Mind games

God’s paradox and other labyrinths of logic

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Some ideas challenge what we think we know—paradoxes twist logic until reason bends or breaks. These classic thought experiments, from ancient puzzles to modern contradictions, expose gaps in philosophy, math, time, and perception. Here are 10 paradoxes that’ll warp your mind and leave you questioning reality.

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If a barber shaves everyone who does not shave themselves, who shaves the barber? If he shaves himself, he must not; if he doesn’t, he must.

This self-referential paradox, posed by Bertrand Russell in 1918, demonstrates a fundamental problem in set theory. It inspired Russell's theory of types, which aimed to avoid such contradictions in formal logic and mathematics. Perhaps the barber will simply choose to grow a beard.

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The statement "This sentence is false" cannot be true or false. If true, then it’s false; if false, then it’s true.

Known since ancient Greece as the Epimenides paradox, it underpins challenges in many logical systems. Although it seems simple at first, deeper thought reveals there is no resolution. Many have tried to solve or circumvent it, yet it remains unsolved.

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If you replace every part of a ship, is it still the same ship? What if you reassemble the old parts into a second ship?

This metaphysical problem dates back to Plutarch. It challenges identity and continuity, and has many analogs in biology (e.g., human cells constantly replacing themselves) and even AI (replicated minds in machines).

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Achilles and a tortoise race each other. As a courtesy, Achilles gives the tortoise a head start. However, Zeno argues Achilles can never catch it, because he must first reach where the tortoise was before, infinitely.

Although this paradox seems crazy and absurd—in real life, obviously Achilles would win the race—what Zeno is pointing to are the infinite gaps between finite numbers. The absurd argument, being that all motion is impossible due to infinite division, helps illustrate the limits of mathematical models of the world.

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If you went back in time and killed your grandfather before your parent was born, how could you exist to do it in the first place?

This classic time travel paradox highlights the problems with causal loops. Theoretical physics offers some resolutions, such as branching timelines (as in the "many-worlds interpretation") or even stranger concepts like "closed time-like curves"—but its true resolution is still debated today.

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The unexpected hanging paradox involves a judge sentencing a prisoner to be hanged on an unknown day of the following week, but the execution must be a surprise. The prisoner logically deduces he cannot be hanged on the last day, nor the day before, and so on, concluding he will not be hanged at all. The next week, to the prisoner’s surprise, the executioner knocks on the prisoner's door at noon on Wednesday.

The unexpected hanging paradox, also known as the surprise test paradox, concerns a person’s expectations about the timing of a future event they are told will occur unexpectedly. It poses a problem in epistemic logic—our knowledge about what we know—and has no widely accepted resolution.

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A time traveler brings a copy of Shakespeare’s Hamlet to the past before Shakespeare wrote it. Who actually authored it?

This paradox suggests that time travel allows the emergence of information or objects with no discernible origin. It is a common trope in science fiction and defies causality, sparking heated debates in temporal logic.

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Can an all-powerful being create a stone so heavy that it cannot lift it?

This simple question highlights one of the main paradoxes behind the concept of omnipotence. Some resolve it by limiting omnipotence to what is logically possible; others reframe omnipotence as maximal power rather than the ability to create contradictions.

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Removing one grain of sand doesn’t make a heap cease to be a heap. So, when does it stop being a heap?

This problem highlights the issue of vague definitions. At its core, it challenges not logic itself, but our use of language and the way we categorize concepts.

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A hotel with infinite rooms is full, but can still accommodate new guests by shifting each one to the next room.

This paradox, created by David Hilbert, illustrates the strange properties of infinite sets—whether rooms or any infinite collection of objects. It is used in set theory to demonstrate how infinities can behave in non-intuitive ways.

Doctor’s order

What's in a name? The fascinating stories behind medical eponyms!

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Have you ever wondered how some medical conditions or terms got their names? Many are eponyms, which is just the fancy word for names borrowed from the people or places connected to their discovery or history. These aren’t just labels, they’re stories! From famous doctors like Parkinson to unexpected connections (hello, Lou Gehrig!), these names make medicine a bit more human. Today, let’s explore some fascinating medical eponyms you’ve probably heard of. Spoiler: some of these might sound oddly familiar for good reason!

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Alzheimer’s disease is a tough one; it’s the most common cause of dementia in older adults. It’s named after Alois Alzheimer, a German doctor who first described the brain changes in a patient in 1906.

The patient had severe memory loss, which turned out to be due to plaques and tangles in the brain. While there’s no cure yet, treatments can help manage symptoms. Now, here’s the twist: Alois didn’t name the disease after himself; others did!

If forgetting your keys worries you, remember that occasional memory lapses are normal. So don’t sweat it unless it’s a daily struggle.

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This disorder, marked by tremors and slowed movement, got its name from James Parkinson, a London doctor. In 1817, he wrote about "shaking palsy" and described six patients with these symptoms. Later, scientists added more details, but the name stuck.

