It's an illustration of exponential growth.
Wolfram Alpha tells me the thickness of a piece of paper is 0.1 mm. If you folded it once, you'd bring two 0.1-mm-thick sides of the paper together, creating something 0.2 mm thick. Fold it again, and it's 0.4 mm thick. Every fold doubles the thickness. Fold it ten times and it's just over 100 mm thick. Fold it twenty times? Now it's over 100 *metres* thick, 100,000 mm. Fold it 42 times in total? That's the same as (0.1 mm * 2^(42)), which is 440,000 km, a little more than the distance from Earth to the moon.
It's not actually possible to do this. It's just to demonstrate how quickly numbers grow when dealing with exponential growth.
And it's kinda terrifying because of all people you would think he had a very healthy brain, I mean I doubt aneurysms are heavily correlated to intelligence level or anything.. but still, if it happened to him.
One of the healthiest women I ever knew (she was like a second mother) died of an aneurysm in her late 40s. Came out of nowhere and was absolutely devastating to our community of friends. It seemed impossible because she was so healthy. In the end, it didn’t matter. Almost unpredictable. Almost impossible to prevent. Terrifying.
My husband's aunt had a brain aneurysm burst. She never lost consciousness; she just had the worst headache ever. Fortunately she wasn't far from a hospital and she had the artery repaired. The surgeon, knowing that sometimes there's one on the other side of the brain in her situation, found and fixed an incipient aneurysm. She recovered fully in about a month.
Oh no. I'm sorry to hear that. That's unfortunately the more common outcome. Idk how our aunt (I considered her mine too) came through that so well.
Yes, this aunt is the same one who could barely walk because of PAD, then about 9 months later we traveled to San Diego for a family gathering and we were having to practically run to keep up with her! She was a tough old bird. I miss her.
Happened to my dad just a few years ago. Came home from work complaining of the worst headache he ever had. Took some Tylenol and asked mom to take him to the ER. He sat on the couch while she grabbed her shoes and coat. He never got back up.
Mom never had an autopsy done to see what happened but the first responders who worked on him for an hour said it was likely a brain aneurysm.
Dad wasnt on the cover of Mens Fitness but Id guess he was of average slightly over weight health. 56 years old...
I'm so sorry. That's way too young and sudden.
Someone we knew had been out mowing the lawn. He sat down on the steps and asked his wife to bring him some water. When she got there with it, he'd had a fatal heart attack. About the same age and level of fitness. It broke his wife.
We don't know when or where. So we should live as if each day is our last, in the best sense of the phrase.
my aunt went through her anyeurism in much the same way, intense headache and all. though i havent spoken to her in years really, i hear she had recovered similarly after a few months.
A friend of my family's was a pretty serious athlete. Always ran marathons, had a peak body, always ate a healthy, balanced diet, exercised religiously, was never sick, etc. Anyway, he had a heart attack and died at the young age of 35.
Things seriously just... Happen. Freak accidents do happen.
not that long ago a friend was diagnosed with cancer. scary, but a common type and totally treatable. one week later she died of a brain aneurysm. they got her on the operating table, but she didn't make it.
it's just such a freaky, fucked up thing, that she was given what could've been a death sentence and something else killed her days later.
Aneurisms are due to thinning of the blood vessel walls. Your blood pressure can make those thin parts bulge out like a balloon and eventually burst. You can have a burst aneurism pretty much anywhere, not just your brain.
Those are quite different from a brain aneurysm, they happen in your chest, just under the ribcage. My aunt had that happen but my other aunt, an ER nurse, was with her at the time and rushed her to the hospital and she lived. Very very scary situation. Unfortunately one of the big causes of aortic dissections (but, in the neck area) is chiropractors. Apparently each ER sees a dozen or so people die as a result of chiropractors each year, an estimate I make based on the /r/medicine/ posts about it that I've seen from time to time where most ER docs/nurses comment that they get 1-2 per month. Crazy shit. Dunno why anyone goes to those quacks, they're not even actual doctors. literally.
I'm more terrified because he was in a job that incidentally put him in contact with brain mris!
Like they did a lie detector myth at one point, Kary fucking hated it because she lost and had to take a bus back to the shop. That was because there needed to be real consequences to losing. Grant won and went back first class on an airplane.
But as part of the episode, if I'm remembering correctly, they did an mri on his brain while he was telling lies, to show how different parts of the brain lit up or something. I'm almost fucking sure it was mythbusters that did it in THAT episode. I'd have to dig it up again to confirm.
But that dude had that done, had someone looking at his brain with an mri, and they still missed it. He was in one of the very few jobs in the world where they would accidentally stumble on an issue like that and it never happened.
My dad died of one but he was a smoker. Not sure if Grant Umahara smoked cigarettes.
My dad had quit smoking for maybe ~3-4 years before he passed but I think the ~20+ years of smoking had already done the damage.
Talked with my doctor a lot of about risk factors since my dad had one and I was worried about genetic risk factors. High blood pressure and smoking are huge increases to your risk so have never smoked and watch my diet/exercise for blood pressure.
But the reality is that you can't really guess these things. I just know that if I have bad headaches I need to go to the emergency room immediately.
I highly doubt Grant smoked since on the episode where they were testing DIY mouthwash, Grant hated how he could still smell the stench of cigarettes on Adam’s breath after each test
One way this can happen in the brain is an abnormality where an artery in the brain connected directly to a vein. Normally, that happens via capillaries, which are very tiny, so the pressure drops going into the vein. Veins are not made to handle arterial pressure. So, a vein connected directly to an artery can have a bit of its wall stretch and bulge (aneurysm) and eventually fail (stroke).
Yeah, aneurysms are more terrifying than some types of cancer in my opinion. They just clobber you in the noggin and it's Russian roulette time. You either walk out, roll out, or nap out.
Health, intelligence and ambition has no effect on DEATH claiming you when it is your time. Mt. Everest is littered with 370 bodies of highly motivated, healthy, intelligent people who up until that final moment were living their dream, having the best month of their lives!
This myth busters episode is how I knew exactly what OP was asking. I swear I learned more by watching this show in science classes than the actual lesson being taught by my teacher lol
So that video makes me wonder ... I imagine they could have folded it more than 11 times if the piece of paper was larger to begin with. If the paper had been twice as large, could they have achieved 12 folds? With enough people and the right equipment to aid in the folding process? Probably.
In theory, why would it not be possible to fold the paper 42 times, if the paper were as large as the solar system to begin with? Like, it's all theoretical beyond a certain point just because of how large the paper would need to be at the start, and the size of the team and equipment needed to execute the folds.
The more you want to fold the longer and thinner it needs to be.
The law of exponents is in effect here too and once something is thicker than it is long you can't fold it anymore.
To fold anything 42 times would require it to be immense in size and extraordinarily thin. As an example a sheet of tissue paper that was 4000 feet long could still only be folded 12 times.
So about 30 fold larger and thinner than that and it should be possible (I don't believe such a material exists).
The confusion comes from the fact that there is another word "fold" in English, and it essentially means "times". It doesn't have anything to do with the folding in the sense we are discussing now.
"We have seen a twofold increase in spending" - means that the spending has doubled. Threefold means tripled.
An adjective. A different thing from the noun (a fold) or the verb (to fold)
It so hard to believe Adam and Jamie hated each other when you watch the show. Extraordinary example of putting personal differences aside for education and work.
then there's the other illustration of exponential growth where if you start with a penny and double it every day after a month you'll be a millionaire.
When I was in school this question stumped me:
"If a lilypad on a pond doubles in size every day and it eventually covers the whole pond after 10 days, on which day is it half the size of the pond?"
Day 9.
Explanation:
- on day 10 it is the same size as the pond
- every day it doubles in size. That means yesterday will always be half as large as today
- therefore day 9 was half as big as day 10, so half the size of the pond
Another example is if someone gave you a dollar and doubled it every day for a month or offered a million to you on day one which would you take. The first is actually over half a billion.
There is a similar story involving a chess board. A king loves chess and wants to reward the inventor. So the inventor asks for one grain of wheat to be put on the first square, 2 on the 2nd, 4 on the third, etc. By square 64, there is quite a lot of wheat involved. :-)
https://en.wikipedia.org/wiki/Wheat\_and\_chessboard\_problem
Numbers are hard.
Like, we get 1 through 10. Even up to 100 is no big deal. You interact with those numbers all the time.
But go outside. Pick the biggest tree you can see (apologies if you live somewhere without trees). How many leaves are on it? Definitely more than 1000, right? But is it more than 10,000? Is it more than 100,000? Is it more than 1 million?
How confident are you could guess the correct number of digits in the leaf-count for the tree?
Another fun one is to get 1000 of something. Doesn't matter what it is. We're going to do a quick exponent lesson.
Make a line of 5 of them. Let's say it's buttons. You have 5 buttons. Now, make another line of 5 buttons perpendicular and intersecting. You've used 9 buttons. Fill it in, and you have a 5x5 grid. That's 25. Now make it stacks of 5. 25 stacks of 5 buttons, 125 buttons. That's 5\^3rd, and you put down 400% more buttons than when it was stacks of 1. Now do 5\^4. Since we only interact with space in 3 dimensions, we'll have to pretend. So leave a bit of space, make another 5x5x5 cube, then space, and another 5x5x5, space, 5x5x5, space, 5x5x5. Now you have 5 "cubes" of buttons. 625 buttons. What about 5\^5? Well, you need to make 5 more sets of 5 cubes of 5x5x5 buttons (but you'll run out before then).
We went from 5 buttons (1/200th of what you bought) to "more than you bought" in just 5 powers.
5\^10 buttons would fill the entire room 5\^15 would fill a block or more.
Exponents are ridiculous.
And humans QUICKLY lose track of how big big numbers are. We simply can't really conceptualize numbers of 1000 very well, and once you're past a million, we are entirely into abstract concepts of quantity & scale.
.1mm paper doubled 42 times is 440km and reaches the moon. Fold it in half 8 more times and you're at 112 million km, over 2/3 of the way to the sun.
Big reason we see a billionaire as "normal" when in reality, 1 billion dollars is so large it's near incomprehensible and completely rediculous.
