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Oct. 27, 2013 By David Knight, SPIEGEL
Two scientists have formalized a theorem regarding the existence of God penned by mathematician Kurt Gödel. But the God angle is somewhat of a red herring -- the real step forward is the example it sets of how computers can make scientific progress simpler.
As headlines go, it's certainly an eye-catching one. "Scientists Prove Existence of God," German daily Die Welt wrote last week.
But unsurprisingly, there is a rather significant caveat to that claim. In fact, what the researchers in question say they have actually proven is a theorem put forward by renowned Austrian mathematician Kurt Gödel -- and the real news isn't about a Supreme Being, but rather what can now be achieved in scientific fields using superior technology.
When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic -- that a higher being must exist. The details of the mathematics involved in Gödel's ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
Even at the time, the argument was not exactly a new one. For centuries, many have tried to use this kind of abstract reasoning to prove the possibility or necessity of the existence of God. But the mathematical model composed by Gödel proposed a proof of the idea. Its theorems and axioms -- assumptions which cannot be proven -- can be expressed as mathematical equations. And that means they can be proven.
That is where Christoph Benzmüller of Berlin's Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, come in. Using an ordinary MacBook computer, they have shown that Gödel's proof was correct -- at least on a mathematical level -- by way of higher modal logic. Their initial submission on the arXiv.org research article server is called "Formalization, Mechanization and Automation of Gödel's Proof of God's Existence."
The fact that formalizing such complicated theorems can be left to computers opens up all kinds of possibilities, Benzmüller told SPIEGEL ONLINE. "It's totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook," he said.
The name Gödel may not mean much to some, but among scientists he enjoys a reputation similar to the likes of Albert Einstein -- who was a close friend. Born in 1906 in what was then Austria-Hungary and is now the Czech city of Brno, Gödel later studied in Vienna before moving to the United States after World War II broke out to work at Princeton, where Einstein was also based. The first version of this ontological proof is from notes dated around 1941, but it was not until the early 1970s, when Gödel feared that he might die, that it first became public.
Now Benzmüller hopes that using such a headline-friendly example can help draw attention to the method. "I didn't know it would create such a huge public interest but (Gödel's ontological proof) was definitely a better example than something inaccessible in mathematics or artificial intelligence," the scientist added. "It's a very small, crisp thing, because we are just dealing with six axioms in a little theorem. … There might be other things that use similar logic. Can we develop computer systems to check each single step and make sure they are now right?"
'An Ambitious Expressive Logic'
The scientists, who have been working together since the beginning of the year, believe their work could have many practical applications in areas such as artificial intelligence and the verification of software and hardware.
Benzmüller also pointed out that there are many scientists working on similar subject areas. He himself was inspired to tackle the topic by a book entitled "Types, Tableaus and Gödel's God," by Melvin Fitting.
The use of computers to reduce the burden on mathematicians is not new, even if it is not welcomed by all in the field. American mathematician Doron Zeilberger has been listing the name Shalosh B. Ekhad on his scientific papers since the 1980s. According to the New York-based Simons Foundation, the name is actually a pseudonym for the computers he uses to help prove theorems in seconds that previously required page after page of mathematical reasoning. Zeilberger says he gave the computer a human-sounding name "to make a statement that computers should get credit where credit is due." "human-centric bigotry" on the part of mathematicians, he says, has limited progress.
Ultimately, the formalization of Gödel's ontological proof is unlikely to win over many atheists, nor is it likely to comfort true believers, who might argue the idea of a higher power is one that defies logic by definition. For mathematicians looking for ways to break new ground, however, the news could represent an answer to their prayers.
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Download mp3 Here are six straight-forward reasons to believe that God is really there. By Marilyn Adamson
Just once wouldn't you love for someone to simply show you the evidence for God's existence? No arm-twisting. No statements of, "You just have to believe." Well, here is an attempt to candidly offer some of the reasons which suggest that God exists.
