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Post 0

Wednesday, September 3 - 12:10pmSanction this postReply
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Thanks for posting this, Ed.

In my go-arounds with the late Nathan Hawking, I fortified the philosophical position that mathematical counting is a conceptual power of awareness -- completely lacking in animals (who are stuck in the perceptual realm). Even the 150+ word vocabulary of Alex the Parrot doesn't seriously threaten this position (see criticisms section near the bottom of the page).

If there are any dissenters -- i.e., folks who still think that animals can do math, or that Alex the Parrot's "bird brain" was "smart" -- then please post here, because I'd like to engage you in debate about it.

Ed




Post 1

Wednesday, September 3 - 1:00pmSanction this postReply
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Hi Ed Thompson,

You know I still think you're out to lunch with regards to your schpiel against animals and counting. You're welcome to launch that lovely topic again in one of the main forums. I might well venture in. It's been kind of beaten to death, though, no?

Well, per the elephant article...I have always wondered about elephant brains. They are so big! Math is probably just a provincial pass time they occasionally dabble in for when they aren't engaged in advanced telepathy and alien reconnaissance. :D

Jordan




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Post 2

Wednesday, September 3 - 9:35pmSanction this postReply
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Jordan, here's a break-down of this 'elehantitis of the brain' article:

Leo Lewis:
The elephant's memory is legendary ...
Sure Leo, but what's your point? Memory is one of the 4 perceptual powers of awareness -- while math is conceptual.

... but in a large, grey surprise to science the mighty Asian elephant turns out to have a distinct flair for maths as well.
 That begs the question that perceivable differences in quantity are "math" -- i.e., that math is something that can be performed without the concept of numbers.

... plenty of animals have been shown to possess basic counting abilities but most animals fail when the numbers get much bigger than three or four or the margin of difference between the available choices become too narrow.

“I couldn’t believe it at first,” said Irie, “They could instantly compare numbers like six and five."
Animals haven't been shown to have counting abilities (which are things which require a concept of numbers) -- instead, they perceive quantity differences up to the limits of their powers of perception. And instant comparisons are perceptual in nature. That should have been a tip-off for the astute mind.

Humans can perceive quantity, too (without "counting"). Our perceptual limit hovers around the ability to perceive 5-10 units of something at the same time. If I put marks on the computer screen, this becomes obvious. You can, for instance, "instantly tell" (read: without counting) how many marks there are when I type:


//

You can even "instantly tell" how many marks there are when I type:

///

And you can instantly tell that the group of 3 marks is larger than the group of 2 marks. Some folks can instantly tell how many marks there are when I type:

//// or /////

Less folks can instantly tell how many marks there are when I type:

/////// or //////

Did you "instantly" notice that I reversed the progression and put the group of more (7) marks before the group of less (6) marks? Due to differences in perceptual awareness (not in differences in "counting" abilities), presumably some animals and some autistic humans can instantly tell how many marks there are when I type:

/////////////////////// or when I type: ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

So, do elephants -- as Leo says -- have "limited but nonetheless impressive mathematical ability"? No, they do not. Is the observation that one elephant can see that seven apples is greater than five 87 times out of a hundred -- and that another elephant can see it 69 times out of a hundred -- any kind of proof of counting? No. 

Elephants, like other animals, merely have the perceptual power of quantity-discrimination -- which is not an ability to do math (though it can appear like it is to the estranged or disenfranchised minds of many professional researchers).

Ed
(Edited by Ed Thompson on 9/03, 9:37pm)




Post 3

Thursday, September 4 - 1:39pmSanction this postReply
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Hi Ed,

Like I said, post anew in one on one of the big boards if you'd really like to venture forth on this topic.

Aside, I do agree that the article is rather unenlightening. Still, my interest in this article really boils down to an interest in different methodologies for assessing mathematical abilities.

Jordan



Post 4

Thursday, September 4 - 4:44pmSanction this postReply
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Here's one who probably can't even count the number of trunks he has: http://www.cbsnews.com/stories/2008/09/04/world/main4416123.shtml



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Post 5

Sunday, September 7 - 4:59amSanction this postReply
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Core Calculations

Science News 8/16/08




Post 6

Sunday, September 7 - 9:47pmSanction this postReply
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From the article Stephen linked to:

It’s possible that U.S. volunteers perceived three or four items at a time — a rapid, nonverbal process called subitizing — in longer strings of items and then combined subitized sets ...
Which explains why credit card numbers are broken up into 4 strings of 4 numbers -- and why the longest continuous string in a phone number is 4 units long. Remembering 4 things isn't just 4 times easier than remembering 16 of them -- because of our ability to "subitize" 4 things (as a single unit) against the contrast of our inability to subitize 16 things (except in very rare cases).

I have a friend who can "see" things in packets of "5" real well. If, say, you were to drop 88 matchsticks on the floor, then he would be able to count them all out in just a few to several seconds (whereas most folks would take at least half a minute or more to count them all out).

He can also tell you, before you strum a given guitar string, just what the musical pitch will sound like -- and how it would sound different if you held down the string at different frets. There are probably folks who could hum out all 88 of the keys of a piano -- or hum the note before you press the various keys you're pointing toward.

All of this is part of our perceptual, not conceptual, powers of awareness.

Ed




Post 7

Wednesday, September 17 - 4:06pmSanction this postReply
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Now, here's a crow who knows his epistemology.







Post 8

Wednesday, September 17 - 5:53pmSanction this postReply
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took ye all this time to find it, huh...



Post 9

Wednesday, September 17 - 8:10pmSanction this postReply
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Well, I now feel as though I've learned something today.



Post 10

Wednesday, September 17 - 8:22pmSanction this postReply
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what - that crows can untie swimsuits??? ;-)



Post 11

Wednesday, September 17 - 11:17pmSanction this postReply
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What? Oh! Uh. Ummm. Excuse me, I was a little distracted there.



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