From the Ted Talk by Colm Kelleher: The science of symmetry
Unscramble the Blue Letters
When you hear the word symmetry, maybe you picture a simple geometric sahpe like a square or a triangle, or the complex pattern on a butterfly's wings. If you are artistically inclined, you might think of the subtle modulations of a Mozart coertcno, or the effortless piose of a prima ballerina. When used in every day life, the word symmetry represents vuage notions of beauty, harmony and balance. In math and snceice, symmetry has a different, and very specific, miennag. In this technical sense, a symmetry is the property of an object. Pretty much any type of object can have symmetry, from tangible things like butterflies, to abstract entities like geometric shapes. So, what does it mean for an object to be symmetric? Here's the definition: a symmetry is a transformation that leaves that object ugcanhend. Okay, that sounds a bit abstract, so let's unpack it. It will help to look at a particular example, like this equilateral triangle. If we rotate our triangle through 120 degrees, around an access through its center, we end up with a triangle that's identical to the original. In this case, the ocjebt is the triangle, and the troaofsmtrinan that leaves the object unchanged is rotation through 120 degrees. So we can say an equilateral tliangre is symmetric with respect to rotations of 120 degrees around its center. If we rtoaetd the triangle by, say, 90 degrees instead, the rotated triangle would look different to the ogniiral. In other words, an equilateral triangle is not symmetric with repscet to rotations of 90 dergees around its cetner. But why do mathematicians and scientists care about symmetries? trnus out, they're enaisetsl in many fields of math and science. Let's take a cosle look at one example: symmetry in biology. You might have noticed that there's a very familiar kind of smyrtmey we haven't mentioned yet: the symmetry of the right and left sides of the human body. The transformation that gives this symmetry is reflection by an inagmariy mirror that slices vertically through the body. Biologists call this bilateral symmetry. As with all symmetries found in living things, it's only amorpipaxte, but still a striking feature of the human body. We humans aren't the only bilaterally symmetric organisms. Many other animals, foxes, sharks, beetles, that butterfly we mentioned earlier, have this kind of symmetry, as do some plants like oicrhd flowers. Other organisms have different symmetries, ones that only become arenpapt when you rotate the organism around its center point. It's a lot like the rotonatial symmetry of the triangle we wcatehd earlier. But when it occurs in animals, this kind of symmetry is known as radial symmetry. For instance, some sea urchins and starfish have panraitedal or five-fold symmetry, that is, symmetry with respect to rationots of 72 degrees around their center. This symmetry also appears in plants, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rotations of 90 degrees, while sea anemones are symmetric when you rotate them at any angle. Some corals, on the other hand, have no symmetry at all. They are completely asymmetric. But why do organisms exhibit these different symmetries? Does body symmetry tell us anything about an animal's lifestyle? Let's look at one particular group: bilaterally symmetric animals. In this camp, we have foxes, beeetls, sharks, biertltufes, and, of course, humans. The thing that unites bilaterally symmetric animals is that their beodis are designed around movement. If you want to pick one direction and move that way, it helps to have a front end where you can group your sensory organs— your eyes, ears and nose. It helps to have your mouth there too since you're more likely to run into food or enemies from this end. You're probably familiar with a name for a gourp of organs, plus a mtouh, mounted on the front of an animal's body. It's called a head. Having a head leads naturally to the development of bilateral symmetry. And it also helps you bluid streamlined fins if you're a fish, aerodynamic wgins if you're a bird, or well coordinated legs for running if you're a fox. But, what does this all have to do with evolution? Turns out, biologists can use these various body symmetries to figure out which animals are related to which. For instance, we saw that starfish and sea urchins have five-fold symmetry. But really what we should have said was auldt starfish and sea ucnrhis. In their larval stage, they're brtlaaiel, just like us hmnuas. For biologists, this is strong evidence that we're more closely related to starfish than we are, to say, corals, or other aailmns that don't exhibit bilateral symmetry at any stage in their development. One of the most fascinating and iarpmtnot problems in biology is rnosctecinrtug the tree of life, discovering when and how the different branches diverged. Thinking about something as simple as body symmetry can help us dig far into our evolutionary past and understand where we, as a species, have come from.
