
Hofstadter – On Number Numbness (1982) [pdf] - rahuljayaraman
https://www.gwern.net/docs/math/1982-hofstadter.pdf
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rendx
"This kind of thing worries me. In a society where big numbers are
commonplace, we cannot afford to have such appalling number ignorance as we
do. Or do we actually suffer from number numbness? Are we growing ever number
to ever-growing numbers?"

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sn41
On a related note: I suspect that humans cannot "guesstimate" numbers greater
than 20 by sight. I have tried this experiment on myself, friends and
relatives and so far no one has succeeded. Take a glance at the next longish
queue and try to guess, are there greater than 50 people or fewer than that?
The first guess is usually wrong.

This is similar to the picture of the logjam in the article. Somehow, we know
abstractly to count, have representations for numbers, and algorithms for
arithmetic, but at a gut level, our instinct for numbers is not very spot-on.

~~~
ZeroGravitas
4 seems to be the limit for accuracy:

[https://en.m.wikipedia.org/wiki/Subitizing](https://en.m.wikipedia.org/wiki/Subitizing)

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AlphaGeekZulu
It would surely be super interesting to forward the questions on the last page
of the PDF (p134-135 in the book) to Alexa, Siri, Cortana and Bixby and post
the answers here...

(I do not use virtual assistants myself, thus the request to anybody who does)

~~~
mda
Tested some, Google assistant has very decent answers.

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dredmorbius
I'd read this many years ago when on my own Hofstadter kick in the late 1980s.
The points of cultivating a basic numeracy are well-made, and sometimes turn
up elsewhere (e.g., numbers / timings all programmers should know).

There are also some blind point revealed in Hofstadter's own awareness. His
comments on the length of account identifiers fails to recognise that the
identifier-space itself is a resource and potential risk surface. When
assessing and trying to archive Google+ content, the fact that the several
billions (10^9) users were represented by 21 digit UUIDs (of which ~19 digits
were significant) was a factor. The notion of an identifier space which can
neither be feasibly exhausted nor searched (contrast: SSNs and phone numbers)
has benefits.

(Phone spam based on random dialing would disappear if the dialing space were
far larger, though as IPv6 critiques note, the idea of a vast an effectively
innumerable space also gives rise to the prospect of attacks from that space.)

In discussing explosive yields, Hofstadter misses the significance of the
inverse cube law. So whilst 1 tonne of C4 killed 214 marines, 10 tonnes would
likely have only about 125% the lethal effect, if detonated at a single point.

(Distributing explosives increases the effective impacts, hence the existence
of cluster munitions and the problems they produce.)

Tools such as GNU unts, or other units-aware calculators, are a great way of
converting easily between different metrics. That's one way of increasing
general numeracy.

It's also helpful to think of "traditional" (non-metric) measures as being
very highly _applied_. 1.2 million litres isn't particularly memorable, but
knowing that an acre-foot of water will raise the level of your one-acre pond
by a foot, that the acre is related to a measure of work (the amount of land a
man and team could plough in a day, literally _Tagwerk_ in German), and that a
foot is, well, roughly a foot, puts the utility back into these measurements.
At a time when quick comparisons were useful and conversions infrequent, and
domain-specific measurements were useful, these made sense.

