7 Classic Paradoxes That Will Blow Your Mind

Mathematical paradoxes, logical paradoxes, semantic ones, and those that make you laugh out loud. All of them put our neurons to work, serving as a refreshing reminder of how reality itself deceives us with its properties and our ways of perceiving it. Math versus physical reality, semantics versus common sense, starving donkeys, Zodiac knights with protection problems, and Greek philosophers tying our minds in knots with seven classic paradoxes that will blow your mind.

In every aspect of our existence, the paradoxical surrounds us as if it were the ironic language with which the Universe reminds us that everything we see, do, and say is subject to laws that considerably falter. Paradoxes challenge common sense and the establishment of a priori judgments, inviting us to rethink situations that seem already resolved from the outset. Brought from the deepest corners of universal human history, even the most classic paradoxes make us modernize our thinking, and that is why we list seven of the most interesting ones here.

The Paradox of Buridan's Ass

It refers to a paradoxical situation in which a donkey that always had well-differentiated options for making a choice is placed exactly between two piles of hay of equal size and quality. His indecision will lead him to starve to death because he cannot make a rational decision about which pile will be his food. Although it has been named in honor of the French philosopher Jean Buridan, the paradox was not originally originated by Buridan but by Aristotle, who exemplifies thought when facing a decision with balanced or too balanced options, with a man who remains immobile with as much thirst as hunger between two tables. One with drinks and another with food.

The paradox is that the supposed equality of conditions can condemn one to choose any option, but the main idea was not that, but rather to always choose the best option. Having two equally 'best' or 'worst' options complicates the picture. One enters complex reasoning cycles, and the end is what we all, members of this existentialist postmodernism, know well: indecision.

Achilles and the Tortoise

Another one from our friend Zeno in pursuit of silencing the Pythagoreans by denying the possibility of movement and talking about the infinite. In the paradox of Achilles and the tortoise, just like in the tale, a tortoise meets someone faster than herself. It is the great Achilles, who will give her a 150-meter head start in a foot race. Some Roman woman in a short dress gives the starting signal, and we start to assume that each runner starts running at a constant speed (one very fast and the other very slow).

After a certain period of time, Achilles has run 150 meters, bringing him to the tortoise's starting point. During this time, the tortoise has advanced a much shorter distance, for example, 20 meters. Achilles will have to run for a while to reach the point where the tortoise was when he started from his 150 meters. By then, the tortoise will have advanced a bit more, showing that every time Achilles reaches the tortoise's previous state, she has already moved.

Therefore, because there is an infinite number of points Achilles must reach where the tortoise has already been, Achilles can never overtake the tortoise. If you are already sharpening your pencil to say no, that experience dictates otherwise, you are right. But that is precisely why this is a paradox. Applying mathematical rules to non-mathematical situations can have strange results, like letting the tortoise escape.

The Surprise Hanging Paradox

Middle Ages, a prison in a castle's dungeon, a condemned man waits to be told on which day of the executioner's schedule he will leave this world. His condemner tells him that the hanging will be one dawn of the next week, but will not tell him when, seeking it to be a surprise until the executioner knocks on his cell door. Upon hearing this sentence, the prisoner feels relieved, because he knows he will escape death. What? Was he also insane? No, on the contrary.

The prisoner reasons that if what he has been told is true and he will be hanged by surprise, the chosen day will not be Friday. Because if by Thursday he has not been hanged, the Friday hanging would not be a surprise. The same happens with Thursday, because if Friday is already eliminated and Wednesday night he is not hanged, Thursday would be obvious. He uses the same to eliminate Wednesday, Tuesday, and Monday, going to sleep peacefully with the fixed idea that he will not be hanged. The following week, Wednesday morning, the prisoner was surprisingly hanged. Do I need to explain why what the King said came true?

If it seemed familiar to you, it is because you have probably experienced it many times, since this paradox is also known as the surprise exam, where, in addition to the premises, the ending almost always ends up being the same: you die, in terms of grades, hanged by the executioner professor.

