A paradox is a statement or idea that contains an inherent contradiction. Some examples are:

The paradox of choice: Buyers want choices, but too much choice is overwhelming and prevents buyers from making a choice.

The paradox of tolerance: A society that tolerates everything must also tolerate intolerance. Is a society that tolerates intolerance tolerant or intolerant?

The chicken and egg paradox: The classic biological paradox: which came first, the chicken or the egg? I’ve always wondered why chickens were chosen for this paradox. No one asks if the kitten or cat came first, the puppy or the dog, or the baby or the adult.

The machine-tool-construction paradox: This is similar to the chicken and egg paradox. Every machine that exists was built using tools made by other machines. How could the first machine have been built if there were no machines before it to make the tools needed to build the first machine?

Perhaps the simplest paradox is the sentence: This sentence is false. If it’s true, then it’s false, and if it’s false, then it’s true, in an endless loop. 

Going in circles

One cause of this paradox is the fact that “This sentence is false” refers to itself in a strange form of circular reasoning. Circular reasoning is a flawed argument where the conclusion of the argument is assumed to be true, and which then uses this conclusion to “prove” the premise.

Examples of circular reasoning are:

John must be guilty because he was arrested. This argument assumes that only guilty people are arrested, and that if someone is arrested, they must be guilty.

You should obey the law because it’s illegal to break the law.  By definition, if you don’t follow the law, you are committing an illegal act, so this statement does not argue anything.

All circular reasoning takes the form: A = B because B = A. The sentence “This sentence is false.” is a one-sentence version of this form.

This is not a heading

One way to resolve “This sentence is false” is to declare it is not really a sentence, or at least not one with any meaning.

It is possible to group words together into a sentence that has no meaning. Noam Chomsky provides a good example: Colorless green ideas sleep furiously. This sentence is grammatically correct but meaningless. Therefore, we could say that the sentence “This sentence is false” is null and void. We thereby sentence this sentence to exile in the land of forbidden sentences.

However, this smacks of circular reasoning, because we’re effectively saying: This sentence is not a sentence because it’s not a sentence. Our desire to resolve this and other paradoxes reflects a larger world-view, that there should be no contradictions in life. However, our entire world is based on contradictions and paradoxes.

Let there be light

One of the most ubiquitous things in our universe is light. However, there is a fundamental contradiction in the nature of light. Depending on how you observe it, light is a wave or a particle. This contradiction in light’s structure is known as wave-particle duality. 

Wave-particle duality relates to another area of physics, quantum mechanics, which has more paradoxes. A principle of quantum mechanics is that a particle can be in more than one place at the same time, a completely paradoxical existence.

It’s big, relatively speaking

Quantum mechanics is the study of the very small: atoms and their components. General relativity, by contrast, is the study of very large objects like planets and galaxies.

Because we live in one universe, there should be one set of rules governing everything. However, there are fundamental contradictions between quantum mechanics and general relativity.

In quantum mechanics, time flows consistently, whereas in general relativity, time can be bent using matter and energy. Quantum mechanics is based on the uncertainty principle, which states that you cannot know the exact speed and location of a subatomic particle at the same time, an idea incompatible with general relativity, where speed and location are both known.

Let’s get small

Quantum mechanics also includes the bizarre concepts of Planck length and Planck time, both enormously small units of measure.

A Planck length is 1.6 × 10⁻³⁵ meters or 0.00000000000000000001 times the size of a proton. If an atom was the size of the earth, a Planck length would be the size of a proton.

Planck time is one 10⁻⁴³ of a second. One unit of Planck time is to a second what a second is to 300 billion trillion years, a time far greater than the age of the universe.

Planck length and Planck time are thought to be the smallest possible intervals that can be measured. If you tried to go any smaller, the laws of physics would break down.

There are also limits on how large space and time can be. Although the universe is very large and very old, it is not infinitely large or old. It is estimated to be 93 billion light-years wide, and 14 billion years old.

The fact that space and time, the most elemental aspects of reality, have an upper and lower limit implies that there is a cosmic minimum and maximum resolution to the universe, much like a TV has a minimum and maximum image resolution, beyond which it cannot go.

Whether these limits are by design or simply an inherit aspect of our reality remains a mystery.

Applied science

Scientists are trying to unify quantum mechanics with general relativity into a grand “theory of everything” that would resolve the fundamental differences between them. Still, despite these differences, each area has led to amazing discoveries.

Applications of quantum mechanics include lasers, electron microscopes, solar cells and quantum computing. General relativity is applied to cosmology (the study of the origin and evolution of the universe), the study of black holes, nuclear fusion (a potential limitless source of clean energy) and GPS (Global Positioning Systems).

The application of GPS is particularly salient. A GPS helps us navigate through new and strange territory; to find our way. This is exactly what a grand unified theory of general relativity and quantum mechanics would do – decode exactly where we fit in the universe.