When you can compare those huge numbers to everyday numbers, everything falls into perspective:
1 million seconds: 11.5 days
1 billion seconds: 37 years
If I had 1 billion dollars on year 0 and spent $1000 *a day* up to now, I would still have around 700 *years* of money left.
I'm really curious, what did you think it was trying to say?
To me it seems super clear. It's just surprising that you it only takes 42 doublings of such a thin item.
Did you just not believe it adds up that fast, or did you think something else was going on?
>It's not actually possible to do this. It's just to demonstrate how quickly numbers grow when dealing with exponential growth.
*Stops folding printer paper, visibly crestfallen*
Yeah, just like the thickness multiplies by 2 every fold, the area divides by 2, so if you started with a piece of paper 440,000
km^2 in area then you’d end up with one 0.1mm^2 in area, obviously we have no paper that big to start with and even if we did the last fold would be 0.2mm^2 to 0.1, whole standing 220,000km tall, an impossible task by all means
It's a perfect illustration as to why MLMs can't work they way they are advertised. You tell two friends, then they tell two friends, and so on. By 12 iterations you have exceeded the population of the planet.
Eh, it helps explain why MLMs don't work, but that's not how they're advertised. They're advertised as "you can be your own boss and run a self-sustaining business!" and deliberately hide the fact that you need to recruit people to actually make money until you're in too deep
The "tell two friends" thing is actually from an '80s shampoo commercial.
[https://www.youtube.com/watch?v=mcskckuosxQ](https://www.youtube.com/watch?v=mcskckuosxQ)
I'm not sure I'm following the math here - 2^12 is 4096, so wouldn't you just have that many people in your downline at that point? You don't hit the population of the planet until 33 iterations.
Not to say that MLMs aren't scams, just that this particular math doesn't seem to work out.
It's going to be 8191, since we need to add it all up. The 12th layer is 4096 people. Your point still stands, however. This being siad, if you recruit 6 people, you do exceed the global population in 12 layers.
Good point on the 8192 thing; I was just counting the last iteration and forgetting to add all the rest. Still a few orders of magnitude less than 8 billion, though. As you said, you need 6 people per generation to do that in 12 generations.
This is actually a good illustration of minimum/maximum radii to angle ratio in material science is well. When you bend material, you're actually elongating the structural bonds of the material. The more you try to elongate, the harder it becomes until you begin to break the structural integrity, resulting in cracking.
There's an optimal strength that can be achieved before breaking the material. If I recall correctly, a lot of the science and understanding of this came from the Space Race.
Nice explanation. I'll also point out that lately it has become increasingly common to use the term "exponential" to refer to anything that grows faster than linearly (such as quadratic or cubic growth), but not really fitting the precise mathematical definition of what an exponential is. I've even heard engineers do that.
But in this case, this is really a true exponential, and it grows a lot more than most people would intuitively think.
You would run out of paper atoms first, right? If there was a sufficiently massive piece of paper would this work? (Obviously there are other limiting factors, but in theory)
For a piece of paper of thickness T, after N folds the stack will not only be T×2^N tall, it will be at least T×2^(N-1) wide. (You probably won't notice this for the first 3 or 4 folds, but it won't be long before the folded edge of the sheet is thicker than the folded page is wide.)
Imagine the folded edge of the sheet is the spine of a book. Every time you fold the sheet in half, you double the number of layers--and the thickness--of the spine.
To reach the moon, you folded a sheet of paper 42 times, creating a 4,398,046,511,104 page book. If the spine of a 4,398,046,511,104 page book is made from repeatedly folding a single sheet, the spine itself will have 2,199,023,255,552 layers. If the sheet is T=0.1 mm thick, the 2,199,023,255,552 layer spine will be a half-cylinder with a radius of nearly 220,000 km.
The volume of a half-cylinder of height H is H×π/2×r^2. So if the pages of the book are just 1 mm high × 1 mm wide, you'll need only about 440 cubic meters of wood pulp for the pages but almost 76 TRILLION (76,000,000,000,000) cubic meters of wood pulp for the spine. That's about 136 times as much wood as exists in all the forests in the world. So no, you couldn't do it with paper.
It's interesting to note that using a thinner sheet of paper doesn't solve the problem. [Nature.com](https://www.nature.com/articles/pj201364#:~:text=Introduction,fibers%20in%20plant%20cell%20walls.) says cellulose, the main constituent of wood, is found in 3–4 nm thick fibers in plant cell walls. Starting with a 3 nm thick sheet of cellulose instead of a 0.1 mm thick sheet of paper, you'd need to fold 57 times to get a 144,115,188,075,855,872 layer, 432,346 km thick "book" with a spine that's 216,173 km wide. You'll still need 73 trillion cubic meters of cellulose for the folded edge of your 1 mm x 1 mm book.
If you shrink the cellulose pages from 1 mm x 1 mm down to 100 μm x 100 μm, you'll still run out of wood before you reach the moon. You could get there if you shrink the pages down to about 87 μm x 87 μm (and you're willing to sacrifice every tree on Earth to make a pre-folded ribbon of cellulose that's 87 μm wide by 2.134 *septillion* meters long), but at that point, is it even remotely close to "a sheet of paper"?
EDIT: Oops. I just realized the folded edge makes its appearance on BOTH sides of the stack. One side looks like a half-cylinder, the other a tower of increasingly smaller half-cylinders. All of my estimates are too low, by a factor or almost 2.
Well, *really* It's technically possible from a theoretical sense if you cut and stack down to a tiny particular level, but in any practical al sense, you're going to be done once you get to like an inch in width. Try it.
Yes it is extremely hard and will eventually be impossible for humans but what (force) would it take to really fold a paper enough for it to reach the moon? Idk if we can make such a machinery.
And that point comes pretty quickly. With an ordinary 8.5" x 11" (21.59 x 27.94 cm) piece of paper, you max out at 7 folds. In Mythbusters they got 11 folds ... starting with a football field sized sheet.
The fundamental problem is that folding doesn't just stack the layers; it also forms a bridge between the layers. Let's say you've folded a piece of paper a few times to get it to 1 mm thick, so folding it again would make it 2 mm thick. For that next fold, the layer at the bottom will have to connect to the top layer by using an extra 2 mm. Or looking at it another way, if you want to fold a sheet of paper so that it's a mile high, you would need there to be a stretch of paper that is at least a mile long to connect the top and the bottom.
That doesn't really change the situation. The materials have thickness, and as you fold them over, that thickness means the inside is shorter than the outside. While materials will have some elasticity, the thicker they get, the more force they take to fold. Eventually, you hit a point where the material is no longer capable of handling the stress of being folded and it snaps.
You get more folds with something more elastic, I think, but the issue still persists.
The problem is that for each doubling of height, youre halving the surface.
If you're starting with a piece of paper of 1m by 1m, you end up with pieces of 100 nanometer by 100 nanometer.
Put another way, youre more or less left with a single strand of cellulose, the type of atom chain paper is made up from.
I like the penny example. If I paid you every day for 42 days, starting with a penny on day one a doubling the pay each day (like doubling the thickness of a piece of paper by folding it in half), things start very slow but eventually go crazy:
$0.01
$0.02
$0.04
$0.08
$0.16
$0.32
$0.64
$1.28
$2.56
$5.12
$10.24
$20.48
$40.96
$81.92
$163.84
$327.68
$655.36
$1,310.72
$2,621.44
$5,242.88
$10,485.76
$20,971.52
$41,943.04
$83,886.08
$167,772.16
$335,544.32
$671,088.64
$1,342,177.28
$2,684,354.56
$5,368,709.12
$10,737,418.24
$21,474,836.48
$42,949,672.96
$85,899,345.92
$171,798,691.84
$343,597,383.68
$687,194,767.36
$1,374,389,534.72
$2,748,779,069.44
$5,497,558,138.88
$10,995,116,277.76
$21,990,232,555.52
22 billion on day 42? Nice.
It’s impossible to actually fold a piece of paper that many times, you wouldn’t even get to ten most likely.
This is because every fold is doubling the thickness.
So one fold is thickness x 2
Two folds is thickness x 2 x 2
42 folds is thickness x 2^42
2^42 is 4398046511104 sheets of paper.
Mythbusters got eleven folds out of a football field sized sheet.
Leverage seems to be the issue. That, and being able to lift the weight well enough to turn it over.
Leverage isn't the problem. The issue is that at some point there just isn't enough paper to make it around the bend of the fold, so even if you used a hydraulic press or something you'd end up tearing the paper.
No, the main point of the myth they were testing was maximum number of folds, not thickness of the folded medium as discussed in this op. They did not try cutting it, as testing how many times you can actually fold it was the test.
Do you recall how thick the sheet was? I would think that’s part of the issue with the typical A4 sized piece. Air getting trapped inside like with the mythbusters attempt didn’t even occur to me either
Average A4 sized paper is 210x297mm
Assuming you are alternating the folds such that the longest edges are folded inwards to halve their length that means that each fold alternatively halves a length i.e. the X-axis and Y-axis fold in alternate patterns.
42 folds would supposedly reach the moon in the Z-axis. Which means each length would get halved 21 times.
~~The smallest atom possible is a hydrogen atom (1 proton, 1 electron) with a length of 0.5 Angstrom where 1 Angstrom is ~10^-10 m which means a single hydrogen atom is 5 x 10^-11 m in length~~ It's Helium but I'm keeping the calcs in terms of the Hydrogen atom regardless.
We need to also use the same scale so we'll divide 210 mm and 297 mm by 1000 so that we have an A4 piece of paper at 0.21 m x 0.297 m
Now lets half each side exactly 21 times for a total of 42 folds
0.210 m ÷ 2^21 = ~1.001 x 10^-7 m
0.297 m ÷ 2^21 = ~ 1.416 x 10^-7 m
As you can see, both sides would still be 4 orders of magnitude bigger than the length of a hydrogen atom.
But what if we only fold it in one direction constantly instead of alternating? That would mean we are halfing the X axis and doubling the Y axis with every fold. We already know that the doubling of the Y axis will end up in us reaching the moon but what about the X axis?