The Arrow Paradox

A direct disciple of Parmenides, Zeno of Elea was a tank of Eleatic concepts, a guard dog of Parmenides and his theses who barked with paradoxes at those who tried to refute his master. In his arrow paradox, this pre-Socratic said that if we fired an arrow and considered its millions of positions during flight as if they were instants, we would realize that the arrow does not move at all, because at every moment taken as an instant it is in a specific position, which nullifies movement itself. A better way to understand this is to think of the frames per second of a short animation. If we take them as still images, movement does not occur.

With this, which seems silly or obvious, Zeno slaps your hypothalamus and tells you: you cannot judge whether an object is at rest or in motion by observing only a single instant. To draw conclusions, you only have to compare the instants that precede or follow it. Just like that, Zeno tied a mental knot for you and brought into play certain ideas about the very concept of speed and its rational definition, leaving at that time an idea like: Is movement a concrete state or only the result of a comparison of states? More on Zeno's paradoxes here.

The Irresistible Force Paradox

What happens when an irresistible force meets an immovable object? This is what the paradox that has a strong intrusion into the realm of logic questions. As with all the paradoxes we have been presenting, the idea is not to think of it as a possible reality, but as an exercise. Known as the paradox of an irresistible or unstoppable force, this postulation comes to confront the current scientific idea that no force is completely irresistible, as well as theoretically asserting that immovable objects do not exist.

This is because an immovable object would still have to have inertia equal to infinity, therefore it should be made of infinite mass. If we take into account a finite universe, such energy for the unstoppable force cannot exist. Anyone who has seen the battle of Shyriu against Seiya will remember the former saying "I possess the hardest fist" and the "most solid shield", with which Pegasus manages to make Shyriu attack himself.

The Interesting Numbers Paradox

Half mathematics, half humor, the paradox of interesting numbers talks about the supposed and subjective nature of interestingness of natural numbers. Not some, but all of them. The denomination of interesting comes from something we all know and even constantly suffer, which is the search for unique properties or special characteristics of certain numbers. And if someone is thinking that a particular number might not be interesting, whoever maintains that natural numbers are always interesting will say no, that the number selected by the one who wants to contradict him is interesting because, for example, it is the number corresponding to the year in which an event occurred or that it is the product of the sum of other natural numbers (also important).

The real demonstration of this statement is given through the division of natural numbers into interesting and boring. In this way, there will always be a number that is the smallest of the boring ones, therefore it will become interesting and therefore it will have to be moved from the group. If this keeps happening, we will find that the group of boring ones will end up empty, implying that all numbers are interesting. The paradoxical thing is that this reduction to the absurd of objective entities has a very strong and ambiguous subjective component, the very fact of being interesting. Now, if the adjective 'interesting' has been subjectively applied to the number and the paradox refers to interesting numbers, how wrong is the main assertion? For more information, check out the specific article about it here at NeoTeo.

The Sorites Paradox

It is time for my favorite paradox, because it puts into play everything we normally say based on common sense (cognitive bias) and the egocentric presumption of the universality of a given knowledge. The author is Eubulides of Miletus, a Greek philosopher also known for his paradoxes. One of the most interesting is the one that formulates the following: At what point does a pile of sand stop being one?

This question always leads us to make deductions about what constitutes a pile of sand. Thus, it is said that two or three grains of sand do not form a pile, that a million do constitute one; that if n grains of sand do not form a pile, adding one more grain will not form one; that if n grains of sand are a pile, removing one grain will still be one. Is the problem with this clear? What is the appropriate measure? What is the interesting number that will inaugurate the existence or not of a pile of sand?

The most accurate answers could be the following: Either there is no such thing as piles, or 1 grain of sand is a pile. By the way, Sorites is the Greek for pile, heap, set. Hence its name, don't think it refers to other equally heapable substances.

Some well-known, others not so much, these seven classic paradoxes always serve to get the head working and think a bit more, because not everything is as it seems and not everything seems what it is, although sometimes it seems everything that it is not and does not seem what it is, which is a paradox in itself.

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