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Math Help - Is it mathematically possible to be 1/3 Italian?

  1. #1
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    Is it mathematically possible to be 1/3 Italian?

    Is it mathematically possible to be 1/3 of an ethnicity? I won't go into how this debate came up between me and my brother-law, and neither of us are smart enough with math to disprove the other on paper, so I'm hoping someone here can provide an answer.

    He says it is NOT possible to be 1/3 mixed ethnicity because, no matter what, our makeup is always a product of two. There can only ever be two contributers, and thus no matter how many hypothetical generations we go up a family tree, and how we slice and dice the possibilities, a person can never become 1/3 of anything.

    I say, since the hypothetical ancestral possibilities are infinite, that no number can be excluded from a possible result, and that there simply has to be some combination, even if it take 100 generations of division, that will result in a person being exactly 1/3 Italian (or substitute your favorite ethnicity).

    Who is right, and can it be proven?
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  2. #2
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    Quote Originally Posted by silverado View Post
    Is it mathematically possible to be 1/3 of an ethnicity? I won't go into how this debate came up between me and my brother-law, and neither of us are smart enough with math to disprove the other on paper, so I'm hoping someone here can provide an answer.

    He says it is NOT possible to be 1/3 mixed ethnicity because, no matter what, our makeup is always a product of two. There can only ever be two contributers, and thus no matter how many hypothetical generations we go up a family tree, and how we slice and dice the possibilities, a person can never become 1/3 of anything.

    I say, since the hypothetical ancestral possibilities are infinite, that no number can be excluded from a possible result, and that there simply has to be some combination, even if it take 100 generations of division, that will result in a person being exactly 1/3 Italian (or substitute your favorite ethnicity).

    Who is right, and can it be proven?
    Unfortunately, your brother. But since you didn't believe him, I'm not sure you will believe me!

    I can point out that your statement, "since the hypothetical ancestral possibilities are infinite, that no number can be excluded from a possible result" is incorrect. There are an infinite number of even numbers (so the "hypothetical ancestral possiblities" are infinite) but you certainly can't say "no number can be excluded from a possible result: any odd number can be excluded.

    Saying that a set contains an infinite collection of numbers does NOT mean that "every number is in it" nor that "we cannot exclulde any number". Another, more relevant example: the set of all numbers of the form m/2^n for m and n positive integers contains an infinitely many numbers but does not contain the number 1/3 because 3 is not 2^n for any n.

    It would be a rather complicated mathematical proof but the basic idea is just what your brother said: If A is purely Italian and B is purely some other ethnicity, then any child will get half his genes from A and half from B and so will be "A/2+ B/2= (A+B)/2" "Italian". If A and B are each "part Italian", you still have (A+ B)/2 and so a "2" in the denominator. No matter how far you go back, 100 generations or 1000, in each step, you will be dividing by a new power of 2. Because you start with integer number of genes ("pure Italian" or "pure non-Italian"), the only thing that ever happens to the denominator is "dividing by 2". You can only have a "power of 2" in the denominator, never a "3".
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  3. #3
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    Well, what I calculated is that it can be very close to 1/3 and get even more close (not sure how should I say it in English).. Well you can be 50% Italian, right? It's when one of your parents is 0 and another one 100%.
    Then if that 50% one mixes up with 0% we get 25%. Then we can mix together 50% and 25% and we get 37,5%... Then again 25% and 37,5% and so on, until we are very close to 33,(3)%, but we'll never get it to be completely equal.
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    Well, what I calculated is that it can be very close to 1/3 and get even more close (not sure how should I say it in English).
    I've since learned that one can get "infinitely close" to 1/3, but never exactly 1/3, because there can never exist a numerator and denominator combination that reduces to exactly 1/3.

    There can however be a numerator and denominator that convert to 33.33333 and so on. A friend of mine showed me how he got to 33.3325 in 12 generations.

    He produced a chart and then commented:
    Now, here is the crucial point as to why it is impossible for one to be exactly one-third a given ethnicity. To get one-third, the denominator (4096 in the example above) would have to be exactly three times the numerators (1365 above, or, in another example some other sum of numerators from the middle column above).

    For the denominator to be exactly three times the numerator, whatever are the prime factors of the numerator, the prime factorization of the denominator would have to include exactly these prime factors plus an additional 3. (For example, if the numerator is 20, with its prime factors 2,2,5, for the fraction to equal one-third, the denominator would need to have the prime factors 2,2,5 plus 3, i.e., have the product 60.)

