The eye color of a grandparent can change the odds a little. While it was once believed that parents with brown eyes could not produce a child with blue eyes, it can — and does! Melanin determines several aspects of our appearance. And while we have the least amount when we enter the world for the first time, remember that babies may be born with eyes of blue, brown, hazel, green, or some other color. You may have heard that babies have more bones than adults.
It's true, and we'll tell you why. Carrots are commonly claimed to keep your eyes healthy, but you may wonder whether this idea is supported by science. This article tells you whether….
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Here is a detailed review of 8 nutrients that can help maintain proper eye function, protect your eyes from damage and fight the negative effects of…. Babies come in all shapes and sizes. As your baby grows, their rate of weight gain will be an important indicator for overall health and development…. Piaget stages of development are the foundation of a well-known theory of early childhood development. We explain each of the four stages and explore…. The science of eye color. Blue, brown, or green: All are beautiful.
Blue eyes are a relatively new phenomenon. Researchers traced blue eyes to a single genetic mutation that occurred between 6, and 10, years ago. People with dark eyes have a lot of melanin in their iris. This dark melanin pigment makes the eyes look brown. And since melanin can absorb light, they look even darker!
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This blue color is made by light scattering when it hits blue eyes or the sky or ocean! The blue color in eyes and water is made by scattering light Image from Pixabay. An iris with a lot of melanin absorbs light, making it appear darker.
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And an iris that has some melanin will absorb some light and scatter the rest, making it appear green. The production of melanin is determined by your DNA. We generally talk about different traits as independent. For example, whether you are tall or short does not affect if you need glasses!
Why Are Babies Born With Blue Eyes?
But the genes for eye, skin, and hair color are different. This is why people typically have either all light features, or all dark features. If one parent has a darker complexion and the other has a lighter complexion, then their children could have a mix of light or dark hair, eyes, and skin. Parents with different complexions can have kids with intermediate colors Image from Flickr. Imagine if there was a region where most people had lighter complexions.
As the population grows and people have babies, the genes for less melanin will become more common. That makes the link between lighter eyes, hair, and skin tighter. Once the guru makes their pronouncement it is common knowledge and every chain of reasoning must terminate at 1 blue eyed person and Z above would have to conclude that they had blue eyes.
All Babies Are Born With Blue Eyes: Fact or Fiction?
From then on every midnight the common knowledge that there are N blue eyed people increments by 1 as everyone sees nobody leaving on the ferry. Stated another way, there's only one stable set of beliefs for the blue eyed people that would allow them to have so many exist on the island indefinitely. That is if each blue eyed person believed not only that they have brown eyes, but also that every other blue-eyed person believed, incorrectly, that they had brown eyes.
Logic reduces this to "all blue-eyes believe that all blues-eyes have brown eyes". The Guru eliminates that particular possibility. Another simple way to understand why the Guru's information is important is thus. Each blue-eyed person knows two sets of information: what the actual situation is on the island both now and in the past , and what would happen in a hypothetical situation.
Each blue-eyed person then needs only to compare the actual situation to a known hypothetical one, and if it matches up, then they take the corresponding action. Consider this: If there were only one blue-eyed person, and the guru never made the announcement, she would not leave on day 1 because she would not know that N is greater than or equal to 1. Now let's add a 2nd blue-eyed person. Blue-eyes 2 would not be able to inductively determine whether or not to leave on night 2, because blue-eyes 2's knowledge of whether or not to leave on night 2 is dependent on what blue-eyes 1 does on night 1 if and only if blue-eyes 1 knows what to do on night 1.
If blue-eyes 1 doesn't know that N is greater than or equal to 1, then blue-eyes 1 doesn't know what to do on night 1, so her lack of leaving gives blue-eyes 2 no new information, since it was an uninformed action and blue-eyes 2's inductive reasoning was dependent on blue-eyes 1 knowing what to do, and so the inductive process never takes off for the hypothetical situation. This means a hypothetical situation for N people cannot be induced. Is it really incomplete on the grounds that Joel hasn't be identified? Explanations of comics leave no more explanation of "Scott" than that he appears to be Randall's friend.
The fact that we don't have a last name for him doesn't make either Scott or those comic explanations incomplete. Similarly, not have a full identifier for "Joel" in this one doesn't, in my opinion, warrant an incomplete tag. I'm removing the tag. If anyone object, revert it. Djbrasier talk , 22 May UTC.
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The proof for this puzzle is incomplete, if not wrong. The theorem is too weak, it should be: "Theorem: N blue eyed people with Nth order knowledge of all N people being logicians, N people having blue eyes, and any blue eyed person will leave as soon as possible after deducing they have blue eyes, will be able to leave on the Nth day. In the theorem as stated, just N blue eyed people will leave on the Nth day, the proof for the inductive steps does not hold.
You need to further assume that the person is able to deduce the hypothesis which should be proven.
In other words, you say X-1 people would leave on the X-1 th day by hypothesis, so the Xth person knows he can leave on the Xth day. But you did not prove that the Xth person can actually deduce this, namely that he has all the information necessary to do so.
Understanding Melanin and Eye Color
Then you have a full proof, since you have now included that they can actually deduce the inductive step. Again, this may seem pedantic, but is really necessary both to be correct and as it illustrates the key of the puzzle, namely the guru gives th order knowledge of someone having blue eyes this is the main problem people have, realizing the concrete piece of information the guru gives.
Jlangy talk , 9 July What I don't follow here is that there's no clarification that the Guru is talking about someone different each time. Just because she says "I see someone with blue eyes" N times doesn't mean that there are N people with blue eyes; she could be talking about the same person every time, or each of two people half the time, etc.
Can anyone clarify this? Thanks - EDIT: Observe the process of comprehension in action I've been thinking about my own brain, with itself, long enough for one day, I'm tired. So, maybe I am indeed just "dumb", as the wiki insists. Clearly, I do not have a perfect understanding of formal logic.
But frankly, my read of this puzzle is that "formal logic" just enables you to jump to ridiculous conclusions. Let's theorize a simpler version of this puzzle. There are now only two people besides the Guru on the island, both with blue eyes. We'll call them Bill and Ted totally bogus, I know. No matter how logical Bill and Ted might be, when Bill hears the Guru say "I see a person with blue eyes" to himself and Ted, and Bill has seen Ted's blue eyes himself, why would Bill assume anything about his own eye color?
It would seem to Bill that Guru was just talking about Ted's eyes, and Ted would believe the reverse. Adding 98 more blue-eyed people, let alone doubling the island's population with irrelevant brown-eyers, hardly reduces the confusion. Knowing Randall is, in general, smarter than me I still do not have the ability to completely accept that he's always right, or that I'm always wrong to ignorantly question his rightness. I have long maintained that certain well-respected "systems of knowledge", of which formal logic is a textbook example, have been respected too well for too long for not-good-enough reasons.