How To Alleviate Suffering And Overcome Your Struggles

Paradoxes have been around since the time of Ancient Greeks and the credit for popularizing them goes to recent logicians. Using logic you can usually find a fatal flaw in the paradox which shows why the seemingly impossible is either possible or the entire paradox is built on flawed thinking. Can you work out the problems in each of the 11 paradoxes below?

#11 – The Omnipotence Paradox

The paradox states that if the being can perform such actions, then it can limit its own ability to perform actions and hence it cannot perform all actions, yet, on the other hand, if it cannot limit its own actions, then that is—straight off—something it cannot do. This seems to imply that an omnipotent being’s ability to limit itself necessarily means that it will, indeed, limit itself.

This paradox is often formulated in terms of the God of the Abrahamic religions, though this is not a requirement. One version of the omnipotence paradox is the so-called paradox of the stone: “Could an omnipotent being create a stone so heavy that even that being could not lift it?” If so, then it seems that the being could cease to be omnipotent; if not, it seems that the being was not omnipotent to begin with. An answer to the paradox is that having a weakness, such as a stone he cannot lift, does not fall under omnipotence, since the definition of omnipotence implies having no weaknesses.

#10 – The Sorites’ Paradox

The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:

1,000,000 grains of sand is a heap of sand. (Premise 1)
A heap of sand minus one grain is still a heap. (Premise 2)
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand.

On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. Peter Unger defends this solution. Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.

#9 – The Interesting number paradox

Claim: There is no such thing as an uninteresting natural number.

Proof by Contradiction: Assume that you have a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of not interesting numbers. Being the smallest number of a set one might consider not interesting makes that number interesting. Since the numbers in this set were defined as not interesting, we have reached a contradiction because this smallest number cannot be both interesting and uninteresting. Therefore the set of uninteresting numbers must be empty, proving there is no such thing as an uninteresting number.

#8 – The arrow paradox

In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher’s paradox—a fletcher being a maker of arrows.

Whereas the first two paradoxes presented divide space, this paradox starts by dividing time – and not into segments, but into points.

#7 – Achilles & the tortoise paradox

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.

#6 – The Buridan’s ass paradox

This is a figurative description of a man of indecision. It refers to a paradoxical situation wherein an ass, placed exactly in the middle between two stacks of hay of equal size and quality, will starve to death since it cannot make any rational decision to start eating one rather than the other. The paradox is named after the 14th century French philosopher Jean Buridan. The paradox was not originated by Buridan himself. It is first found in Aristotle’s De Caelo, where Aristotle mentions an example of a man who remains unmoved because he is as hungry as he is thirsty and is positioned exactly between food and drink. Later writers satirised this view in terms of an ass who, confronted by two equally desirable and accessible bales of hay, must necessarily starve while pondering a decision.

#5 – The unexpected hanging paradox

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week, but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts.

He begins by concluding that the “surprise hanging” can’t be on a Friday, as if he hasn’t been hanged by Thursday, there is only one day left – and so it won’t be a surprise if he’s hanged on a Friday. Since the judge’s sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn’t been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner’s door at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true.

#4 – The barber’s Paradox

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself? Asking this, however, we discover that the situation presented is in fact impossible:

– If the barber does not shave himself, he must abide by the rule and shave himself.
– If he does shave himself, according to the rule he will not shave himself

#3 – Epimenides’ Paradox

This paradox arises from the statement in which Epimenides, against the general sentiment of Crete, proposed that Zeus was immortal, as in the following poem:

They fashioned a tomb for thee, O holy and high one
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in thee we live and move and have our being.

He was, however, unaware that, by calling all Cretens liars, he had, unintentionally, called himself one, even though what he ‘meant’ was all Cretens except himself. Thus arises the paradox that if all Cretens are liars, he is also one, & if he is a liar, then all Cretens are truthful. So, if all Cretens are truthful, then he himself is speaking the truth & if he is speaking the truth, all Cretens are liars. Thus continues the infinite regression.

#2 – The paradox of the court

The Paradox of the Court is a very old problem in logic stemming from ancient Greece. It is said that the famous sophist Protagoras took on a pupil, Euathlus, on the understanding that the student pay Protagoras for his instruction after he had won his first case (in some versions: if and only if Euathlus wins his first court case). Some accounts claim that Protagoras demanded his money as soon as Euathlus completed his education; others say that Protagoras waited until it was obvious that Euathlus was making no effort to take on clients and still others assert that Euathlus made a genuine attempt but that no clients ever came. In any case, Protagoras decided to sue Euathlus for the amount owed.

