Or Are You Real?
Pause for a moment and ask yourself a quietly subversive question.
How do you know that any of this is real?
Your life. Your memories. Your loved ones. The screen before you. Everything and everyone you know. Could it all be a brief hallucination, a flicker of awareness flashing and fading in a vast, indifferent void?
This isn’t a sceptical game from a philosophy seminar. It’s a live problem in modern physics and philosophy, known as the Boltzmann Brain paradox. And once you take it seriously, something surprising happens: the sheer coherence of your experience, its continuing stability, starts to look not like an obvious fact, but like a profound mystery.
Two Ways to Make a Mind
Imagine a universe without intent; just matter, energy, and time. How could a conscious observer arise in such a world?
1. The Hard Way
The universe begins in an awesomely ordered state. Physicists call this Low Entropy. Think of a brand-new deck of cards, perfectly sorted by suit and number. This extreme organisation allows for a complex, long-lasting “game” to follow.
Laws remain stable. Stars form, galaxies evolve, and life stirs on a small planet. Over billions of years, chemistry dreams itself awake, until one day someone sits reading an article about cosmology and doubt. This route demands what philosophers call Fine-Tuning: the idea that the fundamental constants of physics (like gravity) are dialled into a precise, “life-permitting” range.
It yields what we call a normal observer, a mind rooted in an ongoing, stable physical world.
2. The Easy Way
Now picture the opposite extreme: High Entropy. This is the universe after the deck has been shuffled for billions of years. In this world of pure chance, even the shuffled deck will produce a “straight flush” and then another and so on, just by accident. Given enough time, particles randomly arrange themselves into something along the lines of a functioning brain.
That brain would:
• Possess conscious thoughts
• Carry vivid but false memories
• Mistake illusion for reality
And almost instantly, it would dissolve again into the shuffle. That is a Boltzmann Brain.
The Unsettling Arithmetic: A Universe of Ghosts
Here’s the disquieting part: statistically, the easy way is far more common.
It is vastly “cheaper” for nature to generate hallucinating minds than to build a 14-billion-year-old stage for that mind to stand on. If the universe is a blind accident, for every one “real” brain that evolved over billions of years, there should be countless Boltzmann Brains popping into existence.
In a random, unguided cosmos, the “Normal Observers” are a vanishingly small minority. The “Blips” are the rule.
Which leads to a seemingly absurd, yet mathematically very serious, conclusion: If this picture of the universe is right, then you are almost certainly a Boltzmann Brain. You are statistically more likely to be a fleeting ghost than a real human. If that’s so, your trust in reality is a mathematical mistake.
When Fine-Tuning Stops Being Enough
The Fine-Tuning problem already puzzles physicists: why the laws of nature appear calibrated for life. The “Multiverse” is sometimes offered as a tidy answer; that with multiple universes, one like ours eventually appears.
But the Boltzmann Brain paradox in this case suddenly presses harder. Random multiverses produce exponentially more chaotic fluctuations, more opportunities for Boltzmann brains. Now the very scenario meant to explain our existence actually makes our persistent sanity a statistical nonsense. In this way, a universe that explains everything explains nothing. It turns truth itself into a mirage.
A Cosmos Biased Towards Coherence
So perhaps this assumption is wrong, and the universe does not drift aimlessly through probability space. Instead its laws are weighted, not arbitrarily, but towards order, endurance, and intelligibility. Such a universe is not hostile to reason, but profoundly hospitable to it. On such a view:
• The universe begins in Low Entropy for a reason.
• Its laws do not merely allow life but make understanding possible.
• Conscious minds are expected, not accidental.
By “rigging” the start of the universe to be so highly ordered, the “Normal Observers” become the majority, and the fleeting ghosts become the exception. Reality itself is tilted in favour of truth over illusion.
Why Reality Holds Together
Fine-tuning explains the conditions for life. The Boltzmann Brain problem asks why rational life can trust what it perceives. A universe committed to coherence answers both.
• When you lift your hand, it responds.
• When you remember yesterday, it existed.
• When you think, your thoughts are real.
That is not what a cosmic accident would predict. In a cosmic accident, your world should have vanished three sentences ago.
So… What Are We to Make of This?
If being itself tilts towards truth, then the fact that we can reason about the world without watching it collapse is more than the product of blind chance. Instead, it is woven into the structure of reality, minds not merely existing but with the capacity to know. Indeed, the remarkable thing is not just that consciousness occurs. It’s that it endures, anchored to a world intelligible enough to be shared. And if endurance, coherence, and truth are written this deeply into the grain of things, then perhaps the most rational response to the Boltzmann Brain paradox isn’t despair. It is wonder. Not least, it is wonder that we are here at all.
A Tennis Tale with a Twist
A version of this article appears in my book, Twisted Logic: Puzzles, Paradoxes, and Big Questions (Chapman & Hall/CRC Press).
THE WORLD OF BOBBY SMITH, A BUDDING TENNIS PRODIGY
Bobby Smith, a young tennis player, faces daunting odds in his journey to professional status. In his world, 1 in 1,000 schoolboy tennis players make it to the professional ranks.
THE TEST: BOBBY’S GATEWAY TO THE ACADEMY
Bobby takes a crucial test to join the prestigious tennis academy, which serves as a breeding ground for future professionals. Though he passes the test and enters the academy, we must consider what this really indicates about his chances of turning pro.
THE FALLACY: MISINTERPRETING PROBABILITIES
It’s crucial not to confuse the probability of Bobby turning pro (given his academy entry) with the inverse, the probability of him entering the academy if destined to turn pro. While all professionals come from the academy, not all academy members become professionals.
THE GATEKEEPER: A SPECIAL TEST
Bobby is given a test designed to gauge the potential of young tennis players, which is used to determine who will have the privilege of becoming a member of the tennis academy, a training and nurturing ground for aspiring professionals. Bobby takes this test with the goal of securing membership.
THE CHALLENGE: OVERCOMING THE ODDS
The test is taken by a thousand of these budding tennis players, including Bobby, all of whom want to enter the academy. Just 5% of those tested will gain entry to the academy and then fail to become professional players.
Graduation from the academy is also a condition of entry to the professional tour in Bobby’s world. As such, we can rule out anyone who does not gain entry to the academy as a future professional player.
