the question posed in his title.

Now it goes without saying (although I will say it), that if God is omniscient, he knows everything and therefore, perforce, must know all mathematics. These propositions do not, however, require that reality is altogether mathematical, as suggested by Max Tegmark in his book, Our Mathematical Universe. If reality is altogether mathematical, then everything can be quantified, represented by numbers or properties that can put into correspondence with numbers. Is this so?

I invite the reader to suggest things that cannot be quantified by numbers. Here’s my list of a few such: self-awareness, consciousness (“Cogito, ergo sum”), moments of communion with God, The Holy Spirit, Jesus, love of another, shame, anger, pain, happiness, joy, feelings aroused by nature, feelings aroused by music, feelings aroused by intellectual discovery, the literary excellence of a poem, a short story, a novel, boredom on reading blog posts dealing with the reality of mathematics, etc.

Now psychologists might say that most, if not all of the above can be quantified: just use the simple 1-5 scale as, in satisfaction response surveys. I claim that, unlike measuring the mass of a steel ball or its radius, such a procedure would not yield a universal measurement—one person’s “2” might well be another person’s “4”. The qualia referred to in the above items are non-quantifiable, in the sense that a universally applicable measurement cannot be applied.

Let’s explore just one of the above in more detail—feelings aroused by music. In another post, God’s Gift to Man—the Transforming Power of Music, I’ve discussed the emotional and spiritual impact music has had on me, an effect which cannot be explained by mathematical relationships. The Pythagorean harmonies have no place in the dissonances of Bartok, Berlioz or even Mozart (Symphony #40, the Great G-Minor).

The inability of computation–mathematics—to emulate musical creativity is illustrated in a science-fiction story by James Blish, “A Work of Art“. In this tale “mind sculptors” of the future install a recreation of Richard Strauss in a non-musical volunteer. The volunteer thinks of himself as a resurrected Strauss, composes an opera, and then realizes it uses old musical devices and is not creative. At the concert in which the work is premiered, the volunteer knows that the resounding applause is for the mind sculptors, not for his musical work.

The eminent mathematical physicist, Roger Penrose, has said the mind is not a computer. Penrose demonstrates, using Godel’s Incompleteness Theorem and Turing’s Halting Theorem, that the human can know the truth of a mathematical theorem even when a computer can not.

In Shadows of the Mind he gives four types of belief or non-belief in the possibility of Artificial Intelligence (AI), that self-aware intelligence can be programmed by some set of algorithms:

  1. Consciousness is reducible to computation (the view of strong-AI proponents);
  2. Consciousness can be simulated by a computer, but the simulation couldn’t produce “real understanding” (John Searle’s view);
  3. Consciousness can’t even be simulated by computer, but nevertheless has a scientific explanation (Penrose’s own view)
  4. Consciousness doesn’t have a scientific explanation at all (the view of Thomas Nagel—see Mind and Cosmos)

The philosopher John Searle posits, as does Penrose, that consciousness has a scientific explanation , but that it will be an explanation in which consciousness is an “emergent” property of the brain’s biochemistry and biophysics, much as wetness can be explained by theories of surface tension for water.

A quantum computer (i.e. a scientist engaged in quantum computation), Scott Aaronson, has given an amusing and almost-convincing critique of Penrose’s thesis in one of his Physics Lectures. Some of his criticisms can be answered, particularly the one dealing with the Libet experiment, but I don’t propose to engage that discussion here. The critique relies primarily on two features: the activities of the mind are finite, not infinite; a computer which would be allowed to make mistakes would not be bound by Goedel’s Theorem.

Finally, note that Max Tegmark does not show in Our Mathematical Universe how consciousness can be explained as a mathematical phenomenon. He claims that this will be done in the future, but that seems to me very much like a scientism of the gaps.

If mathematics is to be the end-all and be-all of what is, then it seems reasonable to suppose that mathematics is complete in itself—there are no loose ends. A primitive view of Goedel’s and Turing’s theorems suggest that this is not so.

Faith, religion, beauty, love are non-mathematical and above the bounds of logic. As Pope St. John Paul II, said in Fides et Ratio:

Faith and reason are like two wings on which the human spirit rises to the contemplation of truth; and God has placed in the human heart a desire to know the truth—in a word, to know himself—so that, by knowing and loving God, men and women may also come to the fullness of truth about themselves.

So my answer to the question in the title is, God is much more than a mathematician.


Bread From Something Or Nothing? Or, What’s A Miracle?


We interrupt our tour of Summa Contra Gentiles for this brief message.

You’ve heard of the miracle of loaves and fishes? What’s a miracle? How do miracles happen? Read these for a refresher:

A man came from Baal-shalishah bringing the man of God twenty barley loaves made from the first fruits, and fresh grain in the ear. Elisha said, “Give it to the people to eat.”

