There are a lot of things in this world that people don’t understand because, hey, the world is a confusing place. But we can always take solace in the fact that there are some really simple concepts and ideas out there that we can all understand. However, as is often the way with life, when you start to look closely at some of these concepts, you realize that you’ve opened a giant can of worms.
10. The Proof For ’1+1=2′ Is 300 Pages Long
The equation 1+1=2 is probably the very first bit of math that most of us learned, because addition and subtraction are probably the simplest concepts in mathematics. If you have one apple and somebody gives you another, you have two apples. By the same logic, if you have two apples and someone takes one away, you only have one apple. It’s a universal fact of life that transcends barriers like language or race. Which is what makes the following sentence so unbelievable: The proof for 1+1=2 is well over 300 pages long and it wasn’t conclusively proven until the 20th century.
As Stephen Fry explains in this handy clip, in the early 20th century, Bertrand Russell wanted to conclusively prove that mathematics worked, so he decided to start with the simplest concept we know of and went right ahead and proved 1+1=2. However, what sounds like an incredibly simple task actually took the mathematician and philosopher 372 pages of complex sums. The mammoth solution was published as Principia Mathematica across three volumes, which we invite you to read if you aren’t planning on doing anything for the next few weeks.
9. The Definition Of ‘Almost Surely’ Is A Mathematical Nightmare
If we were to say that a given event was almost sure to happen, how would you explain that to a small child? Maybe you’d say that the event was practically guaranteed, but then you’d have to explain what “practically” meant in regards to that sentence, which would just confuse things further. It’s a tough question because the concept of something being “almost sure” to happen is so vague in and of itself.
Luckily for us all, the concept exists within statistical mathematics, which explains it fully. Unluckily, it’s incredibly intimidating at first glance. To quote an online math textbook on the concept:
“In probability theory, a property is said to hold almost surely if it holds for all sample points, except possibly for some sample points forming a subset of a zero-probability event.”
In more basic language, that essentially means that even when an event has a 100 percent chance of occurring, it won’t necessarily occur. For example, if you flipped a coin a million times, statistically, the odds of the coin landing on heads at least once is essentially one. However, there is an infinitesimally small chance that the coin could land on tails every single time. So although the odds of the event happening are for all intents and purposes guaranteed, it is impossible to say that.
8. Defining The Word ‘The’ Is Really Difficult
The word “the” is one of the most commons words in the English language. It’s so ubiquitous that most of us have probably never stopped to think about how strange of a word it actually is.
As discussed here, it’s easily one of the most difficult words to explain to a non-native English speaker because it has such a massive range of applications, some of which are remarkably odd when looked at objectively. To quote:
“Why do we say, ‘I love the ballet,’ but not ‘I love the cable TV?’ Why do we say, ‘I have the flu,’ but not ‘I have the headache?’ Why do we say, ‘winter is the coldest season,’ and not ‘winter is coldest season?’ ”
Think about it - we use the word “the” in dozens of different situations and in reference to many different concepts, ideas, and objects interchangeably. We can use the word to refer to everything from a specific item to an abstract metaphorical concept, and native speakers can instinctively tell when it’s being used incorrectly without thinking about it.
As noted in the linked article above, the dictionary itself lists almost two dozen different ways the word can be used in a sentence correctly, which makes an exact definition of the word that much more difficult to pin down. Don’t believe us? Try defining it yourself in the comments and let us know how it goes.
7. There’s No Universally Accepted Theory On How Bikes Work
Bicycles have existed for over 100 years, and since they were invented we’ve mastered land, sea, and air travel while making impressive headway into space. We have planes that can traverse the globe in a matter of hours, so you’d think that by now we’d have the humble bicycle just about figured out. But oddly, that’s not the case.
As mentioned in this article, scientists have been arguing about how exactly they work, or more specifically, how they stay upright, almost since they were first invented. For a long time, the major theory was that the gyroscopic force of the wheels spinning kept bikes upright, but when scientists built a special bicycle with contraptions attached to it designed to counteract any gyroscopic forces produced by the wheels, it stayed upright and no one could explain how.
There are theories that the bike’s design allows it to steer into a fall and thus correct itself, but they’re still just theories. And because bicycle dynamics isn’t exactly an area of science into which researchers like to invest their time, it’s highly unlikely that we’ll know for sure anytime soon.
6. How Long Is A Piece Of String? It’s Impossible To Know
If someone was to give you a piece of string and ask you how long it was, you’d assume that answering them would be a fairly simple, if rather odd task. But how would you answer that person if they wanted to know exactly how long that piece of string was? That was something comedian Alan Davies wanted to ascertain for a BBC TV special aptly called How Long is a Piece of String? by posing the deceptively simple question to a group of scientists.