    But with the type of inheritance that we are discussing, the denominator will always be a power of 2 (as shown in the first column of numbers in the table above). If a number is a power of two, it prime factorization is some number of twos and can never include a 3. Therefore, the denominator can never be 3 times the numerator and the fraction can never be equal to one-third.
    I think HallsofIvy essentially described the same limitation, I think, but I finally understand after my Professor friend charted it out and explained it to me.
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  5. #5
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    Well, I consider myself as both Canadian and French, not half Canadian half French. My mother is French and my father Canadian. I personally have the 2 passports thus I have 2 nationalities.
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    I'm new to the forum. I found it by searching google for 'can you be 1/3 anything' and decided that I would let others see how i view the debate.

    ok, now to look at this from an entirely different perspective than mathematically...let's look at it scientifically with an open mind...
    you'll have to excuse the graphic content of the first example...
    here's my first example:
    Ok, let's say there is a woman who is 100% Irish. There are two men she likes, one is 100% irish and one is 100% german...both men have sex with her within 2 days...the woman becomes pregnant and has a child. Is the child the product of the irish man or the german man? or is it possible that the child is the product of the combination of both the irishman's and the german man's sperm?? therefore making the child 1/3 german and 2/3 irish....

    Here is my second example:
    Now going along the same hypothesis of the above example, let me lay it out differently...
    Let's say there is a woman who is 100% african. The men she is with, one is 100% irish and one is 100% african. Now if, once again, both men had sex with her within a short period and she became pregnant. It could be possible that the sperm could combine and attempt to make triplets, but if the embryo did not split fully and remained a single embryo almost split into three...making that child 1/3 irish and 2/3 african...no matter how short/long the child would live because of its condition of being 3 children fused into one...(we've seen this happen with a single embryo failing to completely split in two to make twins...it ends up making a single human which has two heads, but a joined spine...etc...)

    From my above hypotheses, I find it completely possible to be considered 1/3 of a certain ethnicity.

    If you have any constructive criticism to my explanations or need it explained further, let me know and I'll try to further elaborate on my theories.
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  7. #7
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    Quote Originally Posted by HaloJDawg View Post
    I'm new to the forum. I found it by searching google for 'can you be 1/3 anything' and decided that I would let others see how i view the debate.

    ok, now to look at this from an entirely different perspective than mathematically...let's look at it scientifically with an open mind...
    you'll have to excuse the graphic content of the first example...
    here's my first example:
    Ok, let's say there is a woman who is 100% Irish. There are two men she likes, one is 100% irish and one is 100% german...both men have sex with her within 2 days...the woman becomes pregnant and has a child. Is the child the product of the irish man or the german man? or is it possible that the child is the product of the combination of both the irishman's and the german man's sperm?? therefore making the child 1/3 german and 2/3 irish....

    Here is my second example:
    Now going along the same hypothesis of the above example, let me lay it out differently...
    Let's say there is a woman who is 100% african. The men she is with, one is 100% irish and one is 100% african. Now if, once again, both men had sex with her within a short period and she became pregnant. It could be possible that the sperm could combine and attempt to make triplets, but if the embryo did not split fully and remained a single embryo almost split into three...making that child 1/3 irish and 2/3 african...no matter how short/long the child would live because of its condition of being 3 children fused into one...(we've seen this happen with a single embryo failing to completely split in two to make twins...it ends up making a single human which has two heads, but a joined spine...etc...)

    From my above hypotheses, I find it completely possible to be considered 1/3 of a certain ethnicity.

    If you have any constructive criticism to my explanations or need it explained further, let me know and I'll try to further elaborate on my theories.
    The fact you don't know whether a child is "half Irish and half German" or "all Irish" doesn't mean that he isn't one or the other! Certainly not "1/3 Irish and 2/3 German".

    And I am very surprised you would talk about being "scientific" and then say "It could be possible that the sperm could combine and attempt to make triplets, but if the embryo did not split fully and remained a single embryo almost split into three...making that child 1/3 irish and 2/3 african...no matter how short/long the child would live because of its condition of being 3 children fused into one"

    No, that can't happen! The chromosomes in the egg cannot match up with those with both sperm nor can some of its chromosomes match up with those from one sperm and other with those from the other. In the very, very rare cases where two sperm enter the egg at the same time (once a sperm enters the egg, its outer surface "hardens" and will not allow other sperm to enter) the egg cannot split and no embryo is formed.
    see
    Fertilization

    "...(we've seen this happen with a single embryo failing to completely split in two to make twins...it ends up making a single human which has two heads, but a joined spine...etc...)"

    No, we haven't seen this happen. Conjoined twins (so-called "Siamese" twins) happen when an egg, fertilized by a single sperm, does not split properly.
    Last edited by HallsofIvy; May 29th 2009 at 06:32 AM.
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