But first consider this. When it comes to the possibility of God's existence, the Bible says that there are people who have seen sufficient evidence, but they have suppressed the truth about God.1 On the other hand, for those who want to know God if he is there, he says, "You will seek me and find me; when you seek me with all your heart, I will be found by you."2 Before you look at the facts surrounding God's existence, ask yourself, If God does exist, would I want to know him? Here then, are some reasons to consider...
1. Does God exist? The complexity of our planet points to a deliberate Designer who not only created our universe, but sustains it today. Many examples showing God's design could be given, possibly with no end. But here are a few:
The Earth...its size is perfect. The Earth's size and corresponding gravity holds a thin layer of mostly nitrogen and oxygen gases, only extending about 50 miles above the Earth's surface. If Earth were smaller, an atmosphere would be impossible, like the planet Mercury. If Earth were larger, its atmosphere would contain free hydrogen, like Jupiter.3 Earth is the only known planet equipped with an atmosphere of the right mixture of gases to sustain plant, animal and human life.
The Earth is located the right distance from the sun. Consider the temperature swings we encounter, roughly -30 degrees to +120 degrees. If the Earth were any further away from the sun, we would all freeze. Any closer and we would burn up. Even a fractional variance in the Earth's position to the sun would make life on Earth impossible. The Earth remains this perfect distance from the sun while it rotates around the sun at a speed of nearly 67,000 mph. It is also rotating on its axis, allowing the entire surface of the Earth to be properly warmed and cooled every day.
And our moon is the perfect size and distance from the Earth for its gravitational pull. The moon creates important ocean tides and movement so ocean waters do not stagnate, and yet our massive oceans are restrained from spilling over across the continents.4
Water...colorless, odorless and without taste, and yet no living thing can survive without it. Plants, animals and human beings consist mostly of water (about two-thirds of the human body is water). You'll see why the characteristics of water are uniquely suited to life:
It has an unusually high boiling point and freezing point. Water allows us to live in an environment of fluctuating temperature changes, while keeping our bodies a steady 98.6 degrees.
Water is a universal solvent. This property of water means that various chemicals, minerals and nutrients can be carried throughout our bodies and into the smallest blood vessels.5
Water is also chemically neutral. Without affecting the makeup of the substances it carries, water enables food, medicines and minerals to be absorbed and used by the body.
Water has a unique surface tension. Water in plants can therefore flow upward against gravity, bringing life-giving water and nutrients to the top of even the tallest trees.
Water freezes from the top down and floats, so fish can live in the winter.
Ninety-seven percent of the Earth's water is in the oceans. But on our Earth, there is a system designed which removes salt from the water and then distributes that water throughout the globe. Evaporation takes the ocean waters, leaving the salt, and forms clouds which are easily moved by the wind to disperse water over the land, for vegetation, animals and people. It is a system of purification and supply that sustains life on this planet, a system of recycled and reused water.6
The human brain...simultaneously processes an amazing amount of information. Your brain takes in all the colors and objects you see, the temperature around you, the pressure of your feet against the floor, the sounds around you, the dryness of your mouth, even the texture of your keyboard. Your brain holds and processes all your emotions, thoughts and memories. At the same time your brain keeps track of the ongoing functions of your body like your breathing pattern, eyelid movement, hunger and movement of the muscles in your hands.
The human brain processes more than a million messages a second.7 Your brain weighs the importance of all this data, filtering out the relatively unimportant. This screening function is what allows you to focus and operate effectively in your world. The brain functions differently than other organs. There is an intelligence to it, the ability to reason, to produce feelings, to dream and plan, to take action, and relate to other people.
The eye...can distinguish among seven million colors. It has automatic focusing and handles an astounding 1.5 million messages -- simultaneously.8 Evolution focuses on mutations and changes from and within existing organisms. Yet evolution alone does not fully explain the initial source of the eye or the brain -- the start of living organisms from nonliving matter.
2. Does God exist? The universe had a start - what caused it? Scientists are convinced that our universe began with one enormous explosion of energy and light, which we now call the Big Bang. This was the singular start to everything that exists: the beginning of the universe, the start of space, and even the initial start of time itself.