BOBBY’S TRIUMPH: ENTERING THE ACADEMY
Fortunately for Bobby, he aces the test and joins the academy. This is a crucial step for him. After all, every professional player in Bobby’s world, as we have noted, is a graduate of the academy.
It might now seem almost certain that he has a bright future ahead in the world of professional tennis. But is this a correct assessment?
Well, it is undeniable that without entrance to the academy there is no way for Bobby to achieve professional status, but he has aced the test and is now a member of the academy. Give the accuracy of the test in sifting talent, can we now look forward with some confidence to his future sporting career?
Well, determining the probability of Bobby becoming a professional tennis player if he scores well enough on the test to gain entry to the academy is a complex matter. It involves factors beyond just his entrance to the academy. Many other elements, such as his dedication, talent, and the competitive environment, play roles in determining his chances. Even so, it does look promising, or does it?
THE FALLACY: AN ILLUSION OF CERTAINTY
Back to the test result, we must be very careful not to confuse the probability of Bobby going on to a professional tennis career given his entrance to the academy with its inverse—the probability that he would enter the academy if he were to go on to attain the professional ranks.
In our example, the probability of his entrance to the academy given that Bobby will make it to professional circles is a sure thing. All future professional players will be graduates of the academy. What we seek to know, however, is something different—it is the probability that Bobby will become a professional player given that he enters the academy. This is a very different question.
Put another way, the fallacy arises from confusing two distinct probabilities:
The probability of a hypothesis being true (Bobby will become a professional tennis player) given some evidence (entrance to the academy).
The probability of the evidence (entrance to the academy) given the hypothesis is true (Bobby will become a professional player).
In simple terms, if we know that Bobby became a professional, he definitely went to the academy. But that’s not what we’re interested in. We want to know the odds of Bobby becoming a professional, given that he got into the academy.
So what is the actual chance that Bobby will become a professional tennis player if he scores well enough on the test to gain entry to the academy?
CALCULATING THE REAL PROBABILITY: BEWARE OF FALSE POSITIVES
When we dig deeper into the data, we uncover some revealing insights. Consider the 5% of students who pass the test and enter the academy but don’t go on to become professional players—they are the ‘false positives’ in our scenario. If we assume 1,000 students take the test, 50 such ‘false positives’ get into the academy.
Add to them the one student who does become a pro (from the original pool of 1,000), and you find that Bobby’s chances of turning pro, even after making it into the academy, are just 1 in 51. This translates to approximately 1.96%.
This will only change if we know some additional information about Bobby.
THE MEDICAL ANALOGY: VIRUS TESTING
Interestingly, this concept aligns with the ‘false positives’ problem in the medical field, particularly in regard to virus testing. Let’s take a group of 1,000 people getting tested for a certain virus. Even with a test accuracy of 95%, about 5% of those tested (50 individuals) will also test positive despite not carrying the virus. On top of these, one individual does have the virus. Thus, if you test positive, the probability of actually carrying the virus is again about 1.96%, unless there is some additional information we need to take into account.
A MATHEMATICAL ASSURANCE: BAYES’ THEOREM
Though we’ve already figured out Bobby’s chances of turning pro, there’s another way to confirm our findings. This alternative method involves Bayes’ theorem. This theorem helps us calculate the updated probability of a hypothesis (in our case, Bobby turning pro) after obtaining new evidence (Bobby entering the academy).
The formula is expressed as follows:
ab/[ab + c (1 − a)]
where
a is the prior probability, i.e. the probability that Bobby will turn pro before we know his test results (0.001, as Bobby is one among 1,000),
b is the probability of Bobby entering the academy if he will turn pro (which is 100%, as all pros in Bobby’s world are academy graduates), and
c is the probability of Bobby entering the academy if he won’t turn pro (which is 50 out of 999, as out of the 999 kids who won’t turn pro, 50 will enter the academy).
By plugging these values into Bayes’ theorem, we confirm that Bobby’s chances of becoming a professional, despite gaining entry to the academy, are not 95% as one might think, but around 1.96%.
CRUNCHING NUMBERS: THE HARD REALITY
To summarise, let’s analyse the situation numerically. Among the 1,000 kids applying for the academy, 50 will be accepted but won’t make it to professional status. One will eventually turn pro. So, out of the 51 kids admitted, only one will become a professional. Therefore, the chance of becoming a professional tennis player if you enter the tennis academy is 1 in 51, or roughly 1.96%, unless there is some additional information that we need to take into account.
THE TWIST: A SUCCESS STORY
Despite the low probability, Bobby turns out to be the exception. He defies the odds and ends up winning the Australian Open under a different name.
CONCLUSION: BEYOND THE NUMBERS
Bobby’s story highlights how statistical probabilities can mislead our intuition. Understanding these concepts is crucial, whether assessing the future of a tennis player or interpreting medical test results. Despite the odds, individuals like Bobby can defy statistics, reminding us that while numbers describe populations, they don’t predetermine individual destinies.
The Hierarchical Cosmological Argument
Most discussions surrounding the “cosmological argument” default to a simplified premise: “Everything has a cause, therefore the universe must have a cause, and that cause is God”. This is usually met with the equally familiar retort: “If everything needs a cause, what caused God?” But that exchange misses the strongest version of the argument entirely. The deepest form of the cosmological argument isn’t about what happened 13.8 billion years ago at the Big Bang. It asks something far more immediate: What is sustaining the universe in existence right now?
This is at the heart of the “Hierarchical Cosmological Argument”. It doesn’t care about the start of the clock; it cares about the “floor” beneath your feet.
1. Borrowed Being: A Universe on Suspenders
We usually picture causation as a linear chain through time, like falling dominoes. But the hierarchical argument concerns simultaneous dependence. Think of a chandelier. It hangs from a chain, the chain from a hook, the hook from a beam, and the beam from the foundation of the house. At no point does the chain support itself. Its “lifting power” is entirely borrowed. If you remove the hook, the chandelier falls immediately, not after a delay, but now.
The claim is that reality has this same vertical structure:
• A tree exists because its molecular structure is held together.
• Molecules depend on the bonding properties of atoms.
• Atoms depend on subatomic particles and quantum fields.
At every level, these things do not exist by their own nature. They are “contingent”—they receive their existence from a deeper layer. This raises a sharp question: Can the entire structure be made of nothing but borrowers?
2. Why the Chain Can’t Be All Mirrors
One response is to suggest an infinite chain of dependence. But adding links to the chain doesn’t explain how the chain is staying in the air.
