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brain, education, linear, logarithms, math, mundurucu, psychology

# 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.

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

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

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

### Re:

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

•
Mr. Applegate, Oct 24th, 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.

•
Anonymous Coward, Oct 24th, 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...?

•
Anonymous Coward, Oct 25th, 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 ???

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

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

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

•
Mr. Applegate, Oct 25th, 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]

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]

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

•
Anonymous Coward, Oct 25th, 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?

•
Mr. Applegate, Oct 26th, 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.

•
Anonymous Coward, Oct 25th, 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?

•
Anonymous Coward, Oct 25th, 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

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

1+9=10/2=5

or, 5±4={1,9}

•
abc gum, Oct 25th, 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

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

### 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.

•
Anonymous Coward, Oct 24th, 2012 @ 7:28pm

### Re: And for bigger numbers ...

In a log scale, 1 billion is actually correct.

•
Emil Ole William Kirkegaard, Oct 24th, 2012 @ 7:53pm

### Re: And for bigger numbers ...

keep in mine https://en.wikipedia.org/wiki/Long_and_short_scales#Comparison

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.

•
abc gum, Oct 25th, 2012 @ 5:49am

### Re: Re: And for bigger numbers ...

"Logarithmic scales makes more sense for large numbers."

This would explain the (brown) logs emanating from the mouths of politicians.

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

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

•
abc gum, Oct 25th, 2012 @ 5:51am

### Re:

"does anyone give a crap about crap like this "

Math is important.

•
Pixelation, Oct 25th, 2012 @ 8:05am

### Re: Re:

"Math is impotant." , unlike spelling. FTFY

•
Anonymous Coward, Oct 25th, 2012 @ 9:49am

### Re: Re: Re:

thats right

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

im sure more people think exponentially that logrithmatically

•
Anonymous Coward, Oct 24th, 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.

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

### Re: Re:

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?!"

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

### Re: Re: Re:

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

•
abc gum, Oct 25th, 2012 @ 5:57am

### Re: Re:

"fat lot of good it will have done me "

Do you {
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.

•
Anonymous Coward, Oct 25th, 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.

•
Anonymous Coward, Oct 25th, 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?

•
Anonymous Coward, Oct 25th, 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...

•
Anonymous Coward, Oct 25th, 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.

•
Anonymous Coward, Oct 24th, 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.

•
Anonymous Coward, Oct 25th, 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.

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

half way between 1 and 9 is 4

•
Anonymous Coward, Oct 25th, 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

•
Anonymous Coward, Oct 25th, 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)

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