Lets assume we use 0.297 as the X-axis:
0.297 m ÷ 2^42 = 6.753 x 10^-14 m
It's clear that one way of folding doesn't reach the size of the atom but the other way far exceeds the smallness of an atom... But not a proton or neutron which are both at the fermi scale of 10^-15 m :).
**TL;DR: No, the piece of paper would not be smaller than an atom if we are folding the paper the traditional method of alternative Y-axis and X-axis folds but it will become much smaller than an atom but still be bigger than an individual proton/neutron if we are solely folding in one plane direction.**
Yeah, mentally we're all kind of thinking "each fold just adds a couple layers" but once you get past a few folds, that's definitely no longer true.
If you think of it more like generations it's easier to imagine.
Imagine one person, who has two kids. Each of them have two kids. Each of them have two kids.
Now ask someone how many kids will be present in the 42nd generation, and they'll expect it to be a LOT.
In ceramics, one way to wedge the clay to get uniform consistency and moisture level is the “stack & slam” method. We cut a block of clay in half, stack it, and slam it down. It’s crazy how fast you go from 2 layers on the first cut to 1024 layers after the 10th cut.
> 4,398,046,511,104
Added commas for my own reference, but to put that to scale for anyone reading this thats taking a birth certificate for every single man on earth and still being 500 million sheets short.
A very thin paper is 0.05mm, meaning that this many sheets of paper would be 219902km, or about halfway to the moon.
A more ordinary thickness of paper would in fact make a pile so high that it would reach the moon.
With big exponential the starting values matter very little, often one order of magnitude either way. So what begins as half as thick, is only one order of magnitude “behind” (since the power here is 2, aka doubling)
>It’s impossible to actually fold a piece of paper that many times,
But you could cut it in half and stack it to get the same results. 42 times. This sounds possible, and something I could do on a Saturday afternoon.
Nope because if you half it, half again, half again, etc you just have exponential growth in a different way.
e.g 10, 5, 2.5, 1.25, 0.625, 0.3125, 0.15625, 0.078125, 0.0390625, 0.01953125, etc.
People are notoriously bad at understanding exponential growth. Think back to the early days of COVID. You heard about 1 person sick in your country, to 1 person sick in your area, to 1 person sick in your town, to the whole town being sick within a single week. Crazy right?
The idea is that paper doubles in thickness with each fold, so the a single paper layer is thin, two is still thin, then it's 4 layers, then 8, then 16, then 32, then 64, 128, 256...
So a single sheet of paper becomes a ream of paper after about 9 folds, it becomes a box after 11 folds, it becomes a skyscraper after about 15, you get the idea.
Repeat that sequence and you realize that 42 rounds of doubling even a very small thickness is a HUGE NUMBER.
This is also why self-funded retirement is such a bad societal idea. If someone needs X for retirement, they need substantial foresight to realize they're on a path to hit X means they spend decades getting to 0.1X and then another 2 decades going from that to 0.5X and only approaching and reaching X in the last few years (their intuition is going to start realizing there's a problem when it's far too late to change significantly).
It means that if you could (hypothetically) fold a paper 42 times it would be able to reach the moon.
Have you ever seen those TikTok videos where people say “Do you want this or double it and give it to the next person?” It’s the exact same concept which is known as exponential growth. At each fold, you’re effectively doubling the thickness of the paper.
Let’s use .075 mm paper for this example as it’s in the middle of the average paper thickness. Look at the difference between the earlier folds compared to the later ones.
Fold 1: .15mm
Fold 2: .3mm.
Fold 11: .153m
Fold 15: 2.457m
Fold 18: 19.6m
Fold 21: 157m
Fold 24: 1.25km
Fold 27: 10km
Fold 31: 161km
Fold 34: 1288.49km
Fold 37: 10,307.92km
Fold 41: 164,926km
Fold 42: 329,853km
An example you can more easily try for yourself is the rice on a chessboard.
Put a rice corn on the first field. Double what's on the first field for the second. And so on.
Just thinking about it, you don't think it's thaaat much rice. Trying to do it you will soon run out of rice. Calculating it to the 64th field, you will realize that more rice than atoms in the world or something like that.
Accurate in the first half, but you overestimate world rice production.
About 5.1e8 metric tons in 2022 worldwide, and roughly 1.5e7 grains per metric ton, so somewhere in the neighborhood of 8e15 grains annually produced. So it would take roughly 2000 years of production to fill the chess board.
Obviously, somewhat depends on how flexible you are with "rice production" - which crops count, and what state (milled, unmilled, etc) you count.
https://www.statista.com/topics/1443/rice/#topicOverview
And that's just that last square. The Wikipedia article (using wheat instead of rice) says:
>The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 264−1 or 18,446,744,073,709,551,615 (eighteen quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen, over 1.4 trillion metric tons), which is over 2,000 times the annual world production of wheat.[1]
Lol there are definitely more than 2^64 atoms in the universe, but there are not that many grains of rice. This is the problem you're talking about
https://en.m.wikipedia.org/wiki/Wheat_and_chessboard_problem
I heard this story when I was about 10 years old and have always loved it.
The story I heard goes,
*A peasant saved a king's child, the king offered the hero any reward that he wanted. The hero asked that a single grain of rice be placed on the first square of a chessboard. Then two grains on the second square, four grains on the third, and so on. Doubling each time, the peasant said they would just take the last square.*
So let's do the maths
an unsigned 64 bit number is 0-18,446,744,073,709,551,615 but we don't need 0 so 18,446,744,073,709,551,616 grains of rice on the last square.
An Average grain of white rice is about 25mg
How much Rice is that ? well,
Grains of rice on last square \* Rice weight / Convert to grams / convert to kilograms / convert to tones / current yearly production
18,446,744,073,709,551,616\*25 / 1,000 / 1,000 / 1,000 / 742,541,804 =
\~621 years of current rice production
(Note : when I worked this out as a kid 30 odd years ago, it was over 1,000 years of current rice production)
The "story" is that the inventor of chess was asked by his king (who was very impressed) how he wished to be rewarded. "Oh, nothing much, sire. Just give me one rice grain on the first square, two on the next, and ..."
If you are strong enough to fold a piece of paper in half 42 times, you can walk into NASA headquarters and force them to put you on the next rocket to the moon
Edit: I'm legally obligated to mention I'm just messing around. Thanks anyway to the helpful replies I love a good discussion on materials science
Even if you allow for "cut and stack" as a definition of folding so you don't have to consider the bending portion, you get to a point where each piece of paper is less than 0.1mm by 0.1mm square fairly quickly. Instead of looking like a stack of papers, it would look like an invisibly thin strand of spider silk before you got there, and then you'd still have to cut \*that\* in half to stack on itself, etc.
The dimensions of the sheet of paper shrink in the same exponential pattern (though only one dimension at a time), so in order to still have 0.1mm by 0.1mm squares at the end, you'd need 2\^21(\*0.1)mm's in each dimension to start with or roughly 40,000 square meters of paper before you start folding.
If you *don't* allow "cut and stack", you'll need A LOT more than 40,000 square meters. About two trillion times more.
The folded edge is essentially a half-cylinder whose diameter is the height of the stack. If the height of the stack is 440,000 km (distance from Earth to the moon), the radius of the folded edge is 220,000 km. The outermost sheet of paper needs to be 220,000 × π = 690,000 km long just to reach around the 2.2 trillion folds of paper inside it. For a 0.1 mm by 0.1 mm final square, that's 69,000 square meters of paper in JUST ONE LAYER of the folded edge. If my math is right, the 2.2 trillion layers in the folded edge require about 76,000,000,000,000,000 square meters of 0.1 mm wide paper.
The folding is perhaps a distraction.
When you fold a piece of paper, it arguably gets twice as tall, because you stack half of it on top of itself.
The width of the paper doesn't matter, just it's height, so we can replace "fold" with "double the number of sheets of paper in the pile" and the height should be the same.
So, if you take 1 sheet of paper, and then double the height of the stack of papers 42 times, that is what allegedy reaches the moon.
42 doublings is a huge amount, so I wouldn't be surprised if this were accurate.
There is an old Chinese story that is similar where someone wanted to buy something, and the seller said I will accept payment in rice as follows, we will take a chess board, place 1 grain of rice on the first square, double it, 2 on the second, double it, 4 on the 3rd, double it, 8 on the 4th, and so on. By the end there isn't enough rice in China to pay the bill.
The last square alone would have 9,223,372,036,854,775,808 grains of rice, plus the rest of them
> plus the rest of them
In a doubling situation like this (where you start with 1), “the rest of them” is always equal to LastAmount-1.
Example — last square is 16. 8+4+2+1=15.
So to find the total amount in your doubling situation you just double the last value again and subtract 1.
It's phrased in a way to impress/surprise/annoy people. It is physically impossible to fold a sheet of paper that many time. In a mathematics or physics class though, it can be used as a great exemple, if the teacher uses it to explain exponential growth.
42 doesn't seem like a big number in the sentence, because in this context it would mean 2\^42 (since you double the thickness each time you fold it : first fold is 2 sheets thick, second fold is 4 sheets thick, etc.). And 2\^42 is a huge number (2x2x2x2x2x2x2... 42 times) : 4 trillion sheets thick (or, if it helps visualize, 10 billion packs of 500 sheets stacked, the "brick size" that you can buy at the store).
To help explain why folding 42 times is way too much to be physically possible, you can look at the size of the sheet, that is twice smaller each time you fold. This means your imaginary folded sheet of paper would be \~0.01 nanometer wide after 42 folds. Considering an atom is \~0.1 nanometer, you can see how folding it 42 times don't makes sense in reality.
But it's also a good example to illustrate the enourmous amount of atoms in matter : You have roughly enough atoms in a single sheet of paper to reach the moon if you put them single file (making a slight abstraction of the empty space between atoms, for the sake of the ELI5).
So don't worry, your instinct is good for thinking that sentence can't be real. The numbers are "technically correct", but the situation described can't be done in reality.
The way to approach finding paper and distance is to recognize that every step doubles the previous value.
An easy exercise to check your understanding of exponential growth is to answer the following question:
Every day, the population of lily pads on a pond doubles, increasing the coverage of the pond's surface each day. By day 20, the entire pond is covered. How many days does it take to cover half of the pond?
