OT Surprising Mathematical Result

[keno]

Fold in half a VERY LARGE dollar bill, thickness 0.0043 inches, 100 times. Putting aside the impossibility of folding a piece of paper that many times, what would you guess is the thickness of the final product?

keno

[Sandy]

Interesting question.

You would be setting up a progression of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 80,192,..... since on each fold, you would be doubling the number of previous folds, and hence doubling the previous thickness. So by the time you got to 100 folds, you would have zillions of doubled thickness. Hence, you would be a zillions times the .0043 inches, which would yield a surprisingly large number. I don't know what, but it would be very large, I would guess, possibly approaching infinity if it really got out of hand. I guess that it would be easy to figure our using sequences, and limits, but I am too old to even think about that.

Anyway, without thinking any further, I would say the answer is surprisingly LARGE.

Simple Sandy

PS- Hope that you are doing well.

PPS- Do I win a little prize for my thoughts above, or am I just a moron??

[keno]

moron.

From a former math teacher I expect an ANSWER. From an economist I expect a theory.

keno

[Sandy]

By using my post above, after only 13 folds, you would have 80,192 of the original thickness. That would be 80,192 X .0043 = 344.8256 inches, and you barely have begun. My final answer is it would be approaching infinity. It would take you a very, very long time to even try to write down how big it would be getting. In fact, you couldn't, as it would be increasing so fast. Think infinity...


Sandy

[nationsgirl]

146 Billion Light Years

2 to the 100th power * .043 / 5280 / 12 / 365 / 24 /186000//3600/1000000000

[Sandy]

Ok- answer- infinity.................(or close)...... :)



Moron Mirman

[znfdl]

2^100 = 1.26765E+30
Thickness = 0.0043
Answer = 5.4509E+27


Oh by the way I am an Economist and proud of it ;)

[Bill Bove]

what's a dollar :confused:

[Sandy]

2^100 = 1.26765E+30
Thickness = 0.0043
Answer = 5.4509E+27


Oh by the way I am an Economist and proud of it ;)

Yeah, but because you are an Economist, you will change your answer in a couple of months anyway, and besides, you have no pressure on you, as economists are never right anyway. :) I was a high school math teacher, so Keno holds me to a higher standard. Little does he know that I got fired as I couldn't add. :)

By the way znfdl, does your answer take into consideration inflation or which party is in office? :rolleyes: :)


Moron Mirman

[Sandy]

what's a dollar :confused:

Excellent point. As a Serotta Ottrott ST owner, dollars are not even allowed in my house. I start at $100. I have standards, you know! :rolleyes:


Snobbish Serotta Sandy

[William]

Interesting question.

You would be setting up a progression of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 80,192,..... since on each fold, you would be doubling the number of previous folds, and hence doubling the previous thickness. So by the time you got to 100 folds, you would have zillions of doubled thickness. Hence, you would be a zillions times the .0043 inches, which would yield a surprisingly large number. I don't know what, but it would be very large, I would guess, possibly approaching infinity if it really got out of hand. I guess that it would be easy to figure our using sequences, and limits, but I am too old to even think about that.

Anyway, without thinking any further, I would say the answer is surprisingly LARGE.

Simple Sandy

PS- Hope that you are doing well.

PPS- Do I win a little prize for my thoughts above, or am I just a moron??

Sandy,

Let's test your theory, though in an easier manner to complete.

I will open a bank account on the 1st of the month. Each day you make a deposit. On day one you deposit a penny. On day two deposit two pennies. Day three four pennies, day four eight pennies, day five sixteen pennies, and so on. Double the amount each day and let's see what we have accumulated by the end of the month. This will be fun. :banana:

I'll open the account right away and you be ready on the first. :) What do you say? Let's show the forum how a real experiment is done.




