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Hair: Newsletter Challenge (07/12/05)

Posted July 12, 2005 7:00 AM

The question as it appears in the 07/05 edition of Specs & Techs from GlobalSpec:

You come home to find the kids arguing yet again (and it's just the beginning of summer vacation… sigh)! This time they're arguing about, of all things, whether any two people on the planet have the exact same number of strands of hair on their heads. Your daughter contends it's a common occurrence; but your son says, "No way! Well… maybe in the case of twins it's possible, but otherwise, people are like snowflakes, no two are exactly the same." When your daughter says she can prove it, your son challenges her to do so. Can she?

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Power-User

Join Date: Feb 2005
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#1

Hair count challenge

07/12/2005 9:10 AM

Do the math. If everyone had a different number of hairs on their head, one person would have 1 hair, 1 person 2, the next 3, and so on up to 6 billion (est). Since the average hair diameter is .001 inches, and even if you assume a dense pack with no space between hairs, you would need 4712 sq. in. of headspace or 33 sq feet of headspace to fit all that hair. Roughly an 8 ft diameter head.

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Guru
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#2
In reply to #1

Re:Hair count challenge

07/12/2005 11:40 AM

Isn't the sensible answer that there is a distribution of the number of hairs on people's heads and so for any given number of hairs, probablility maths shows us that more than one person would have the same number of hairs?

However, what I suspect "my" daughter is about to do is bring in Frank from two doors down and sit him next to her grandfather ... and point out that that both have NO hairs on their heads. And to rub it in, she'll mention that she's looked up on the internet the number of completely bald people in the world.

Then we'll get into the age-old debate of whether zero can be considered a number...and whether black is actually a colour. That should keep us all entertained for the entire summer holidays!

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The Engineer
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#4
In reply to #2

Re:Hair count challenge

07/12/2005 1:46 PM

You'd be hard pressed to find a truly bald person. Most balding people lose hair off the crown of their head. Those who appear completely bald shave the rest of their hair. I think shaved hairs still count, so the daughter couldn't make that argument. That first response (8 foot head) is the only way I can see of proving it.

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#5
In reply to #4

Truly bald

07/12/2005 1:55 PM

Yes, there are folks who are tryly bald (and beyond): Alopecia Areata. While this does nothing to answer the Challenge Question, I felt it was important to clear up a misconception.

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The Engineer
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#6
In reply to #5

Re:Truly bald

07/12/2005 2:28 PM

Yes, I guess that people with this disease would have the same number of hairs on their head. So I guess this would make the earlier point valid. I still think the other explanation is stronger.

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#3
In reply to #1

Re:Hair count challenge

07/12/2005 12:08 PM

I know some people with heads that big.........

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#7

Hair

07/12/2005 3:59 PM

Well right out of the gate the easiest way for her to win the bet is to stand two bald guys side by side and if they are truley as bald as cue balls, she wouldn't enen need to count anything. Aside from that the average head has 100,000 hairs, there is 6,000,000,000 people on the planet. to me the math, based on those two numbers alone is that there is 60,000 people on the planet with the same number of hair as me.

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#8

Your hairs are numbered...

07/13/2005 10:27 AM

This is an important learning lesson for your son. When discussing anything with a woman, you MUST first define the challenge. He is claiming a difference, "like snowflakes," but she only claimed "exact same number of strands." His point may well be valid; it would be impossible for her to find (and prove) that any two people had the same head, pattern, number, color, texture, etc. as even completely bald men have different hair follicle patterns where their hair 'used to be,' But the challenge from her is only quantity. Non issue on several fronts.

1) The above-mentioned totally bald men, whether by genetic disorder, disease, or chemo, would all be zero (well, assuming we count 'zero' as a 'number' of strands...;)

2) Everything up from there is a statistical distribution on a curve, with many millions of identical quantity.

3) Straight mathematical analysis would also prove that it would be impossible for even the 6+ billion around now, not counting history, to each have a different number of hairs, as the average (back to sadistics) is less than 150,000, resulting in many people needing to have around 40,000 heads, each, to hold all the hairs they would require to be 'differently haired' starting with the first guy to have 400,000 or so, requiring his second head based on max density on the first one, and going from there...and Sinbad thought the hydra was something - can you imagine Tina Turner with 40,000 mouths?

4) The average human loses 40-100 hairs every day, at different rates, resulting in a shift throughout any given hour as to which people have the same number of hairs at that moment.

5) Some of us aren't growing those hairs back, and continue to slide down the curve toward the 'retired engineer's zone'...where most hairs have been pulled out solving the world's great problems, not to mention the occasional GlobalSpec challenge question...;)

PS - lucky for us, only private suckers are sinking millions into those amazingly unsuccessful 'embryo stem cell' boondoggles, though they're still trying to add our tax money to throw into the pit-of-no-treatements (a true zero, as in none, except disasterous new cancers created)... BUT, amid the hundreds of disease treatments and cures developed from adult stem cells is: more hair on-the-way...http://my.webmd.com/content/article/9 3/102390.htm?z=1728_00000_1000_nb_01 too bad it's just for mice right now, eh? ;)

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Power-User

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#9

For certain.

07/13/2005 10:31 AM

1) The number of people on the earth outweigh the average maximum hairs on your head(80K-140K) by a large factor. A good analogy is like having 140K chairs in a game of musical chairs. When you have 6 billion people playing, there's a lot of sitting on laps that is going on. 2) The probability of two randomly picked people sharing the same number is then at least 1:140,000 and it's interesting to note that by calculating the probability of a match occuring, if you were to get 441 people together, there would be a greater than 50% chance of a match within the group. How's that for an AP Statistics grad?

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Commentator

Join Date: May 2005
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#10

Hair challenge

07/18/2005 4:00 AM

By my estimate, there will exist at any one time 17% of the global population with exactly the same number of hair strands. 12% of he population will be totally bald, and the remaining 71% will differ.....Having said that, 78% of statistics are made up on the spot (including this one!) Hope this helps

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#11
In reply to #10

Re:Hair challenge

07/18/2005 11:25 AM

As Homer says: "Oh, people can come up with statistics to prove anything, Kent. 14% of people know that."

Homer Simpson that is, not the bard of Greecean epics.

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#12

And the Answer is...

08/02/2005 1:26 PM

As written in the 7/19 issue of Specs & Techs from GlobalSpec:

Sure she can, using proof by contradiction as the basis of her argument. Assume, for purposes of the proof, that person number 1 has one hair on his head, the next person has two, the next person has three, and on it goes. Given the total population of planet earth (billions of people), a point will be reached (rather quickly, actually) when there is not enough room on a human scalp to hold all the hair. So theoretically, there are thousands upon thousands of people who have the exact same number of hairs growing on their heads. (And undoubtedly, those with the most can be seen in shampoo ads.) So your daughter wins this one.

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