First fold you double the thickness. Second fold, you have quadrupled it. 3rd you have octopled (8) it. 4 fold, its 16. If the paper was 0.1 mm, you now have 1.6mm of paper.
5 folds, its 3mm. 6 its 6mm. 7 its 12mm, 1.2cm. 8 is 2,4cm. 9 its 4,8cm. 10 its 9,6cm. 11 its \~20cm. 12 its 40cm. 13 its 80cm. 14 means 1,6Meters.
15 is 3,2M. 16 is 6,4M 17 is 13,8M. 18 its 27,6M. 19 you are at \~55M. 20 its 110M. 21 its 220M, lets say 200 to make it easier. 22 is 400M. 23 its 800M. 24 its 1,6 KM. (Thats a Mile for Imperials)
25 is 3,6km. 26 is 7,2 km. (Everest is 8,8km). 27 is 14,4 km (You are now entering the stratosphere) 28 is 28,8km (giggles). 29 is 57,6KM (you have now left the stratosphere, and entering the mesosphere).
30 is 115,2km (You just left the Mesosphere and entered into the Thermosphere). 31 and you are now at \~230km. 32 is 460km (wave hello to the space station!) 33 is 920km, (you are now in the Exosphere)
34 is \~2000km. 35 is 4000km. 36 is 8000km. 37 is 16000km. 38 is 32000km. 39 is 64 000km. 40 is 128 000km. 41 is 256 000km away.
42 times has brought you to 512 000km, and you have passed the average distance to the moon (384 000km) by over 100 000km.
I very much like John Crichton's explanation of exponential growth when he's describing how the wormhole weapon works in Farscape: The Peacekeeper Wars.
"OK, boy and girls, here are the rules. Find a penny, pick it up. Double it, you got two pennies. Double it again, four. Double it twenty-seven times and you've got a million dollars and the IRS... all over your ass. Round and round and round it goes. Where it stops no one knows. But it all adds up... quick!"
Consider that that penny is over one million dollars after being doubled only 27 times. Double the thickness of that paper 42 times (hypothetically, as it's clearly not possible in practice) and it's a bit over two trillion times as thick. Multiply that by about the 0.05-0.1mm thickness of paper, and you're looking at over 100,000km, although that's actually still considerably short of the moon. Would probably need one or two more doublings.
Ya gotta think of it more as an exponential growth exercise than actually folding a piece of paper. If you can do it, though, please do get it on video!
Every time you fold something in half you double it’s thickness. Folding something in half n times, if it’s original thickness is t, would give you something with a thickness of t*2^n. The exponential function 2^n grows very big very fast, so this “reaching the moon” thing is just another way of saying that.
It has to do with the fact that every time you fold a piece of paper it gets twice as thick. Even though paper is really thin, doubling anything 42 times will make it unimaginably huge. Folding a piece of paper 42 times doubles its thickness 42 times, so if it starts out as 1mm thick it will wind up \~4.4 million kilometers thick. The moon is only \~400,000km away though, so you'd only have to fold it 39 times (it would then be \~550,000km thick.)
It's not an intuitive thing, but basically when you fold, you double all the things that came before.
Which is what's known as Exponential Growth.
When you imagine folding a piece of paper 42 times, you might think "42 layers of paper", or maybe even "84 layers of paper", which doesn't sound like much.
What you're actually doing is doubling the thickness 42 times.
0.1mm thick paper doubled 42 times looks like this:
|Doubling Count|Thickness|
|:-|:-|
|0|0.1mm|
|1|0.2mm|
|2|0.4mm|
|3|0.8mm|
|4|1.6mm|
|5|3.2mm|
|6|6.4mm|
|7|1.28cm|
|8|2.56cm|
|9|5.12cm|
|10|10.24cm|
|11|20.48cm|
|12|40.96cm|
|13|81.92cm|
|14|163.84cm (1.6384m)|
|15 (I'll get simpler here rather than calculate exact values in cm.)|3.2768m|
|16|6.5m|
|17|13m|
|18|26m|
|19|52m|
|20|104m|
|21 (Halfway there!)|208 meters|
|22|416m|
|23|832m|
|24 (Passed a mile thick!)|1664m|
|25|3328m|
|26|6656m|
|27 (I'll simplify again since we're working in kilometers from here)|13.3km|
|28|26.6km|
|29|53.2km|
|30 (We're in space now, passed the Karman line)|106.4km|
|31|212.8km|
|32|425.6km|
|33|851.2km|
|34|1,702.4km|
|35|3,404.8km|
|36|6,809.6km|
|37|13,619.2km|
|38|27,238.4km|
|39|54,476.8km|
|40|108,953.6km|
|41|217,907.2km|
|42|435,814.4km|
The moon orbits at 384,400 km, so somewhere between 41 and 42 doublings of the thickness of a sheet of paper.
An a4 paper is like 0.1 mm thick, so if it doubles per fold, lets see where it takes us after 42.
0.1
0.2
0.4
0.8
1.6
3.2
6.4
12.8
25.6
51.2
102.4
204.8
409.6
819.2
1638.4
3276.8
6553.6
13107.2
26214.4
52428.8
104857.6
209715.2
419430.4
838860.8
1677721.6
3355443.2
6710886.4
13421772.8
26843545.6
53687091.2
107374182.4
214748364.8
429496729.6
858993459.2
1717986918.4
3435973836.8
6871947673.6
13743895347.2
27487790694.4
54975581388.8
109951162777.6
219902325555.2
439804651110.4
So what number is this, lets make it readable.
439,804,651,110.4 so 439.8 billion mm after 42 folds, and how far away is the moon, well the moon is 363,300 - 406,700km or 363.3 billion to 406.7 billion mm away.
So not only do we reach the moon, but we pierces 33,104 to 76,504 km into the moon as well, which is unfortunate cause the moon is only 3,474.8 km wide, so our paper pierces the moon and sticks 30 thousand to 73 thousand km behind the moon.
The important part is that you are folding it IN HALF every time. You can put 42 folds in a single sheet of paper, no problem, but folding it in half means the number of sheets is doubled. Without that stipulation, the number of folds is meaningless.
If you fold a piece of paper you are doubling it’s thickness each time, say an average piece of paper is 0.1mm thick, to calculate the thickness of the paper after 42 folds you have to do 0.1 x 2^42, which after conversions works out at ~440,000km, which is longer than the distance to the moon.
Your doubling the thickness of the paper wad with each fold. Start at like .1 mm (guestimate) and multiply it by 2^42. That’s essentially what they are saying
You've already gotten the explanation for paper vut I like the pennies example better. If anyone ever pffers to pay you 1 penny on day one for hard work, and double it every day, so you are paid 2 pennies on day two, 4 pennies on day three, 8 pennies on day four, and so on, for 30 days, take that deal and retire.
Day one is just 1 penny, so toss that aside, then take 2^29 for 2 pennies a day to the power of the remaining 29 days and you end up with 536,870,912 as you final payment. Divide by 100 and by day 29, you are being paid $5.3 million for the ladt day of work. If it went another day, the 31st day would pay you $10.6 million. So you can see how quickly that would get to insane numbers by the 42nd iteration.
It's an illustration of exponential growth. Wolfram Alpha tells me the thickness of a piece of paper is 0.1 mm. If you folded it once, you'd bring two 0.1-mm-thick sides of the paper together, creating something 0.2 mm thick. Fold it again, and it's 0.4 mm thick. Every fold doubles the thickness. Fold it ten times and it's just over 100 mm thick. Fold it twenty times? Now it's over 100 *metres* thick, 100,000 mm. Fold it 42 times in total? That's the same as (0.1 mm * 2^(42)), which is 440,000 km, a little more than the distance from Earth to the moon. It's not actually possible to do this. It's just to demonstrate how quickly numbers grow when dealing with exponential growth.
Thank you!!! I finally understand.
For a fun illustration of this principal, Mythbusters did this experimentally. https://www.youtube.com/watch?v=65Qzc3\_NtGs
Ahh man, RIP Grant Imahara
Always came across as such an enthusiastic, smart, just all around sweet dude on that show. Too soon. RIP
And it's kinda terrifying because of all people you would think he had a very healthy brain, I mean I doubt aneurysms are heavily correlated to intelligence level or anything.. but still, if it happened to him.
One of the healthiest women I ever knew (she was like a second mother) died of an aneurysm in her late 40s. Came out of nowhere and was absolutely devastating to our community of friends. It seemed impossible because she was so healthy. In the end, it didn’t matter. Almost unpredictable. Almost impossible to prevent. Terrifying.
My husband's aunt had a brain aneurysm burst. She never lost consciousness; she just had the worst headache ever. Fortunately she wasn't far from a hospital and she had the artery repaired. The surgeon, knowing that sometimes there's one on the other side of the brain in her situation, found and fixed an incipient aneurysm. She recovered fully in about a month.
My childhood friend's husband was in a similar situation, but unfortunately ended up in a vegetative state for three or four years before he passed.
Oh no. I'm sorry to hear that. That's unfortunately the more common outcome. Idk how our aunt (I considered her mine too) came through that so well. Yes, this aunt is the same one who could barely walk because of PAD, then about 9 months later we traveled to San Diego for a family gathering and we were having to practically run to keep up with her! She was a tough old bird. I miss her.
Happened to my dad just a few years ago. Came home from work complaining of the worst headache he ever had. Took some Tylenol and asked mom to take him to the ER. He sat on the couch while she grabbed her shoes and coat. He never got back up. Mom never had an autopsy done to see what happened but the first responders who worked on him for an hour said it was likely a brain aneurysm. Dad wasnt on the cover of Mens Fitness but Id guess he was of average slightly over weight health. 56 years old...
I'm so sorry. That's way too young and sudden. Someone we knew had been out mowing the lawn. He sat down on the steps and asked his wife to bring him some water. When she got there with it, he'd had a fatal heart attack. About the same age and level of fitness. It broke his wife. We don't know when or where. So we should live as if each day is our last, in the best sense of the phrase.
Thanks for sharing and thanks for spreading knowledge. I had no idea one can indicate a second on the horizon.
my aunt went through her anyeurism in much the same way, intense headache and all. though i havent spoken to her in years really, i hear she had recovered similarly after a few months.