Astrophysicist Robert Jastrow, a self-described agnostic, stated, "The seed of everything that has happened in the Universe was planted in that first instant; every star, every planet and every living creature in the Universe came into being as a result of events that were set in motion in the moment of the cosmic explosion...The Universe flashed into being, and we cannot find out what caused that to happen."9
Steven Weinberg, a Nobel laureate in Physics, said at the moment of this explosion, "the universe was about a hundred thousands million degrees Centigrade...and the universe was filled with light."10
The universe has not always existed. It had a start...what caused that? Scientists have no explanation for the sudden explosion of light and matter.
3. Does God exist? The universe operates by uniform laws of nature. Why does it? Much of life may seem uncertain, but look at what we can count on day after day: gravity remains consistent, a hot cup of coffee left on a counter will get cold, the earth rotates in the same 24 hours, and the speed of light doesn't change -- on earth or in galaxies far from us.
How is it that we can identify laws of nature that never change? Why is the universe so orderly, so reliable?
"The greatest scientists have been struck by how strange this is. There is no logical necessity for a universe that obeys rules, let alone one that abides by the rules of mathematics. This astonishment springs from the recognition that the universe doesn't have to behave this way. It is easy to imagine a universe in which conditions change unpredictably from instant to instant, or even a universe in which things pop in and out of existence."11
Richard Feynman, a Nobel Prize winner for quantum electrodynamics, said, "Why nature is mathematical is a mystery...The fact that there are rules at all is a kind of miracle."12
4. Does God exist? The DNA code informs, programs a cell's behavior. All instruction, all teaching, all training comes with intent. Someone who writes an instruction manual does so with purpose. Did you know that in every cell of our bodies there exists a very detailed instruction code, much like a miniature computer program? As you may know, a computer program is made up of ones and zeros, like this: 110010101011000. The way they are arranged tell the computer program what to do. The DNA code in each of our cells is very similar. It's made up of four chemicals that scientists abbreviate as A, T, G, and C. These are arranged in the human cell like this: CGTGTGACTCGCTCCTGAT and so on. There are three billion of these letters in every human cell!!
Well, just like you can program your phone to beep for specific reasons, DNA instructs the cell. DNA is a three-billion-lettered program telling the cell to act in a certain way. It is a full instruction manual.13
Why is this so amazing? One has to ask....how did this information program wind up in each human cell? These are not just chemicals. These are chemicals that instruct, that code in a very detailed way exactly how the person's body should develop.
Natural, biological causes are completely lacking as an explanation when programmed information is involved. You cannot find instruction, precise information like this, without someone intentionally constructing it.
5. Does God exist? We know God exists because he pursues us. He is constantly initiating and seeking for us to come to him. I was an atheist at one time. And like many atheists, the issue of people believing in God bothered me greatly. What is it about atheists that we would spend so much time, attention, and energy refuting something that we don't believe even exists?! What causes us to do that? When I was an atheist, I attributed my intentions as caring for those poor, delusional people...to help them realize their hope was completely ill-founded. To be honest, I also had another motive. As I challenged those who believed in God, I was deeply curious to see if they could convince me otherwise. Part of my quest was to become free from the question of God. If I could conclusively prove to believers that they were wrong, then the issue is off the table, and I would be free to go about my life.
I didn't realize that the reason the topic of God weighed so heavily on my mind, was because God was pressing the issue. I have come to find out that God wants to be known. He created us with the intention that we would know him. He has surrounded us with evidence of himself and he keeps the question of his existence squarely before us. It was as if I couldn't escape thinking about the possibility of God. In fact, the day I chose to acknowledge God's existence, my prayer began with, "Ok, you win..." It might be that the underlying reason atheists are bothered by people believing in God is because God is actively pursuing them.
I am not the only one who has experienced this. Malcolm Muggeridge, socialist and philosophical author, wrote, "I had a notion that somehow, besides questing, I was being pursued." C.S. Lewis said he remembered, "...night after night, feeling whenever my mind lifted even for a second from my work, the steady, unrelenting approach of Him whom I so earnestly desired not to meet. I gave in, and admitted that God was God, and knelt and prayed: perhaps, that night, the most dejected and reluctant convert in all of England."
