[HN Gopher] Who was Aleph Null? (2013)
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Who was Aleph Null? (2013)
Author : guerrilla
Score : 62 points
Date : 2021-10-11 08:35 UTC (3 days ago)
(HTM) web link (bit-player.org)
(TXT) w3m dump (bit-player.org)
| hungryforcodes wrote:
| I LOVE this stuff. After reading the article it's not more clear,
| but my mind has more tinder to kindle it's imagination.
| dcminter wrote:
| Actually if you look through the comments at the foot of that
| page, John Francis makes it clear that the author was Richard
| Parkins of Cambridge, UK: http://www.zen224037.zen.co.uk/
| dosman33 wrote:
| For a second I was thinking of Aleph One of this site from way
| back when:
| https://web.archive.org/web/19980214102549/http://undergroun...
|
| Interesting read regardless.
| afandian wrote:
| I was thinking of another Aleph One who made both ARM processor
| upgrades [0] and biofeedback boxes [1]
|
| [0]
| http://chrisacorns.computinghistory.org.uk/32bit_UpgradesA2G...
|
| [1] http://www.aleph1.co.uk/about-us.html
| 1MachineElf wrote:
| That's a cool site. How did you discover it? What happened to
| it?
| guerrilla wrote:
| It's the homepage of the author of the phrack article. See my
| other comment.
| perl4ever wrote:
| Aleph one bottles of beer on the wall! Aleph one bottles of
| beer! Take aleph null down Pass them around
| Aleph one bottles of beer on the wall!"
|
| https://math.bu.edu/people/jeffs/aleph-null.html
| mzs wrote:
| "under the pseudonym 0"
|
| http://www.zen224037.zen.co.uk/
| moomin wrote:
| Why am I not surprised it was Richard Parkin?
|
| Charles Lang, is of course, a good candidate for "Archimedes"
| but I'm suspecting it may be David Wheeler, an incredible
| polymath that seemed to be beyond the cutting edge on every
| frontier of computer science for his entire career.
| bitwize wrote:
| Apparently (per a comment in the article) Parkins was a
| member of a group called the Archimedeans and "Archimedes" is
| a composite character representing questions asked or points
| raised by his fellow Archimedeans.
| kevinwang wrote:
| Nice
| mcbuilder wrote:
| You can really get a sense of his humor from his website: "55
| years ago I first used Occam's Razor. Since then I have used no
| other."
| michaelcampbell wrote:
| These stories fascinate me; I remember how giddy I was when the
| famous "Mel" programmer's identity was discovered, even though I
| have zero need to know, nor even any relationship with any of the
| story. Other than said fascination.
| jacquesm wrote:
| That guy 'Mel' has amazing name recognition. On par with
| Mitnick (but for much better reasons).
|
| If you don't know how Mel is:
|
| https://en.wikipedia.org/wiki/The_Story_of_Mel
| mewse-hn wrote:
| The story of Mel explained (2015):
|
| https://jamesseibel.com/the-story-of-mel/
| bawolff wrote:
| I thought this was going to be about the stack smashing guy.
| guerrilla wrote:
| Aleph One wrote "Smashing The Stack For Fun And Profit." [1] I
| found this Aleph Null through a citation in "The UNIX Time-
| Sharing System" by Dennis Ritchie and Ken Thompson [2]
|
| In case anyone doesn't know, Aleph-null is the cardinality of
| the natural numbers and Aleph-one is the cardinality of the
| countable ordinal numbers. On the continuum hypothesis, aleph-
| one would equal the cardinality of the continuum (i.e. reals.)
|
| 1. http://phrack.org/issues/49/14.html
|
| 2. https://news.ycombinator.com/item?id=28826870
| bialpio wrote:
| I think you have a mistake in your aleph-one summary, if I
| recall correctly aleph-zero is the cardinality of countably
| infinite set (like natural numbers), and aleph-one is for
| uncountably infinite sets. It's been a while though so I may
| be misremembering.
|
| Edit: PEBKAC, parent is correct.
| guerrilla wrote:
| I am also rusty, but I believe both statements are true but
| mine may be more precise as there is more than one
| uncountable infinite set and the set of all countable
| ordinal numbers is an uncountable infinite set.
| brobdingnagians wrote:
| The cardinality of Real numbers is 2^Aleph_Null.
| Continuum hypothesis is equivalent to saying that it is
| equal to Aleph_One. But that is debated :) [Debated in
| the sense that you could accept one or the other, but it
| is independent of ZF and there should be a good reason to
| accept one or the other]
|
| https://en.wikipedia.org/wiki/Aleph_number#Aleph-one
| guerrilla wrote:
| > but it is independent of ZF
|
| Yeah, if I recall that's why forcing was invented, to
| specifically prove that C and CH were independent of ZF.
| Yeah: [1]
|
| 1. https://en.wikipedia.org/wiki/Paul_Cohen#Continuum_hyp
| othesi...
| bialpio wrote:
| You're right, I got thrown off by the "countable" part in
| the "set of countable ordinal numbers", which is indeed
| uncountably infinite.
| Sniffnoy wrote:
| Unless guerrilla's comment was edited and you're referring
| to an older version, guerrilla's comment is completely
| correct.
|
| Aleph_1 doesn't refer to uncountable cardinals in general,
| it's a _specific_ uncountable cardinal. More specifically,
| it is, as guerrilla says, the number of countable ordinals.
| moomin wrote:
| Aleph-0 is the naturals (countable). (And many other
| things, like integers, rationals, algebraic numbers)
|
| Aleph-1 is the reals (uncountable), aka 2^Aleph-0. (Also
| any multi-dimensional (finite dimensions) complex space.)
|
| Aleph-2 is 2^Aleph-1 &c
|
| The continuum hypothesis is that there isn't an infinite
| cardinality between 0 and 1.
| Sniffnoy wrote:
| This is incorrect, and a common misconception.
|
| Aleph_1 refers to the second-smallest infinite cardinal,
| whether that's equal to 2^(aleph_0) or not. (Aleph_1 is
| also equal, as has been mentioned, to the number of
| countable ordinals.)
|
| The continuum hypothesis, in stating that there are no
| infinite cardinals inbetween aleph_0 and 2^(aleph_0), is
| equivalent to the statement that 2^(aleph_0) = aleph_1.
|
| The series you refer to is denoted by the Hebrew letter
| bet, not aleph. So bet_0 = aleph_0, bet_1 = 2^(bet_0),
| bet_2 = 2^(bet_1), etc. But that is not how the aleph
| numbers work.
| klyrs wrote:
| Some of us prefer to assume the continuum hypothesis just
| for the sake of this notation... but it turns out that
| the continuum hypothesis is still pretty hot.
|
| https://www.quantamagazine.org/how-many-numbers-exist-
| infini...
| Sniffnoy wrote:
| "Assuming the continuum hypothesis for the sake of this
| notation" is being deliberately obfuscatory, encouraging
| confusion, and requiring other mathematicians to do extra
| work to translate your results to the more general
| context. There's perfectly good notation for the bet
| series, and no need to use aleph as a substitute when
| that simply isn't what it means.
| Greek0 wrote:
| Do we know who the stack-smashing Aleph One was?
| skeletron wrote:
| https://en.wikipedia.org/wiki/Elias_Levy
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