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  • 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.

Hey, Vsauce. Michael here. Let's take a moment to recognize

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    林宜悉 に公開 2021 年 01 月 14 日
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