Imagine a room of mirrors. Each mirror reflects light but produces none. You can add a thousand mirrors, or an infinite sea of them, but without a light source, the room remains pitch black. An infinite chain of “borrowers” does not explain the gift of existence; it merely postpones the explanation forever.
If everything has existence only because something else “lends” it, then existence itself becomes a miracle without a source. At that point, one must either accept that reality is a “Brute Fact”, meaning it exists for no reason at all, or admit there is a foundation.
3. From Potentiality to Pure Act
To sharpen this, classical philosophy looks at the difference between Potentiality and Actuality. Everything we encounter is a mixture of both. A coffee bean is actually a bean but potentially a cup of espresso. It cannot “upgrade” itself; it requires something already actual (hot water and pressure) to flip the switch from potential to actual. If the universe is just a vast collection of these “switches,” there must be a First Mover that isn’t a mixture of potential and act. There must be something that is Pure Actuality:
• It has no “unrealised potential.”
• It doesn’t need to be “switched on” by anything else.
• It doesn’t just have existence; its very nature is existence.
4. Why call the First Cause “God”?
Why call this source “God” rather than a fundamental field of physics? Because anything described by physics is composite—it is a “LEGO set” of parts, laws, and properties. If a thing has parts, it depends on those parts to exist. It is still borrowing its being.
Whatever sits at the absolute bottom of the hierarchy must be:
1. Undivided (Non-composite): It cannot have parts, or it would depend on them. It is a single, seamless reality.
2. Necessary: It cannot not exist; it is the ground that allows everything else to be.
3. Unique: There can only be one “Pure Act,” as two would require a difference to distinguish them, and difference implies composition.
When classical theists speak of God, they aren’t talking about a “super-being” living inside the universe. They are talking about the substance of reality itself, the “Hook” from which the entire chain of physics hangs.
5. The Cost of Denial
Does this argument compel belief? Not like a mathematical trap. You can always walk away. But walking away has a price. To reject the foundation, you must accept that at the very bottom of reality, reason simply stops. You must accept that the “mirrors” are reflecting light that comes from nowhere. You must embrace ultimate arbitrariness as the source of all order.
Or you can ask: Why is there, right now, something rather than nothing? Why has the world not vanished into nothingness while you were reading this sentence?
The Hierarchical Cosmological Argument provides a real and meaningful answer to both questions. It is, for this reason, an argument that quite simply refuses to go away.
From Possibility to Necessity
The God Logic: Why Possibility Implies Necessity.
Many arguments for God’s existence ask us to look out: at the intricate dance of galaxies, the fine-tuning of physical constants, the sheer improbability of life, and far more. These arguments frame God as a hypothesis to be inferred from the evidence.
But there is also another, radically different argument, one that has perplexed and fascinated philosophers for nearly a millennium. It requires no telescope or microscope. It looks instead to the very nature of meaning, possibility, and reality itself.
This is the Ontological Argument. First formulated by St. Anselm of Canterbury in the 11th century, its claim is as startling as it is profound: if you can coherently conceive of God, then God must exist not only in your mind but in reality.
The Definition: The Unsurpassable Limit of Thought
Anselm begins not with a statement of faith, but with a definition rooted in logic:
God is “that than which nothing greater can be conceived”.
This isn’t a poetic flourish; it is a strict logical boundary. To grasp it, imagine ranking all conceivable things by their “greatness”, not in terms of size or moral character, but of their perfection or fullness of being.
Consider these examples of how we intuitively understand “greatness” in this philosophical context:
• A being that possesses consciousness is greater than one that does not.
• A being that is all-powerful is greater than one with limitations.
• A being that exists independently is greater than one that depends on something else for its existence.
Now, push this concept to its absolute limit. If you can think of a being, and then imagine a greater one, you have not yet conceived of God. By definition, God is the logical ceiling, the maximal and unsurpassable case.
The Pivot: Why Existence in Reality is a Perfection
Here we arrive at the argument’s crucial and most debated step. Ask yourself a simple question: which is greater, something that exists only as an idea, or something that exists in reality as well?
Imagine the most perfect island, complete with pristine beaches, ideal weather, and untold riches. Now, which is greater: the idea of this island in your mind, or this island existing in the actual world?
Everything screams that reality is superior. An imagined masterpiece lacks what a real one possesses: actuality.
Anselm applies this directly to his definition of God.
1. We have a coherent idea of God as the greatest conceivable being.
2. But if this being existed only in our minds, it would not be the greatest conceivable being. We could conceive of something greater: the same being, but with the added perfection of existing in reality.
3. This creates a logical contradiction: the greatest conceivable being would not be the greatest conceivable being.
Since contradictions are logically impossible, the initial premise, that God exists only as an idea, must be false. Therefore, if the concept of God is coherent, God must exist in reality.
The Modern Upgrade: From Possibility to Necessity
For centuries, many philosophers dismissed Anselm’s argument as a clever but flawed “proof by definition”. The most famous early objection came from the monk Gaunilo, who argued that if Anselm was right, one could define a “perfect island” into existence.
Philosophers have since noted a key distinction: an island has no intrinsic maximum. For any “perfect” island, we can always conceive of a “greater” one. God, as a being of maximal perfection, is not subject to this flaw.
In the 20th century, philosophers like Alvin Plantinga revived the argument using the tools of modal logic—the logic of possibility, necessity, and contingency. This modern version is widely considered more robust.
It proceeds as follows:
1. Possibility: It is at least logically possible that a “maximally great being” exists. A being is maximally great if it is all-powerful, all-knowing, and morally perfect in every possible world. To refute this, one must show the concept is logically incoherent, like a “married bachelor”.
2. Necessity: A key attribute of a maximally great being is that it would exist necessarily. It could not be a contingent being that just happens to exist, as depending on anything else for its existence would be an imperfection.
3. The Axiom: A foundational principle of modal logic states that “If it is possible that a necessary being exists, then that necessary being does exist”.
4. Conclusion: Therefore, if the existence of a maximally great being is even logically possible, even 0.0000000000000000001% possible, or far less, it must actually exist.
As such, the modern argument shifts the debate from whether existence is a “perfection” to a starker question:
Is the concept of a maximally great being logically coherent?