Lewis went on to write a book titled, "Surprised by Joy" as a result of knowing God. I too had no expectations other than rightfully admitting God's existence. Yet over the following several months, I became amazed by his love for me.
6. Does God exist? Unlike any other revelation of God, Jesus Christ is the clearest, most specific picture of God revealing himself to us. Why Jesus? Look throughout the major world religions and you'll find that Buddha, Muhammad, Confucius and Moses all identified themselves as teachers or prophets. None of them ever claimed to be equal to God. Surprisingly, Jesus did. That is what sets Jesus apart from all the others. He said God exists and you're looking at him. Though he talked about his Father in heaven, it was not from the position of separation, but of very close union, unique to all humankind. Jesus said that anyone who had seen Him had seen the Father, anyone who believed in him, believed in the Father.
He said, "I am the light of the world, he who follows me will not walk in darkness, but will have the light of life."14 He claimed attributes belonging only to God: to be able to forgive people of their sin, free them from habits of sin, give people a more abundant life and give them eternal life in heaven. Unlike other teachers who focused people on their words, Jesus pointed people to himself. He did not say, "follow my words and you will find truth." He said, "I am the way, the truth, and the life, no one comes to the Father but through me."15
What proof did Jesus give for claiming to be divine? He did what people can't do. Jesus performed miracles. He healed people...blind, crippled, deaf, even raised a couple of people from the dead. He had power over objects...created food out of thin air, enough to feed crowds of several thousand people. He performed miracles over nature...walked on top of a lake, commanding a raging storm to stop for some friends. People everywhere followed Jesus, because he constantly met their needs, doing the miraculous. He said if you do not want to believe what I'm telling you, you should at least believe in me based on the miracles you're seeing.16
Jesus Christ showed God to be gentle, loving, aware of our self-centeredness and shortcomings, yet deeply wanting a relationship with us. Jesus revealed that although God views us as sinners, worthy of his punishment, his love for us ruled and God came up with a different plan. God himself took on the form of man and accepted the punishment for our sin on our behalf. Sounds ludicrous? Perhaps, but many loving fathers would gladly trade places with their child in a cancer ward if they could. The Bible says that the reason we would love God is because he first loved us.
Jesus died in our place so we could be forgiven. Of all the religions known to humanity, only through Jesus will you see God reaching toward humanity, providing a way for us to have a relationship with him. Jesus proves a divine heart of love, meeting our needs, drawing us to himself. Because of Jesus' death and resurrection, he offers us a new life today. We can be forgiven, fully accepted by God and genuinely loved by God. He says, "I have loved you with an everlasting love, therefore I have continued my faithfulness to you."17 This is God, in action.
Does God exist? If you want to know, investigate Jesus Christ. We're told that "God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life."18
God does not force us to believe in him, though he could. Instead, he has provided sufficient proof of his existence for us to willingly respond to him. The earth's perfect distance from the sun, the unique chemical properties of water, the human brain, DNA, the number of people who attest to knowing God, the gnawing in our hearts and minds to determine if God is there, the willingness for God to be known through Jesus Christ. If you need to know more about Jesus and reasons to believe in him, please see: Beyond Blind Faith.
If you want to begin a relationship with God now, you can. This is your decision, no coercion here. But if you want to be forgiven by God and come into a relationship with him, you can do so right now by asking him to forgive you and come into your life. Jesus said, "Behold, I stand at the door [of your heart] and knock. He who hears my voice and opens the door, I will come into him [or her]."19 If you want to do this, but aren't sure how to put it into words, this may help: "Jesus, thank you for dying for my sins. You know my life and that I need to be forgiven. I ask you to forgive me right now and come into my life. I want to know you in a real way. Come into my life now. Thank you that you wanted a relationship with me. Amen."
God views your relationship with him as permanent. Referring to all those who believe in him, Jesus Christ said of us, "I know them, and they follow me; and I give them eternal life, and they shall never perish, and no one shall snatch them out of my hand."20
Looking at all these facts, one can conclude that a loving God does exist and can be known in an intimate, personal way.