Hofstadter – On Number Numbness (1982) [pdf]
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Re: Hofstadter – On Number Numbness (1982) [pdf]
#2"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?"
Re: Hofstadter – On Number Numbness (1982) [pdf]
#3It 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)
Re: Hofstadter – On Number Numbness (1982) [pdf]
#4On 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.
Re: Hofstadter – On Number Numbness (1982) [pdf]
#5On 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 abstra…
4 seems to be the limit for accuracy:
Re: Hofstadter – On Number Numbness (1982) [pdf]
#6It 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)
Tested some, Google assistant has very decent answers.
Re: Hofstadter – On Number Numbness (1982) [pdf]
#7I'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.