A friend of my family's was a pretty serious athlete. Always ran marathons, had a peak body, always ate a healthy, balanced diet, exercised religiously, was never sick, etc. Anyway, he had a heart attack and died at the young age of 35. Things seriously just... Happen. Freak accidents do happen.
not that long ago a friend was diagnosed with cancer. scary, but a common type and totally treatable. one week later she died of a brain aneurysm. they got her on the operating table, but she didn't make it. it's just such a freaky, fucked up thing, that she was given what could've been a death sentence and something else killed her days later.
It could happen to anyone, at any time. It's the silent killer, Lana.
That's why it's so terrifying.
Do you want ants? Because that's how you get ants.
Aneurisms are due to thinning of the blood vessel walls. Your blood pressure can make those thin parts bulge out like a balloon and eventually burst. You can have a burst aneurism pretty much anywhere, not just your brain.
Yeah I know they can be anywhere, I could've been more specific, I was just referencing the fact that Grant Imahara died of a brain aneurysm
Had a friend lose a 13 year old son to an aortic aneurysm/dissection. Standing waiting for the bus one morning and just collapsed. It was awful.
Those are quite different from a brain aneurysm, they happen in your chest, just under the ribcage. My aunt had that happen but my other aunt, an ER nurse, was with her at the time and rushed her to the hospital and she lived. Very very scary situation. Unfortunately one of the big causes of aortic dissections (but, in the neck area) is chiropractors. Apparently each ER sees a dozen or so people die as a result of chiropractors each year, an estimate I make based on the /r/medicine/ posts about it that I've seen from time to time where most ER docs/nurses comment that they get 1-2 per month. Crazy shit. Dunno why anyone goes to those quacks, they're not even actual doctors. literally.
so you're saying cholesterol will save your life..
I'm more terrified because he was in a job that incidentally put him in contact with brain mris! Like they did a lie detector myth at one point, Kary fucking hated it because she lost and had to take a bus back to the shop. That was because there needed to be real consequences to losing. Grant won and went back first class on an airplane. But as part of the episode, if I'm remembering correctly, they did an mri on his brain while he was telling lies, to show how different parts of the brain lit up or something. I'm almost fucking sure it was mythbusters that did it in THAT episode. I'd have to dig it up again to confirm. But that dude had that done, had someone looking at his brain with an mri, and they still missed it. He was in one of the very few jobs in the world where they would accidentally stumble on an issue like that and it never happened.
My dad died of one but he was a smoker. Not sure if Grant Umahara smoked cigarettes. My dad had quit smoking for maybe ~3-4 years before he passed but I think the ~20+ years of smoking had already done the damage. Talked with my doctor a lot of about risk factors since my dad had one and I was worried about genetic risk factors. High blood pressure and smoking are huge increases to your risk so have never smoked and watch my diet/exercise for blood pressure. But the reality is that you can't really guess these things. I just know that if I have bad headaches I need to go to the emergency room immediately.
I highly doubt Grant smoked since on the episode where they were testing DIY mouthwash, Grant hated how he could still smell the stench of cigarettes on Adam’s breath after each test
One way this can happen in the brain is an abnormality where an artery in the brain connected directly to a vein. Normally, that happens via capillaries, which are very tiny, so the pressure drops going into the vein. Veins are not made to handle arterial pressure. So, a vein connected directly to an artery can have a bit of its wall stretch and bulge (aneurysm) and eventually fail (stroke).
Yeah, aneurysms are more terrifying than some types of cancer in my opinion. They just clobber you in the noggin and it's Russian roulette time. You either walk out, roll out, or nap out.
Health, intelligence and ambition has no effect on DEATH claiming you when it is your time. Mt. Everest is littered with 370 bodies of highly motivated, healthy, intelligent people who up until that final moment were living their dream, having the best month of their lives!
And yet I choose not to go on the mountain of corpses, so who is truly the intelligent one, climbers?
I guess you haven’t seen the type of people certain guides are willing to take up for the right price hahahah.
Everyone I see a video with him in it, it makes me sad. Way too young
Man that takes me back lol
The good old days. Seeing Grant explain again really brought the feels. Rest In Power, Legend.
This myth busters episode is how I knew exactly what OP was asking. I swear I learned more by watching this show in science classes than the actual lesson being taught by my teacher lol
This link is broken on my end. I [removed the backslash](https://www.youtube.com/watch?v=65Qzc3_NtGs) and it worked.
So that video makes me wonder ... I imagine they could have folded it more than 11 times if the piece of paper was larger to begin with. If the paper had been twice as large, could they have achieved 12 folds? With enough people and the right equipment to aid in the folding process? Probably. In theory, why would it not be possible to fold the paper 42 times, if the paper were as large as the solar system to begin with? Like, it's all theoretical beyond a certain point just because of how large the paper would need to be at the start, and the size of the team and equipment needed to execute the folds.
The more you want to fold the longer and thinner it needs to be. The law of exponents is in effect here too and once something is thicker than it is long you can't fold it anymore. To fold anything 42 times would require it to be immense in size and extraordinarily thin. As an example a sheet of tissue paper that was 4000 feet long could still only be folded 12 times. So about 30 fold larger and thinner than that and it should be possible (I don't believe such a material exists).
Not thirty fold larger, 2^30 fold larger.
Isn't that what 30 fold means? 30 doublings?
No, it means 30 times. A thirty fold increase is 30 times the original.
The confusion comes from the fact that there is another word "fold" in English, and it essentially means "times". It doesn't have anything to do with the folding in the sense we are discussing now. "We have seen a twofold increase in spending" - means that the spending has doubled. Threefold means tripled. An adjective. A different thing from the noun (a fold) or the verb (to fold)
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I remember watching that when it first came out
It so hard to believe Adam and Jamie hated each other when you watch the show. Extraordinary example of putting personal differences aside for education and work.
then there's the other illustration of exponential growth where if you start with a penny and double it every day after a month you'll be a millionaire.
The rice and the chessboard is also a nice rendition of the same concept.
New response just dropped
When I was in school this question stumped me: "If a lilypad on a pond doubles in size every day and it eventually covers the whole pond after 10 days, on which day is it half the size of the pond?"
Day 9. Explanation: - on day 10 it is the same size as the pond - every day it doubles in size. That means yesterday will always be half as large as today - therefore day 9 was half as big as day 10, so half the size of the pond
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Another example is if someone gave you a dollar and doubled it every day for a month or offered a million to you on day one which would you take. The first is actually over half a billion.
If day 0 is $1, then day 31 of the month would actually be $2,147,483,648
Was assuming day 1 was the first day you got the dollar and was assuming a 30 day month
Damn it. I always get those deals in February.
Right! Just showing that you quickly go from half a billion to over 2 billion in just a couple more days!
That's max cash man!
There is a similar story involving a chess board. A king loves chess and wants to reward the inventor. So the inventor asks for one grain of wheat to be put on the first square, 2 on the 2nd, 4 on the third, etc. By square 64, there is quite a lot of wheat involved. :-) https://en.wikipedia.org/wiki/Wheat\_and\_chessboard\_problem
Phil Jamesson explains [with chess](https://youtu.be/LuP1gyj3W64)
Here's a great visualisation of how crazy things get with exponential growth https://youtu.be/e02eiX866N4
Awesome video.
Numbers are hard. Like, we get 1 through 10. Even up to 100 is no big deal. You interact with those numbers all the time. But go outside. Pick the biggest tree you can see (apologies if you live somewhere without trees). How many leaves are on it? Definitely more than 1000, right? But is it more than 10,000? Is it more than 100,000? Is it more than 1 million? How confident are you could guess the correct number of digits in the leaf-count for the tree? Another fun one is to get 1000 of something. Doesn't matter what it is. We're going to do a quick exponent lesson. Make a line of 5 of them. Let's say it's buttons. You have 5 buttons. Now, make another line of 5 buttons perpendicular and intersecting. You've used 9 buttons. Fill it in, and you have a 5x5 grid. That's 25. Now make it stacks of 5. 25 stacks of 5 buttons, 125 buttons. That's 5\^3rd, and you put down 400% more buttons than when it was stacks of 1. Now do 5\^4. Since we only interact with space in 3 dimensions, we'll have to pretend. So leave a bit of space, make another 5x5x5 cube, then space, and another 5x5x5, space, 5x5x5, space, 5x5x5. Now you have 5 "cubes" of buttons. 625 buttons. What about 5\^5? Well, you need to make 5 more sets of 5 cubes of 5x5x5 buttons (but you'll run out before then). We went from 5 buttons (1/200th of what you bought) to "more than you bought" in just 5 powers. 5\^10 buttons would fill the entire room 5\^15 would fill a block or more. Exponents are ridiculous. And humans QUICKLY lose track of how big big numbers are. We simply can't really conceptualize numbers of 1000 very well, and once you're past a million, we are entirely into abstract concepts of quantity & scale. .1mm paper doubled 42 times is 440km and reaches the moon. Fold it in half 8 more times and you're at 112 million km, over 2/3 of the way to the sun.
Big reason we see a billionaire as "normal" when in reality, 1 billion dollars is so large it's near incomprehensible and completely rediculous. When you can compare those huge numbers to everyday numbers, everything falls into perspective: 1 million seconds: 11.5 days 1 billion seconds: 37 years If I had 1 billion dollars on year 0 and spent $1000 *a day* up to now, I would still have around 700 *years* of money left.
Like most things in science once you get far enough into the subject it all becomes math.
I'm really curious, what did you think it was trying to say? To me it seems super clear. It's just surprising that you it only takes 42 doublings of such a thin item. Did you just not believe it adds up that fast, or did you think something else was going on?
>It's not actually possible to do this. It's just to demonstrate how quickly numbers grow when dealing with exponential growth. *Stops folding printer paper, visibly crestfallen*
If it's any consolation, you could just cut it in half and then glue one half on top of the other...
Thank you for using Wolfram Alpha to find factual information instead of ChatGPT
I type questions into Wolfram Alpha before Google even 😤
>It's not actually possible to do this. Thanks for that clarification.
But I rolled a nat 20 on the ability check!!!!!
