English subtitles

← An unexpected tool for understanding inequality: abstract math

Get Embed Code
26 Languages

Showing Revision 12 created 03/08/2019 by Brian Greene.

  1. The world is awash
    with divisive arguments,
  2. conflict,
  3. fake news,
  4. victimhood,
  5. exploitation, prejudice,
    bigotry, blame, shouting
  6. and minuscule attention spans.
  7. It can sometimes seem
    that we are doomed to take sides,
  8. be stuck in echo chambers
  9. and never agree again.
  10. It can sometimes seem
    like a race to the bottom,
  11. where everyone is calling out
    somebody else's privilege
  12. and vying to show that they
    are the most hard-done-by person
  13. in the conversation.
  14. How can we make sense
  15. in a world that doesn't?
  16. I have a tool for understanding
    this confusing world of ours,

  17. a tool that you might not expect:
  18. abstract mathematics.
  19. I am a pure mathematician.

  20. Traditionally, pure maths
    is like the theory of maths,
  21. where applied maths is applied
    to real problems like building bridges
  22. and flying planes
  23. and controlling traffic flow.
  24. But I'm going to talk about a way
    that pure maths applies directly
  25. to our daily lives
  26. as a way of thinking.
  27. I don't solve quadratic equations
    to help me with my daily life,
  28. but I do use mathematical thinking
    to help me understand arguments
  29. and to empathize with other people.
  30. And so pure maths helps me
    with the entire human world.
  31. But before I talk about
    the entire human world,

  32. I need to talk about something
    that you might think of
  33. as irrelevant schools maths:
  34. factors of numbers.
  35. We're going to start
    by thinking about the factors of 30.
  36. Now, if this makes you shudder
    with bad memories of school maths lessons,
  37. I sympathize, because I found
    school maths lessons boring, too.
  38. But I'm pretty sure we are going
    to take this in a direction
  39. that is very different
    from what happened at school.
  40. So what are the factors of 30?

  41. Well, they're the numbers that go into 30.
  42. Maybe you can remember them.
    We'll work them out.
  43. It's one, two, three,
  44. five, six,
  45. 10, 15 and 30.
  46. It's not very interesting.
  47. It's a bunch of numbers
    in a straight line.
  48. We can make it more interesting
  49. by thinking about which of these numbers
    are also factors of each other
  50. and drawing a picture,
    a bit like a family tree,
  51. to show those relationships.
  52. So 30 is going to be at the top
    like a kind of great-grandparent.
  53. Six, 10 and 15 go into 30.
  54. Five goes into 10 and 15.
  55. Two goes into six and 10.
  56. Three goes into six and 15.
  57. And one goes into two, three and five.
  58. So now we see that 10
    is not divisible by three,
  59. but that this is the corners of a cube,
  60. which is, I think, a bit more interesting
  61. than a bunch of numbers
    in a straight line.
  62. We can see something more here.
    There's a hierarchy going on.

  63. At the bottom level is the number one,
  64. then there's the numbers
    two, three and five,
  65. and nothing goes into those
    except one and themselves.
  66. You might remember
    this means they're prime.
  67. At the next level up,
    we have six, 10 and 15,
  68. and each of those is a product
    of two prime factors.
  69. So six is two times three,
  70. 10 is two times five,
  71. 15 is three times five.
  72. And then at the top, we have 30,
  73. which is a product
    of three prime numbers --
  74. two times three times five.
  75. So I could redraw this diagram
    using those numbers instead.
  76. We see that we've got
    two, three and five at the top,
  77. we have pairs of numbers
    at the next level,
  78. and we have single elements
    at the next level
  79. and then the empty set at the bottom.
  80. And each of those arrows shows
    losing one of your numbers in the set.
  81. Now maybe it can be clear

  82. that it doesn't really matter
    what those numbers are.
  83. In fact, it doesn't matter what they are.
  84. So we could replace them with
    something like A, B and C instead,
  85. and we get the same picture.
  86. So now this has become very abstract.