William :D

[CNY rider]

Yeah, but because you are an Economist, you will change your answer in a couple of months anyway, and besides, you have no pressure on you, as economists are never right anyway. :) I was a high school math teacher, so Keno holds me to a higher standard. Little does he know that I got fired as I couldn't add. :)

By the way znfdl, does your answer take into consideration inflation or which party is in office? :rolleyes: :)


Moron Mirman


Economists are the people who bring us inflation reports ex-inflation (i.e. CPI but let's not count food and gasoline, it's not like people really use much of those things anyway!) :banana:

[Sandy]

Great idea. But why open a new account? We can just use one that you already have. Just give me the account number and I will make my first withdrawal, ....I mean deposit...... :rolleyes:


So Super $$$$$$$ Slick So Serotta Sandy

[William]

Great idea. But why open a new account? We can just use one that you already have. Just give me the account number and I will make my first withdrawal, ....I mean deposit...... :rolleyes:


So Super $$$$$$$ Slick So Serrota Sandy

Not a bad idea. But, Rhea Basset wants to be involved in this little experiment. She'll stop by your place each day. Just put the money in her saddle bags. Give her a little pat on the head, maybe a belly rub, and then she'll deliver it to me..I mean the bank for deposit.

BaaWoo!!!
BaaWoo!!!




William :banana:

[Sandy]

Now that sounds even better. After a few pats on the head and belly rubs, Rhea Basset will choose to live here with me. I will have a great dog AND new saddle bags. :)


Seemingly Steadily Slicker Serotta Sandy

[znfdl]

Yeah, but because you are an Economist, you will change your answer in a couple of months anyway, and besides, you have no pressure on you, as economists are never right anyway. :) I was a high school math teacher, so Keno holds me to a higher standard. Little does he know that I got fired as I couldn't add. :)

By the way znfdl, does your answer take into consideration inflation or which party is in office? :rolleyes: :)

Sandy:

I also have done graduate studies in Math, but I try to keep that quiet.

Economists are always right, as we have the lattitude to change our assumptions. ;)

As for inflation, I leave that to Fly.

[William]

Now that sounds even better. After a few pats on the head and belly rubs, Rhea Basset will choose to live here with me. I will have a great dog AND new saddle bags. :)


Seemingly Steadily Slicker Serotta Sandy


You are so super sly Serotta Sandy. :no:




William ;)

[Karin Kirk]

I'm not an economist, but I'm a geologist and I always say that only those two professions are good at thinking about very large numbers.

I whipped up a quick Excel spreadsheet, with 0.0043 times two, repeated 100 times. I can't do math in my head at all, but I can do it with Excel. I got the same answer as znfdl, which is 5.45 with 27 zeros after it.

Let's see... that comes out to 14 billion light years - off one order of magnitude from nation's girl.

Yo, Sandy. Just because a number is large, does not mean it's more or less infinity! Think big, pal! :)

[Sandy]

Yo, Karin. I realized that the number was really really big, but still finite, so certainly it could be a lot larger. I just thought that it would be so large, that at that point it wouldn't make much difference, one way or the other. I think that the answer given by you and/or znfdl are estimates anyway.

So consider my weight- If it was doubled 100 times, do you really think that Dave could ever make me a bike that wouldn't fall apart as soon as I sat on it??? Although my weight would be finite, couldn't we just say infinity, as it would be so large, anyway. Heck, the earth might just fall out of orbit because of the added weight!! :rolleyes: :)


Weightless in space,


Sandy

[djg]

Fold in half a VERY LARGE dollar bill, thickness 0.0043 inches, 100 times. Putting aside the impossibility of folding a piece of paper that many times, what would you guess is the thickness of the final product?

keno

What do you mean by "a VERY LARGE dollar bill"? Do they come in different sizes? Did I miss something in one of Annheida Ride's posts?

So the doubling thing is a big number, but it's pretty straightforward, nu? I thought the surprising mathematical result was going to have to do with accounting, systematically, for the folds themselves.

[Sandy]

Big enough to fold it 100 times. I folded it 2 times and I was too weak to go any further. :)


So Strong So Serotta Sandy

[djg]

[QUOTE=znfdl

I also have done graduate studies in Math, but I try to keep that quiet.

[/QUOTE]

Geek. ;)

[Karin Kirk]

Yo, Karin. I realized that the number was really really big, but still finite, so certainly it could be a lot larger. I just thought that it would be so large, that at that point it wouldn't make much difference, one way or the other. I think that the answer given by you and/or znfdl are estimates anyway.