Open Cloze
When you hear the word symmetry, maybe you picture a simple geometric _____ like a square or a triangle, or the complex pattern on a butterfly's wings. If you are artistically inclined, you might think of the subtle modulations of a Mozart ________, or the effortless _____ of a prima ballerina. When used in every day life, the word symmetry represents _____ notions of beauty, harmony and balance. In math and _______, symmetry has a different, and very specific, _______. In this technical sense, a symmetry is the property of an object. Pretty much any type of object can have symmetry, from tangible things like butterflies, to abstract entities like geometric shapes. So, what does it mean for an object to be symmetric? Here's the definition: a symmetry is a transformation that leaves that object _________. Okay, that sounds a bit abstract, so let's unpack it. It will help to look at a particular example, like this equilateral triangle. If we rotate our triangle through 120 degrees, around an access through its center, we end up with a triangle that's identical to the original. In this case, the ______ is the triangle, and the ______________ that leaves the object unchanged is rotation through 120 degrees. So we can say an equilateral ________ is symmetric with respect to rotations of 120 degrees around its center. If we _______ the triangle by, say, 90 degrees instead, the rotated triangle would look different to the ________. In other words, an equilateral triangle is not symmetric with _______ to rotations of 90 _______ around its ______. But why do mathematicians and scientists care about symmetries? _____ out, they're _________ in many fields of math and science. Let's take a _____ look at one example: symmetry in biology. You might have noticed that there's a very familiar kind of ________ we haven't mentioned yet: the symmetry of the right and left sides of the human body. The transformation that gives this symmetry is reflection by an _________ mirror that slices vertically through the body. Biologists call this bilateral symmetry. As with all symmetries found in living things, it's only ___________, but still a striking feature of the human body. We humans aren't the only bilaterally symmetric organisms. Many other animals, foxes, sharks, beetles, that butterfly we mentioned earlier, have this kind of symmetry, as do some plants like ______ flowers. Other organisms have different symmetries, ones that only become ________ when you rotate the organism around its center point. It's a lot like the __________ symmetry of the triangle we _______ earlier. But when it occurs in animals, this kind of symmetry is known as radial symmetry. For instance, some sea urchins and starfish have ___________ or five-fold symmetry, that is, symmetry with respect to _________ of 72 degrees around their center. This symmetry also appears in plants, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rotations of 90 degrees, while sea anemones are symmetric when you rotate them at any angle. Some corals, on the other hand, have no symmetry at all. They are completely asymmetric. But why do organisms exhibit these different symmetries? Does body symmetry tell us anything about an animal's lifestyle? Let's look at one particular group: bilaterally symmetric animals. In this camp, we have foxes, _______, sharks, ___________, and, of course, humans. The thing that unites bilaterally symmetric animals is that their ______ are designed around movement. If you want to pick one direction and move that way, it helps to have a front end where you can group your sensory organs— your eyes, ears and nose. It helps to have your mouth there too since you're more likely to run into food or enemies from this end. You're probably familiar with a name for a _____ of organs, plus a _____, mounted on the front of an animal's body. It's called a head. Having a head leads naturally to the development of bilateral symmetry. And it also helps you _____ streamlined fins if you're a fish, aerodynamic _____ if you're a bird, or well coordinated legs for running if you're a fox. But, what does this all have to do with evolution? Turns out, biologists can use these various body symmetries to figure out which animals are related to which. For instance, we saw that starfish and sea urchins have five-fold symmetry. But really what we should have said was _____ starfish and sea _______. In their larval stage, they're _________, just like us ______. For biologists, this is strong evidence that we're more closely related to starfish than we are, to say, corals, or other _______ that don't exhibit bilateral symmetry at any stage in their development. One of the most fascinating and _________ problems in biology is ______________ the tree of life, discovering when and how the different branches diverged. Thinking about something as simple as body symmetry can help us dig far into our evolutionary past and understand where we, as a species, have come from.
