DailyDirt: Logarithmic Thinking Is Natural

from the urls-we-dig-up dept

Most of us have been taught to understand math-related topics in a linear way, but that might not be the way our brains are hard-wired. Kids actually tend to have an innate number scale that is logarithmic, so even though they know how to count to ten (or even twenty), they'll actually think more along the lines of one, many, lots of many's, and then OMG so many that's like infinity. Here are just a few links on logarithmic thinking to ponder. If you'd like to read more awesome and interesting stuff, check out this unrelated (but not entirely random!) Techdirt post.
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Filed Under: brain, education, linear, logarithms, math, mundurucu, psychology


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  • icon
    Watchit (profile), 24 Oct 2012 @ 5:42pm

    Man, people are really stupid. Halfway between 9 is 4.5!

    link to this | view in chronology ]

    • identicon
      Anonymous Coward, 24 Oct 2012 @ 6:09pm

      Re:

      halfway between ONE and NINE... not ZERO & 9.

      link to this | view in chronology ]

    • identicon
      Mr. Applegate, 24 Oct 2012 @ 7:15pm

      Response to: Watchit on Oct 24th, 2012 @ 5:42pm

      Yep. Some people sure are stupid.

      9-1=8

      8/2=4

      4+1=5

      5 is half way between 1 and 9

      Who knew.

      link to this | view in chronology ]

      • identicon
        Anonymous Coward, 24 Oct 2012 @ 8:24pm

        Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

        Counting on fingers: 1,2,3,4,5
        Next hand: 1,2,3,4
        So halfway between them is...?

        link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 9:38am

          Re: Re: Response to: Watcht on Oct 24th, 2012 @ 5:42pm

          except your first finger should be 2 not 1..

          between 1 AND 9 is not math, like '1 and 1 = 2' its the difference between the digits 1 and the digit 9..

          start at 1 your first count is 2, when you get to 9 how many fingers are you holding up thats right 8 fingers..

          half of 8 is ???

          link to this | view in chronology ]

          • identicon
            Anonymous Coward, 25 Oct 2012 @ 4:43pm

            Re: Re: Re: Response to: Watcht on Oct 24th, 2012 @ 5:42pm

            "your first finger should be 2 not 1". Ohhhhkayyyy...

            link to this | view in chronology ]

        • identicon
          Mr. Applegate, 25 Oct 2012 @ 1:36pm

          Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

          OK, try this. What number is half way between 20 and 40?

          Did you say 30? Why?

          High Number [40] less[-] low number [20] = Spread [20]

          Spread [20] divided by[/] 2[2] = Half of spread [10]

          Half of spread [10] added to [+] low number [20] = Halfway point [30]

          So now with What number is half way between 1 and 9?

          High Number [9] less[-] low number [1] = Spread [8]

          Spread [8] divided by [/]2 [2] = Half of spread [4]

          Half of spread [4] added to [+] low number [1] = Halfway point [5]

          link to this | view in chronology ]

          • identicon
            Anonymous Coward, 25 Oct 2012 @ 4:45pm

            Re: Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

            Wouldn't it be easier to just add 20 and 40 and divide by 2?

            link to this | view in chronology ]

            • identicon
              Mr. Applegate, 26 Oct 2012 @ 4:46am

              Re: Re: Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

              Yes, but I was trying to explain WHY the answer is 5 (or 30). That solution was offered and rejected, I attempting to explain it a different way.

              In math sometimes you have to prove your answer in more than one way, especially if people don't understand the concept.

              link to this | view in chronology ]

      • identicon
        Anonymous Coward, 25 Oct 2012 @ 5:47am

        Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

        9 is not a number (in octal) so I am not sure how you can count that high?

        link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 9:41am

          Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

          9 in octal is 10 !!! half of 10 is 5

          octal 2 is 2
          octal 9 is 10

          the difference between 2 (octal) and 10 (octal) is 8 octal, half of 8 octal is 4 (O)..

          9 is a number in octal it's digits are 10

          link to this | view in chronology ]

      • identicon
        carlos carmona, 8 Jun 2015 @ 9:30pm

        Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm

        1 2 3 4 5 6 7 8 9
        1 1 1 1 0 1 1 1 1

        Even simpler explanation for visual learners

        link to this | view in chronology ]

  • identicon
    Emil Ole William Kirkegaard, 24 Oct 2012 @ 7:07pm

    1+9=10/2=5

    or, 5±4={1,9}

    link to this | view in chronology ]

    • identicon
      abc gum, 25 Oct 2012 @ 5:44am

      Re:

      I realize what you attempted to write, however brackets are required in order to be correct.

      (1+9=10)/2=5 otherwise one might suggest that 1+9=5

      link to this | view in chronology ]

  • identicon
    azlibertarian, 24 Oct 2012 @ 7:21pm

    And for bigger numbers ...

    many (so-called) educated adults in answering the question:

    "What number is halfway between one million and one trillion?"

    ... will give the answer "1 billion" (which is only approx 1/1000 of the way).