Protagoras argued that if he won the case he would be paid his money. If Euathlus won the case, Protagoras would still be paid according to the original contract, because Euathlus would have won his first case.

Euathlus, however, claimed that if he won then by the court’s decision he would not have to pay Protagoras. If on the other hand Protagoras won then Euathlus would still not have won a case and therefore not be obliged to pay. The question is: which of the two men is in the right?

#1 – The unstoppable force paradox

The Irresistible force paradox, also the unstoppable force paradox, is a classic paradox formulated as “What happens when an irresistible force meets an immovable object?” The paradox should be understood as an exercise in logic, not as the postulation of a possible reality. According to modern scientific understanding, no force is completely irresistible, and there are no immovable objects and cannot be any, as even a minuscule force will cause a slight acceleration on an object of any mass. An immovable object would have to have an inertia that was infinite and therefore infinite mass. Such an object would collapse under its own gravity and create a singularity. An unstoppable force would require infinite energy, which does not exist in a finite universe.

Bonus – Olbers’ Paradox

In astrophysics and physical cosmology, Olbers’ paradox is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. It is one of the pieces of evidence for a non-static universe such as the current Big Bang model. The argument is also referred to as the “dark night sky paradox” The paradox states that at any angle from the earth the sight line will end at the surface of a star. To understand this we compare it to standing in a forest of white trees. If at any point the vision of the observer ended at the surface of a tree, wouldn’t the observer only see white? This contradicts the darkness of the night sky and leads many to wonder why we do not see only light from stars in the night sky.

P.S. If you liked this post then you’ll like my books as well. You can get them on Amazon.

Whether you’re trying to survive an intensive college schedule or just want to seem smarter in front of your friends, you can do a lot of things to both look and be smarter.

Here are ten simple tricks for boosting your real (and perceived) brain power.

Read Faster and Better

Obviously, one of the best ways to boost your intelligence is to read more! You can read faster (and thus consume more knowledge) by getting your speech mechanism out of the equation. So give your mouth something to do, like eating, humming, or chewing gum to get through that stuff quickly. Then, take some time to absorb and reflect on what you read to keep it in your memory. Whether it’s War and Peace or just the Wikipedia Random button, you’ll be surprised by how much more you learn when you’re reading not just fast, but well.

Speak Up

The more you can contribute to a conversation, a meeting, or other discourse, the smarter you’ll come off. Even if it means admitting ignorance or asking questions, you’ll still look better than if you stay silent—and you might actually learn something in the process. Expressive speech is key: you can boost your credibility a lot by simply making sure you speak with an engaging tone. Change your pitch and volume as necessary, and try to minimize the number of pauses as you speak. A little confidence goes a long way.

Don’t Fall Prey to BS

When someone’s trying to convince you of something, they can often resort to logical fallacies, appeals to your emotion, and other “workarounds”. Learn the most common forms of BS so you can detect them as they come up. By knowing what they are, you’ll also be able to avoid dishing out those same fallacies yourself, which can be a big hit to your credibility if someone catches you.

Focus on What You Know

When engaged in a heated discussion with your friends, you’re bound to stumble upon a few holes in your knowledge. It’s okay to admit when you don’t know something, but if you’re feeling particularly self-conscious and want to keep up the appearance of intelligence, the key is emphasizing what you do know. If you’re in an argument, don’t stress disagreement so much as agreement—that way, you aren’t straying away from things you know about. You’re stressing the parts you do know while still taking part in the discussion.

Get Some Exercise

A healthy body means a healthy brain. So, in between all the reading and mind-expanding, make sure you’re leading a healthy physical life, too. That means eating right and getting regular exercise. A number of studies. have shown links between regular activity and intellecual capacity, productivity, and creativity. Will spending all day at the gym make you smarter? Not quite, but sitting around all day will not only kill you, but hinder your brain from being at its absolute best.