So consider my weight- If it was doubled 100 times, do you really think that Dave could ever make me a bike that wouldn't fall apart as soon as I sat on it??? Although my weight would be finite, couldn't we just say infinity, as it would be so large, anyway. Heck, the earth might just fall out of orbit because of the added weight!! :rolleyes: :)


I hear ya, Sandy. I'm still not too keen on calling a large number "infinite" just because it's so large that it's crazy, impractical, or unwieldy. In your example, your weight is just waaaaay outside the parameters of even Dave's super-strong frames. I think I'm just being overly literal here, and you are looking at things from a more practical point of view.

Now, what would happen if we started out with two kittens, and doubled the number of kittens in the house every day. After a year, how much kibble would they consume?

[Richard]

interesting factoid -- I believe the practical limit for folding any paper in half, regardless of starting size, is 7 times.

[Karin Kirk]

interesting factoid -- I believe the practical limit for folding any paper in half, regardless of starting size, is 7 times.

Oh, the Mythbusters had fun with that one. They used a piece of paper that was like the size of a football field and were able to fold it a dozen or so times. I don't remember the exact number, but they busted the myth!

[bcm119]

With apologies to Anheida-

If you took a Federal Reserve Note and folded it 100 times, it would probably just turn back into thin air, since thats what its made outta anyway.

[Marron]

"The Logic of Failure" which devotes considerable attention to the problem human brains have with compounding anything and the consequence there of, and the new book by Nassim Taleb," The Black Swan".

[keno]

kudos. And Marron, this particular problem came from a book by Scott Plous, "The Psychology of Judgment and Decision Making". The person answering is to give a high and low figure and his degree of confidence that the actual answer falls between the two. Hard to imagine that few in a billion would think that the answer, in somewhat humanly familiar terms, would be in light years, let alone 14+ billion of them.

To prove your point, Marron, I was recently with a group of several executives whose average annual compensation is over a million bucks (and make $100,000,000-type decisions with some regularity) and I posed the problem. One guessed "a few inches", another said "alot", a third said "it's irrelevant", and the rest were similarly noteworthy. But, then again, they're making the big bucks while I could answer the question and never did.

Taleb's stuff is great, BTW. If you like great investment thinking, take a look at www.efficientfrontier.com.

keno

[Xyzzy]

http://www.mersennewiki.org/index.php/List_of_known_Mersenne_primes

Kinda makes 5450897580981386426435823783.1168 inches seem miniscule.

PS - Some of those files have pretty big numbers. We are not responsible if your browser acts a bit funky.

[Xyzzy]

I whipped up a quick Excel spreadsheet, with 0.0043 times two, repeated 100 times. I can't do math in my head at all, but I can do it with Excel. I got the same answer as znfdl, which is 5.45 with 27 zeros after it.
Just for fun, check out bc (http://www.gnu.org/software/bc/), or a similar arbitrary precision calculator:

$ echo '2^100*.0043' | bc
5450897580981386426435823783.1168

[keno]

the folding factoid answer is interesting. http://pomonahistorical.org/12times.htm

keno

[vaxn8r]

With apologies to Anheida-

If you took a Federal Reserve Note and folded it 100 times, it would probably just turn back into thin air, since thats what its made outta anyway.
+/- 1

Beat me to it ;)

[Ahneida Ride]

BEAT ME TO IT.

They are FRN'S not dollars and the method of our enslavement.
Inflation is a tax and the most oppressive !!!!!

[gasman]

BEAT ME TO IT.

They are FRN'S not dollars and the method of our enslavement.
Inflation is a tax and the most oppressive !!!!!


True, but every country has an economy based on Euros,Yuan, etc.

What is the alternative ? Trading for goods and services without money ?

[Sandy]

kudos. And Marron, this particular problem came from a book by Scott Plous, "The Psychology of Judgment and Decision Making". The person answering is to give a high and low figure and his degree of confidence that the actual answer falls between the two. Hard to imagine that few in a billion would think that the answer, in somewhat humanly familiar terms, would be in light years, let alone 14+ billion of them.