Where the Real Dispute Lies
This is what makes the ontological argument so intellectually potent. It bypasses debates over empirical evidence and forces the sceptic into a very specific corner.
To reject the argument, it is not enough to say, “I see no evidence for God”, even if you don’t. One must be prepared to argue that the very idea of a maximally great being is as logically self-contradictory as a four-sided triangle.
If the concept is even possibly coherent, however, the logic compels the conclusion that such a being exists necessarily and, therefore, actually. That is a far heavier burden of proof for the atheist than is commonly assumed.
The Takeaway
The ontological argument does not present God as another object to be found within the universe. It presents God as the very ground of reality, a being whose nature, if coherent, if even possible at all, does not permit non-existence.
And if God is possible, even 0.0000000000000000001% possible, then we are led to the inescapable logical conclusion that God exists.
Performance, Putts, and Parables
A version of this article appears in my book, Twisted Logic: Puzzles, Paradoxes, and Big Questions (Chapman and Hall/CRC Press, 2024).
THE PROBLEM OF LOSS AVERSION
Loss aversion, a key concept in behavioural economics, explains our tendency to prefer avoiding losses over acquiring equivalent gains. This principle is illustrated in diverse settings, from biblical parables to professional sports.
LOSS AVERSION IN THE VINEYARD
The Gospel of Matthew in the New Testament of the Bible relates the Parable of the Workers in the Vineyard. Here’s a breakdown of the parable:
Setting: A landowner goes out early in the morning to hire workers for his vineyard.
Early Morning Hiring: The landowner hires the first group of workers at daybreak, agreeing to pay them a denarius for the day’s work, which was a typical day’s wage at the time.
Subsequent Hirings: Throughout the day, the landowner hires additional groups of workers. He goes out again at the third hour (around 9 a.m.), the sixth hour (noon), the ninth hour (3 p.m.), and even the 11th hour (5 p.m.) to hire more workers. With these groups, he doesn’t specify an exact wage, but promises to pay them ‘whatever is right’.
End of the Day—Payment Time: When evening comes, the workers line up to receive their wages, starting with those who were hired last. To everyone’s surprise, the workers hired at the 11th hour receive a full day’s wage (a denarius).
Discontent among the First Hired: Seeing this, the workers who were hired first expect to receive more than their agreed-upon denarius. However, they too receive the same wage. This leads to grumbling against the landowner. They feel it’s unfair that they worked the whole day, bearing the heat, and yet received the same as those who worked just an hour.
Landowner’s Response: The landowner points out that he did not cheat the first workers; he paid them the agreed-upon wage.
Reference Points and Relative Outcomes: The workers who commenced early had a clear reference point; a denarius for a day’s toil. Despite receiving the agreed wage, they perceived receiving the same pay as those who worked less as a loss. Observing others receiving equivalent wages for fewer hours of work framed their wages in this way. This episode underlines the significance of reference points in human decisions, emphasising the relational aspect of outcome evaluations, surpassing absolutes. The dissatisfaction emanating from the early workers is a classic example of loss aversion. It is a central feature of modern Prospect Theory, albeit some 2,000 years ahead of its time.
BENCHMARKS AND BEHAVIOUR
An intriguing study on the behaviour of New York City cab drivers focused on how they decided the duration of their work shifts in relation to their daily earnings. Contrary to the expectations set by traditional economic theories, which suggest workers would maximise their hours on days with higher demand (and thus potential earnings), the study discovered that cab drivers tended to work fewer hours on days where they were earning more per hour and worked longer hours on less lucrative days. This behaviour aligns more closely with the concept of setting earning targets—drivers tended to end their shifts once they reached a certain income goal, regardless of how quickly they achieved it. This finding, led by Colin Camerer and Linda Babcock, challenged the rational agent model in economics, suggesting that real-world decisions are influenced more by psychological factors and personal benchmarks than traditional economics would expect.
BENCHMARKS ON THE GOLF COURSE
In the game of professional golf, the reference point takes on a very different aspect. This time the problem does not arise because those playing for just a couple of holes earn the same as those who complete four rounds. Instead, the problem arises from the so-called ‘Par’ assigned to each hole, which is a benchmark indicating the number of strokes that a skilled golfer, typically a ‘scratch golfer’ – who plays without any handicap – is expected to take to complete that particular hole under standard playing conditions. While the total number of shots should be the player’s real concern in most competitions, regardless of the assigned ‘par’ scores, the fear of failing to achieve par on individual holes may trigger the influence of loss aversion. In this case, the aversion is to underperforming expectations.
FINDING EVIDENCE OF LOSS AVERSION
Contrary to what might seem rational, analysis of more than 2.5 million putts, with detailed measurements of initial and final ball placement, reveals that professional golfers are indeed significantly influenced by the artificial par reference point. Specifically, it can be shown from the data that golfers are less accurate when putting to score better than par on a hole than when aiming for par. The data suggests, as such, that professional golfers exert more effort to avoid missing par on a hole than in scoring better than par. But why? Their only true objective in most competitions should be to minimise the number of shots taken, regardless of the ‘par’ assigned to each hole.
A paper published by Devon Pope and Maurice Schweitzer in the American Economic Review in 2011 examines a range of possible explanations, systematically eliminating them one by one until the true cause becomes evident. They conclude that golfers view par as their ‘reference’ score. Therefore, a missed par putt is perceived by golfers, perhaps subconsciously, as a more significant loss than a missed ‘birdie’ putt, i.e. one shot better than par. The reality is that par is an artificial construct; all that really matters in strokeplay competitions is the total number of shots taken. This implicit mental bias, however, leads to irrational behaviour during the game, with golfers unable to adjust their strategy even when made aware of this bias.
Interestingly, the researchers also observed a tendency for equivalent ‘birdie’ putts to come up slightly short of the hole in comparison to par putts, further confirming the hypothesis that a fear of a loss to par impacts the players’ putting strategies.
EXPLORING ALTERNATIVE EXPLANATIONS
Despite the compelling evidence for loss aversion, alternative explanations were considered. The possibility that birdie putts might originate from more precarious positions, for example, was explored. However, comprehensive data and rigorous analysis ruled out competing theories.
DYNAMICS OF LOSS AVERSION ACROSS TOURNAMENT ROUNDS
Interestingly, the accuracy gap between par and birdie putts varied across the tournament rounds. It was largest during the initial round and decreased significantly by the fourth round. This fluctuation suggests that the influence of loss aversion and the salience of the par reference point are neither automatic nor immutable and may be affected by factors such as competitor scores later in the tournament.