Talk to Yourself

While mumbling to oneself is often looked at the behavior of a crazy person, a recent study showed that talking out loud to yourself can help give you a temporary cognitive boost when trying to find something. The theory behind it: when you give yourself verbal labels to a task you’re performing, you focus better on the task at hand at any given moment. So when you feel the need to open your mouth, don’t fight the urge—it might help you get things done faster.

Learn a Second Language

People who know a second or third language are often perceived as smart by others, but research shows that it can actually make you smarter, too. If you know a second language, you’re able to adapt to and switch between certain mental tasks better than those that only know one, so if you want to give your brain a real boost, learning a new language is a real (and useful!) way to do so. It’s not actually hard to do, either: all you need is this simple four step method to learn in just a few months.

Do Things the Hard Way

Technology really has made our lives easier, but sometimes it’s worth doing things the hard way. Take GPS navigation, for example: it’s great that you can essentially never get lost, but if you rely on it too much, you’ll never truly learn your way around. Instead, wean yourself off your GPS dependency and actually learn your way around town, develop a sense of direction, and learn to navigate using your brain. Doing things the hard way can help keep your brain sharp, so don’t be afraid to forgo the easy stuff once in a while.

Know What Won’t Make You Smarter

There’s a lot of work going into researching what makes us smarter—much of which we’ve mentioned here—but it’s also important to know what won’t make you smarter. Check out our list of nine stubborn brain myths that just won’t die to see just a few examples, like “the internet is making us dumber” (it isn’t, if you use it properly), “listening to classical music makes children smarter” (unlikely), or that “brain games make you smarter” (don’t waste your time). The less time you spend on silly myths, the more time you can spend actually expanding your brain, so get these out of your system now.

Just Believe You Can Be Smarter

The last step? Just believe you can be smarter. Studies have shown that this simple belief can actually make it true. That isn’t to say you should be pompous: you need to assume you aren’t that great yet, which will leave you open to learning new things and asking new questions—the exact sort of things that can make you smarter. But it’ll never happen if you believe your intelligence is somehow fixed, so once that roadblock is gone, you may find you’re much freer to pursue the level of intelligence you want. If you’re having trouble doing that, it may be time to recalibrate your reality—attitude is everything.

As always thanks for reading and until next time.

P.S. If you liked this post then you’ll like my books as well. You can get them on Amazon.

The relationship between our minds and our bodies is exceedingly complex, and often functions in ways that we simply haven’t yet found a way to understand or explain in purely scientific terms. For decades, studies on the placebo effect have shown that patients who believed they were getting a treatment responded in ways that were similar or the same to those who were actually getting a treatment, showcasing an unexpected level of power of the brain over the body.

While the placebo effect itself is a fascinating topic of study, there are a lot of very practical and perhaps even inspirational lessons that can be taken away from this phenomenon and applied to everyday life. Here are just a few that we think are especially powerful that offer insights into motivation, mindfulness, and even happiness that we can all stand to benefit from.

Belief is often more powerful than reality

When researchers study the placebo effect, they often find that those who aren’t given a particular treatment improve in many of the same ways as those that are, simply because they believe that they are being treated, not because they’re getting any real medical help. While believing things, even very strongly, doesn’t always cause them to be true, it can have a marked impact on how we see and experience the world, often much more so than things that are regarded as fact. Belief can, in many ways, be a much more powerful force than reality, coloring our perceptions, pushing us forward, and changing what we feel is possible to accomplish.

Life is all about perception

The placebo effect is all about perception, as people respond to an outside stimulus in a way that isn’t congruent with the effect the stimulus should actually have on the body (in many cases, there should be no effect at all). This reaction isn’t exclusive to issues of healthcare, however, as a number of studies have shown. People perceive a wine to taste better when they believe it’s expensive, and they get a greater health benefit from doing something if they believe it qualifies as exercise. How we think about something can entirely change how we react and how it affects us, whether it’s something as simple as enjoying wine or something much more complex like getting along with a boss, caring for an aging parent, or coping with the stresses of everyday life. The placebo effect teaches us that we can choose how things, whether bad or good, in the outside world affect us. That’s an incredibly powerful piece of knowledge to have.

