LL-L "Numeralia" 2009.01.09 (02) [E]

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L O W L A N D S - L - 09 January 2009 - Volume 02
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From: M.-L. Lessing <marless at gmx.de>
Subject: LL-L "Numeralia" 2009.01.07 (02) [E]

Dear Heather,



that blind spot at 7+8 is interesting! Is it commutative, i.e. is 8+7 just
as bad as 7+8? I found as a child that it helped to add the smaller
number to the greater... a little :-)



I read the New scientist article too, and it is astonishing that even
a savant uses what we call "eselsbrücken" ("asses' bridges") in german when
dealing with numbers. Human mind does not love abstract concepts, it wants
touchable, visible things, at least analogies, examples, comparisons.
Probably because of this a great part of the world escapes us. (This idea
always sends a shiver down my back :-) Not that I am greedy for nature's
mysteries, I am a quiet person and can leave things uninvestigated quite
well; but the idea that we might look at nature's wonders in a totally wrong
way or from a wrong direction frightens me. It is not a matter of knowledge,
but of love.)



About numbers: Is your number line equidistant? I mean, is the "space"
between n and n+1 the same everywhere? The question tells you that mine is
not, and I have a general suspicion that humans count in a logartihmic way.
Not strictly, of course. On my number line, I stand at 0, and 0 to 20 takes
about the same space as 20 to 100. 100 to 1000 is just as long as 1 to 100
was, and 1000 to 1 million also. The higher the numbers, the smaller the
distance between them seems. The far away numbers shrink with "perspective".
A multiple of 10 is scaled into the number axis, reducing the distances at
certain values. I have rarely asked people about their inner number line
(and it is only in this discussion I realize that it seems a somewhat
private matter to me :-)), but I should be surprised if anybody on his or
her number line found the "visible" distance between 598077 and 598086
exactly that between 1 and 10. Arithmetically of course it is the same. But
is is not felt the same. -- Maybe this is a reason why we just shrug
shoulders when, as happens everywhere now, bank losses or government
spending just switches from millions to billions, while a factor 1000 seems
much more significant when a thing costs either 1 Euro orr 1000 Euro. This
is insanity, as a factor 1000 is much more important when the number
multiplied is high already, but.... As Luc wrote, humans in hunter-gatherer
societies need not count above "eins, zwei, drei, viele". Great numbers are
dim from perspective, and we always stand at 0. Figuratively of course :-)



Is it so?



Hartlich!



Marlou


From: heatherrendall at tiscali.co.uk <heatherrendall at tiscali.co.uk>
Subject: LL-L "Numeralia" 2009.01.06 (08) [E]

from heather Rendall  heatherrendall at tiscali.co.uk

re the whole of Marlou's reply

Brilliant! What a lovely reply because it takes what I described and then
moves one step on!

I do agree that numbers are greatly affected by how we learn them. In my 20s
I had a shop and discovered that my mind went a total blank whenever I had
to add anything with a unit 7 to anything with a unit 8  i.e. 7 + 18  or 58+
17   or 37 +8 and I couldn't work out for a long time why. Then one
Christmas I found myself playing Cribbage with my mother, where cards have
to add up to 15 so 7s and 8s are important / useful cards to have. I found
my mind blanking out in exactly the same way at the end of each round as my
mother added up my totals for me. Despite the fact that I had been conscious
enough of the addition to make sure I kept the right cards, I appear to have
given up in the face of my mother's quicker arithmetic! And so never got
round to actually adding 7 + 8 = 15. Or was it that I has never been allowed
to say it!

We used to play a lot of family games using dice and I do see combinations
of numbers as on the faces of dice

o                     o             o

o          +                o                          =  8

o                    o              o

In the New Scientist  last week (Jan 3rd)  was a v interesting article by
Daniel Tammet the autistic savant who not only excels at numbers but
languages as well. For him numbers have 'texture'!
Heather

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From: R. F. Hahn <sassisch at yahoo.com>
Subject: Numeralia

Folks,

For those of you that are not already familiar with it, the German
term *Eselsbrücke
*("asses' bridge") denotes a mnemonic device.

Regards,
Reinhard/Ron
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