But his servant objected, “How can I set this before a hundred?” Elisha again said, “Give it to the people to eat, for thus says the LORD: You will eat and have some left over.”

He set it before them, and when they had eaten, they had some left over, according to the word of the LORD.

After this, Jesus went across the Sea of Galilee. A large crowd followed him, because they saw the signs he was performing on the sick. Jesus went up on the mountain, and there he sat down with his disciples. The Jewish feast of Passover was near. When Jesus raised his eyes and saw that a large crowd was coming to him, he said to Philip, “Where can we buy enough food for them to eat?”

He said this to test him, because he himself knew what he was going to do.

Philip answered him, “Two hundred days’ wages worth of food would not be enough for each of them to have a little.”

One of his disciples, Andrew, the brother of Simon Peter, said to him, “There is a boy here who has five barley loaves and two fish; but what good are these for so many?”

Jesus said, “Have the people recline.” Now there was a great deal of grass in that place. So the men reclined, about five thousand in number. Then Jesus took the loaves, gave thanks, and distributed them to those who were reclining, and also as much of the fish as they wanted. When they had had their fill, he said to his disciples, “Gather the fragments left over, so that nothing will be wasted.”

So they collected them, and filled twelve wicker baskets with fragments from the five barley loaves that had been more than they could eat.

When the people saw the sign he had done, they said, “This is truly the Prophet, the one who is to come into the world.” Since Jesus knew that they were going to come and carry him off to make him king, he withdrew again to the mountain alone.

So I’m visiting a church and the deacon (I think) mounted the high ambo to give the homily. “Today’s reading is all about food,” he said. He mentioned “foodies” and food television and celebrity chefs. “Imagine you were one of the characters in the story,” he offered. “Imagine you were one of the loaves and fishes waiting to be handed out.”

It was at that point that I stopped listening and started thinking about what the passages—for these are the readings today—really meant.

Let’s accept the reported events occurred. How could they? God cannot do the impossible. He can’t, for instance, make himself not exist. That means if miracles like this are going to happen, there are only one of two ways that I see.

Now we know that matter and energy are related; E = mc2 and all that. So the first way would be to take existing equivalent masses or energies and convert them to the desired form—and in the require short time. So, rocks or grassy fields or whatever (mass or energy from elsewhere in the universe would have to be transported, and that requires even more work) are rearranged, via some mechanism, into sufficient bread or bread and fish to feed a multitude. Given what we know about nuclear physics, that would require a magnificent amount of energy. Think of the apparatus required to manipulate just one atom. Here were talking many.

How many? A good spherical cow problem. Should be able to get within an order of magnitude or two the mass involved, and thus a rough count of subatomic particles, and thus some idea of how to rearrange what’s on hand and what that would cost in terms on energy. Since I’m writing this right now this morning and in a hurry, I’ll leave this as a homework problem. The answer will be incomprehensibly beyond any human capacity.

The second way would be to create the masses (of bread or fish) ex nihilo. That requires infinite energy. Nothing is no thing, not some thing. Energy is something, and so is existing mass. So creating from nothing obviously requires Omnipotence. Nothing else could do it.

Point is, given that these events happened, if they happened by manipulating existing mass and energy, it would require something very like magic (but not). Like God. And if the masses were created from nothing, only God could do it.

Now there are other instances of creation ex nihilo and no reports of missing mass or flashing lights or anything like that. And there is nothing we know that would allow nuclear reactions to occur this quickly. This is circumstantial evidence, of course, but it does hint toward ex nihilo. And God. Of course, even rearranging mass points toward God.

And that’s what these passages are really about.

Since I wrote this as a replacement post and, as I said, in a hurry, I may update it as the day goes along.


This Week In Doom: Crunchy Yummy Babies And A New Circle Of Hell

At a Planned Parenthood auction.

At a Planned Parenthood auction.

There’s not much to enjoy about this week’s doom, except to note that things are speeding up. Perhaps we need a pseudo-quantified measure of our acceleration into the abyss?

Crunchy Yummy

From the Center for Inquiry’s (the group that used to be CSICOP) Cause & Effect Friday email:

Fighting Back Against the Scheme to Take Down Planned Parenthood

The religious right, in its zeal to take away women’s rights to make their own reproductive decisions, has long sought to bring about the end of Planned Parenthood, a vital organization that provides a wide variety of necessary health services, including HIV and cancer screenings, to millions of women. The latest manifestation of this campaign took the form of heavily doctored “undercover” videos that falsely purported to implicate Planned Parenthood in the selling of fetal body parts for profit. These deceptively edited videos have given religious right allies in Congress the fodder they seek to strike a potentially fatal blow to Planned Parenthood, with threats of legislation that would end all federal funding to this important organization.

