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Hey, Vsauce. Michael here. The title of this video is misspelled in honour of mistakes. Mistakes are everywhere; they surround us like air. To err is human. Faults, flaws, faux pas, fumbles and fallacies are as much a part of who we are today as the stuff we've gotten right.

For instance, if a knight knocked your knuckle or knifed your knee, why would there be so many "k"s? Well, the "k"s are silent by mistake. The original old English forms of these words were pronounced with "k" sounds: K-nife, K-night, K-nee. But that's a bit of a mouthful to say, and because reading and writing weren't as common hundreds of years ago, people just pronounced words the way they wanted to, regardless of spelling.

Spelling is fun. Warren G knows what I'm talking about. In the fourth verse of his "What's Next", he asks what's next. What's next, what's N-X-E-T? Spelling isn't the only thing we get wrong. The history of science is a graveyard of dead and abandoned ideas. Fritz Machlup coined the phrase "Half-life of knowledge". The amount of time it takes for half of the knowledge within a field to be superseded by new, better ideas or to simply be shown untrue.

Donald Hebb famously estimated that the half-life of knowledge in psychology is just five years. Humans are awesome, don't get me wrong, but we tend to believe that what we currently think we know about the universe is reasonably correct, even though statistics aren't on our side. Previous generations incorrectly thought the exact same thing about what they used to think was true.

My favourite examples of the ubiquity of mistakes are production errors in popular songs. They're like humbling Easter eggs, just waiting to be found. For instance, Buffalo Springfield's "For What It's Worth". 26 seconds in, the "be" in the lyric "beware" is clipped, as is the "p" in "people" at 1:24 minute. Once you hear the mistake, it's tough to unhear it.

In "Hey Jude", Paul McCartney misses a chord. And if you listen closely, you can clearly hear him say "F**ing hll". Seriously, it's in the actual song. Go listen to it. In fact, there's an entire website that chronicles mistakes in Beatles' songs.

Take a look at this 700-year-old prayer book. A monk wrote it on fresh, clean paper. I'm kidding, of course. He scraped the ink off an older manuscript, cut the pages and rotated them before writing all over them. A mistake? Well, kind of. Recent multispectral images of the prayer book have revealed that the old manuscript he erased was a previously unknown copy of a work by Archimedes. It was called "The Method" and laid out the heart of calculus thousands of years before Newton and Leibniz.

If that one monk hadn't erased that one book, would we be hundreds, thousands of years mathematically and technologically more advanced today than we currently are? It's hard to say. All that is certain is that we would continue to make ridiculous mistakes, like the Mars Climate Orbiter. This 327.6 million dollar expedition burned up in the red planet's atmosphere because, when calculating flight manoeuvres, NASA used the agreed-upon metric units, while Lockheed Martin used the imperial system.

This is Neil Armstrong taking humankind's first steps on the Moon. It's about the best footage we have. The original tapes containing the highest quality recording of that moment have been lost. They were probably recorded over by later test missions. Ten years ago, Sergio Martinez became lost in the woods while hunting outside of San Diego. Hoping to attract the attention of rescuers, he lit a small fire. But that fire quickly got out of control and became a giant Cedar Fire. It destroyed 300,000 acres of land, 2,322 homes and killed 15 people.

The man carrying a wounded soldier in this painting, based on a photograph taken during World War I, is Henry Tandey, an English recipient of the Victoria Cross. Four years after the event in this image, Tandey caught a wounded German soldier in his gun sights. But rather than kill the man, Tandey took pity on his wounded state and spared his life. The German he allowed to live was this man. Later, the man whose life he spared wore his mustache shorter but still had the same name: Adolf Hitler.

In 1918, did Henry Tandey miss a chance to kill Hitler? Detailed researchers found that the exact days their units were in the same location don't quite match up. The story is apocryphal, but what is known is that Hitler owned a copy of the painting of Tandey, and in 1938, when meeting with Neville Chamberlain, Hitler pointed to Tandey and told Chamberlain: "That man came so close to killing me in 1918 that I thought I should never see Germany again."

So, who's wrong? Maybe Hitler confirmed the story merely because he hoped to make up extra evidence that providence had kept him alive to pursue his goals. Either way, someone is mistaken. Missed opportunities are a bummer. Obsessing over them is not healthy, but regret is a powerful emotion. How do you deal with regret, with guilt? Can you?

In the early morning hours on a bench outside a hotel in Anaheim this summer, Ze Frank told me something I am going to paraphrase. I love this metaphor. Stuff in your past is like a carving on the bark of a sapling. Over time, the scar, the carving won't go away. Because of the way trees grow, it won't go up or down much either; it'll just stay right where it began. It might even get darker. But it won't get bigger. You, however, can. You can keep growing, doing more things, more branches, being more things. The wound won't get smaller, but you can make it a smaller part of who you are. Maybe regrets are like that.

They stick around forever, like arborglyphs. Or maybe they make like a tree and leaf. A red or purple leaf in the autumn. As days get shorter and chlorophyll production decreases, the yellow and orange carotenoids, which are always in leaves, appear as the green fades. But red and purple leaves are the interesting ones.

As winter approaches, it would seem to be a good time for trees to conserve energy, but some trees do the opposite. Instead of giving up, they spend extra energy producing anthocyanins to turn their leaves red and purple hues. These colours protect their leaves from sun damage before their nutrients can all be used and may also be a defence against insects looking for a parasitic home. A way for the tree to tell the insects: "Yes, I am in part dying but not without a fight. I am still very much vital."

Drought and even turn a kit applied by man can bring about these colors prematurely. When you look at beautiful autumn colours, you are looking at stress. But the bigger the fight the trees put up, the more energy they put into their defences at the very end, the more brilliant their colours will be. Winter will eventually come. But scientifically, the brightest, deepest, most remarkable colours come from not giving up too easily or quickly.

And as always, thanks for watching.