# 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]

If you’d like to read more awesome and interesting stuff, check out this unrelated (but not entirely random!) Techdirt post.

Filed Under: brain, education, linear, logarithms, math, mundurucu, psychology

## Comments on “DailyDirt: Logarithmic Thinking Is Natural”

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

## Re: Re:

halfway between ONE and NINE… not ZERO & 9.

## Re: 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.

## Re: 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…?

## Re: 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 ???

## Re: Re: Re:

^{2}Response to: Watcht on Oct 24th, 2012 @ 5:42pm“your first finger should be 2 not 1”. Ohhhhkayyyy…

## Re: 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]

## Re: Re: Re:

^{2}Response to: Watchit on Oct 24th, 2012 @ 5:42pmWouldn’t it be easier to just add 20 and 40 and divide by 2?

## Re: Re: Re:

^{3}Response to: Watchit on Oct 24th, 2012 @ 5:42pmYes, 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.

## Re: 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?

## Re: 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

1+9=10/2=5

or, 5?4={1,9}

## Re: 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

## 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.

## Re: And for bigger numbers ...

In a log scale, 1 billion is actually correct.

## 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.

## 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.

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

## Re: Re:

“does anyone give a crap about crap like this “

Math is important.

## Re: Re: Re:

“Math is impotant.” , unlike spelling. FTFY

## Re: Re: Re: Re:

thats right

im sure more people think exponentially that logrithmatically

## Re: 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.

## Re: 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?!”

## Re: Re: Re: Re:

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

## Re: 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.

## Re: 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.

## Re: 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?

## Re: 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…

## Re: 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.

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.

## Re: 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.

half way between 1 and 9 is 4

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

## 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)

## 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