IMPLICATIONS: BENEFICIAL KNOWLEDGE FOR FORECASTERS AND PSYCHOLOGISTS
This unique insight into professional golfer behaviour has profound implications. It provides valuable information for sports forecasters or even those betting on the match in-play. Moreover, it serves as critical knowledge for sports psychologists working with professional golfers. If these psychologists could find a way to subtly reframe a golfer’s perception of a birdie putt, they could significantly improve a golfer’s performance and earnings over time.
CONCLUSION: PERSISTENCE OF BENCHMARKS AND LOSS AVERSION
This analysis demonstrates that even in a high-stakes, competitive market setting, loss aversion persists among experienced agents. Even top-performing golfers in the study displayed signs of this enduring bias, highlighting its pervasive influence in decision-making scenarios.
The concept has, of course, much broader significance than in competitive sports or even at the workplace. It has been shown to exist in so many of our personal choices and perceptions. By considering how we respond in our own lives to artificial benchmarks and reference points, it has the potential to significantly improve our everyday decisions and actions for the better.
A spoiler-free guide; including the Secret Traitor twist
How to Win the New Traitors
At first glance, The Traitors looks like a game about spotting liars. Watch a little longer and you realise it’s something else entirely. It’s a game about how people react to uncertainty, who feels safe to keep around, and when being right actually makes you dangerous.
The latest UK format adds an elegant complication: the Secret Traitor. Alongside the familiar, visible (to viewers) Traitors, there is now one extra player who knows who the Traitors are, but is unknown to everyone else, including them. This Secret Traitor provides a shortlist of candidates for the visible Traitors to eliminate from. This twist doesn’t just add drama. It changes how the game should be played.
1. Stop Playing Detective
The most common mistake, especially among Faithfuls, is treating the game like a puzzle to be solved. That instinct is understandable. It’s also usually fatal.
You don’t win The Traitors by proving who the Traitors are. You survive by not giving the group a reason to get rid of you. Those are very different skills. Players who sound sharp, confident, and decisive often leave early — not because they’re wrong, but because they look like future trouble. Being useful is safer than being impressive.
2. Confidence Is Riskier Than Being Wrong
Nothing raises eyebrows faster than certainty.
- Confident Faithfuls look like they might organise votes later.
- Confident Traitors look like they know more than they should.
- Confident Secret Traitors don’t stay secret for long.
The safest tone is calm uncertainty:
- Ask rather than accuse.
- Share doubts instead of conclusions.
- Be willing to change your mind out loud.
People rarely banish someone for being unsure. They often banish people who sound settled.
3. What the Secret Traitor Changes
The Secret Traitor quietly removes a comforting illusion: that the Traitors are a tight, informed unit acting with shared purpose. They aren’t, and this has three knock-on effects:
Strange behaviour is harder to interpret
Not every odd move is a “tell” anymore. Some confusion is baked into the structure.
Traitors have less control than they did
Knowing that someone else has influence, but not knowing who, makes bold play risky.
Blending in becomes even more powerful
Players who don’t dominate discussions or force narratives are harder to justify removing. The game shifts away from detection and towards social equilibrium.
4. How to Play the Secret Traitor
The Secret Traitor sits in the most powerful position, and the most precarious one.
The key is restraint. Don’t look clever. Your strength is invisibility. The moment others think you’re steering outcomes, you’re vulnerable. So make decisions that feel obvious. When influencing eliminations, aim for choices that don’t spark debate. If no one talks about your move, it’s probably a good one.
Let others absorb the drama. If tension follows a decision, allow louder players to carry it. Stay adjacent, not central. Think in weeks, not days. Short-term manoeuvring is tempting. Longevity comes from patience. The best Secret Traitor move is often the one nobody notices.
5. Likeability Outlasts Insight
The players who last tend to do small things well:
- They listen.
- They acknowledge others’ worries.
- They soften disagreements instead of sharpening them.
- They don’t insist on being heard.
Someone who’s “probably right but irritating” is far more at risk than someone who’s “possibly wrong but calming”. In this game, people vote out threats, not errors.
6. Why Players Really Get Banished
Most banishments aren’t about guilt or innocence. They happen because someone is:
- Too intense
- Too articulate
- Too eager
- Too early
There’s a real paradox here: good reasoning increases danger unless it’s carefully disguised as reflection. Often, the smartest thing to do is stop just before you land the point.
Final Thought: It’s Not a Mystery — It’s a Social Test
The Traitors isn’t about uncovering truth. It’s about managing fear, comfort, and trust in a group that never has enough information. The Secret Traitor twist simply makes that reality harder to ignore.
If you want to survive, and maybe win:
- Be understandable, not dazzling.
- Be flexible, not fixed.
- And remember that how you make people feel matters more than what you know.
That’s the real game, secret or otherwise.
Can prediction markets find missing MH370?
Confronting uncertainty.
For more than a decade, Malaysia Airlines Flight MH370 has occupied a strange place in the modern imagination: a wound that has never closed. A plane with 239 people on board does not simply vanish in the 21st century, or at least it shouldn’t. And yet it did!
Now, once again, the southern Indian Ocean is being searched.
A quiet, highly technical operation is underway, led by Ocean Infinity, under a renewed “no-find, no-fee” agreement with the Malaysian government. Its vessel, Armada 86 05, is deploying autonomous underwater vehicles capable of descending nearly 20,000 feet, scanning the seabed with sonar, magnetometers, and high-resolution 3D mapping. The target zone, around 5,800 square miles, has been refined using years of accumulated analysis.
There are no dramatic press conferences this time, no daily briefings. Just machines slipping silently into black water, searching terrain no human will ever see.
What we know, and what we still don’t
MH370 disappeared on 8 March 2014, forty minutes after take-off from Kuala Lumpur bound for Beijing. Military radar later showed the Boeing 777 deviating sharply from its planned route, flying south for hours into one of the most remote regions on Earth. Satellite data confirmed continued flight, but not where it ended, or why.
The largest multinational search in aviation history followed, at enormous cost. It failed to locate the main wreckage or flight recorders. And yet the evidence is no longer a blank page.