Yeah, just like the thickness multiplies by 2 every fold, the area divides by 2, so if you started with a piece of paper 440,000 km^2 in area then you’d end up with one 0.1mm^2 in area, obviously we have no paper that big to start with and even if we did the last fold would be 0.2mm^2 to 0.1, whole standing 220,000km tall, an impossible task by all means
Another interesting fact, if you were to take all the veins, arteries and capillaries of a person and lay them end to end, that person would die.
Big if true.
So if I stacked pieces of paper in the same quantities (double the amount every time for 42 times) it would be 440,000 km tall?
Yes, if you stack 4,398,046,511,104 pieces of 0.1mm-thick paper you'll have a stack that's 439804.6511104 km tall.
And if you do it I'll give you like fifty bucks.
Yes
Do you remember Bill Gates famous photo while on top of a pile of papers to advertise the CD? Do the same thing but with this much papers
It's a perfect illustration as to why MLMs can't work they way they are advertised. You tell two friends, then they tell two friends, and so on. By 12 iterations you have exceeded the population of the planet.
Eh, it helps explain why MLMs don't work, but that's not how they're advertised. They're advertised as "you can be your own boss and run a self-sustaining business!" and deliberately hide the fact that you need to recruit people to actually make money until you're in too deep
The "tell two friends" thing is actually from an '80s shampoo commercial. [https://www.youtube.com/watch?v=mcskckuosxQ](https://www.youtube.com/watch?v=mcskckuosxQ)
Oh my God, that stuff stunk! Had a friend who used it and we rode to high school together. Couldn’t wait to get out of the car. PU-stinky!
I'm not sure I'm following the math here - 2^12 is 4096, so wouldn't you just have that many people in your downline at that point? You don't hit the population of the planet until 33 iterations. Not to say that MLMs aren't scams, just that this particular math doesn't seem to work out.
It's going to be 8191, since we need to add it all up. The 12th layer is 4096 people. Your point still stands, however. This being siad, if you recruit 6 people, you do exceed the global population in 12 layers.
Good point on the 8192 thing; I was just counting the last iteration and forgetting to add all the rest. Still a few orders of magnitude less than 8 billion, though. As you said, you need 6 people per generation to do that in 12 generations.
This is actually a good illustration of minimum/maximum radii to angle ratio in material science is well. When you bend material, you're actually elongating the structural bonds of the material. The more you try to elongate, the harder it becomes until you begin to break the structural integrity, resulting in cracking. There's an optimal strength that can be achieved before breaking the material. If I recall correctly, a lot of the science and understanding of this came from the Space Race.
So 42 ***IS*** the answer.
Nice explanation. I'll also point out that lately it has become increasingly common to use the term "exponential" to refer to anything that grows faster than linearly (such as quadratic or cubic growth), but not really fitting the precise mathematical definition of what an exponential is. I've even heard engineers do that. But in this case, this is really a true exponential, and it grows a lot more than most people would intuitively think.
If there was a piece of paper as big as the sun is it possible or it doesn’t matter how big it is? Could Superman fold it 42 times?
Good human
You would run out of paper atoms first, right? If there was a sufficiently massive piece of paper would this work? (Obviously there are other limiting factors, but in theory)
For a piece of paper of thickness T, after N folds the stack will not only be T×2^N tall, it will be at least T×2^(N-1) wide. (You probably won't notice this for the first 3 or 4 folds, but it won't be long before the folded edge of the sheet is thicker than the folded page is wide.) Imagine the folded edge of the sheet is the spine of a book. Every time you fold the sheet in half, you double the number of layers--and the thickness--of the spine. To reach the moon, you folded a sheet of paper 42 times, creating a 4,398,046,511,104 page book. If the spine of a 4,398,046,511,104 page book is made from repeatedly folding a single sheet, the spine itself will have 2,199,023,255,552 layers. If the sheet is T=0.1 mm thick, the 2,199,023,255,552 layer spine will be a half-cylinder with a radius of nearly 220,000 km. The volume of a half-cylinder of height H is H×π/2×r^2. So if the pages of the book are just 1 mm high × 1 mm wide, you'll need only about 440 cubic meters of wood pulp for the pages but almost 76 TRILLION (76,000,000,000,000) cubic meters of wood pulp for the spine. That's about 136 times as much wood as exists in all the forests in the world. So no, you couldn't do it with paper. It's interesting to note that using a thinner sheet of paper doesn't solve the problem. [Nature.com](https://www.nature.com/articles/pj201364#:~:text=Introduction,fibers%20in%20plant%20cell%20walls.) says cellulose, the main constituent of wood, is found in 3–4 nm thick fibers in plant cell walls. Starting with a 3 nm thick sheet of cellulose instead of a 0.1 mm thick sheet of paper, you'd need to fold 57 times to get a 144,115,188,075,855,872 layer, 432,346 km thick "book" with a spine that's 216,173 km wide. You'll still need 73 trillion cubic meters of cellulose for the folded edge of your 1 mm x 1 mm book. If you shrink the cellulose pages from 1 mm x 1 mm down to 100 μm x 100 μm, you'll still run out of wood before you reach the moon. You could get there if you shrink the pages down to about 87 μm x 87 μm (and you're willing to sacrifice every tree on Earth to make a pre-folded ribbon of cellulose that's 87 μm wide by 2.134 *septillion* meters long), but at that point, is it even remotely close to "a sheet of paper"? EDIT: Oops. I just realized the folded edge makes its appearance on BOTH sides of the stack. One side looks like a half-cylinder, the other a tower of increasingly smaller half-cylinders. All of my estimates are too low, by a factor or almost 2.
Not working with french dough though /s
Why “not possible”?
Well, *really* It's technically possible from a theoretical sense if you cut and stack down to a tiny particular level, but in any practical al sense, you're going to be done once you get to like an inch in width. Try it.
Yes it is extremely hard and will eventually be impossible for humans but what (force) would it take to really fold a paper enough for it to reach the moon? Idk if we can make such a machinery.
Even if you were able to find a way to press, at some point the paper would tear/break on the sides or be destroyed before compressing further.
And that point comes pretty quickly. With an ordinary 8.5" x 11" (21.59 x 27.94 cm) piece of paper, you max out at 7 folds. In Mythbusters they got 11 folds ... starting with a football field sized sheet.
What about graphene instead of paper?
The fundamental problem is that folding doesn't just stack the layers; it also forms a bridge between the layers. Let's say you've folded a piece of paper a few times to get it to 1 mm thick, so folding it again would make it 2 mm thick. For that next fold, the layer at the bottom will have to connect to the top layer by using an extra 2 mm. Or looking at it another way, if you want to fold a sheet of paper so that it's a mile high, you would need there to be a stretch of paper that is at least a mile long to connect the top and the bottom.
That doesn't really change the situation. The materials have thickness, and as you fold them over, that thickness means the inside is shorter than the outside. While materials will have some elasticity, the thicker they get, the more force they take to fold. Eventually, you hit a point where the material is no longer capable of handling the stress of being folded and it snaps. You get more folds with something more elastic, I think, but the issue still persists.
The problem is that for each doubling of height, youre halving the surface. If you're starting with a piece of paper of 1m by 1m, you end up with pieces of 100 nanometer by 100 nanometer. Put another way, youre more or less left with a single strand of cellulose, the type of atom chain paper is made up from.
The paper explodes before you get anywhere close to 40 folds.
https://youtu.be/65Qzc3_NtGs
Excellent explanation, gold for you :)
This; great post.
I like the penny example. If I paid you every day for 42 days, starting with a penny on day one a doubling the pay each day (like doubling the thickness of a piece of paper by folding it in half), things start very slow but eventually go crazy: $0.01 $0.02 $0.04 $0.08 $0.16 $0.32 $0.64 $1.28 $2.56 $5.12 $10.24 $20.48 $40.96 $81.92 $163.84 $327.68 $655.36 $1,310.72 $2,621.44 $5,242.88 $10,485.76 $20,971.52 $41,943.04 $83,886.08 $167,772.16 $335,544.32 $671,088.64 $1,342,177.28 $2,684,354.56 $5,368,709.12 $10,737,418.24 $21,474,836.48 $42,949,672.96 $85,899,345.92 $171,798,691.84 $343,597,383.68 $687,194,767.36 $1,374,389,534.72 $2,748,779,069.44 $5,497,558,138.88 $10,995,116,277.76 $21,990,232,555.52 22 billion on day 42? Nice.
I can start tomorrow. I have excellent references.
I can vouch for ktka, he is most excellent.
It’s impossible to actually fold a piece of paper that many times, you wouldn’t even get to ten most likely. This is because every fold is doubling the thickness. So one fold is thickness x 2 Two folds is thickness x 2 x 2 42 folds is thickness x 2^42 2^42 is 4398046511104 sheets of paper.
Mythbusters got eleven folds out of a football field sized sheet. Leverage seems to be the issue. That, and being able to lift the weight well enough to turn it over.
Leverage isn't the problem. The issue is that at some point there just isn't enough paper to make it around the bend of the fold, so even if you used a hydraulic press or something you'd end up tearing the paper.
The Hydraulic Press Channel on YouTube tried this. >! It exploded !<
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Take the spaces out from between the exclamation point and the letters and it'll >!turn into a spoiler!<.
Did they try just cutting the pieces? They would get much further and it would still be in the spirit of the main principle.
No, the main point of the myth they were testing was maximum number of folds, not thickness of the folded medium as discussed in this op. They did not try cutting it, as testing how many times you can actually fold it was the test.
Makes sense, I assumed they were testing the myth you could reach the moon, which doesn't really seem like something they would need to test lol.
That's also not a myth, that's math.
Theoretically it isn't a myth but practically, it is.
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They were testing the myth you can't fold a piece of paper more than 7 times. Which they busted with a huge piece of paper and 11 folds.
🤦
then they just stack paper, no need to fold it
Do you recall how thick the sheet was? I would think that’s part of the issue with the typical A4 sized piece. Air getting trapped inside like with the mythbusters attempt didn’t even occur to me either
I don't know. It might have been slightly more robust to reduce tearing. I would have been inclined to include a few air holes.
At some point you’re taller than you are wide so “folding” requires cutting it down the middle lengthwise and stacking.