  87. The numbers have turned into letters.
  88. But there is a point to this abstraction,
  89. which is that it now suddenly
    becomes very widely applicable,
  90. because A, B and C could be anything.
  91. For example, they could be
    three types of privilege:
  92. rich, white and male.
  93. So then at the next level,
    we have rich white people.
  94. Here we have rich male people.
  95. Here we have white male people.
  96. Then we have rich, white and male.
  97. And finally, people with none
    of those types of privilege.
  98. And I'm going to put back in
    the rest of the adjectives for emphasis.
  99. So here we have rich, white
    non-male people,
  100. to remind us that there are
    nonbinary people we need to include.
  101. Here we have rich, nonwhite male people.
  102. Here we have non-rich, white male people,
  103. rich, nonwhite, non-male,
  104. non-rich, white, non-male
  105. and non-rich, nonwhite, male.
  106. And at the bottom,
    with the least privilege,
  107. non-rich, nonwhite, non-male people.
  108. We have gone from a diagram
    of factors of 30

  109. to a diagram of interaction
    of different types of privilege.
  110. And there are many things
    we can learn from this diagram, I think.
  111. The first is that each arrow represents
    a direct loss of one type of privilege.
  112. Sometimes people mistakenly think
    that white privilege means
  113. all white people are better off
    than all nonwhite people.
  114. Some people point at superrich
    black sports stars and say,
  115. "See? They're really rich.
    White privilege doesn't exist."
  116. But that's not what the theory
    of white privilege says.
  117. It says that if that superrich sports star
    had all the same characteristics
  118. but they were also white,
  119. we would expect them
    to be better off in society.
  120. There is something else
    we can understand from this diagram

  121. if we look along a row.
  122. If we look along the second-to-top row,
    where people have two types of privilege,
  123. we might be able to see
    that they're not all particularly equal.
  124. For example, rich white women
    are probably much better off in society
  125. than poor white men,
  126. and rich black men are probably
    somewhere in between.
  127. So it's really more skewed like this,
  128. and the same on the bottom level.
  129. But we can actually take it further

  130. and look at the interactions
    between those two middle levels.
  131. Because rich, nonwhite non-men
    might well be better off in society
  132. than poor white men.
  133. Think about some extreme
    examples, like Michelle Obama,
  134. Oprah Winfrey.
  135. They're definitely better off
    than poor, white, unemployed homeless men.
  136. So actually, the diagram
    is more skewed like this.
  137. And that tension exists
  138. between the layers
    of privilege in the diagram
  139. and the absolute privilege
    that people experience in society.
  140. And this has helped me to understand
    why some poor white men
  141. are so angry in society at the moment.
  142. Because they are considered to be high up
    in this cuboid of privilege,
  143. but in terms of absolute privilege,
    they don't actually feel the effect of it.
  144. And I believe that understanding
    the root of that anger
  145. is much more productive
    than just being angry at them in return.
  146. Seeing these abstract structures
    can also help us switch contexts

  147. and see that different people
    are at the top in different contexts.
  148. In our original diagram,
  149. rich white men were at the top,
  150. but if we restricted
    our attention to non-men,
  151. we would see that they are here,
  152. and now the rich, white
    non-men are at the top.
  153. So we could move to
    a whole context of women,
  154. and our three types of privilege
    could now be rich, white and cisgendered.
  155. Remember that "cisgendered" means
    that your gender identity does match
  156. the gender you were assigned at birth.
  157. So now we see that rich, white cis women
    occupy the analogous situation
  158. that rich white men did
    in broader society.
  159. And this has helped me understand
    why there is so much anger
  160. towards rich white women,
  161. especially in some parts
    of the feminist movement at the moment,
  162. because perhaps they're prone
    to seeing themselves as underprivileged
  163. relative to white men,
  164. and they forget how overprivileged
    they are relative to nonwhite women.
  165. We can all use these abstract structures
    to help us pivot between situations

  166. in which we are more privileged
    and less privileged.
  167. We are all more privileged than somebody
  168. and less privileged than somebody else.
  169. For example, I know and I feel
    that as an Asian person,
  170. I am less privileged than white people
  171. because of white privilege.
  172. But I also understand
  173. that I am probably among
    the most privileged of nonwhite people,
  174. and this helps me pivot
    between those two contexts.
  175. And in terms of wealth,
  176. I don't think I'm super rich.
  177. I'm not as rich as the kind of people
    who don't have to work.
  178. But I am doing fine,
  179. and that's a much better
    situation to be in
  180. than people who are really struggling,
  181. maybe are unemployed
    or working at minimum wage.
  182. I perform these pivots in my head

  183. to help me understand experiences
    from other people's points of view,
  184. which brings me to this
    possibly surprising conclusion:
  185. that abstract mathematics
    is highly relevant to our daily lives
  186. and can even help us to understand
    and empathize with other people.
  187. My wish is that everybody would try
    to understand other people more
  188. and work with them together,
  189. rather than competing with them
  190. and trying to show that they're wrong.
  191. And I believe that abstract
    mathematical thinking
  192. can help us achieve that.
  193. Thank you.

  194. (Applause)