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.- Ask second graders to map out a few numbers on a blank line from 1 to 1,000 -- and you'll see that 7yo kids tend to space out the numbers in a logarithmic pattern. Fourth graders won't make the same number line map as these second graders, and it's apparently not too hard to un-learn logarithmic scales since many adults don't remember what a log scale graph is. [url]
- RadioLab has a nice podcast about how kids learn their numbers, switching from logarithmic thinking to more linear thinking. Young kids and even infants notice large changes (such as when quantities double), but they're not so good at exact amounts and small differences. [url]
- It's not just little kids. Some cultures think in logarithmic scales -- such as an Amazonian indigene group, the Mundurucu. Actually, logarithmic thinking may lie dormant in all of us, whenever we estimate quantities or deal with extremely large numbers. [url]
- What number is halfway between 1 and 9? Most formally educated adults say 5, but another answer (from kids) is 3. [url]
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Filed Under: brain, education, linear, logarithms, math, mundurucu, psychology
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Response to: Watchit on Oct 24th, 2012 @ 5:42pm
9-1=8
8/2=4
4+1=5
5 is half way between 1 and 9
Who knew.
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Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
Next hand: 1,2,3,4
So halfway between them is...?
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Re: Re: Response to: Watcht on Oct 24th, 2012 @ 5:42pm
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 ???
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Re: Re: Re: Response to: Watcht on Oct 24th, 2012 @ 5:42pm
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Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
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]
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Re: Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
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Re: Re: Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
In math sometimes you have to prove your answer in more than one way, especially if people don't understand the concept.
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Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
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Re: Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
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
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Re: Response to: Watchit on Oct 24th, 2012 @ 5:42pm
1 1 1 1 0 1 1 1 1
Even simpler explanation for visual learners
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or, 5±4={1,9}
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(1+9=10)/2=5 otherwise one might suggest that 1+9=5
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And for bigger numbers ...
"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.
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Re: And for bigger numbers ...
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Re: And for bigger numbers ...
million = 10e6
milliard = 10e9
billion = 10e12
billiard = 10e15
trillion = 10e18
so 10e6+10e18=1000000000001000000 half way is 1000000000001000000/2 = 500000000000500000.
Logarithmic scales makes more sense for large numbers.
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Re: Re: And for bigger numbers ...
This would explain the (brown) logs emanating from the mouths of politicians.
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Math is important.
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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?!"
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Re: Re:
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.
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Re: Re: Re:
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.
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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...
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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.
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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
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all our senses are logarithmic, makes sense to perceive the world that way
even gravity pulls you down in an almost logarithmic fashion (9.8mts/sec^2)
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The Last Word
“Math is important.