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Maybe.

It has defeated some of the greatest mathematicians and scientists of the last 400 years who have devoted hundreds of thousands of hours to prove it is not mere conjecture.

It all started innocently enough, (if cannonballs are ever innocent), when Sir Walter Raleigh simply wanted to know the ultimate way to pack cannonballs in the hold of his ship.

In 1611, German astronomer Johannes Kepler, best known for figuring out planetary motions, responded by saying just pile them up the same way that grocers stack oranges.

Namely, in the folds of another sphere below.

Now if you or I were asked, without knowing it was called face centered cubic packing, we might have said something like, "Yeah, I think that's probably the best way."

But when Kepler said it, it was genius.

It apparently takes more geniuses to prove it, which is the only way a conjecture can become a theorem.

(For example, the dropped piece of toast always falling on the buttered side down is mere conjecture, although I would award it theory like status.)

If you can ever squeeze drama out of this obsessive desire to prove Kepler right, author George Szpiro does it with, "Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World."

Turns out there are endless ways to pack spheres in a Euclidean  space and over the last four hundred years those minds went through all of them.

And now they're, well sort of "cheating" by using computers.

In 1953 Hungarian, László Fejes-Tóth showed that given sufficient computing power the problem could be solved.

Now, the American mathematician, Thomas Hales has either done it, or we're not quite sure, pending further scrutiny.

So what is finally the point in proving Kepler's conjecture so it can land in the prestigious Annals of Mathematics?

Is it as Albert Einstein said:

"Curiosity has its own reason for existing."

Or is it as Sir George Mallory said:

"Because it is there."

I know this group knows how to pack many astute answers into a rectangular box.

At least that would be my conjecture, which should take at least one day to prove.

J. Peterman

 

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49 Members’ Opinions
January 05, 2011 12:13 AM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Surely a debate about packing your cannon balls should be about boxer shorts vs. Y-fronts.

January 05, 2011 12:48 AM
29971 10photoviewsCom-100First-comFirst-photo Lee LaFontaine said...

The minds of women, at least some of them, are much more compicated, and fascinating, and the minds of mere mathmaticians.

January 05, 2011 2:47 AM
10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1Hr-10Hr-5 Stoney said...


Wonder how long it took for someone to try to take a ball from the bottom of the pile.

January 05, 2011 3:07 AM
Atticus_1 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 Bert said...

"Dr. Posin's Giants," a textbook authored by the host of a public tv kids show in Chicago in the 1950's, still sits next to my desk. One chapter devoted to the respective father of each great scientific theory. AND it has diagrams, drawn as if on a blackboard, to assist. Learned more there than in any classroom or from any textbook....

January 05, 2011 3:45 AM
Stage_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 JALOPKIN said...

STONEY:  Its just like the End-Stand Canned Dog Food Display at the Grocery Store ... There is one Mullet in every crowd .......  Usually, its an Eight year old Kid, but I have seen Adults do it too .......

January 05, 2011 5:30 AM
Com-100Com-300Com-500First-comHr-1 bebe said...

That photo is very aesthetically pleasing.................late meeting day,please send a cannonball my way as it would be much more pleasant............................great day all............

January 05, 2011 5:39 AM
Myself 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Spring Fragrance said...

Hazel....!! hahaha...surely that is a loaded statement?
 
On topic, just a few days ago, I posed a somewhat similar question, epistemologically, to RY here.        http://www.petermanseye.com/photos/292891
If I recall, he thinks round into squares is easier.
 
My choice of conjecture to be elevated to a theory is the 50-50-90 rule. Everytime there is a 50-50 chance of getting something right, there is a 90% probability you'll get it wrong
 
 

January 05, 2011 6:58 AM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Eeeeeeek! Panic! Son just 'phoned - is it OK if we come and visit for a long weekend, see you Thursday evening. Better start tidying up.

January 05, 2011 7:49 AM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

Just shake the darn thing, and the spheres will come to rest neatly piled in the optimum arrangement.


I had to re-read" face centered cubic packing"; my first attempt saw a "P" instead of "C".

January 05, 2011 7:58 AM
Atticus_1 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 Bert said...

