How do we know the genetic code? (Part 4)

When we last left off, we were feeling a little bummed.  Gregor Mendel never received the recognition he deserved for discovering the basic laws of heredity, at least not while he was alive.  August Weismann was struggling against criticisms of his theory, which said that inheritance passed from parent to child solely through gametic cells in a process known as fertilization that was essentially meiosis in reverse.  And it was clear that had Weismann (or anyone else, for that matter) just known about Mendel’s work, the burgeoning field of genetics would be poised to take a giant leap forward.  Why’s that?  Because Weismann and others had observed that, during fertilization, chromosomes come together from both parents in a way that was very similar to Mendel’s theoretical explanation of how heredity in pea plants worked.  Mendel lacked the intimate knowledge of chromosomes that Weismann had, but Weismann lacked the knowledge of heredity that Mendel had.  Once the two pieces of the puzzle were put together, it would be clear:  the inheritance of genetic traits from one generation to the next is determined solely by the chromosomes that interact when a sperm and an egg unite.

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How do we know the genetic code? (Part 3)

Last time, we explored the work of Friedrich Miescher and his discovery of DNA, but we didn’t talk about how DNA stores information about the traits we display and inherit.  That’s because at first no one had any idea that DNA was really all that important.  People just assumed it was yet another cellular substance in a deluge of substances being discovered during that period.  However, at roughly the same time that Miescher was doing his work, other scientists were finding new ways to observe never before seen structures and processes in cells.  But it was a long time before anyone suspected that these cellular observations were related to DNA.  This is a recurring theme in science:  researchers in different fields find themselves studying different aspects of the same phenomenon, and it often takes decades for scientists to put all the pieces together to give an accurate context for all of their data.

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How do we know the genetic code? (Part 2)

In part 1, we looked at how DNA in our cells can cause cascades of effects that eventually show up as observable traits, like hair color or sickle cell anemia.  As an example, we looked at how a specific group of letters in some people’s DNA can lead, through a series of steps, to those people having blue eyes:

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How do we know the genetic code? (Part 1)

Over the course of the next few posts, I hope to tell you the story behind one of the most important codebreaking efforts in history.  The code at the center of this story does not concern itself with assassination conspiracies or terrorist plots.  There is no political intrigue or corporate espionage.  No couriers are relieved of their parcels (or their lives) during a clandestine midnight ride.  The code of which I speak isn’t really much of a code at all; its message can be read in the very faces of those who carry it.  And every single one of us, and everyone we know or have ever known or will ever know, carries this code with us.

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How do we know that sin²&#952+cos²&#952=1?

I’m already late for this week’s post and I’m nowhere near done with the one I intended to post.  So here’s a really quick post for the time being.  You can probably already answer it yourself if you think a little bit about it.  The equation sin^2\theta+cos^2\theta=1 may or may not be familiar to you from geometry or trigonometry, but it’s dead easy to prove.  We use good old “soh cah toa.”  For those of you scratching your heads in bemusement at this point, soh cah toa is a mnemonic for “sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.”  A few of you may really be puzzled now.  What I’m referring to is the definitions of the sine, cosine and tangent functions.  They’re defined in terms of the lengths of the sides of a right triangle, as seen below:

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How do we know that diamond and graphite are different structures of carbon?

In the first part of this post, I explained how scientists found out in the late 18th century that diamond, graphite, and charcoal were all made of carbon.  As a quick explanation of how such different materials could be made of the same element, I put up the following photo, showing that diamond and graphite actually have vastly different structures:

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How do we know that the angles of a triangle add up to 180 degrees?

I know I promised last time that I’d explain how we know about the different structures of diamond and graphite, but that one’s not quite ready yet.  Plus, the last post was really long, so I figured I’d give your brain a little rest and do some high-school geometry (some of you might not consider that a “rest,” but I promise to make it as painless as I can).  The fact that you can unfold a triangle to make a straight line (180 degrees) has been known since ancient times, and it’s been the subject of some really ingenious proofs and some fundamental advances in math over the years.  I wanted to take a moment to present you with two proofs:  one that I just made up on the fly, and one from Euclid.  The proofs are neat, and they give some insight into how mathematicians think about problems; but more importantly, I’ve got a couple of other HDWKI’s planned that will use some of these properties of triangles, so it helps to have a decent understanding of them now, so those posts don’t stretch on to eternity.

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