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 spilme geometric shape like a square or a triangle, or the complex pratten on a butterfly's wings. If you are ailistcrtaly inclined, you might think of the subtle modulations of a Mozart cnetrcoo, or the effortless poise of a prima blniaelra. 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 obejct can have symmetry, from tangible things like butterflies, to abstract eiietnts like geometric shapes. So, what does it mean for an object to be symmetric? Here's the definition: a stmmryey is a tfarsiotomrann that leaves that object uhnacgned. Okay, that snodus 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 acescs 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 dereegs. So we can say an equilateral taligrne is symmetric with rscpeet to rotations of 120 degrees around its center. If we rotated the triangle by, say, 90 degrees instead, the retoatd 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 cetenr. But why do mathematicians and scientists care about symmetries? Turns out, they're essential in many fields of math and scincee. 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 mteonnied 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. botsgliois call this bilateral symmetry. As with all seiremtmys found in liivng things, it's only ampiaorxtpe, 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 rnooattial symmetry of the triangle we watched earlier. But when it ocurcs in animals, this kind of symmetry is known as ridaal 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 pnatls, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to rtoitnaos of 90 degrees, while sea aneeomns are setyirmmc when you rtotae them at any angle. Some corals, on the other hand, have no symmetry at all. They are completely atiemrsymc. 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 fxeos, beetles, skhras, 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 ledas 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? truns out, biologists can use these various body symmetries to fgiure out which animals are retaeld 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 laarvl stage, they're bilateral, just like us humans. For biologists, this is strong evidence that we're more cseloly 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, dcrvesnioig when and how the different branches diverged. Thinking about something as simple as body symmetry can help us dig far into our enovrliaotuy past and understand where we, as a species, have come from.

Open Cloze

When you hear the word symmetry, maybe you picture a ______ geometric shape like a square or a triangle, or the complex _______ on a butterfly's wings. If you are ____________ inclined, you might think of the subtle modulations of a Mozart ________, or the effortless poise of a prima _________. 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 ______ can have symmetry, from tangible things like butterflies, to abstract ________ like geometric shapes. So, what does it mean for an object to be symmetric? Here's the definition: a ________ is a ______________ that leaves that object _________. Okay, that ______ 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 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 _______. So we can say an equilateral ________ is symmetric with _______ to rotations of 120 degrees around its center. If we rotated the triangle by, say, 90 degrees instead, the _______ 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 ______. But why do mathematicians and scientists care about symmetries? Turns out, they're essential in many fields of math and _______. 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 _________ 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. __________ call this bilateral symmetry. As with all __________ found in ______ 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 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 __________ symmetry of the triangle we watched earlier. But when it ______ in animals, this kind of symmetry is known as ______ 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 ______, as you can see for yourself by slicing through an apple horizontally. Some jellyfish are symmetric with respect to _________ of 90 degrees, while sea ________ are _________ when you ______ them at any angle. Some corals, on the other hand, have no symmetry at all. They are completely __________. 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 _____, beetles, ______, 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 _____ 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? _____ out, biologists can use these various body symmetries to ______ out which animals are _______ 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 ______ stage, they're bilateral, just like us humans. For biologists, this is strong evidence that we're more _______ 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, ___________ when and how the different branches diverged. Thinking about something as simple as body symmetry can help us dig far into our ____________ past and understand where we, as a species, have come from.

Solution

  1. discovering
  2. respect
  3. degrees
  4. leads
  5. sounds
  6. rotational
  7. unchanged
  8. radial
  9. foxes
  10. transformation
  11. anemones
  12. asymmetric
  13. larval
  14. closely
  15. ballerina
  16. pattern
  17. living
  18. sharks
  19. biologists
  20. turns
  21. concerto
  22. figure
  23. rotations
  24. rotated
  25. related
  26. occurs
  27. center
  28. rotate
  29. object
  30. symmetries
  31. simple
  32. plants
  33. triangle
  34. science
  35. symmetric
  36. evolutionary
  37. symmetry
  38. access
  39. mentioned
  40. entities
  41. approximate
  42. artistically

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