    No wonder politicos can fool much of the public. The difference between a billion and a trillion doesn't seem like much logarithmically.

    link to this | view in chronology ]

  • identicon
    Anonymous Coward, 24 Oct 2012 @ 8:08pm

    Seriously, does anyone give a crap about crap like this crap?

    link to this | view in chronology ]

  • identicon
    Anonymous Coward, 24 Oct 2012 @ 8:16pm

    im sure more people think exponentially that logrithmatically

    link to this | view in chronology ]

    • identicon
      Anonymous Coward, 24 Oct 2012 @ 8:30pm

      Re:

      And I don't think about this crap at all because it doesn't matter. Not to me, anyway. I live, survive, get through my day just fine without thinking about any of this stuff. And when I die, fat lot of good it will have done me to know what number is halfway between 1 and 9.

      link to this | view in chronology ]

      • identicon
        Pixelation, 24 Oct 2012 @ 10:08pm

        Re: Re:

        "And I don't think about this crap at all because it doesn't matter."

        Except when Dirty Harry says, "I have 5 bullets in my gun and I've fired halfway between 1 and 9. Ask yourself did he fire 3 shots or 5? Feel lucky punk?!"

        link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 4:57pm

          Re: Re: Re:

          Sorry, I don't believe in Dirty Harry. Debbie Harry, however, is a different matter.

          link to this | view in chronology ]

      • identicon
        abc gum, 25 Oct 2012 @ 5:57am

        Re: Re:

        "fat lot of good it will have done me "

        Do you {
        balance your checkbook
        do your own taxes
        calculate a budget
        look for bargains while shopping
        home improvement projects
        } ?

        Your claims are possibly born out of ignorance, but more likely are simple trolling.

        link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 4:52pm

          Re: Re: Re:

          Balance my checkbook- No. I don't have a checkbook.
          Do my own taxes- No.
          Calculate a budget- Sort of. I at least have enough sense to put my needs before my wants.
          Look for bargains while shopping- Yes, assuming it's something I need or want.
          Home improvement projects- Nah.

          link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 4:55pm

          Re: Re: Re:

          "Your claims are possibly born out of ignorance". Okay, then, enlighten me: when I die (or more importantly, after I die), what good will it have done me to know what number lies halfway between 1 and 9?

          link to this | view in chronology ]

      • identicon
        Anonymous Coward, 25 Oct 2012 @ 9:56am

        Re: Re:

        so you dont think you have $20 dollars in your pocket, you know money can buy fuel for your car, but you dont know how much, and you cant work out how far you will be able to go for your $20, or if you even need to spend all of that $20 on fuel, but keep some for some more drugs and beers..

        your not sure if what you are paying for your beers and drugs is alot or not much, nor can you work out if you are being pain as much as you should or if you are being screwed by your boss.

        what a hell you must live in...

        link to this | view in chronology ]

        • identicon
          Anonymous Coward, 25 Oct 2012 @ 4:47pm

          Re: Re: Re:

          "So you don't think you have $20 in your pocket...". No, I know for a FACT that I don't have $20 in my pocket currently.

          link to this | view in chronology ]

  • identicon
    Anonymous Coward, 24 Oct 2012 @ 11:29pm

    Actually the logarithmic perception principle is physiologically important because it allows our range limited senses differentiate a larger range of stimuli. Google Weber–Fechner law.

    link to this | view in chronology ]

    • identicon
      Anonymous Coward, 25 Oct 2012 @ 10:10am

      Re:

      its that our senses are capable of differentiating such a wide range of stimuli that the log scale is required.

      otherwise it would be impossible to hear a pin drop and a really loud rock band on a linear scale, log scale is necessary for the dynamic range of human senses.

      link to this | view in chronology ]

  • identicon
    Anonymous Coward, 25 Oct 2012 @ 9:30am

    half way between 1 and 9 is 4

    link to this | view in chronology ]

  • identicon
    Anonymous Coward, 25 Oct 2012 @ 9:45am

    climb a 9000 foot mountain, when you get 1000 up set your altimeter to zero (set it from asl to agl), then clime to the top, what does your altimeter read now ?? 8000 good you did not fall...

    what is half of 8000 feet ?? lets see 8000/2 = 4000

    or just clime up 9 stairs, start counting between 1 and 9 and work out how many steps you took (8) then do the math 1/2 x 8/1 = 4

    link to this | view in chronology ]

  • identicon
    Anonymous Coward, 25 Oct 2012 @ 10:02am

    all our senses are logarithmic, makes sense to perceive the world that way

    we see, hear, feel, smell, taste logarithmicly, this is to achieve a far higher dynamic range in our senses. it's the same reason earthquakes are scaled logarithmically, for the dynamic range it provides (7 of the scare is 10 times bigger than 6).. nature tends to act in a logarithmic manner as well.

    even gravity pulls you down in an almost logarithmic fashion (9.8mts/sec^2)

    link to this | view in chronology ]


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