Parkinson’s is caused by a lack of dopamine in the brain, which acts like a chemical messenger for movement. Modern treatments include medications and therapies to improve quality of life. James would probably marvel at today’s advances. Remember, staying active helps keep your body and brain sharp!

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Joseph Babinski’s name lives on through a simple but revealing reflex test. In 1896, he noticed that stroking the foot’s sole made the toes fan out in babies but curl in adults. If adults show the baby's response, it signals a problem in the nervous system.

It’s an important tool for diagnosing brain or spinal cord issues. Babinski’s discovery is still used in clinics worldwide. Don’t you simply want to try it out right now? Who knew feet could reveal so much?

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Named after Dr. Thomas Hodgkin, this type of cancer affects the lymphatic system, your body’s drainage network.

In 1832, Hodgkin described several patients with swollen lymph nodes and weight loss. Though rare, it’s one of the most treatable cancers today. Treatments include chemotherapy, radiation, or newer immunotherapies.

Hodgkin’s curiosity paved the way for breakthroughs in cancer care. So, if you ever hear the term, know it’s backed by a history of determined research. Science sure knows how to make lemonade out of lemons!

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Crohn’s disease is an inflammatory bowel disease that can mess with your digestion. It’s named after Dr. Burrill Crohn, who, in 1932, described cases of severe intestinal inflammation. The exact cause? That’s still a mystery, but genes, environment, and immune system quirks play a role.

Symptoms may include pain, diarrhea, and weight loss, but treatments like medications or surgery can help. Burrill wasn’t the sole researcher on this, but his name took the spotlight. If your stomach’s giving you trouble, you’re not alone. Crohn’s is actually more common than you’d think.

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Do you usually feel weak and tired for no clear reason? Thomas Addison might have an answer.

In 1855, he linked strange fatigue and weight loss to damaged adrenal glands. These glands, above your kidneys, produce hormones that keep you balanced. Addison’s disease happens when they don’t, leading to symptoms like low blood pressure and craving salty snacks. Can you relate? Thankfully, hormone replacement therapy can fix this.

Addison’s knack for connecting the dots helps countless people manage their symptoms today. So next time you grab chips, thank your adrenal glands!

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This thyroid condition got its name from Robert J. Graves, an Irish doctor, in the 1830s. It causes hyperthyroidism, leading to weight loss, anxiety, and even bulging eyes.

Graves was a pioneer, and his work brought attention to autoimmune diseases. Though not life-threatening, it can feel quite overwhelming without treatment, which includes medications or sometimes surgery.

Graves didn’t seek fame; his patients’ relief was all he wanted. If your energy feels through the roof, maybe get that thyroid checked; it might just be doing overtime.

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You may know this one as ALS, or amyotrophic lateral sclerosis. But its former name was after Lou Gehrig, a beloved baseball player. Of course, he wasn’t the one to discover it, but the one who got it.

Diagnosed in 1939, Gehrig brought attention to this muscle-weakening condition. It affects the nerves controlling voluntary movements like walking or talking. While the cause is still unclear, ongoing research holds promise.

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Antoine Marfan, a French pediatrician, described this connective tissue disorder in 1896. It affects the body’s scaffolding and makes people tall with long limbs and sometimes heart issues. Famous figures like Abraham Lincoln are thought to have had it!

Early diagnosis is key since heart complications can be serious. Treatments, including regular check-ups and medications, help manage symptoms. Marfan’s legacy ensures people with this syndrome lead long, full lives.

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Harvey Cushing, an American neurosurgeon, found this hormone imbalance in 1932. It happens when cortisol levels are sky-high, causing weight gain, round faces, and mood changes.

The condition often results from a tumor in the adrenal or pituitary glands. Cushing’s meticulous work brought clarity to these puzzling symptoms.

Today, surgery or medications can restore balance. If stress feels like it’s taken over your body, it might be time for a check-up. Cushing showed us that even hormones need boundaries!

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Named after Georges Gilles de la Tourette, this condition is marked by repetitive movements or sounds called tics. He described it in 1885 while working with neurologist Jean-Martin Charcot.

Though it can be tricky to live with this syndrome, many people lead successful, fulfilling lives. Treatment often combines therapy and medications. Tourette’s work laid the foundation for understanding neurological quirks. If you know someone with tics, patience, and kindness go a long way. After all, everyone’s brain dances to its own rhythm!

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Syndromes are not the only things named after the people who first described them. That also happens with some drugs.

Named after the Wisconsin Alumni Research Foundation (WARF), warfarin actually started as rat poison! In the 1920s, scientists discovered its blood-thinning properties after cattle ate spoiled clover. It became a life-saving drug for preventing blood clots and strokes.

Don’t worry, it’s safe for humans in controlled doses. If you’re on it, take pride in modern medicine’s quirky history. Just remember to follow your doctor’s orders to stay safe!