An entry contained in a blog
Time for a little pet peeve. I’ve gotten numerous emails that say something like, “In your last blog…” when what they mean is, “In your last blog entry…”
A blog is a collection of entries (or posts). The set of possible entries is only countably infinite, but the set of possible blogs has the cardinality of the continuum.
(In practice, the positivity of the cosmological constant does impose an upper bound of about 210^122 on the number of possible blogs. But that’s merely a contingent fact about our universe, and is not intrinsic to the notion of blog. Logically, there’s no reason for a blog ever to end — even though any particular entry, including this one, must.)
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Comment #1 April 7th, 2006 at 6:53 am
If a blog can be infinite in principle, a blog entry can also be infinite in principle. Instead of adding more and more new entries to the blog, one could just edit one entry adding more and more things to it. So the set of all possible blog entries has the cardinality of the continuum.
Comment #2 April 7th, 2006 at 7:14 am
Alejandro: That’s a valuable insight — thanks!
But I construe “entry” as meaning “entry at a particular time” — so that if you edit an entry, then in effect it becomes a different entry. In other words, I’m unwilling to regard the union of all edits to an entry over the course of eternity as itself an entry, even though that union is part of the blog. The reason I take this route is that I want to affirm what’s arguably the First Law of Blogging: that every entry must be consumable by readers in a finite amount of time.
Comment #3 April 7th, 2006 at 9:47 am
So but what about all those comments, are they not part of an ‘entry’ ?
Comment #4 April 7th, 2006 at 10:24 am
So but what about all those comments, are they not part of an ‘entry’ ?
Sorry, dude. Is the DVD commentary track part of the movie? Is the Talmud part of the Bible?
Comment #5 April 7th, 2006 at 11:18 am
I disagree. The size (number of entries) of a blog is not bounded, but it can only be arbitrarily large, not infinite. So the set of all blogs remains countable.
Comment #6 April 7th, 2006 at 12:12 pm
Scott,
blog ‘entries’ are not static text like the bible.
What if the ‘entry’ contains hot-linked images or other dynamic content (e.g. stock ticker)?
Comment #7 April 7th, 2006 at 12:31 pm
Would not a blog need a unique identifier (such as an IP address and a directory name, all of which are finite) in order to ever be read or written?
Comment #8 April 7th, 2006 at 12:59 pm
Also, it’s not so clear how to order blogs so as to yield a predecessor function.
Comment #9 April 7th, 2006 at 1:00 pm
I completely agree with you Scott – I think this is one of your better blogs.
Comment #10 April 7th, 2006 at 1:02 pm
So a blog can’t contain another blog? When a blogger sets up rss feeds for the comments in individual blog entries, are those feeds themselves blogs? Or would that lead to problems involving Russell’s Paradox?
Comment #11 April 7th, 2006 at 1:33 pm
I completely agree with you Scott – I think this is one of your better blogs.
🙂
I was waiting for someone to crack that one…
Comment #12 April 7th, 2006 at 1:38 pm
What if the ‘entry’ contains hot-linked images or other dynamic content (e.g. stock ticker)?
Would not a blog need a unique identifier (such as an IP address and a directory name, all of which are finite) in order to ever be read or written?
Alright, alright, alright…
I’ve already thought of several responses to these questions that make what I’ve written true. But I’m sure you can do the same on your own. 😉
Comment #13 April 7th, 2006 at 1:42 pm
Also, it’s not so clear how to order blogs so as to yield a predecessor function.
An ordering of blogs? Let’s see: Shtetl-Optimized, Quantum Pontiff, …
Seriously, if you assume the Axiom of Choice, you can do this even for a continuum of blogs. But why do you need to?
Comment #14 April 7th, 2006 at 2:39 pm
>the set of possible blogs has
>the cardinality of the continuum.
huh?
I didn’t get that. I think the cardinality is Aleph-Zero… Do I need to show a gödel numbering for blogs to show that?
Comment #15 April 7th, 2006 at 3:05 pm
> I didn’t get that.
