11 ms·
Who was Aleph Null? (2013)
- michaelcampbell 5y agoThese 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 5y agoThat 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 https://en.wikipedia.org/wiki/The_Story_of_Mel
- mewse-hn 5y agoThe story of Mel explained (2015): https://jamesseibel.com/the-story-of-mel/ https://jamesseibel.com/the-story-of-mel/
- bawolff 5y agoI thought this was going to be about the stack smashing guy.
- guerrilla 5y agoAleph 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 http://phrack.org/issues/49/14.html 2. https://news.ycombinator.com/item?id=28826870 https://news.ycombinator.com/item?id=28826870
- bialpio 5y agoI 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.
- moomin 5y agoAleph-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 5y agoThis 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 5y agoSome 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-infinity-proof-moves-math-closer-to-an-answer-20210715/ https://www.quantamagazine.org/how-many-numbers-exist-infini...
- Sniffnoy 5y ago"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 5y agoDo we know who the stack-smashing Aleph One was?
- skeletron 5y agohttps://en.wikipedia.org/wiki/Elias_Levy https://en.wikipedia.org/wiki/Elias_Levy
- dosman33 5y agoFor a second I was thinking of Aleph One of this site from way back when: https://web.archive.org/web/19980214102549/http://underground.org/ https://web.archive.org/web/19980214102549/http://undergroun... Interesting read regardless.
- 1MachineElf 5y agoThat's a cool site. How did you discover it? What happened to it?
- guerrilla 5y agoIt's the homepage of the author of the phrack article. See my other comment.
- afandian 5y agoI 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/Aleph1_ARM320.html http://chrisacorns.computinghistory.org.uk/32bit_UpgradesA2G... [1] http://www.aleph1.co.uk/about-us.html http://www.aleph1.co.uk/about-us.html
- mzs 5y ago"under the pseudonym ℵ₀" http://www.zen224037.zen.co.uk/ http://www.zen224037.zen.co.uk/
- moomin 5y agoWhy 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 5y agoApparently (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 5y agoNice
- mcbuilder 5y agoYou 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."
- hungryforcodes 5y agoI LOVE this stuff. After reading the article it's not more clear, but my mind has more tinder to kindle it's imagination.
- dcminter 5y agoActually 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/ http://www.zen224037.zen.co.uk/
- hungryforcodes 5y agoNice catch, I didn't see that while skimming the comments.
- hungryforcodes 5y agoOK why did I get downvoted for this one?
- perl4ever 5y agoAleph 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 https://math.bu.edu/people/jeffs/aleph-null.html
- Someone 5y agoFTA: “ℵ0 is also listed as the author of a 1973 book review in SP&E. The book under review is Games Playing with Computers, by A. G. Bell.” I tried finding out what those initials stand for, but couldn’t find an answer. If it happens to be Alexander Graham Bell, I give it a decent chance that’s a pseudonym, too.