4 — Qualitative Change: What Number Cannot Measure

October 25, 2017 — Compared to making money by investing in the market, the economic changes discussed last week—in the upgrades of power over different forms of “fire,” from wood, to charcoal, to chemistry, electricity, nuclear, and fusion—occur as jumps. They create new fields of potential that did not exist before, and cannot be understood in terms of the past.



  1. (TBA) Topics will include geometry (irreducibly global measures) and biology (examples of non-quantitative change).

  2. Preparation for next week — before watching the assigned video for next week, write short (one sentence) definitions of “flat” and “straight.”

Reading for next class: Watch the video Riemann: The Habilitation Dissertation

Showing 6 reactions

Please check your e-mail for a link to activate your account.
  • Jason Ross
    commented 2017-11-03 14:53:46 -0400
    On the question of beauty and morality versus raw self-interest, I think that if you consider the greatest of discoveries and innovations, they do not find their origin in “self-interest” as understood by, say, Adam Smith. What drove Kepler through his years of agonizingly difficult work was not a desire for self-advancement, but a desire to KNOW, to discover. The same is true for Mendeleyev, Einstein, etc.
    Among those great thinkers who did achieve a very comfortable life (such as Giuseppe Verdi or the painter Frederic Church), do you think it was a desire for income that drove them?
  • Jason Ross
    commented 2017-11-03 14:51:27 -0400
    Hi Gregory,
    The number of real numbers is infinite, but a higher order infinite than the infinite number of whole numbers. The distinction is between the “countable infinite” and the continuum.
    These are all the same type of infinite:
    • counting numbers, fractions, points on graph paper (with whole number coordinates)
    This infinite (the discrete / countable infinite) is smaller than the continuous infinite.
    Does that address your question?
  • David Harold Chester
    followed this page 2017-10-29 02:36:01 -0400
  • Gregory Unger
    commented 2017-10-25 13:51:41 -0400
    Is the appeal to beauty or to morality more effective at helping people understand economics? Or just raw self-interest?
  • Gregory Unger
    commented 2017-10-25 13:36:01 -0400
    Hi Jason, how many of these “extra-infinite” decimal numbers can there be?
  • Benjamin Deniston
    followed this page 2017-10-24 14:45:56 -0400

Donate Volunteer Get updates