The answer was, rather ironically, “it depends,” because the exact definition of how long something is depends on who you ask. Mathematicians told the comedian that a piece of string could theoretically be of infinite length, while physicists told him that due to the nature of subatomic physics and the fact that atoms can technically be in two places at once, measuring the string precisely is impossible.
5. Yawning
Yawning is a puzzling phenomenon. Even the simple act of talking about it is enough to make some people do it (some of you are probably doing it right now). There really is no other bodily function quite like it.
Now, some of you reading this may be aware of the long-standing theory that the purpose of yawning is to keep us alert by forcing our bodies to take in an extra large gulp of oxygen. That makes sense, because we mostly yawn when we’re tired or bored, situations where an extra burst of energy would come in handy.
The thing is, experiments have conclusively disproven that theory over the years. In fact, there is no universally agreed upon theory for why we actually yawn, even though everyone does it. A commonly accepted theory is that yawning actually cools down the brain, because various experiments have shown that one of the few things to actually change in the body during a yawn is the temperature of the brain itself.
4. Left And Right Have Been Confusing Philosophers For Years
How would you explain the concept of left and right to someone who had no idea what those words meant? Would you explain it in terms of your relative position to a well-known stationary landmark? Or maybe you’d think outside the box and refer to the rotation of the Earth or something comparably massive and unchanging. But what if you were talking to an alien whose planet rotated differently to our own, or one who didn’t have eyes? It’s a question that has been intriguing philosophers for years because, without an agreed upon point of reference, it’s incredibly difficult to define what left and right actually are.
For example, consider the work of German philosopher Immanuel Kant, who once said, “Let it be imagined that the first created thing were a human hand, then it must necessarily be either a right hand or a left hand.”
However, with only one hand, it’s impossible to explain which hand it is without another one present. Think about it for a second - right and left hands are clearly very different from one another, but if you were to describe them, the descriptions would be literally identical because they’re the same. Only they aren’t because, as Kant himself put it, a left hand can’t fit into a right-handed glove, so there is a difference between them. However, said difference is practically impossible to put into words without the other hand being present.
If you think we’re over-complicating this, we should point out that there is literally a 400-page book on the philosophy of right and left, aptly called The Philosophy Of Right And Left. That’s more pages than it took to work out 1+1=2.
3. We Enjoy Things For Reasons Other Than Enjoyment
Enjoyment is a weird thing because it’s so subjective - for every person who loves a given food, song, or movie, there’s another person who adamantly hates it. You’d think that the reason we enjoy things is because it feels good in some way, but scientists have conclusively proven that that’s only half the story.
For example, people can be fooled into thinking they love a certain food or wine just by telling them it’s really expensive. The same can be said for objects - people will instinctively choose an expensive product over a cheaper one purely because of the price. Enjoyment is barely even a factor. In marketing, this is known as the “Chivas Regal effect,” named for the scotch of the same name which saw sales explode after they simply raised the price of their product.
To further illustrate the point, there’s a famous experiment where wine experts were fooled into thinking a cheap bottle of wine was an exceptional vintage just by switching the labels. Their enjoyment of the product wasn’t based on some deeply held love and appreciation of wine - it was based entirely on the fact that they were told it was good wine. Which, to be honest, is much easier.
2. Some Mosquitoes Bite People Because Of Their Clothes
If you’ve ever been bitten by a mosquito, chances are someone nearby has given you a recycled explanation for why the insect decided to ruin your day. Maybe they said that you smelled good, or that you had a particular blood type, or maybe they just told you that your shirt makes you look like a victim. We’re not being facetious with that list, by the way - they’re all things that scientists believe can cause mosquitoes to find you more attractive.
As a recent Smithsonian article details, 20 percent of people seem to be strangely attractive to mosquitoes, and no one is really in agreement as to why. The simple answer would appear to be that it’s something in a person’s blood that attracts mosquitoes. However, it would appear that the mosquitoes are actually attracted by a chemical signal given off by the body. It’s present in around 85 percent of us - which also explains why some people seem invisible to mosquitoes - and it indicates what your blood type is.
Another, stranger theory is that mosquitoes are naturally attracted to darker, more vivid colours. In other words, it’s actually been theorized - and in some cases shown - that mosquitoes will bite people because they like their shirt.
1. Rock-Paper-Scissors Is The Most Serious Game In The World
Nothing could be simpler than a game of rock-paper-scissors; it’s the easiest way to decide any argument because it’s basically just random chance, right?
Well, not if the dozens of papers written about the subject are to be believed. The game has become a favourite research topic of psychologists because of how intertwined rock-paper-scissors is with subconscious human responses and game theory. As a result, dozens of strategies exist to help players get an edge in the game - including playing blindfolded to avoid being subconsciously influenced by an opponent’s body language.
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