Science is a process by which  humans try to understand reality.

And sometimes, that process spits out paradoxes. Observations seem to defy  the laws we’ve established.

Like a diluted batch of acid that  corrodes steel way better than a concentrated batch of the same acid. Or a coastline with as many different  lengths as there are ways to measure it. But often, scientific paradoxes  don’t mean we were entirely wrong about the world, just  that we were missing something.

So let’s dive into five paradoxes that  have plagued researchers for decades. [♪ INTRO] Our first paradox comes from statistics, which might sound more “math” than “science.” But stats are a critical component of  pretty much every experimental study, whether you’re looking for  a new subatomic particle, or the best way to treat kidney stones. Speaking of which, let’s say  you’re a kidney stone scientist. And you’re in the middle of a study examining two different kidney stone treatments.

We’ll call them Treatment A and Treatment B. And you’re testing both treatments on two different types of kidney stones: large and small. When you get your results, you  find Treatment A seems to be more effective than Treatment B at  dealing with large kidney stones, and also more effective at  treating small kidney stones.

So Treatment A should be  the best treatment, right? Except, when you look at your combined dataset… small and large kidney stones mixed together… Treatment B comes out on top. Turns out, you’ve stumbled onto a  classic example of Simpson’s paradox, when trends you observe in  subpopulations can disappear when you look at the whole  population, or vice versa.

This paradox was first observed  at the turn of the 20th century, but was lost in the literature until 1951, when British statistician Edward  H. Simpson described it in a paper. He didn’t actually call it a “paradox”, though.

Or name it after himself. Both of those bits came later. While Simpson’s paradox can be  confusing, it has a simple solution: it means you haven’t taken  all variables into account.

There’s another factor at play that's having a strong effect on your statistical comparison. Let’s look back at our kidney stone story, which is based on a real study that’s often used as an example of Simpson’s Paradox. In that study, Treatment A was open surgery, and Treatment B was minimally invasive surgery.

And the hidden factor here is that doctors weren’t randomly assigning patients to each treatment. The size of the kidney stones actually  affected the treatment being recommended. Large kidney stones are more likely  to be treated by open surgery, while small kidney stones  are more likely to be treated by a minimally invasive procedure.

Plus, treating a large kidney stone is more likely to fail than  treating a small kidney stone. So Treatment A worked better  than Treatment B in most cases, but because Treatment A was  disproportionately prescribed for large kidney stones…which  are more failure-prone than small kidney stones…Treatment  A was also going to record a larger number of failures than Treatment B. That’s why Treatment B seemed to do  better in the overall population.

It wasn’t really the better option; it just overwhelmingly got  assigned to the easiest cases. So Simpson’s paradox is only  a paradox at first glance. If you look closer, it vanishes.

Meanwhile, our next paradox  occurs when you look too close. How long is the coastline of Alaska? Well, if you ask the National Oceanic  and Atmospheric Administration, better known as NOAA, Alaska has  about 10,000 kilometers of coastline.

But wait. According to a different  measurement from the same agency, that distance is closer to 55,000 kilometers. With a discrepancy that large,  you might think some poor soul was just really bad at taking measurements.

But no. One of them just used a smaller ruler. To explain this coastline paradox, we have to take another dive into the world of mathematics.

Specifically, the world of infinitely  complex shapes called fractals. The more you zoom in on a fractal,  the more features its edge reveals. Or surface, if you’re working with  something 3D like Romanesco broccoli.

That means the length of that  edge is practically infinite, because the more you zoom in, the more nooks and crannies  you can find to measure. Coastlines may be the best  real world example of this. Benoit Mandelbrot… the mathematician  who coined the term ‘fractal’… developed his ideas while writing  a paper on the British coastline.

But there are plenty of other  fractals in nature, too. Including ones where the coastline  paradox might actually matter. For example, a 2017 study compares  cell membranes to coastlines, in the sense that they also seem to get longer and more featured the closer you look.

The authors applied this insight to  a phenomenon called cell migration, which is essential for understanding how organs are formed in a developing embryo. And in order to successfully migrate, the cells have to unfold parts of  those super intricate surfaces to form tiny protrusions called…and I  mean this 100% seriously…blebs. So in a way, a paradox that was originally  about coastlines is helping us learn a bit more about how we go from being  a bunch of cells to, well, ourselves.

For our next paradox, let’s  jump into some fluid dynamics. Not the dynamics of the cool, refreshing  water off the coast of Britain, but a liquid that’s way more  associated with Britain. Tea.

This particular paradox is known  as Einstein’s tea leaf paradox. Yes, Albert Einstein, of  upending-our-entire-concept-of-gravity fame. But this paradox has nothing to do with  relativity…which is itself full of paradoxes… or any of the other physics revelations  Einstein is most famous for.

If you make your tea using loose  tea leaves instead of bags, you’ve probably seen this phenomenon in action. But you might not have realized  what you saw was super weird. Normally, when a bunch of solid  bits are dispersed in water, and then you stir that water, the bits  get pushed toward the cup’s walls.

This is why centrifuges work for  getting solids out of solution. But anyone who’s stirred a cup of loose leaf knows those leaves don’t end up hugging the walls. Instead, the more you stir, the more they  end up settling in the center of the cup.

The exact opposite of where they should be. This paradox was first described  in 1857 by James Thomson, the older and less famous brother of the  guy who would later become Lord Kelvin. Thomson attributed the  phenomenon to secondary flow, which is a fluid dynamics term for a weaker flow superimposed onto the primary one.

Basically, his idea was that some  other force was moving the leaves in a different direction, away from the  centrifugal force caused by stirring. He blamed friction on the bottom of  the cup, and he wasn’t entirely wrong. But the correct solution for the  paradox came about in a 1926 paper by, you guessed it: Albert Einstein.

