• Posts
  • RSS
  • ◂◂RSS
  • Contact

  • Make Truncation be Rounding

    May 22nd, 2016
    ideas, math  [html]
    When I see a number like "183" the first thing I see is a "1". If I'm looking very quickly, perhaps scanning a column of numbers, that might be all I see, and I'll approximate this number as "100" when "200" would be closer. Yes, truncation isn't the same thing as rounding, but wouldn't things be a lot easier if it were? Let's make it be that way.

    To interpret a number today, you multiply each column by the size it represents and add them up:

    number 100s 10s 1s sum
    100 1 0 0 1*100 + 0*10 + 0*1
    120 1 2 0 1*100 + 2*10 + 0*1
    121 1 2 1 1*100 + 2*10 + 1*1
    129 1 2 9 1*100 + 2*10 + 9*1
    125 1 2 5 1*100 + 2*10 + 5*1

    With this new system, we still do this, but in each column our available options range from -5 to 4 instead of 0 to 9.

    number 100s 10s 1s sum
    100 1 0 0 1*100 + 0*10 + 0*1
    120 1 2 0 1*100 + 2*10 + 0*1
    121 1 2 1 1*100 + 2*10 + 1*1
    129 1 3 -1 1*100 + 3*10 + -1*1
    125 1 3 -5 1*100 + 3*10 + -5*1

    Here are a few more examples:

    old notation new notation
    0 0
    4 4
    7 1-3
    579 1-4-2-1
    432 432
    1999 200-1

    And here's a program to calculate these:

    def to_new_notation(x):
      digits = []
      carry = False
      for digit in reversed([
            int(x) for x in str(x)]):
        if carry:
          digit += 1
          carry = False
    
        if digit >= 5:
          digit -= 10
          carry = True
    
        digits.append(digit)
    
      if carry:
        digits.append(1)
    
      digits.reverse()
      return digits
    

    Update 2016-05-25: Truncation isn't actually rounding in this system unless you allow both 5 and -5 as digits. Thanks to Marius for pointing this out.

    Comment via: google plus, facebook

    Recent posts on blogs I like:

    Collections: The Queen’s Latin or Who Were the Romans? Part IV: The Color of Purple

    This is the fourth part (I, II, III) of our series asking the question “Who were the Romans?” and contrasting the answer we get from the historical evidence with the pop-cultural image of the Romans as a culturally and ethnically homogeneous society typic…

    via A Collection of Unmitigated Pedantry July 23, 2021

    The Leakage Problem

    I’ve spent more than ten years talking about the cost of construction of physical infrastructure, starting with subways and then branching on to other things, most. And yet there’s a problem of comparable size when discussing infrastructure waste, which, …

    via Pedestrian Observations July 23, 2021

    Songs about terrible relationships

    [Spoilers for several old musicals.] TV Tropes lists dozens of examples of the “I want” song (where the hero of a musical sings about their dream of escaping their small surroundings). After watching a bunch of musicals on maternity leave, I’m wondering h…

    via The whole sky July 17, 2021

    more     (via openring)


  • Posts
  • RSS
  • ◂◂RSS
  • Contact