full transcript

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 shape like a suraqe or a triangle, or the complex pattern on a butterfly's wgnis. If you are artistically inclined, you might think of the subtle miaolodunts of a morazt 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 acasbtrt entities like geoirmtec 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 aecscs through its cetner, we end up with a triangle that's iacdtneil to the original. In this case, the oejcbt is the triangle, and the tsrooinmfraatn 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 tilagrne by, say, 90 degrees instead, the rotated triangle would look different to the original. In other wodrs, an equilateral triangle is not symmetric with respect to riatontos 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 liivng things, it's only approximate, but still a striking ftauere of the hmuan body. We humans aren't the only bilaterally symmetric ogsnirams. Many other animals, foxes, srkhas, beetles, that butterfly we mentioned eielrar, have this kind of symmetry, as do some plants like orchid fowrles. 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 wcheatd earlier. But when it occurs in animals, this kind of sremytmy is known as radial symmetry. For instance, some sea urchins and starfish have pentaradial or five-fold symmetry, that is, symmetry with rpecset to rotations of 72 degrees around their center. This symmetry also apaeprs in plants, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rotations of 90 drgeees, 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 fxoes, beltees, sharks, butterflies, and, of course, humans. The thing that unites bilaterally symmetric amnials is that their bidoes are designed around movement. If you want to pick one doirtcein and move that way, it helps to have a front end where you can gorup your soresny 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 bluid 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 aludt 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 clsoely related to srtafish 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 fnicanaistg and important problems in biology is reconstructing the tree of life, dersoniivcg 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 shape like a ______ or a triangle, or the complex pattern on a butterfly's _____. If you are artistically inclined, you might think of the subtle ___________ of a ______ 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 ________ entities like _________ 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 ______ through its ______, we end up with a triangle that's _________ 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 triangle is symmetric with respect to rotations of 120 degrees around its center. If we rotated the ________ by, say, 90 degrees instead, the rotated triangle would look different to the original. In other _____, an equilateral triangle is not symmetric with respect to _________ 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 ______ things, it's only approximate, but still a striking _______ of the _____ body. We humans aren't the only bilaterally symmetric _________. Many other animals, foxes, ______, beetles, that butterfly we mentioned _______, have this kind of symmetry, as do some plants like orchid _______. 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 _______ earlier. But when it occurs in animals, this kind of ________ is known as radial symmetry. For instance, some sea urchins and starfish have pentaradial or five-fold symmetry, that is, symmetry with _______ to rotations of 72 degrees around their center. This symmetry also _______ in plants, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rotations of 90 _______, 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 _____, _______, sharks, butterflies, and, of course, humans. The thing that unites bilaterally symmetric _______ is that their ______ are designed around movement. If you want to pick one _________ and move that way, it helps to have a front end where you can _____ your _______ 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 _____ 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 _____ 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 _______ related to ________ 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 ___________ and important problems in biology is reconstructing the tree of life, ___________ 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


  1. object
  2. mozart
  3. beetles
  4. group
  5. respect
  6. square
  7. identical
  8. modulations
  9. earlier
  10. living
  11. fascinating
  12. degrees
  13. center
  14. wings
  15. bodies
  16. sharks
  17. geometric
  18. appears
  19. words
  20. feature
  21. build
  22. human
  23. animals
  24. direction
  25. abstract
  26. transformation
  27. starfish
  28. sensory
  29. access
  30. watched
  31. adult
  32. triangle
  33. rotations
  34. flowers
  35. closely
  36. discovering
  37. symmetry
  38. foxes
  39. organisms

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.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
equilateral triangle 3
bilateral symmetry 3
bilaterally symmetric 3
sea urchins 3
object unchanged 2
human body 2
body symmetry 2
symmetric animals 2

ngrams of length 3

collocation frequency
bilaterally symmetric animals 2


Important Words


  1. abstract
  2. access
  3. adult
  4. aerodynamic
  5. anemones
  6. angle
  7. animals
  8. apparent
  9. appears
  10. apple
  11. approximate
  12. artistically
  13. asymmetric
  14. balance
  15. ballerina
  16. beauty
  17. beetles
  18. bilateral
  19. bilaterally
  20. biologists
  21. biology
  22. bird
  23. bit
  24. bodies
  25. body
  26. branches
  27. build
  28. butterflies
  29. butterfly
  30. call
  31. called
  32. camp
  33. care
  34. case
  35. center
  36. close
  37. closely
  38. completely
  39. complex
  40. concerto
  41. coordinated
  42. corals
  43. day
  44. degrees
  45. designed
  46. development
  47. dig
  48. direction
  49. discovering
  50. diverged
  51. earlier
  52. ears
  53. effortless
  54. enemies
  55. entities
  56. equilateral
  57. essential
  58. evidence
  59. evolution
  60. evolutionary
  61. exhibit
  62. eyes
  63. familiar
  64. fascinating
  65. feature
  66. fields
  67. figure
  68. fins
  69. fish
  70. flowers
  71. food
  72. fox
  73. foxes
  74. front
  75. geometric
  76. group
  77. hand
  78. harmony
  79. head
  80. hear
  81. helps
  82. horizontally
  83. human
  84. humans
  85. identical
  86. imaginary
  87. important
  88. inclined
  89. instance
  90. jellyfish
  91. kind
  92. larval
  93. leads
  94. leaves
  95. left
  96. legs
  97. life
  98. lifestyle
  99. living
  100. lot
  101. math
  102. mathematicians
  103. meaning
  104. mentioned
  105. mirror
  106. modulations
  107. mounted
  108. mouth
  109. move
  110. movement
  111. mozart
  112. naturally
  113. nose
  114. noticed
  115. notions
  116. object
  117. occurs
  118. orchid
  119. organism
  120. organisms
  121. organs
  122. original
  123. pattern
  124. pentaradial
  125. pick
  126. picture
  127. plants
  128. point
  129. poise
  130. pretty
  131. prima
  132. problems
  133. property
  134. radial
  135. reconstructing
  136. reflection
  137. related
  138. represents
  139. respect
  140. rotate
  141. rotated
  142. rotation
  143. rotational
  144. rotations
  145. run
  146. running
  147. science
  148. scientists
  149. sea
  150. sense
  151. sensory
  152. shape
  153. shapes
  154. sharks
  155. sides
  156. simple
  157. slices
  158. slicing
  159. sounds
  160. species
  161. specific
  162. square
  163. stage
  164. starfish
  165. streamlined
  166. striking
  167. strong
  168. subtle
  169. symmetric
  170. symmetries
  171. symmetry
  172. tangible
  173. technical
  174. thinking
  175. transformation
  176. tree
  177. triangle
  178. turns
  179. type
  180. unchanged
  181. understand
  182. unites
  183. unpack
  184. urchins
  185. vague
  186. vertically
  187. watched
  188. wings
  189. word
  190. words