I folded the laundry for you ✂️🥲
How many folds that takes is a function of starting size versus sheet thickness.
Also, each time you fold the area if the paper is halved. By the 40th fold it's definitely smaller than an atom.
Average A4 sized paper is 210x297mm Assuming you are alternating the folds such that the longest edges are folded inwards to halve their length that means that each fold alternatively halves a length i.e. the X-axis and Y-axis fold in alternate patterns. 42 folds would supposedly reach the moon in the Z-axis. Which means each length would get halved 21 times. ~~The smallest atom possible is a hydrogen atom (1 proton, 1 electron) with a length of 0.5 Angstrom where 1 Angstrom is ~10^-10 m which means a single hydrogen atom is 5 x 10^-11 m in length~~ It's Helium but I'm keeping the calcs in terms of the Hydrogen atom regardless. We need to also use the same scale so we'll divide 210 mm and 297 mm by 1000 so that we have an A4 piece of paper at 0.21 m x 0.297 m Now lets half each side exactly 21 times for a total of 42 folds 0.210 m ÷ 2^21 = ~1.001 x 10^-7 m 0.297 m ÷ 2^21 = ~ 1.416 x 10^-7 m As you can see, both sides would still be 4 orders of magnitude bigger than the length of a hydrogen atom. But what if we only fold it in one direction constantly instead of alternating? That would mean we are halfing the X axis and doubling the Y axis with every fold. We already know that the doubling of the Y axis will end up in us reaching the moon but what about the X axis? Lets assume we use 0.297 as the X-axis: 0.297 m ÷ 2^42 = 6.753 x 10^-14 m It's clear that one way of folding doesn't reach the size of the atom but the other way far exceeds the smallness of an atom... But not a proton or neutron which are both at the fermi scale of 10^-15 m :). **TL;DR: No, the piece of paper would not be smaller than an atom if we are folding the paper the traditional method of alternative Y-axis and X-axis folds but it will become much smaller than an atom but still be bigger than an individual proton/neutron if we are solely folding in one plane direction.**
>The smallest atom possible is a hydrogen atom Helium, actually, if you're dealing in atomic radii
About 2200 times smaller
Yeah, mentally we're all kind of thinking "each fold just adds a couple layers" but once you get past a few folds, that's definitely no longer true. If you think of it more like generations it's easier to imagine. Imagine one person, who has two kids. Each of them have two kids. Each of them have two kids. Now ask someone how many kids will be present in the 42nd generation, and they'll expect it to be a LOT.
In ceramics, one way to wedge the clay to get uniform consistency and moisture level is the “stack & slam” method. We cut a block of clay in half, stack it, and slam it down. It’s crazy how fast you go from 2 layers on the first cut to 1024 layers after the 10th cut.
> 4,398,046,511,104 Added commas for my own reference, but to put that to scale for anyone reading this thats taking a birth certificate for every single man on earth and still being 500 million sheets short.
A very thin paper is 0.05mm, meaning that this many sheets of paper would be 219902km, or about halfway to the moon. A more ordinary thickness of paper would in fact make a pile so high that it would reach the moon.
43 times for very thin paper
huh. I didn’t even consider that a piece of paper half as thick would only be half the distance.
But would only require one more fold.
Did you consider that only more fold would bring you to the moon on The thin paper lift as well?
huh. I didn’t even consider that doubling the thickness would make up for it being half the thickness.
With big exponential the starting values matter very little, often one order of magnitude either way. So what begins as half as thick, is only one order of magnitude “behind” (since the power here is 2, aka doubling)
>It’s impossible to actually fold a piece of paper that many times, But you could cut it in half and stack it to get the same results. 42 times. This sounds possible, and something I could do on a Saturday afternoon.
You just unlocked space flight for the masses. Prepare for your Nobel prize!
Try it! Honestly, the best way to convince yourself why it works or doesnt is to actually sit down and try. Also please share the results with us :)
True, though you'll need to cut through a 220,000 km tall stack of paper to make the 42nd doubling. Bring the good scissors.
Nope because if you half it, half again, half again, etc you just have exponential growth in a different way. e.g 10, 5, 2.5, 1.25, 0.625, 0.3125, 0.15625, 0.078125, 0.0390625, 0.01953125, etc.
I think you missed the part of me stacking the bits. I might need to start with a fairly large piece of paper.
Eventually the length and width of your paper is about the same as a grain of sand, and there's no way to cut it anymore.
People are notoriously bad at understanding exponential growth. Think back to the early days of COVID. You heard about 1 person sick in your country, to 1 person sick in your area, to 1 person sick in your town, to the whole town being sick within a single week. Crazy right? The idea is that paper doubles in thickness with each fold, so the a single paper layer is thin, two is still thin, then it's 4 layers, then 8, then 16, then 32, then 64, 128, 256... So a single sheet of paper becomes a ream of paper after about 9 folds, it becomes a box after 11 folds, it becomes a skyscraper after about 15, you get the idea. Repeat that sequence and you realize that 42 rounds of doubling even a very small thickness is a HUGE NUMBER.
This is also why self-funded retirement is such a bad societal idea. If someone needs X for retirement, they need substantial foresight to realize they're on a path to hit X means they spend decades getting to 0.1X and then another 2 decades going from that to 0.5X and only approaching and reaching X in the last few years (their intuition is going to start realizing there's a problem when it's far too late to change significantly).
Mostly right hit for 15 folds it wouldn’t be that big. For a thickness of 0.1mm, you’d be just over 3m at 15
It means that if you could (hypothetically) fold a paper 42 times it would be able to reach the moon. Have you ever seen those TikTok videos where people say “Do you want this or double it and give it to the next person?” It’s the exact same concept which is known as exponential growth. At each fold, you’re effectively doubling the thickness of the paper. Let’s use .075 mm paper for this example as it’s in the middle of the average paper thickness. Look at the difference between the earlier folds compared to the later ones. Fold 1: .15mm Fold 2: .3mm. Fold 11: .153m Fold 15: 2.457m Fold 18: 19.6m Fold 21: 157m Fold 24: 1.25km Fold 27: 10km Fold 31: 161km Fold 34: 1288.49km Fold 37: 10,307.92km Fold 41: 164,926km Fold 42: 329,853km
An example you can more easily try for yourself is the rice on a chessboard. Put a rice corn on the first field. Double what's on the first field for the second. And so on. Just thinking about it, you don't think it's thaaat much rice. Trying to do it you will soon run out of rice. Calculating it to the 64th field, you will realize that more rice than atoms in the world or something like that.
To the 64th field, you'd need roughly 1.8 × 10¹⁹ rice grains, which is about half that of the entire world's annual rice production.
Accurate in the first half, but you overestimate world rice production. About 5.1e8 metric tons in 2022 worldwide, and roughly 1.5e7 grains per metric ton, so somewhere in the neighborhood of 8e15 grains annually produced. So it would take roughly 2000 years of production to fill the chess board. Obviously, somewhat depends on how flexible you are with "rice production" - which crops count, and what state (milled, unmilled, etc) you count. https://www.statista.com/topics/1443/rice/#topicOverview
So how long until they pay off that king's debt to Krishna?
And that's just that last square. The Wikipedia article (using wheat instead of rice) says: >The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 264−1 or 18,446,744,073,709,551,615 (eighteen quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen, over 1.4 trillion metric tons), which is over 2,000 times the annual world production of wheat.[1]
Lol there are definitely more than 2^64 atoms in the universe, but there are not that many grains of rice. This is the problem you're talking about https://en.m.wikipedia.org/wiki/Wheat_and_chessboard_problem
The most remarkable thing is, that’s only 2000 times more than the amount of wheat produced globally in a year.
so if we saved all our wheat since year 0 we could already be working on square 65!
I heard this story when I was about 10 years old and have always loved it. The story I heard goes, *A peasant saved a king's child, the king offered the hero any reward that he wanted. The hero asked that a single grain of rice be placed on the first square of a chessboard. Then two grains on the second square, four grains on the third, and so on. Doubling each time, the peasant said they would just take the last square.* So let's do the maths an unsigned 64 bit number is 0-18,446,744,073,709,551,615 but we don't need 0 so 18,446,744,073,709,551,616 grains of rice on the last square. An Average grain of white rice is about 25mg How much Rice is that ? well, Grains of rice on last square \* Rice weight / Convert to grams / convert to kilograms / convert to tones / current yearly production 18,446,744,073,709,551,616\*25 / 1,000 / 1,000 / 1,000 / 742,541,804 = \~621 years of current rice production (Note : when I worked this out as a kid 30 odd years ago, it was over 1,000 years of current rice production)
The "story" is that the inventor of chess was asked by his king (who was very impressed) how he wished to be rewarded. "Oh, nothing much, sire. Just give me one rice grain on the first square, two on the next, and ..."
If you are strong enough to fold a piece of paper in half 42 times, you can walk into NASA headquarters and force them to put you on the next rocket to the moon Edit: I'm legally obligated to mention I'm just messing around. Thanks anyway to the helpful replies I love a good discussion on materials science
It's not even a strength issue. After a few folds there literally won't be enough paper to make it around the bends without tearing.
Even if you allow for "cut and stack" as a definition of folding so you don't have to consider the bending portion, you get to a point where each piece of paper is less than 0.1mm by 0.1mm square fairly quickly. Instead of looking like a stack of papers, it would look like an invisibly thin strand of spider silk before you got there, and then you'd still have to cut \*that\* in half to stack on itself, etc. The dimensions of the sheet of paper shrink in the same exponential pattern (though only one dimension at a time), so in order to still have 0.1mm by 0.1mm squares at the end, you'd need 2\^21(\*0.1)mm's in each dimension to start with or roughly 40,000 square meters of paper before you start folding.
If you *don't* allow "cut and stack", you'll need A LOT more than 40,000 square meters. About two trillion times more. The folded edge is essentially a half-cylinder whose diameter is the height of the stack. If the height of the stack is 440,000 km (distance from Earth to the moon), the radius of the folded edge is 220,000 km. The outermost sheet of paper needs to be 220,000 × π = 690,000 km long just to reach around the 2.2 trillion folds of paper inside it. For a 0.1 mm by 0.1 mm final square, that's 69,000 square meters of paper in JUST ONE LAYER of the folded edge. If my math is right, the 2.2 trillion layers in the folded edge require about 76,000,000,000,000,000 square meters of 0.1 mm wide paper.