Egyptians at least 2,000 BC were fantastic mathematicians, engineers, and they knew the laws of physics. To teach thousands of illiterate slaves how to move giant stone blocks up scaffolding with military precision meant they had to have working models, for illustrative purposes. Sure wish wood held up as well as stone, but even in dry climates wood, like most things organic, deteriorates. I would give a small fortune (emphasis on SMALL, I just sent the IRS a 4th quarter payment) to discover them, or even to see them.....

January 05, 2011 8:12 AM
Atticus_1 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 Bert said...

The cannon balls at Fort Sumter, Gettysburg, & assuredly at Arlington National Cemetery are stacked just as described in the "face-centered cubic packing" theorem.

The minds of women process information differently, not necessarily better or worse than the minds of men. It's similar to a prism, both viewers "see" reality, BUT perspective, life experience, and "the gender thing" matter. Had we had women in critical positions of historical leadership, decisions would not have been such that bravado trumped brains. I'm thinking their sons are seen more as treasure, and less as some testosterone-generated conduit to continue the family/country military tradition.

more on the honor roll
January 05, 2011 8:20 AM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

Bert,


That slaves were the workforce for the pyramids etc, is conjecture.


I believe, another theory holds, supporting the idea that these monumental building projects were the "public works projects" of their day.

January 05, 2011 8:21 AM
Pecos_tommy 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Tommy Typical said...

Be it a stack of gumballs in a gumball machine in front of an innocent child or a photo of cannonballs in a war from the history books or some alignment of molecules in the development of something far more sinister, the solution of "problems" such as this have the innocent genius of the Keplers and the Einsteins and the Hales of the world taken from the realm of satisfying curiosity to a world of practical use. A better mousetrap to make life better or a weapon to destroy used by a fanatic on those pesky Kurds or Tibetans. Evil is a thief that steals from mankind the creativity and the rewards from the highest levels of intellectual endeavor and innocents are killed in greater numbers and more diabolical ways. Be it a serial killler or a rogue nation-state, the enemy has been empowered with the same devices that the best of humanity have.  God with unlimited power is a beautiful thing. Flawed humans with god-like power is the most dangerous thing. An ancient but persistent and ever increasing problem that must be solved. The future in my opinion requires knowledge but also a wisdom that humans have not quite shown to date.

January 05, 2011 9:02 AM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Miss Blue~ re: your 7.49 - Hahaha!

January 05, 2011 9:34 AM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

Why are biscuits round?


I need to test a theory.


If I use a square  for a biscuit cutter, instead of the traditional round one, will I get more sweet potato biscuits out of the first dough roll-out and avoid successive rollouts, thereby saving time and avoiding the possibility of a few tough biscuits from the last roll-out.


Hummm....

January 05, 2011 9:42 AM
Pecos_tommy 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Tommy Typical said...

Miss Blue- At the last BA meeting, I stated clearly that I am Tommy-I am a breadaholic. If you have butter and jam, my dear. I will be happy to test any theory regarding biscuits.  

January 05, 2011 9:43 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 


The picture reminds me of the saying:


"It's cold enough to freeze the balls off a brass monkey"


OK, before anyone thinks I'm an advocate for frozen monkeys, know that a "Brass Monkey" was the 4 X 4 base upon which cannon balls were stacked awaiting their destiny. When it would freeze, the brass would contract at a differing rate than the iron cannon balls, throwing the neat pile slighly askew from the cold causing the balls to tumble off their perch.

January 05, 2011 9:47 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 
"For example, the dropped piece of toast always falling on the buttered side down is mere conjecture, although I would award it theory like status"
 
Carried forward, the buttered side falls down in greater proportion, according to square foot price of the flooring. The higher the cost, the more likely it is to fall buttered/jellied/mayo'd and mustard/(add your favorite spread)...down.

January 05, 2011 9:58 AM
4224 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 RoadYacht said...

and Ummgawa, do not forget the modifying factor of pet hair on the buttered side down; is it a further attractant? Does it amplify gravity,or merely redirect the downward force?

January 05, 2011 9:59 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 
Pythagoras' Pick-Up Line:
 
"Hi, my name's Pythagoras. Perhaps you've heard of my theorem?"