To prove your point, Marron, I was recently with a group of several executives whose average annual compensation is over a million bucks (and make $100,000,000-type decisions with some regularity) and I posed the problem. One guessed "a few inches", another said "alot", a third said "it's irrelevant", and the rest were similarly noteworthy. But, then again, they're making the big bucks while I could answer the question and never did.

Taleb's stuff is great, BTW. If you like great investment thinking, take a look at www.efficientfrontier.com.

keno

So what was wrong with my answer or nationsgirl's answer? The 2 to the 100th power times the thickness of the bill she gave is the most precise answer given. I didn't give such a precise answer as I wanted to place emphasis on how really astonishingly large the number is. Don't we get a little bit of credit?


Sad Sandy

[keno]

no.

keno

[Sandy]

You are tough! When I grow up and get big and strong, and am the first to be able to actually do the 100th folding of the bill, I am going to be sure that you are inside that bill someplace--fold 45 or so.... :)



Superman Serotta Sandy

[Bud_E]

Ok- answer- infinity.................(or close)...... :)



Moron Mirman

FWIW I came up with the same answer! ( And I was a math major ) :banana:

[Sandy]

Actually, my analysis was correct, but I decided not to actually quantify the answer, as the given number might not project the enormity of the actual answer, so I just gave my analysis, and said that it would be really large. As the answer is clearly finite as 100 is a finite number (or close), I just threw out infinity to describe how really large it is, knowing that the number was finite. I think that next time I will just keep quiet.


Silent Sandy

[Kevan]

and I don't think mathmatics had anything to do with it.

Signed,

Doubled over laughing Kevan

[stevep]

way way back for a time i was a substitute math teacher.
i used to use similar example to entertain classes.
a man rescued the daughter of a wealtyhy shah. the shah offered the man any prize he wished.
the man simply asked for a 31 day month calendar to be produced.
on the 1st day a single piece of rice, the 2nd- 2 pieces, 3rd 4, 4th 8 and double the pieces until the calendar is completed.
the shah quickly agreed because he did not really understand a geometric progression.

i kinda forget the answer in the end but its a lot. easy enough to calculate...never mind 100 times.
i think it came out to more rice than has been produced in history...or some such. the shah probably put the guy to death when he realized he had been outsmarted.

[William]

way way back for a time i was a substitute math teacher.
i used to use similar example to entertain classes.
a man rescued the daughter of a wealtyhy shah. the shah offered the man any prize he wished.
the man simply asked for a 31 day month calendar to be produced.
on the 1st day a single piece of ride, the 2nd- 2 pieces, 3rd 4, 4th 8 and double the pieces until the calendar is completed.
the shah quickly agreed because he did not really understand a geometric progression.

i kinda forget the answer in the end but its a lot. easy enough to calculate...never miond 100 times.
i think it came out to more rice than has been produced in history...or some such. the shah probably put the guy to death when he realized he had been outsmarted.

Which reminds me, it's the 22nd Sandy. Rhea Basset will be by to pick up her $41,943.04. I think for Wednesday you should switch to cashiers checks since here on out things will be getting heavy. Hey, she's not a LLama you know...




William :rolleyes:

[Sandy]

Which reminds me, it's the 22nd Sandy. Rhea Basset will be by to pick up her $41,943.04. I think for Wednesday you should switch to cashiers checks since here on out things will be getting heavy. Hey, she's not a LLama you know...




William :rolleyes:

So William, would you mind a cashiers check drawn on Milk Bone Biscuits Bank of America?? If the check is no good (bet on it), Rhea Basset can always eat it! :) :)


Sandy

[Bud_E]

Actually, my analysis was correct, but I decided not to actually quantify the answer, as the given number might not project the enormity of the actual answer, so I just gave my analysis, and said that it would be really large. As the answer is clearly finite as 100 is a finite number (or close), I just threw out infinity to describe how really large it is, knowing that the number was finite. I think that next time I will just keep quiet.


Silent Sandy

I was agreeing with your answer ! Your description communicated the correct answer to me just as clearly as going to the trouble of figuring it out to the last digit ( + or - 3 mm ). :beer: