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<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 11pt; font-family: Arial;">===========================================<br>
L O W L A N D S - L - 09 January 2009 - Volume 02<span style="color: rgb(102, 102, 102);"><br>
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<p class="MsoNormal" style="margin-bottom: 12pt;"><span style="font-size: 11pt; font-family: Arial;"><br>
From: <span class="ep8xu"><span><span style="color: rgb(91, 16, 148);">M.-L.
Lessing</span></span></span><span class="hccdpe"> </span><span class="ldacoc"><<a href="mailto:marless@gmx.de">marless@gmx.de</a>></span><br>
Subject: <span class="hccdpe">LL-L "Numeralia" 2009.01.07 (02) [E]</span></span></p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">Dear Heather,</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">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
:-)</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">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.) </span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">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 :-)</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">Is it so?</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">Hartlich!</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-size: 13.5pt;">Marlou</span></p>
<p class="MsoNormal"><span style="font-size: 11pt; font-family: Arial;"><br></span></p><div style="margin-left: 40px;"><span style="font-size: 11pt; font-family: Arial;">
<span style="color: rgb(0, 0, 153);">From: <a href="mailto:heatherrendall@tiscali.co.uk" target="_blank">heatherrendall@tiscali.co.uk</a> <</span><a style="color: rgb(0, 0, 153);" href="mailto:heatherrendall@tiscali.co.uk" target="_blank">heatherrendall@tiscali.co.uk</a><span style="color: rgb(0, 0, 153);">></span></span><br style="color: rgb(0, 0, 153);">
<span style="font-size: 11pt; font-family: Arial; color: rgb(0, 0, 153);">
Subject: LL-L "Numeralia" 2009.01.06 (08) [E]</span><span style="font-size: 10pt; font-family: Arial; color: rgb(0, 0, 153);"></span></div>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">from heather Rendall <a href="mailto:heatherrendall@tiscali.co.uk" target="_blank">heatherrendall@tiscali.co.uk</a></span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">re the whole of Marlou's
reply</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">Brilliant! What a lovely
reply because it takes what I described and then moves one step on!</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">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!</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">We used to play a lot of
family games using dice and I do see combinations of numbers as on the faces of
dice </span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">o
o o</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">o
+
o
= 8</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">o
o
o</span></p>
<p style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">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'!</span></p>
<div style="margin-left: 40px; color: rgb(0, 0, 153);"><span style="font-size: 11pt; font-family: Arial;">Heather</span><br style=""></div><div style="color: rgb(0, 0, 153);"><br><span style="color: rgb(0, 0, 0);">----------</span><br style="color: rgb(0, 0, 0);">
<br style="color: rgb(0, 0, 0);"><span style="font-size: 11pt; font-family: Arial; color: rgb(0, 0, 0);">From: R. F. Hahn <<a href="mailto:sassisch@yahoo.com" target="_blank">sassisch@yahoo.com</a>><br>
Subject: </span><span style="color: rgb(0, 0, 0);">Numeralia</span><br style="color: rgb(0, 0, 0);"><br style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">Folks,</span><br style="color: rgb(0, 0, 0);"><br style="color: rgb(0, 0, 0);">
<span style="color: rgb(0, 0, 0);">For those of you that are not already familiar with it, the German term </span><i style="color: rgb(0, 0, 0);">Eselsbrücke </i><span style="color: rgb(0, 0, 0);">("asses' bridge") denotes a mnemonic device.</span><br style="color: rgb(0, 0, 0);">
<br style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">Regards,</span><br style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">Reinhard/Ron</span><br style="color: rgb(0, 0, 0);"><br style=""></div>
<p class="MsoNormal">
<span style=""></span></p>