Solution
wings
adult
mouth
build
approximate
urchins
symmetry
triangle
turns
group
essential
humans
shape
reconstructing
object
pentaradial
rotations
poise
orchid
rotated
imaginary
original
meaning
animals
apparent
butterflies
close
transformation
bodies
respect
rotational
important
concerto
bilateral
science
center
vague
watched
beetles
unchanged
degrees
Original Text
When you hear the word symmetry, maybe you picture a simple geometric shape like a square or a triangle, or the complex pattern on a butterfly's wings. If you are artistically inclined, you might think of the subtle modulations of a Mozart concerto, or the effortless poise of a prima ballerina. When used in every day life, the word symmetry represents vague notions of beauty, harmony and balance. In math and science, symmetry has a different, and very specific, meaning. In this technical sense, a symmetry is the property of an object. Pretty much any type of object can have symmetry, from tangible things like butterflies, to abstract entities like geometric shapes. So, what does it mean for an object to be symmetric? Here's the definition: a symmetry is a transformation that leaves that object unchanged. Okay, that sounds a bit abstract, so let's unpack it. It will help to look at a particular example, like this equilateral triangle. If we rotate our triangle through 120 degrees, around an access through its center, we end up with a triangle that's identical to the original. In this case, the object is the triangle, and the transformation that leaves the object unchanged is rotation through 120 degrees. So we can say an equilateral triangle is symmetric with respect to rotations of 120 degrees around its center. If we rotated the triangle by, say, 90 degrees instead, the rotated triangle would look different to the original. In other words, an equilateral triangle is not symmetric with respect to rotations of 90 degrees around its center. But why do mathematicians and scientists care about symmetries? Turns out, they're essential in many fields of math and science. Let's take a close look at one example: symmetry in biology. You might have noticed that there's a very familiar kind of symmetry we haven't mentioned yet: the symmetry of the right and left sides of the human body. The transformation that gives this symmetry is reflection by an imaginary mirror that slices vertically through the body. Biologists call this bilateral symmetry. As with all symmetries found in living things, it's only approximate, but still a striking feature of the human body. We humans aren't the only bilaterally symmetric organisms. Many other animals, foxes, sharks, beetles, that butterfly we mentioned earlier, have this kind of symmetry, as do some plants like orchid flowers. Other organisms have different symmetries, ones that only become apparent when you rotate the organism around its center point. It's a lot like the rotational symmetry of the triangle we watched earlier. But when it occurs in animals, this kind of symmetry is known as radial symmetry. For instance, some sea urchins and starfish have pentaradial or five-fold symmetry, that is, symmetry with respect to rotations of 72 degrees around their center. This symmetry also appears in plants, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rotations of 90 degrees, while sea anemones are symmetric when you rotate them at any angle. Some corals, on the other hand, have no symmetry at all. They are completely asymmetric. But why do organisms exhibit these different symmetries? Does body symmetry tell us anything about an animal's lifestyle? Let's look at one particular group: bilaterally symmetric animals. In this camp, we have foxes, beetles, sharks, butterflies, and, of course, humans. The thing that unites bilaterally symmetric animals is that their bodies are designed around movement. If you want to pick one direction and move that way, it helps to have a front end where you can group your sensory organs— your eyes, ears and nose. It helps to have your mouth there too since you're more likely to run into food or enemies from this end. You're probably familiar with a name for a group of organs, plus a mouth, mounted on the front of an animal's body. It's called a head. Having a head leads naturally to the development of bilateral symmetry. And it also helps you build streamlined fins if you're a fish, aerodynamic wings if you're a bird, or well coordinated legs for running if you're a fox. But, what does this all have to do with evolution? Turns out, biologists can use these various body symmetries to figure out which animals are related to which. For instance, we saw that starfish and sea urchins have five-fold symmetry. But really what we should have said was adult starfish and sea urchins. In their larval stage, they're bilateral, just like us humans. For biologists, this is strong evidence that we're more closely related to starfish than we are, to say, corals, or other animals that don't exhibit bilateral symmetry at any stage in their development. One of the most fascinating and important problems in biology is reconstructing the tree of life, discovering when and how the different branches diverged. Thinking about something as simple as body symmetry can help us dig far into our evolutionary past and understand where we, as a species, have come from.