A flaperon, part of a wing control surface, was recovered on Réunion Island in 2015 and identified by investigators as almost certainly originating from MH370. Additional fragments, judged “very likely” to be from the aircraft, later washed up along the East African coast and Indian Ocean islands. Oceanographers refined drift models. Satellite analysts revisited the data again and again. The picture narrowed, even if it never snapped fully into focus.
This is where MH370 now sits: not in a fog of ignorance, but in a haze of probability.
Why this search feels different
Ocean Infinity has been here before. A 2018 seabed search came up empty. An earlier phase of this renewed effort was paused due to weather. Scepticism is not only understandable; it is rational. What has changed is not just technology, but synthesis.
The current search area reflects years of accumulated judgment across disciplines: aviation, satellite communications, oceanography, wreck recovery. It is, in effect, the best collective guess we can now make about where the aircraft lies.
And that brings me back to an idea I first explored in this context nearly ten years ago.
The problem of the “lone expert”
We like to imagine breakthroughs coming from a single decisive insight: the brilliant analyst, the overlooked data point, the final piece of the puzzle. But MH370 resists that narrative. No single expert, model, or dataset has been enough.
In problems like this, where uncertainty is vast and information fragmented, history suggests a different approach can work better: aggregating judgment.
In 1968, when the US Navy submarine USS Scorpion was lost, the search area was overwhelming. Instead of relying on one authoritative theory, experts were asked to make independent probabilistic assessments. When those assessments were combined, the wreck was found within a few hundred metres of the predicted location. The lesson is not mystical. It is practical. Groups of informed people, when aggregated properly, can outperform even the best individual experts.
In a sense, Ocean Infinity’s search already embodies this idea. But it does so informally, behind closed doors. A structured mechanism, such as a carefully designed prediction market restricted to qualified experts, can help surface neglected hypotheses, test assumptions, and dynamically re-weight search priorities as new information emerges.
This is not about “betting” in some probability exercise on tragedy. It is about recognising that uncertainty itself can be measured, and that human judgment, when pooled intelligently, is a tool rather than a weakness. The wisdom of the crowd is often greater than even its strongest member.
Confronting uncertainty
For the families and friends of the 239 people on board, this search is about being able to say, finally, this is where they are. It is about burial, mourning, and the end of limbo. For the rest of us, MH370 is a reminder of something deeply unsettling: that even in an age of satellites, big data, and constant connectivity, parts of the world, and parts of our systems, remain frighteningly opaque.
If Ocean Infinity succeeds, it will be a triumph of persistence and engineering. If it fails, the story should not end in resignation. The question then becomes not “why didn’t we look harder?”, but “did we think hard enough about how we look at all?”
The challenge is a great one – it is about how we should confront uncertainty, share knowledge, and search together when no one has the full answer.
And that question, unlike the aircraft, has never really disappeared.
Masterpiece or Miracle?
The Shroud of Turin is perhaps the only object on Earth that can make an avuncular nuclear physicist and a mild-mannered medieval historian lose their respective tempers at the same formal dress dinner party.
At first glance, it hardly looks like much: a long strip of ancient linen, faintly marked with the shadowy image of a man who appears to have been crucified. And yet this quiet, unassuming cloth has been examined, tested, photographed, scanned, and debated more than any artefact in history. As we approach 2026, we are arguably no closer to consensus than when it was first photographed in 1898. In some regards, we’re further away.
That’s because the Shroud refuses to sit still. Just when one side thinks it has won the argument, new evidence seems to pop up.
The straightforward case: A medieval masterpiece
If you’re sceptically inclined, the Shroud looks like a solved problem.
In 1988, three independent laboratories, in Oxford, Zurich, and Arizona, used radiocarbon dating to analyse samples from the cloth. All three placed it firmly in the medieval period, between 1260 and 1390 AD. That date lines up almost perfectly with the Shroud’s first clear appearance in the historical record, in 1354, in the French village of Lirey.
Even contemporaries were suspicious. The local bishop, Pierre d’Arcis, wrote to the Pope claiming the Shroud was a fake and that an artist had confessed to producing it. Medieval Europe, after all, was awash with relics; splinters of the True Cross, drops of holy blood, and saints’ bones by the cartload. Pilgrims meant money, and holy objects meant pilgrims.
Seen this way, the Shroud becomes an extraordinary but entirely human achievement: a brilliantly executed forgery from a period when forgery flourished. Apply the redoubtable Occam’s Razor, and the simplest explanation seems obvious. No miracle required, just a once-in-a-millennium artist.
And yet… the cloth itself won’t cooperate
The trouble is that when scientists actually look at how the image is formed, the neat medieval explanation begins to feel less neat.
In 1978, a team of American scientists was given unprecedented access to the cloth. They arrived expecting to find paint, pigment, or dye. What they found instead was baffling:
• The Photographic Negative: When Secondo Pia photographed the Shroud in 1898, he realised the image works like a negative; the light and dark values are reversed. Only when flipped does it look like a realistic human face. Medieval artists were talented, but deliberately painting a negative image centuries before the invention of photography?
• The Three-Dimensionality: The intensity of the image corresponds precisely to how far the cloth would have been from a body beneath it. Feed the image into a NASA VP-8 image analyser and, unlike any 2D painting or photograph, it produces a coherent 3D topographical map of a human form.
• The Microscopic Surface: The discolouration sits only on the outermost surface of the linen fibres, about 200 nanometres thick. It doesn’t bleed through the cloth. Modern laboratories struggle to reproduce this effect even with lasers. A medieval brush simply shouldn’t be capable of it.
At this point, even hardened sceptics tend to pause. But what about the 1988 studies?
The 2024 plot twist
For decades, the 1988 carbon dating has been the sceptic’s knockout punch. But in 2024, a new study reopened the fight.
Italian researcher Liberato De Caro used Wide-Angle X-ray Scattering (WAXS) to analyse how the linen’s cellulose structure has degraded over time. The results were startling: structurally, the Shroud’s fibres look almost identical to first-century linen recovered from the siege of Masada (c. 55–74 AD).
If this method holds up, it lends significant weight to the “Medieval Repair Hypothesis”. This theory suggests the 1988 samples, taken from a corner that had been heavily handled, burned in a 16th-century fire, and repaired by nuns, were not representative of the cloth as a whole. The date might be correct for the sample, but wrong for the Shroud.
While WAXS is a relatively new technique in the world of archaeology, it has turned what was once “settled science” back into a live debate.