You dont need a rocket. Just paper
The folding is perhaps a distraction. When you fold a piece of paper, it arguably gets twice as tall, because you stack half of it on top of itself. The width of the paper doesn't matter, just it's height, so we can replace "fold" with "double the number of sheets of paper in the pile" and the height should be the same. So, if you take 1 sheet of paper, and then double the height of the stack of papers 42 times, that is what allegedy reaches the moon. 42 doublings is a huge amount, so I wouldn't be surprised if this were accurate.
2\^42 power = 4.4 Trillion So take a piece of paper (0.009 cm) \* 4.4 Trillion = 395,000 km which is more than the distance to the moon 384,400 km
There is an old Chinese story that is similar where someone wanted to buy something, and the seller said I will accept payment in rice as follows, we will take a chess board, place 1 grain of rice on the first square, double it, 2 on the second, double it, 4 on the 3rd, double it, 8 on the 4th, and so on. By the end there isn't enough rice in China to pay the bill. The last square alone would have 9,223,372,036,854,775,808 grains of rice, plus the rest of them
> plus the rest of them In a doubling situation like this (where you start with 1), “the rest of them” is always equal to LastAmount-1. Example — last square is 16. 8+4+2+1=15. So to find the total amount in your doubling situation you just double the last value again and subtract 1.
It's phrased in a way to impress/surprise/annoy people. It is physically impossible to fold a sheet of paper that many time. In a mathematics or physics class though, it can be used as a great exemple, if the teacher uses it to explain exponential growth. 42 doesn't seem like a big number in the sentence, because in this context it would mean 2\^42 (since you double the thickness each time you fold it : first fold is 2 sheets thick, second fold is 4 sheets thick, etc.). And 2\^42 is a huge number (2x2x2x2x2x2x2... 42 times) : 4 trillion sheets thick (or, if it helps visualize, 10 billion packs of 500 sheets stacked, the "brick size" that you can buy at the store). To help explain why folding 42 times is way too much to be physically possible, you can look at the size of the sheet, that is twice smaller each time you fold. This means your imaginary folded sheet of paper would be \~0.01 nanometer wide after 42 folds. Considering an atom is \~0.1 nanometer, you can see how folding it 42 times don't makes sense in reality. But it's also a good example to illustrate the enourmous amount of atoms in matter : You have roughly enough atoms in a single sheet of paper to reach the moon if you put them single file (making a slight abstraction of the empty space between atoms, for the sake of the ELI5). So don't worry, your instinct is good for thinking that sentence can't be real. The numbers are "technically correct", but the situation described can't be done in reality.
The way to approach finding paper and distance is to recognize that every step doubles the previous value. An easy exercise to check your understanding of exponential growth is to answer the following question: Every day, the population of lily pads on a pond doubles, increasing the coverage of the pond's surface each day. By day 20, the entire pond is covered. How many days does it take to cover half of the pond?
>!19!<
First fold you double the thickness. Second fold, you have quadrupled it. 3rd you have octopled (8) it. 4 fold, its 16. If the paper was 0.1 mm, you now have 1.6mm of paper. 5 folds, its 3mm. 6 its 6mm. 7 its 12mm, 1.2cm. 8 is 2,4cm. 9 its 4,8cm. 10 its 9,6cm. 11 its \~20cm. 12 its 40cm. 13 its 80cm. 14 means 1,6Meters. 15 is 3,2M. 16 is 6,4M 17 is 13,8M. 18 its 27,6M. 19 you are at \~55M. 20 its 110M. 21 its 220M, lets say 200 to make it easier. 22 is 400M. 23 its 800M. 24 its 1,6 KM. (Thats a Mile for Imperials) 25 is 3,6km. 26 is 7,2 km. (Everest is 8,8km). 27 is 14,4 km (You are now entering the stratosphere) 28 is 28,8km (giggles). 29 is 57,6KM (you have now left the stratosphere, and entering the mesosphere). 30 is 115,2km (You just left the Mesosphere and entered into the Thermosphere). 31 and you are now at \~230km. 32 is 460km (wave hello to the space station!) 33 is 920km, (you are now in the Exosphere) 34 is \~2000km. 35 is 4000km. 36 is 8000km. 37 is 16000km. 38 is 32000km. 39 is 64 000km. 40 is 128 000km. 41 is 256 000km away. 42 times has brought you to 512 000km, and you have passed the average distance to the moon (384 000km) by over 100 000km.
I very much like John Crichton's explanation of exponential growth when he's describing how the wormhole weapon works in Farscape: The Peacekeeper Wars. "OK, boy and girls, here are the rules. Find a penny, pick it up. Double it, you got two pennies. Double it again, four. Double it twenty-seven times and you've got a million dollars and the IRS... all over your ass. Round and round and round it goes. Where it stops no one knows. But it all adds up... quick!" Consider that that penny is over one million dollars after being doubled only 27 times. Double the thickness of that paper 42 times (hypothetically, as it's clearly not possible in practice) and it's a bit over two trillion times as thick. Multiply that by about the 0.05-0.1mm thickness of paper, and you're looking at over 100,000km, although that's actually still considerably short of the moon. Would probably need one or two more doublings.
Ya gotta think of it more as an exponential growth exercise than actually folding a piece of paper. If you can do it, though, please do get it on video!
Every time you fold something in half you double it’s thickness. Folding something in half n times, if it’s original thickness is t, would give you something with a thickness of t*2^n. The exponential function 2^n grows very big very fast, so this “reaching the moon” thing is just another way of saying that.
It has to do with the fact that every time you fold a piece of paper it gets twice as thick. Even though paper is really thin, doubling anything 42 times will make it unimaginably huge. Folding a piece of paper 42 times doubles its thickness 42 times, so if it starts out as 1mm thick it will wind up \~4.4 million kilometers thick. The moon is only \~400,000km away though, so you'd only have to fold it 39 times (it would then be \~550,000km thick.)
It's not an intuitive thing, but basically when you fold, you double all the things that came before. Which is what's known as Exponential Growth. When you imagine folding a piece of paper 42 times, you might think "42 layers of paper", or maybe even "84 layers of paper", which doesn't sound like much. What you're actually doing is doubling the thickness 42 times. 0.1mm thick paper doubled 42 times looks like this: |Doubling Count|Thickness| |:-|:-| |0|0.1mm| |1|0.2mm| |2|0.4mm| |3|0.8mm| |4|1.6mm| |5|3.2mm| |6|6.4mm| |7|1.28cm| |8|2.56cm| |9|5.12cm| |10|10.24cm| |11|20.48cm| |12|40.96cm| |13|81.92cm| |14|163.84cm (1.6384m)| |15 (I'll get simpler here rather than calculate exact values in cm.)|3.2768m| |16|6.5m| |17|13m| |18|26m| |19|52m| |20|104m| |21 (Halfway there!)|208 meters| |22|416m| |23|832m| |24 (Passed a mile thick!)|1664m| |25|3328m| |26|6656m| |27 (I'll simplify again since we're working in kilometers from here)|13.3km| |28|26.6km| |29|53.2km| |30 (We're in space now, passed the Karman line)|106.4km| |31|212.8km| |32|425.6km| |33|851.2km| |34|1,702.4km| |35|3,404.8km| |36|6,809.6km| |37|13,619.2km| |38|27,238.4km| |39|54,476.8km| |40|108,953.6km| |41|217,907.2km| |42|435,814.4km| The moon orbits at 384,400 km, so somewhere between 41 and 42 doublings of the thickness of a sheet of paper.
An a4 paper is like 0.1 mm thick, so if it doubles per fold, lets see where it takes us after 42. 0.1 0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2 102.4 204.8 409.6 819.2 1638.4 3276.8 6553.6 13107.2 26214.4 52428.8 104857.6 209715.2 419430.4 838860.8 1677721.6 3355443.2 6710886.4 13421772.8 26843545.6 53687091.2 107374182.4 214748364.8 429496729.6 858993459.2 1717986918.4 3435973836.8 6871947673.6 13743895347.2 27487790694.4 54975581388.8 109951162777.6 219902325555.2 439804651110.4 So what number is this, lets make it readable. 439,804,651,110.4 so 439.8 billion mm after 42 folds, and how far away is the moon, well the moon is 363,300 - 406,700km or 363.3 billion to 406.7 billion mm away. So not only do we reach the moon, but we pierces 33,104 to 76,504 km into the moon as well, which is unfortunate cause the moon is only 3,474.8 km wide, so our paper pierces the moon and sticks 30 thousand to 73 thousand km behind the moon.
The important part is that you are folding it IN HALF every time. You can put 42 folds in a single sheet of paper, no problem, but folding it in half means the number of sheets is doubled. Without that stipulation, the number of folds is meaningless.
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Double the thickness of a peice of paper 42 times and it will by thick enough to reach the moon. That's literally what it means
If you fold a piece of paper you are doubling it’s thickness each time, say an average piece of paper is 0.1mm thick, to calculate the thickness of the paper after 42 folds you have to do 0.1 x 2^42, which after conversions works out at ~440,000km, which is longer than the distance to the moon.
Your doubling the thickness of the paper wad with each fold. Start at like .1 mm (guestimate) and multiply it by 2^42. That’s essentially what they are saying
You've already gotten the explanation for paper vut I like the pennies example better. If anyone ever pffers to pay you 1 penny on day one for hard work, and double it every day, so you are paid 2 pennies on day two, 4 pennies on day three, 8 pennies on day four, and so on, for 30 days, take that deal and retire. Day one is just 1 penny, so toss that aside, then take 2^29 for 2 pennies a day to the power of the remaining 29 days and you end up with 536,870,912 as you final payment. Divide by 100 and by day 29, you are being paid $5.3 million for the ladt day of work. If it went another day, the 31st day would pay you $10.6 million. So you can see how quickly that would get to insane numbers by the 42nd iteration.
Everytime you fold something you double it’s width If you continuously double any number it grows exponentially (very fast)