As skeptics who believe in the importance of facts, we want to help make it clear that these video “stings” are ideological propaganda, and their claims have no basis in reality. Fetal tissue, freely donated to medical research by fully informed patients, has long provided incredible possibilities for discovering treatments for some of the cruelest diseases that afflict human beings, such as Parkinson’s. Under current law, such tissue cannot be sold, but “reasonable payments associated with the transportation, implantation, processing, preservation, quality control, or storage” can be made. That was all these deceptive videos showed. The New York Times editorialized this week, “Lawmakers responding by promoting their own anti-choice agenda are rewarding deception and putting women’s health and their constitutionally protected rights at risk.”

Let’s not let this underhanded scheme undo a great organization that provides such crucial health services to so many women. Tell your Members of Congress to stop the attacks on Planned Parenthood, and to stand up for women’s health and women’s rights.

This rather depressed me. And you have to feel sorry for these folks. So determined are they to hold onto immorality, that any evidence, even that which is false, is sufficient. They eagerly jettison reason, logic, observation, everything. “Heavily doctored” videos forsooth! They create that absurdity—the videos are plain and easily seen to be so—and then use it to imply to themselves that “editing” means “lies.” This gives them excuse not to watch the videos—and thus it removes the need to confront evil.

For the sake of completeness: killing a life inside a mother is not a “health service”, it is the opposite. A “women’s rights to make their own reproductive decisions” cannot be made in isolation of the man who impregnated her, and the “right” to kill her child is the point in dispute. If, as should happen in a just country, Planned Parenthood disappeared, women would still be able to get mammographies etc.

Utilitarianism (a tenet of liberalism and libetarianism) must lead, and has led, to tyranny and evil: the ends cannot justify the means. The law does not and cannot decide what is evil or immoral. Of course, when the law fails to conform to human nature, as ours does, then the end must come. It is only a question of when. If Planned Parenthood gets away with this, which is likely, it will be much sooner than later.

Done With Dante

Dante’s Divine Comedy ‘offensive and should be banned’

The classic work should be removed from school curricula, according to Gherush 92, a human rights organisation which acts as a consultant to UN bodies on racism and discrimination.

Dante’s epic is “offensive and discriminatory” and has no place in a modern classroom, said Valentina Sereni, the group’s president…

“The Prophet Mohammed was subjected to a horrific punishment — his body was split from end to end so that his entrails dangled out, an image that offends Islamic culture,” she said.

Homosexuals are damned by the work as being “against nature” and condemned to an eternal rain of fire in Hell.

I’m offended that thinking Islam might be offended should justify that Dante should be banned. Therefore the UN may not ban. Homosexuals aren’t damned: those who commit homosexual acts, which are obviously against nature, and do not seek forgiveness are damned. As we all are unless we also ask for grace.

The Past Is History

Activist group shovels ground at Confederate General Nathan Bedford Forrest’s grave

On July 22 a group of protesters from the Commission on Religion and Racism (CRR) used a shovel and “dug up a patch of grass next to” Confederate General Nathan Bedford Forrest’s Memphis statue, saying they hope others “follow suit and dig him up.”

NAACP still pushing to sandblast Confederate leaders from Stone Mountain

Once the Confederate Battle Flag came down on the grounds of the South Carolina Capitol complex, the Left had won their great victory and everyone could go home and get on with their lives, right? (I’ll pause for a moment so everyone can finish laughing.) Of course not. Nothing is ever truly going to be enough, and the NAACP has been on a push for more than a week with a larger target in mind. A much, much larger target. They would like the 90 by 190 foot sculpture at Stone Mountain Park in Georgia sandblasted from the face of the mountain. Rising 400 feet above the ground, it’s the largest, highest outdoor relief sculpture in the world and depicts Jefferson Davis, Robert E. Lee and Stonewall Jackson.

Orwell says, “There was never a Confederacy.” Yet another symptom of believing “truth” is decided by the powerful.

One Party Shall Rule Them All

Ted Cruz on the Senate floor: Mitch McConnell’s a liar and our new majority is a cronyist fraud

Sample quote: “[This majority] does get things done, but it listens to one and only one voice: That is, the voice of the Washington cartel, of the lobbyists on K Street, of the big money and big corporations.” This guy is talking about his own caucus.

Prediction about the effect of this speech: none. There is also thus no reason to discuss the Iran deal.


The Remnant: Ever Wonder Why Gmarriage Is Only Legal in Post Christian Nations?


Today’s post is at The Remnant: “Ever Wonder Why Gmarriage Is Only Legal in Post Christian Nations?

Have you noticed that gmarriage—government-defined marriage—is legal only in post-Christian nations? Why this is so in a moment, but first a brief review of where we stand.

The Netherlands were the first to pretend that two men (or two women) can be married, making it the law of the land in 2001. Belgium followed close at heel in 2003, with the flight from reality gaining momentum in 2005 with Canada and Spain. As of this writing, there are twenty-four countries mandating gmarriage, with Finland, Ireland, Mexico, and the United States the latest entries.

Go there to read the rest. Albert Jay Nock would: you should, too.

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