Two explanations, both extraordinary
And so we arrive at an uncomfortable fork in the road.
Option A: The Natural Miracle. The Shroud is the product of a medieval mind with an understanding of anatomy, chemistry, optics, and image encoding that apparently wouldn’t be rediscovered for another five centuries.
Option B: The Supernatural Miracle. It is the physical trace of an unknown energetic event, something closer to a burst of radiation than a brushstroke, leaving behind a microscopic imprint of a body at the moment of resurrection.
Neither option is tidy. Both stretch the sceptical mind in different ways.
Why the Shroud won’t let us go
In the end, the Shroud of Turin may tell us more about ourselves than about the past. For some, it confirms a suspicion that faith manufactures its own evidence. For others, it offers a rare and unsettling hint that reality might be stranger than our models allow.
What seems clear is this: the Shroud does not behave like a painting, a photograph, or any known medieval artefact. It sits stubbornly at the boundary between belief and scepticism, history and physics, the proverbial ghost at the senior common room dinner table.
And perhaps that’s why, as we leave behind the year 2025, it still refuses to be neatly folded away.
A Bayesian Evaluation of Shakespeare’s Othello
OTHELLO: THE BACKGROUND
Created by William Shakespeare, ‘Othello’ is a play centred around four main characters: Othello, a general in the Venetian army; his devoted wife, Desdemona; his trusted lieutenant, Cassio; and his manipulative ensign, Iago. Iago’s plan forms the central conflict of the play. Driven by jealousy and a large helping of evil, Iago seeks to convince Othello that Desdemona is conducting a secret affair with Cassio. His strategy hinges on a treasured keepsake, a precious handkerchief which Desdemona received as a gift from Othello. Iago conspires successfully to plant this keepsake in Cassio’s lodgings so that Othello will later find it.
UNDERSTANDING OTHELLO’S MINDSET
Othello’s reaction to this discovery can potentially take different paths, depending on his character and mindset. If Othello refuses to entertain any possibility that Desdemona is being unfaithful to him, then no amount of evidence could ever change that belief.
On the other hand, Othello might accept that there is a possibility, however small, that Desdemona is being unfaithful to him. This would mean that there might be some level of evidence, however overwhelming it may need to be, that could undermine his faith in Desdemona’s loyalty.
There is, however, another path that Othello could take, which is to evaluate the circumstances objectively and analytically, weighing the evidence. But this balanced approach also has its pitfalls. A very simple starting assumption that he could make would be to assume that the likelihood of her guilt is equal to the likelihood of her innocence. That would mean assigning an implicit 50% chance that Desdemona had been unfaithful. This is known as the ‘Prior Indifference Fallacy’. If the prior probability is 50%, this needs to be established by a process better than simply assuming that because there are two possibilities (guilty or innocent), we can ascribe automatic equal weight to each. If Othello falls into this trap, any evidence against Desdemona starts to become very damning.
THE LOGICAL CONTRADICTION APPROACH
An alternative approach would be to seek evidence that directly contradicts the hypothesis of Desdemona’s guilt. If Othello could find proof that logically undermines the idea of her infidelity, he would have a solid base to stand on. However, there is no such clear-cut evidence, leading Othello deeper into a mindset of anger and suspicion.
BAYES’ THEOREM TO THE RESCUE
Othello might seek a strategy that allows him to combine his subjective belief with the new evidence to form a rational judgement. This is where Bayes’ theorem comes in. Bayes’ theorem allows, as we have seen in previous chapters, for the updating of probabilities based on observed evidence. The theorem can be expressed in the following formula:
Updated probability = ab/[ab + c (1 − a)]
In this formula, a is the prior probability, representing the likelihood that a hypothesis is true before encountering new evidence. b is the conditional probability, describing the likelihood of observing the new evidence if the hypothesis is true. And finally, c is the probability of observing the new evidence if the hypothesis is false. In this case, the evidence is the keepsake in Cassio’s lodgings, and the hypothesis is that Desdemona is being unfaithful to Othello.
APPLYING BAYES’ THEOREM TO OTHELLO’S DILEMMA
Now, before he discovers the keepsake (new evidence), suppose Othello perceives a 4% chance of Desdemona’s infidelity (a = 0.04). This represents his prior belief, based on his understanding of Desdemona’s character and their relationship. Of course, he is not literally assigning percentages, but he is doing so implicitly, and here we are simply making these explicit to show what might be happening within a Bayesian framework.
Next, consider the probability of finding the keepsake in Cassio’s room if Desdemona is indeed having an affair. Let’s assume that Othello considers there is a 50% chance of this being the case (b = 0.5).
Finally, what is the chance of finding the keepsake in Cassio’s room if Desdemona is innocent? This would in Othello’s mind require an unlikely series of events, such as the handkerchief being stolen or misplaced, and then ending up in Cassio’s possession. Let’s say he assigns this a low probability of just 5% (c = 0.05).
BAYESIAN PROBABILITIES: WEIGHING THE EVIDENCE
Feeding these values into Bayes’ equation, we can calculate the updated (or posterior) probability of Desdemona’s guilt in Othello’s eyes, given the discovery of the keepsake. The resulting probability comes out to be 0.294 or 29.4%. This suggests that, after considering the new evidence, Othello might reasonably believe that there is nearly a 30% chance that Desdemona is being unfaithful.
IAGO’S MANIPULATION OF PROBABILITIES
This 30% likelihood might not be high enough for Iago’s deceitful purposes. To enhance his plot, Iago needs to convince Othello to revise his estimate of c downwards, arguing that the keepsake’s presence in Cassio’s room is a near-certain indication of guilt. If Othello lowers his estimate of c from 0.05 to 0.01, the revised Bayesian probability shoots up to 67.6%. This change dramatically amplifies the perceived impact of the evidence, making Desdemona’s guilt appear significantly more probable.
DESDEMONA’S DEFENCE STRATEGY
On the other hand, Desdemona’s strategy for defending herself could be to challenge Othello’s assumption about b. She could argue that it would be illogical for her to risk the discovery of the keepsake if she were truly having an affair with Cassio. By reducing Othello’s estimate of b, she can turn the tables and make the presence of the keepsake testimony to her innocence rather than guilt.