January 05, 2011 10:06 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 


Here's a mathmatical limeric:


((12 + 144 + 20


 + (3 * 4^(1/2)))


 / 7)


+ (5 * 11)


= 9^2 + 0

January 05, 2011 10:14 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 


RY- it increases the likelyhood of it falling buttered side down exponential to the frequency of the day in between the times the floor is swept. If floor is swept once a week, the likelyhood of it falling spread down increases as each day passes, at zenith on the sixth day. If it's a long haired cat, well, I haven't done the calculations. Lots of hair means it doesn't matter which side falls down. If swept every day the likelyhood of it falling is equally proportionate to the time when the cat is in the house and if you are eating over top of it.


Now the likelyhood of it falling on the cat buttered side down, if your cat is always under your feet, may be uncalculatable, but may be in direct proportion of how much said cat likes buttered bread.

January 05, 2011 10:14 AM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Much to the delight of the cat, instead of being a Domestic Goddess, I've been playing aroung trying to stack my glass marbles. Ummgawa is right about the brass monkey - you need some sort of frame at the base.
Miss Blue~ Iv'e made square bisquits for years, for the reasons you cite.

January 05, 2011 10:21 AM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Can anybody come here and crawl round the floor in search of my marbles? I seem to have lost most of them. Cat - the culprit of chasing them to under furniture is busy licking butter off her fur from my dropped slice of toast. Today is not going well.

January 05, 2011 10:25 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

Answer:
 
A Dozen, a Gross and a Score,
plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more.


January 05, 2011 10:32 AM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

It has been long known = I haven't bothered to check the references
It is known = I believe
It is believed = I think
It is generally believed = My colleagues and I think
There has been some discussion = Nobody agrees with me
It can be shown = Take my word for it
It is proven = It agrees with something mathematical
Of great theoretical importance = I find it interesting
Of great practical importance =This justifies my employment
Of great historical importance =This ought to make me famous
Some samples were chosen for study = The others didn't make sense
Typical results are shown = The best results are shown
Correct within order of magnitude = Wrong
The values were obtained empirically. The values were obtained by accident
The results are inconclusive......... The results seem to disprove my hypothesis
Additional work is required.......... Someone else can work out the details
It might be argued that.............. I have a good answer to this objection
The investigations proved rewarding.. My grant has been renewed

--- From: chris@labtam.labtam.oz.au (Chris Taylor)
Special Category: Definitions and terms A brief guide to Scientific literature

January 05, 2011 10:36 AM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 


RY- if you increase the possibility that the dropper of the buttered toast/bread/bagle or whatever edible vehicle might be holding the subject condiment might like cat hair in his/her favorite consumable. That might cause the likelyhood of the drop to decrease. If one considers that the presence of cat hair is a non issue, then one could extrapolate that the likelyhood might decrease to zero, and improper handling of buttered bread might disappear alltogether.


I, for one, don't like cat hair, even on a cat. I don't have an inside cat. I don't eat buttered bread outside, especially around our cat.


 


The possibilities are endess.

January 05, 2011 10:54 AM
Pecos_tommy 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Tommy Typical said...

Kinky called my partner yesterday and informed us that Little Jewford is coming to town on the 20th when he will join us for our book signing. I say T for Texas T for Tennessee. Posted a picture on my Eye Site that the boys allowed us to use. He will be signing his latest book and the classic What Would Kinky Do? Subtitle-How to unscrew a screwed-up world. With a new congress, it seems appropriate. I am wearing boots today.

January 05, 2011 12:01 PM
10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewHr-1Hr-10Hr-5 Mooseloop said...

Creation of the human world on Oct. 23, 4004??! How naive of James Ussher!
Anyone who has read Jean Auel knows that it was much earlier than that!
What a card! Ussher must have been also writing one of his hip-hop songs at the same
moment as that theory! Ha!
 
Stacking balls is one of those theoretical dilemmas that does not relate to my life at all.
I can see why the ship captains of the 1600-1700's would be concerned, but do we really need to know the theorem for the optimum count? I cannot imagine my grocer consulting a mathmatical equation to stack up those oranges, apples, and plums in such neat piles!
 