Einstein figured out it’s also the friction  between the water and the wall of the cup, not just the bottom of the cup,  which causes that secondary flow. Because of this friction,  the velocity of the water is slower at the bottom of  the cup than at the top. So while a centrifugal force initially  pushes the water and the tea leaves away from the center of the  cup, and towards the walls, that difference in velocity causes water  in the center of the cup to rise upward.

Since they’re just along for the ride,  the leaves wind up traveling in an arc. First towards the walls, then down,  and finally towards the center. If we only apply this solution to the  tea that started this whole mystery, it’s pretty much just a fun fact.

Luckily, it has applications well beyond  the stuff we use to flavor our water. For example, the principles  behind this paradox have been applied in biology to separate  blood plasma out of solution… which is great for medical  tests that specifically require plasma samples separated from  red or white blood cells. I myself haven’t looked into how they do that, but I’m now picturing a vampire holding a teacup full of blood and  stirring very vigorously.

And before we head over to our next example, all science needs funding. So here’s an ad. Thanks for watching SciShow and  learning new science stuff with us!

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And right now, SciShow viewers can save 20% off an annual subscription  at brilliant.org/scishow. The namesake of our next paradox,  English scientist Michael Faraday, was so good at discovering contradictions that he actually has two paradoxes to his name. But today we’re going to talk  about his electrochemistry paradox.

In 1830, Faraday found that while  diluted nitric acid corroded steel, concentrated nitric acid  did basically nothing to it. This was a little odd, because  you’d expect concentrated versions of any substance to have more of an  effect than their diluted counterpart. Faraday thought so too, so he took a closer look.

When he scratched the surface of the  steel before dipping it back into concentrated acid, bubbles would  form and appear on the surface, but only for a moment. He concluded the paradox had something to do with a property on the steel’s surface. He suggested that it had  become “passive”, somehow… but he couldn’t explain why.

The paradox remained unsolved  for more than a hundred years, but Faraday wasn’t too far off. It turns out, the surface of the steel becomes oxidized when exposed to concentrated nitric acid. Oxidation is a chemical process  where a substance loses electrons.

Electrons, rather famously,  are negatively charged. Meanwhile, either the stronger or  the more concentrated an acid is, the more hydrogen ions you have floating around. And yes I did say “or”, because  “strong” and “concentrated” aren’t synonyms in Chemistry Land.

An acid’s strength determines  how easily the hydrogens pop off the rest of the acid molecule. But those molecules are usually  floating around in some amount of water. So you can have a strong  acid that’s super diluted, or a weak acid that’s super concentrated.

Nitric acid, for the record, is a strong acid. Anyway, hydrogen ions are positively  charged, and opposite charges attract. So the hydrogens from the nitric acid wind up pulling the electrons off of  the iron atoms in the steel.

But when a metal is oxidized, it has  slightly different chemical properties. Which means it won’t react with  an acid in the exact same way. Dipping a piece of steel in concentrated  nitric acid oxidizes the surface very quickly, forming a protective film that keeps the  rest of the steel safe from corrosion.

And that film is so thin, it  looks like nothing happened. Meanwhile, a more diluted version of that  same acid isn’t as capable of oxidizing the metal, so instead of making a protective  surface, it just corrodes as normal. We still use this phenomenon,  which we now call passivation, to create metals that are  more resistant to corrosion.

This has been especially useful for  things like implantable medical devices, because these devices need to  sit inside a messy human body and work for a really long time without corroding. Every paradox we’ve discussed  so far has already been solved. But not this one.

The Faint Young Sun Paradox  still confounds scientists, because it deals with something that happened way before any of us were around to witness it. Based on studies of some very old rocks, scientists know the Earth had liquid  water as early as 4 billion years ago. And for water to remain liquid on Earth’s surface, it needs to be kept at a warm temperature.

That’s why when astronomers look for  water on planets that are not the Earth, they focus on the planets that are just  the right distance from their star. But the thing is, that “just  right” distance…or more accurately, range of distances…moves over  the course of a star’s life. It moves farther out as the star  ages and becomes more luminous.

And roughly 4 billion years ago, our  Sun was about 25% weaker than it is now. Its so-called “Habitable Zone” had not yet  moved out to where the Earth’s orbit is. Meaning the Earth should have  been completely frozen over.

Which we know it wasn’t. Even more confusingly, parts of Mars’s surface are chock full of evidence that they were  also covered in liquid water at the time. And Mars’s orbit is even further out than Earth’s!

We’ve known about the Faint  Young Sun Paradox since 1972, when Carl Sagan and George  Mullen first wrote about it. And over the decades, a lot of scientists have proposed reasons for how this could have worked. The most probable hypothesis involves  some kind of greenhouse effect.

High concentrations of carbon dioxide  in both Earth and Mars at the time… probably leftover from their own messy formations… were able to compensate for the weaker sunlight and trap enough heat to keep water liquid. But there have been plenty of other ideas, too. Maybe since our Moon was a  lot closer to Earth back then, it generated a sufficient boost in  heat through stronger tidal forces.

Sagan and Mullen hypothesized  that the Earth’s atmosphere had a higher concentration of ammonia. But that’s less likely,  because ammonia breaks down really quickly in any amount of sunlight. Each of those is reasonable, but  the only thing we know for sure is that something was different  about Earth back then.

The more we learn about the world,  the more there is to uncover. But that’s not necessarily a bad thing. A paradox is just a puzzle to solve…just  the kind of thing that science is made for!

And the act of untangling these paradoxes often teaches us something new about the world. Meanwhile, you can teach us! We’d love to hear about your favorite  scientific paradox, if you’ve got one. [♪ OUTRO]