CONCLUSION: THE TIMELESS BAYESIAN
Shakespeare’s ‘Othello’ was written about a century before Thomas Bayes was born. Yet the complex interplay of trust, deception, and evidence in the tragedy presents a classic case study in Bayesian reasoning.
Shakespeare was inherently Bayesian in his thinking. The tragedy of the play is that Othello was not!
In a Nutshell
Atheism is often advanced as the intellectually cautious position, promising fewer commitments and no metaphysical extravagance. It’s just matter, laws, and chance. That restraint can feel like a virtue.
But caution cuts both ways. When we step back and ask which worldview best explains the world we actually observe, atheism turns out not to be modest at all. It repeatedly asks us to accept extraordinary coincidences across independent domains of reality, encompassing physics, consciousness, knowledge, and morality, while ruling out the one kind of unifying explanation that would make these features far less surprising.
A note on method
I am not in this nutshell proposing an argument for absolute certainty, nor an attempt to “prove” God from a single premise. Rather, this is an exercise in explanatory comparison.
The question is not, therefore, whether atheism is possible, but whether it is the most plausible account of the world we find ourselves in. Which hypothesis best explains the total evidence with the fewest unexplained coincidences? It is a question we routinely ask in science, history, and everyday reasoning.
1. A universe balanced on a knife-edge
Modern physics has revealed that the universe is balanced on a razor’s edge. Many fundamental constants, such as the strength of gravity, the expansion rate of the vacuum, the ratios among fundamental forces, must lie within extraordinarily narrow ranges for stars, chemistry, and life to exist at all. Small deviations would not merely produce a different kind of life; they would eliminate complexity entirely.
Perhaps more striking still, the universe is not only life-permitting but intelligible. It behaves according to stable, elegant mathematical structures, precisely the conditions required for minds capable of understanding it.
Atheism typically responds with “brute luck” or appeals to a speculative multiverse. Invoking luck at this scale functions less as an explanation than as a placeholder. Multiverse proposals, meanwhile, tend to shift the problem upward: why should a universe-generator exist that is itself so delicately configured as to produce even one intelligible, life-friendly world?
Theism offers a simpler expectation. If reality is grounded in a rational mind, a law-governed, life-friendly universe is exactly what we should expect to find. Every worldview will face some brute facts, but the claim here is comparative: theism leaves fewer and less arbitrary ones than atheism.
2. The harmony of mind and world
We are conscious. That alone is a deep mystery. But the more striking fact is how well our minds work.
- Our intentions reliably guide our actions.
- Our perceptions generally track reality.
- Our abstract reasoning uncovers deep truths about a physical world billions of light-years away.
Evolution can explain why certain behaviours aid survival. It is much harder, on a purely unguided picture, to see why our cognition should be so broadly truth-tracking, extending far beyond survival needs into higher mathematics, theoretical physics, and objective ethics. Naturalistic accounts exist, of course, but they tend to treat this expansive reliability as an unexpected bonus rather than something to be anticipated.
If atheism is true, the harmony between the “logic” of the stars and the “logic” of our minds is a colossal stroke of luck. If theism is true, it looks intentional.
3. The crisis of reason
Atheism inherits a quiet but serious epistemic problem. If our cognitive faculties are merely the unintended by-products of survival-driven processes, why should we trust them to deliver truth rather than merely useful delusions?
Even if evolution yields some degree of reliability, the more tightly our minds are tuned to reproductive success alone, the more puzzling it becomes that they also seem fitted for grasping deep, abstract truths about logic, mathematics, and metaphysics. If a worldview makes it plausible that our reasoning is unreliable in principle, then confidence in science and philosophy becomes precarious.
Theism offers a more stable foundation. If reality is grounded in a rational Creator, it is reasonable to expect that our faculties are generally fit for truth, even if imperfectly so.
4. Truths that aren’t negotiable
Most of us treat certain truths as objective and binding. Mathematical truths are not social conventions; moral truths are not merely tribal habits.
Many atheistic accounts can explain why we feel bound by morality, as a product of biology or social evolution. What they struggle to explain is why there really are stance-independent moral truths at all, or why a universe composed solely of particles in motion should contain genuine “oughts” rather than merely ingrained preferences.
On theism, moral and mathematical truths reflect the rational and moral structure of the Mind behind the universe. They are not accidents; they are foundational.
5. A world saturated with value
There are countless ways reality could have been devoid of value:
- nothingness,
- sterile laws incapable of complexity,
- life without consciousness,
- minds without the capacity for love or beauty.
Yet we inhabit a world saturated with meaning and moral seriousness. It is deeply flawed and often painful, yes, but unmistakably value-laden. Atheism typically treats this as a fortunate but ultimately inexplicable outcome of blind processes. Theism treats it as the point.
6. Why Christianity?
General theism points to a Mind; Christianity points to a Face.
Christianity makes the striking claim that God’s nature is revealed in history through the life, death, and resurrection of Jesus. What is immediately noticeable is how counter-intuitive this story is.
- A crucified Messiah was a scandal within Second Temple Judaism.
- A God revealed through weakness and self-giving love was an absurdity in Roman power-culture.
This is not the kind of narrative one invents to gain influence. At the centre of the faith stands a historical claim: the Resurrection. Once theism is taken seriously as a framework, the Resurrection becomes a historical question: what best explains the sudden transformation of the disciples and the birth of a movement grounded in a “victory” achieved through execution?
7. The shape of divine goodness
The Cross gives Christianity its philosophical depth. If God is perfectly good, how would divine love confront a world of guilt and suffering? Not through detached judgment, but through solidarity.
In the Cross, power is redefined as love willing to suffer for the sake of the beloved. It does not deny suffering; it insists that suffering is not final.
Why I am not an atheist: in a nutshell
In a few words, I am not an atheist because atheism asks me to believe that:
- a finely tuned, intelligible universe exists for no reason;
- consciousness and truth-seeking minds emerged by a fluke;
- objective moral and mathematical truths are binding but ultimately groundless;
- value pervades reality ultimately without foundation.
Theism does not answer every question; no worldview does. But it explains so much more with fewer and less arbitrary brute facts.
This is not a rejection of reason in favour of faith. It is an appeal to reason in its fullest sense: the search for the best explanation of reality as a whole.
And perhaps the most remarkable fact of all is not that we ask these questions, but that we exist in a universe intelligible enough, and meaningful enough, to ask them at all.
Professor Leighton Vaughan Williams 