Sometimes you get in your own way

Belief is a powerful force, but sometimes the power it wields over us can actually hold us back and keep us from meeting our goals. The placebo effect can work in two ways: one that motivates, heals, and helps, and the other that can induce self-doubt, destructive thoughts, and keep success at bay. If you believe you can’t accomplish something because you’re not smart enough, good enough, or fast enough, these beliefs may become a self-fulfilling prophecy and you may fail not because you truly can’t do something, but because the doubt and uncertainty caused by your beliefs trips you up or makes you overly cautious. Take a child who is struggling with learning as an example. If he or she is told they will never grasp a concept, are stupid, and should just give up, eventually this message will sink in and the child will give up, regardless of his or her actual abilities.

There truly is power in positive thinking

If the placebo effect teaches us anything, it’s that there is something to be said for positive thinking. It may not bring you unlimited riches or the perfect life, but it can have an effect on your happiness, relationships, and, of course, your health. Studies have shown that positive thinking can help you control stress, lower rates of depression, and may even result in a longer life span. So believing in the best outcome may just be what you need to get your life on track.

Anything is possible, if you put your mind to it

As cliché and saccharine as it may be, there is truth in this old adage. Many things seem impossible until someone really puts effort into showing how they can be done. Take runner Roger Bannister as an example. Roger decided he would set the world record for running a mile, with the goal of a time that was under 4 minutes. People told him it wasn’t possible; after all, no one had ever done it before. In 1954, Bannister completed a mile run in 3 minutes and 59 seconds. Within a year of breaking this previously unheard of barrier, more than 30 other runners had also run with similar times. All it took was someone changing the beliefs surrounding the achievement to make others see it as a possibility, something we can all take note of in our own lives.

We often become reliant on outside factors to empower ourselves

As the placebo effect shows, we often believe we need some form of outside input, a medicine or surgery say, to feel better. In reality, it may be enough to believe that we’ll get better, allow ourselves to heal, and let time take its course than looking for an outside solution to a problem. While help and support from others can be great, real motivation has to come from within. You have to want something for yourself or believe that it will happen to really make any progress.
Humans aren’t always rational.

Like the half-human, half-Vulcan Spock in the classic Star Trek series, humans are constantly battling against their emotional side when trying to make logical, rational decisions. Often — perhaps too often — emotions win out, influencing our decisions on everything from business to buying a car. The way we react and the things we choose are rarely entirely rational or easily explicable to others. Our brains work in mysterious ways, as the placebo effect clearly demonstrates, so never forget to account for the effects of our ever powerful emotions in any situation, both in our own reactions and those of others. It may just give you a deeper understanding of a situation, temper your actions, and help you prepare for the unexpected.

You can choose your level of happiness in life

You can choose to believe a medication will work or believe it will do nothing at all, but as the placebo effect shows us, sometimes hoping for the best will actually increase the likelihood that these things will come to pass. You can choose your beliefs and in turn, choose the ways in which things affect you in your everyday life. If you believe that being stuck in a traffic jam is the worst thing in the world, it will be, raising your levels of stress and making you angry. But if you choose to believe that any delay can be an opportunity, you’ll be less stressed, more happy, and may use that extra time on the road to think, learn a language, tackle a book on tape, or just enjoy some music. Being happy isn’t just something that happens, it’s something you can choose.

What you think is just as important as what you do

Thoughts, even if we don’t act on them, have a big impact on our outlook on the world, what we do end up doing, and our overall level of happiness. They are incredibly powerful, often more so than we’re willing to readily admit. One lesson you can take away from the placebo effect is that your thoughts are just as important as your actions. After all, in placebo studies, doing an essentially empty task (taking a sugar pill) can have the same effect as actually doing something, because of a particular line of thinking. You can apply this to other areas of life as well, making sure careful and purposeful thoughts always precede any actions you take.

Life’s obstacles are rarely as insurmountable as they seem

If people can see a change in their health, or at least their perception of it, from doing nothing at all except thinking that they should feel better, than there really isn’t much in life that can’t be conquered (or at least managed) by changing the way you think. Think you’ll never complete a task? That you can’t get ahead in your career? That you’ll never get over a breakup? While we might all feel this way from time to time, framing your thoughts with respect to the bigger, overall picture of your life can change how you see your ability to push through. And, as we’ve already discussed, it doesn’t hurt to truly believe that you can do these things either.

As always thanks for reading and until next time.

P.S. If you liked this post then you’ll like my books as well. You can get them on Amazon.