Scott seems to understand a blog as an infinite sequence of entries
B = E1, E2, …
Use a variant of Cantor’s diagonal replacement …
Comment #16 April 7th, 2006 at 3:34 pm
huh?
I didn’t get that.
As I said — in principle, there’s no reason for a blog ever to end. And if it doesn’t, it can encode an arbitrary real number.
Comment #17 April 7th, 2006 at 3:52 pm
Oh, I see. The problem is I see a blog as a blog in a given point of the time. At any point, it’s finite.
Comment #18 April 7th, 2006 at 6:43 pm
I am glad we are finally having this important discussion.
If the cardinality of the set of blogs is the continuum, then there are blogs that are not recursively enumerable. What does this say about strong AI?
Comment #19 April 7th, 2006 at 6:54 pm
The blog-counting argument is correct, but I believe there is only one possible sequence of entries for this blog.
Prove me wrong.
Comment #20 April 7th, 2006 at 7:50 pm
Hi Luca,
I am glad we are finally having this important discussion.
Me too!
If the cardinality of the set of blogs is the continuum, then there are blogs that are not recursively enumerable. What does this say about strong AI?
I don’t think anything. For given infinite time, it’s easy to create a non-r.e. blog. You just measure a state of the form (|0>+|1>)/sqrt(2) every day and post the result.
Comment #21 April 7th, 2006 at 7:58 pm
The blog-counting argument is correct, but I believe there is only one possible sequence of entries for this blog.
Prove me wrong.
Well, do you accept indeterminism about any future event? If so, then I can prove you wrong by blogging about that event when and if it happens.
But I would think the burden would be on you to predict my next entry.
Comment #22 April 7th, 2006 at 8:51 pm
Thanks Scott, now I have a better understanding of how you come up with your posts.
Comment #23 April 8th, 2006 at 6:42 am
In your next entry, you should talk about the biggest blog which is not describable in just one entry.
Comment #24 April 8th, 2006 at 9:07 am
>What does this say about
>strong AI?
Nothing, because it says nothing about the process of writring actual blogs in actual languages, only about “possible” blogs.
Comment #25 April 8th, 2006 at 12:44 pm
I meant the smallest blog not describable in just one entry, of course. D’oh.
Comment #26 April 8th, 2006 at 8:05 pm
An aside: I like the way verbs like “to post” become nouns “the post” so easily these days. I like living in time when if nothing else, at least language is fluid.
Comment #27 April 8th, 2006 at 8:56 pm
I like living in time when if nothing else, at least language is fluid.
Language has always been fluid. Otherwise, how did American English become so different from British English in 200 years?
Comment #28 April 9th, 2006 at 9:10 pm
Language has always been fluid. Otherwise, how did American English become so different from British English in 200 years?
Freedom Scott, Freedom.
Comment #29 April 9th, 2006 at 10:36 pm
Hi Scott,
BTW, do you have any job offer for the next year?
Comment #30 April 9th, 2006 at 11:00 pm
BTW, do you have any job offer for the next year?
I decided to spend another year in Waterloo, either at the university or at Perimeter. I like it here.
Comment #31 April 10th, 2006 at 4:36 pm
>>Language has always been fluid. >>Otherwise, how did American English >>become so different from British >>English in 200 years?
>Freedom Scott, Freedom.
I believe you mean “errors”, my dear chap.
Comment #32 April 10th, 2006 at 7:22 pm
>Freedom Scott, Freedom.
I believe you mean “errors”, my dear chap.
Do people not get sarcasm?
Or, if this fellow did get the sarcasm, is it generally considered humorous (or humourous, as the case may be) to respond to sarcasm as if it were not sarcasm?
Comment #33 April 13th, 2006 at 2:08 am
>Or, if this fellow did get the
>sarcasm, is it generally considered
>humorous (or humourous, as the case
>may be) to respond to sarcasm as if
>it were not sarcasm?
I couldn’t possibly comment on what passes for humour in the colonies.
Comment #34 April 22nd, 2006 at 2:58 pm
See this post, and comments 763 to 768.