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.