Hey, Vsauce. Michael here. Let’s take a moment to recognize the heroes who count. Canadian Mike Smith holds the world record for the largest number counted to in one breath – 125. But the world record for the largest number ever counted to belongs to Jeremy Harper from Birmingham, Alabama. In order to set the record, Harper never left his apartment. He got regular sleep, but from the moment he woke up in the morning until the moment he went to bed at night, Harper did nothing but count. He streamed the entire process over the Internet and raised money for charity while doing it, but after three months of counting all day, every day, he finally reached the world record – 1 million. Now, a million might not sound like a lot, but think of this way. One thousand seconds is about 17 minutes, but a million seconds is more than 11 days. And a billion seconds, well, that’s more than 31 years. There’s no full video online of Harper counting all the way to a million, but you can watch John Harchick count all the way to 100,000, if you have 74 hours to spare. John also has some other channels.

One involves more than 300 videos of himself eating carrots. Another, more than 3,000 videos of himself drinking water. Many of John’s videos literally have no views. They are as lonely as a video on YouTube can get. A great way to find such videos is a website made by Jon van der Kruisen. This website auto plays videos on YouTube that no one has yet watched.

John and Jeremy, as well as Mike, the one breath counter counted like this. 1, 2, 3, 4, 5, 6, 7 and so on. But that’s not the only way to count. And it doesn’t seem to be the one we’re born with. Additive counting is the one we’re all familiar with, where each next step is just one added to the last. But what if we multiply it by a number instead? Well, that kind of counting is logarithmic, from “arithmos” meaning number and “logos” meaning ratio, proportion. On this scale, similar distances are similar proportions. One is a third of three and three is a third of nine. Four is a third of 12 and so on. Our brains perceive the world around us on a logarithmic scale.

It’s believed that almost all of our senses are multiplicative, not additive. For example, how loud we perceive a sound to be. Two boomboxes playing at the same volume don’t sound twice as loud as one. In order to make a sound that is perceived as being about twice as loud as one boombox, you actually need ten times as many, so 10. And to double that loudness, you would need a hundred. And to double that loudness, you would need a thousand. Having an intuitive sense of logarithmic scales built into your brain is probably an advantage when it comes to natural selection and survival, because often proportion matters more than absolute value. For example, “is there one lion hiding over there in the shadows or two?” is a very different question than “are there ninety six lions about to attack us or ninety seven?” Sure, in both cases I’m just talking about one extra lion, but adding one lion to one lion, doubles the threat.

Adding one lion to 96, well, that’s basically nothing. Logarithmic thinking and feeling may explain why life seems to speed-up as we get older. It seems like I was a child for ever. And in college, in my early 20’s, just whizzed by. And logarithmically, that makes sense, because each new year that I live is the smaller fraction of all the other years I’ve already lived. When you turn 2 years old, the last year of your life is half your life. But when you turn 81, that last year that you’ve lived, well, that’s just a tiny part of the other 80 that you know. Logarithmic thinking isn’t always helpful, especially in scenarios where proportion doesn’t logically matter but we, nonetheless, act like it does.

One of my favorite examples is the psychophysics of price paradox. This is something almost all of us do. Researchers found consistently that people are willing to put a lot of effort into saving 5 dollars of a 10 dollar purchase, but they won’t put much effort into saving 5 five dollars of a 2,000 dollar purchase. It’s 5 dollars saved either way, but our natural obsession with proportion leads us astray. Take a look at these pictures.

Can you tell how many objects are in each of them? You probably can. It’s like really easy. You can tell if there are zero, one, two, three or four objects in a photo without even needing to count. How are you doing that? Is it some sort of sixth sense? No. Psychologists call it “subitizing.” We can, intuitively, at a glance, determine whether there are about four or fewer objects in a photo. This has been part of human culture for a very long time and it may be the reason so many tally systems from all over the world all through history wind up having to do something different when counting the number five. When estimating or comparing amounts above 4, the brain uses what’s known as an approximate number system. It’s a psychological ability we have. It’s about 15 percent accurate. It two amounts are at least 15 percent different, we can tell. So, for example, 100 objects and 115 or a thousand and 1,150 or 1,200. If you wanna test the accuracy of your approximate number system Panamath has a pretty good test. We often take linear additive counting for granted, but it’s not granted to us.

We aren’t born with it. We are, however, born with the ability to subitize and use an approximate number system. Children younger than the age of three can tell, without counting, that this line of 4 coins contains fewer coins than this line of 6, even if you spread the 4 coins out into a line that is physically bigger, longer than this line of 6. However, mysteriously, around the age of 3.5, children lose this ability and begin saying that this line of 6 coins contains fewer coins than this long line of just 4 coins, possibly because around this age the physical world of objects, physical sizes, is more salient in their minds. But then, when they begin to learn linear counting, they reverse back and begin again correctly saying that this line of 6 contains more coins than this line of 4, around the age of 4. The smallest physical thing science could ever hope to observe is the Planck length. In order to look at anything smaller, you’d need to have so much energy concentrated in such a small area a black hole would form and you would lose whatever you were looking at. Okay, with that in mind, here’s a question.

What number is halfway in-between 1 and 9. 5 seems like the obvious answer. There are four numbers on either side of 5, it’s halfway between, right? Well, if you ask this question of a young child or a member of a culture that doesn’t teach a linear additive number line, their answer will be 3. You see, they are exhibiting the human mind’s natural logarithmic tendency, because 3 in that sense makes sense. Three is three times larger than 1, and 9 is three times larger than 3. Three is in the middle, proportionately. But what if we took that logarithmic number line and change the one to be the smallest thing we can observe, the Planck length, and the nine to be the largest thing we can observe, the observable universe. What would go in the middle? Well, as it turns out, we would. The number of Planck lengths you could stretch across a brain cell is equal to the number of your brain cells it would take to stretch all the way across the observable universe.

sold So, welcome to the middle. And as always, thanks for watching. Hello again. The YouTube channel Field Day recently gave me an opportunity to explore Whittier, Alaska, one of the strangest places humans call home. To see why and to see me investigate, talk to the locals, click the link in this video’s description or on the annotation here on this video. It was really fun, so give it a little lookie look..

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