Scientists have made enormous advances using both these areas, despite the fact that they contradict each other. There is no conflict between progress and contradiction. Science takes the best of both worlds, large and small.

Feeling conflicted

Contradictions are useful not just in science but in life. We live with, indeed we thrive, with contradictions.

We must be assertive but flexible. We must be independent but social. We judge but are compassionate. We seek challenges but also comfort. We must fit within society but also question the status quo and change it. We have free will, but are strongly influenced by others and outside forces.

Through these contradictions, we grow and mature. We do not need to choose one or the other – we need both.

Intelligence 2.0

Both science and humanity are facing their own paradox with the explosive growth of AI (artificial intelligence). DallE and MidJourney AI create astounding images from descriptive text. ChatGPT gives detailed, coherent responses to questions and requests, including general queries, poems and short stories.

Here is an example of an image created using MidJourney:

Have cake, will eat it too

Depending on what output you are observing, AI sometimes produces superior output than a human can, and sometimes does not. To resolve this paradox, we can have AI and humans working together.

A chess player working with an AI will play better than a person or an AI separately. Doctors work with AI medical systems such as IBM’s Watson to diagnose diseases.

There is a particularly remarkable example of humans working with AI. Music historians, musicologists, composers and computer scientists created an AI to analyze Beethoven’s unfinished 10th symphony and all his other works. Based on the patterns the AI found, it generated a musical score on what it thought the remainder of the unfinished symphony should be. The musicians constantly reviewed and updated the AI’s score using their extensive human musical skills. You can see a portion of the remarkable final result here.

We can go even further. Humans are not only working well with AIs, they are combining different AI systems together to produce complex new forms. People have used ChatGPT to write descriptive stories, then copied these descriptions into an AI image generator, creating completely original graphic novels. Similar combinations of AIs can create sounds and videos. In the near future, we may be able to use a single AI to instantly create entire movies with coherent stories, images, music and sound.

I think, therefore I doublethink

As we’ve seen, in science and in life, we use contradictory approaches to solve problems and answer difficult questions. This is doublethink, the ability to hold two contradictory thoughts simultaneously, a concept from George Orwell’s dystopian classic 1984.

Doublethink is illustrated in a scene in the novel where Winston, held captive by O’Brien, says that two and two are four. O’Brien calmly responds:

“Sometimes, Winston. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. You must try harder. It is not easy to become sane.”

Doublethink surely is not a good thing, then, is it?

It depends – in fact, you can use doublethink to describe itself:

• Doublethink is a dangerous form of thinking that leads to contradictory ideas.
• Doublethink is a productive form of thinking that leads to new ideas and tangible benefits.

Both of these things are true, and not true.

The Big Question

Science uses doublethink to describe the nature of light and reality. But could doublethink answer the question of what gives life meaning and purpose, and whether God exists?

On these ultimate questions, the main belief systems include:

Theism – The belief that God exists and is the source of all meaning and morality.

Atheism – The belief that God does not exist. Life has no meaning or we must invent one.

Agnosticism – The belief that we cannot know if God exists or not. Life may or may not have meaning.

Humanism – The belief in the worth and dignity of humans individually and collectively, rather than God, with an emphasis on critical thinking, reason, individual freedom and free thought, and the scientific method.

Ignosticism – This is similar to agnosticism in that it states that it’s impossible to know if God exists. However, it goes further by saying that the question itself is meaningless, because it’s impossible to know exactly what God is or what the nature of his existence could be.

All these views have their strengths and weaknesses. For me, the three most compelling are humanism, agnosticism and theism.

But which one of these is “correct”?

Quantum theology

I suggest a new belief system, quantheism, which states that depending on the observer and the situation, God exists or does not exist.

When we observe the awesome complexity of the universe, the planets, stars and galaxies, the incredible variety of life, and the sense of community and history within our faith, God flows into existence.

When we see that most people, including millions of children and other innocents, suffer in poverty, misery, war, natural disasters and disease, often dying young, God slips out of existence.

When we recognize the challenge of knowing that there must be a right and wrong, but not having an outside source of morality, God flows into existence. When we observe that people can behave rightly or wrongly regardless of whether they are religious or secular, God fades away.

When we struggle between these two views, we are agnostic, and God moves into a quantum state, neither existing nor not existing.

Theism provides an order and structure to the world, a sense of wonder, a belief that there is more out there than what we experience with our physical senses; it give us a sense of hope, of connection to an infinite guiding force, and the knowledge that this life is not all there is.

Humanism gives us rational thought, the scientific method, personal freedom, tolerance, self-determination, and personal responsibility.

Agnosticism gives us the freedom to doubt, and freedom from absolutes.

So am I a theist, humanist, or agnostic?

Sometimes I am a theist. Sometimes I am humanist. Sometimes I am agnostic. Sometimes I am all of them at once.

It is not easy to become sane.