For the most stuff in the smallest space, consult anyone who has moved many times! I can bet you that I can get more stuff into a car trunk (boot, Hazel), or into a suitcase, than the average person! I have moved so many times that I can just look at a pile of stuff and mentally "see" where what will fit, and what will not! When I go to the beach with my 4-5 gal pals, they always stand back and ask me to pack the car! Anyone moving soon? I'll help if I can. No charge. I love the satisfaction of getting it all in there! Others into that?

January 05, 2011 12:42 PM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

RY


There are those of us, just slightly out of round, who roll out of formation, sending all postulates and theorems out the window.

January 05, 2011 1:04 PM
1-dscn1106-4 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 PARK4 said...

Miz Hazel: I thought biscuits are round because that's the shape of the refrigerated tube that they come in, you know, the one Pillsbury makes?  Then there's the notion that it's easier to make a round dough thing than it is to make a square dough thing, if you don't have cutters on hand.  Especially for someone without any baking skills whatsoever (that would be me), in spite of the fact that I regularly watch Top Chef and Chopped...........The truth is, I really shouldn't comment on any topic that involves the word "cubic."  My eyes see the word, but nothing further happens...;)   

January 05, 2011 1:06 PM
10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1Hr-10Hr-5 Stoney said...


Wholey Balls!

January 05, 2011 1:18 PM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

PARK4~ I have a stainless steel thing in my kitchen that was, I believe, part of a cover for a ventilation system. It's 12 inches x 12 inches of two inch square grid & is a brilliant bisquit cutter.

January 05, 2011 1:18 PM
29971 10photoviewsCom-100First-comFirst-photo Lee LaFontaine said...

Miss blue-Loved what you said; I used to be in the grant business, too. It was fascinating...but occasionally disappointing.

January 05, 2011 1:19 PM
10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Lynn830 said...

Mooseloop, Some people have a visual sense and others do not.  And it seems to be genetic.  My son and I can pack a moving van so that nothing moves.  Stuff is also padded when needed and tied in.  And nothing breaks.  A friend of my son and his father moved a truck full of stuff from Virginia to New México and wondered why so much was broken.  It was simple: everything was packed loosely, nothing was padded and nothing was tied down.  That is a recipe for disaster.
There are so many conjectures and occasional assertions in mathematics that it is amazing.  Eventually they get solved or disproven.  And frequently they add to the knowledge of mathematics and arithmetic, and then get a practical application that makes our lives easier.  Hooray for mathematicians.  That's a tough profession.

January 05, 2011 1:20 PM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

 


Park4


Upon further examination, it would seem the squares' corners would have the tendency to break off; besides, I find a soft round shape more pleasing than an angular square one.


I will share with you my very simple recipe for sweet potato biscuits....I'll send it via e-message later in the evening.


How are you feeling? Last I heard you were battling a sinus infection.


Stoney...


male primogeniture?

January 05, 2011 1:21 PM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Sorry, I forgot, CUBIC ~ the instructions Noah got for building the ark were even worse than what we get these days with flat-pack furniture.

January 05, 2011 1:40 PM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

 
HL....   

Posterior probability dictates the biscuits only become" approximately" cubic or cylindrical upon completion of baking. With my recipe, I find ¼ handbreadth about the right thickness for the prebaked dough.

January 05, 2011 1:51 PM
Com-100Com-300Com-500First-comHr-1Hr-10Hr-5 hazel leese said...

Miss Blue et al~ biscuits/bisquits morph in the oven. Who cares as long as they taste OK? You have to keep the ones that are the "right" shape  for visitors.

January 05, 2011 3:16 PM
28961 10photoviewsCom-100Com-300Com-500First-comFirst-photoFirst-videoHr-1 Ummgawa said...

 


A biscuit can look like a runt-over-possum as long as it's hot and there is butter and honey present.

January 05, 2011 3:31 PM
Myself 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Spring Fragrance said...

Miss Blue 10.32 AM....I like that!!


Mooeseloop...haha!! When can you ship? I could do with some help right now as am moving right now.  Like you, I have moved countless times in my last decade or so. The worst was relocating to a different country.


2+2=5? New perspective, empirical and observable, perfectly logical....


A western anthropologist is told by a Voohooni (??) that 2+2=5.
The anthropologist asks him how he knows this. The tribesman says, "By counting, of course. First I tie two knots in a cord. Then I tie two knots in another cord. When I join the two two cords together, I have five knots.

January 05, 2011 4:12 PM
Stage_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1Hr-10Hr-5 JALOPKIN said...

Five Knots Maximum, Pulling Out of The Harbour .......
 
and
 
If I am Not makin' Catheads ... I roll my dough out to about an inch thickness, and cut it into Squares with a Tableknife ...  Some of the Bisquits have one rounded edge, sorta ... but they eat just as Good .......
 

January 05, 2011 4:29 PM
Pecos_tommy 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 Tommy Typical said...

Ivan- No wake zones always give me trouble-
***
When Dooley Wilson (Sam) tickled the ivory and played it again. All the solutions to all the problems (that didn't amount to a hill of beans in the end) were solved. So sing-
 
This day and age we're living in
Gives cause for apprehension
With speed and new invention
And things like fourth dimension.

Yet we get a trifle weary
With Mr. Einstein's theory.
So we must get down to earth at times
Relax relieve the tension


And no matter what the progress
Or what may yet be proved
The simple facts of life are such
They cannot be removed.]


You must remember this
A kiss is just a kiss, a sigh is just a sigh.
The fundamental things apply
As time goes by.


And when two lovers woo
They still say, "I love you."
On that you can rely
No matter what the future brings
As time goes by.


Moonlight and love songs
Never out of date.
Hearts full of passion
Jealousy and hate.
Woman needs man
And man must have his mate
That no one can deny.


It's still the same old story
A fight for love and glory
A case of do or die.
The world will always welcome lovers
As time goes by.


Oh yes, the world will always welcome lovers
As time goes by.


© 1931 Warner Bros. Music Corporation, ASCAP

January 05, 2011 5:20 PM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

 
Ohrwurm  !!!

January 05, 2011 6:52 PM
Com-100Com-300Com-500First-comHr-1 bebe said...

PARK...................I hope you are well on the way to being mended sinus wise....................I love round biscuits w/ butter..........mmmmmmmmmmmmmmmm......................
 
MISS BLUE..................have you ever tried James Beard's cream biscuits? I just have a feeling you may have & if so, aren't they wonderful & tender & soooooooooooo easy it feels like cheating..............they also make a great top for chicken potpie........................
 
STONEY................People have "axed" for things all day.............please make it stop.
 
Hope JAX & PL are feeling better too......................
 
 

January 05, 2011 7:44 PM
Poison_dart_frog_2 10photoviewsCom-100Com-300Com-500First-comFirst-photoHr-1 Miss Blue said...

Bebe, nice to see you!


I have not tried that particular recipe, but, it seems very much like one I have used from the American Heritage Cook Book.

January 05, 2011 10:40 PM
4224 10photoviews10videoviewsCom-100Com-300Com-500First-comFirst-photoFirst-reviewFirst-videoHr-1Hr-10Hr-5 RoadYacht said...

as my wife was fond of saying,about my dog's appetite;round is a shape

Prime Web

Goldbach's Conjecture

Goldbach's Conjecture singnet.com Take a look at an interesting article we found.

Euler's Mathematical Contributions

Euler's Mathematical Contributions suite101.com Take a look at an interesting article we found.

What is Kepler's conjecture

What is Kepler's conjecture knowledgerush.com Take a look at an interesting article we found.

Honor Roll


The cannon balls at Fort Sumter, Gettysburg, & assuredly at Arlington National Cemet...

-Bert

Jan. 05, 2011 8:12 AM

read full opinion



Poll

Which conjecture should be elevated to theory?

  • If something seems too good to be true, it probably is If something seems too good to be true, it probably is 38%
  • The probability of anything happening is in inverse ratio to its desirability The probability of anything happening is in inverse ratio to its desirability  8%
  • The other line moves faster The other line moves faster  15%
  • When all else fails, read the instructions When all else fails, read the instructions 31%
  • You tell us You tell us 8%

Yesterday's Discussion

Humming, which goes back in time, may now have health benefits.

 

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