possibility. Sorry I missed your earlier email.
Please let me know what procedure I need to do to participate in the
phone call. If it is just a matter of someone calling me, my phone
number is 612-333-1251.
Thanks!
And of these shall I speak to those eager, That quality of wisdom that all the wise wish And call creative qualities And good creation of the mind The all-powerful truth Truly and that more & better ways are discovered Towards perfection --Zarathustra.
Please let me know what procedure I need to do to participate in the
phone call. If it is just a matter of someone calling me, my phone
number is 612-333-1251.
Thanks!
Anyway, I like having a few different things to work on in case any of
the items get stuck -- e.g. I was relying on help from a Media Lab guy
who practically disappeared when school got going. I may have to go
track him down in person to get any more help from him before next
summer (and going to visit him is a good excuse to visit the media
lab). The other locale I want to get to is Bloomington, Indiana, to
visit the Editors of a relatively new book "Understanding Knowledge as
a Commons".
Florida seems like a not-unrealistic possibility for sometime this
year -- I get together a few times a year with Aaron Krowne who lives
in Atlanta. Next time I talk to him I'll see what his schedule is
looking like. (My main career goal at present is to shake myself
loose of my local side-job so I can travel way more...)
FYI, my sister is currently on staff for a program called Philosophy
Talk, out of San Fransisco -- this Sunday at 10 AM Pacific the show is
on "Mathematics and the Mind". Will be streamed here:
http://planetmath.cc.vt.edu/~jcorneli/pmhdm-paper.pdf
I would be interested in getting your opinions on this idea and
thoughts on how to finish the paper off in a convincing style.
http://planetmath.cc.vt.edu/~jcorneli/acadia.ogg
MP3 version will follow -- but it takes a little while to copy from
the CD to my hard drive. After I listen to it, I'll put segmented
versions in the usual place.
(It occurs to me that a double billing featuring them and Dreamland
Faces would be quite something...)
1 bottle of Czech beer
1 long-pulled shot of Italian espresso
1 snifter cheap British gin
1 glass French white wine (alternatively: 1 glass Spanish red)
1 shot Kirschwasser (German cherry liqueur)
Shake first four ingredients gently with ice and pour into a large
beaker. Float the liqueur over the top. Serve a slice of orange or
lime. Drink through a straw.
The actual title of this drink is the "V for Vendetta". Its primary
purpose is to give whoever consumes it a whopping headache. It also
lowers psychic barriers, so that while under the influence, the
imbiber should be subjected to a reconditioning program, e.g. to fight
fascism in all its forms. May raise or lower IQ via an undisclosed
formula involving a 20-sided die and data on the choice of orange or
lime slice.
"Happy juice" would be a very different recipe... Melon juice,
cucumber juice, lychee juice, coconut milk, nuts... these things all
tend to make me feel pretty happy. I'd happily try a beverage with
those ingredients, anyway!
Some place in the middle: recently I made green tea ice cream again,
and tried making a green tea ice cream/sake float. Tasty, if
intoxicating!
I had a good time at the reunion -- only now I am sad that I don't
regularly spend more time hanging out with the family!
Now that summer is winding up (hot even so) I've done some assessment
of whot I did...
http://gathatoulie.blogspot.com/2007/08/how-i-spent-my-summer-vacation.html
The main point being that I haven't found a new job, but I have
clarified at least three possible arenas to explore for careerish
opportunities. The 3 aren't exactly mutually exclusive (yet, anyway);
but the most likely one is probably to "keep pursuing this nonprofit
stuff" using some of the new contacts I made. However, making the
nonprofit work is definitely going to be a team effort and I'm not
quite sure what state the team is in at present. The other
exploratory possibilities are looking more like grad school (or at
least something scholarly), the primary challenge there being
monetary.
However - it is easy to get stalled out thinking about various
"options" for the future; and since I've been home largely I've been
thinking about other things. Perhaps that's due somewhat to the heat.
In particular: I did some more music and writing -- had my third ever
performance last night -- here are some photos of me and the group
taken by an hombre by name of Dave Stagner during the show:
http://www.flickr.com/photo_zoom.gne?id=1327411504&context=set-72157601874720725&size=l
http://www.flickr.com/photo_zoom.gne?id=1327392398&context=set-72157601874720725&size=l
http://www.flickr.com/photo_zoom.gne?id=1326507205&context=set-72157601874720725&size=l
http://www.flickr.com/photo_zoom.gne?id=1327424616&context=set-72157601874720725&size=l
When the sound files are available (I forgot my recorder and another
audience member captured the sound and will mail me a cd!) I'll upload
it as "Session B" to:
http://planetmath.cc.vt.edu/~jcorneli/everything/novel/
(I don't remember whether I sent you that link before or not.)
Actually despite the common wisdom that it is hard to publish things,
I am considering the possibility of trying to raise funds by getting
this work or something based on it published (for money). Seeing as
how I've been spending a lot of time writing over the last couple of
years that doesn't seem quite as unrealistic as it might be if I just
said "oh, I know, I'll write a book and have it published and make
thousands of dollars..." -- although admittedly my situation isn't all
that dissimilar.
I don't know if there is a ton of other newness around here. I've
noticed myself feeling a little jaded as I look at the random college
students who've just showed up (confessedly, ogle might be a better
word) and think about how little I feel I have in common with them.
On the other hand, my friendships with my neighbors are as good as
ever if not better, and I have been cooking and sharing a lot of
tastyl food lately, emphasizing things from the garden. Today I
bought the other ingredients to combine with mounds of basil that we
got out of our garden, to make a year's supply of pesto.
Anyway I do hope I can figure out a good way to come spend some more
time visiting you all down in Santa Fe this fall. Some of the things
I've been hoping to see develop oughta start developing soon. Will
probably be able to think more clearly about all that when this latest
heat wave goes away.
Love,
Joe
PS. Hi to Greg -- I'm glad I met him. Hope to have more time to visit
soon!
Wav format would be good. Thanks again & hope to see you around.
http://planetmath.org/encyclopedia/UniversalNetsInCompactSpacesAreConvergent.html
Anaphora seems to comes up a lot in math. This is in the usual
"textual" way --
E.g. in this definition, ($(x_\alpha)_{\in \alpha \mathcal{A}}$
refers to the same thing whereever it appears, and also sets
notation like \alpha or \mathcal{A} which will be used seperately
later.
and also in a "hypertextual" way
What the heck is a "universal net" anyway, and what are its
properties? -- properties of these and other defined terms will be
needed by a reader who wants to follow this theorem and proof.
On PlanetMath, hypertextual ultra-long-range references are dealt with
in interface by hyperlinks to entries that define or discuss the terms
being linked. In typical mathematics writing, these links aren't
hard-coded but are "implied" (i.e. the reader is expected to be able
to find or just know the definition on their own).
Combining these two features, the author feels free to introduce terms
like \alpha_0 which have not been explicitly defined anywhere.
Understanding what this sort of conglomerate symbol is supposed to
mean requires some "domain knowledge". Really, this goes for what
happens when any locally scoped definition is made (as in "for every
$x\in X$ we would find neighborhoods $U_x$" -- the reader is assumed
to know what a "neighborhood $U_x$" has to do with an element $x$).
These are probably the main linguistic issues. Math text is written
in a "compressed form" and can't be understood without background
information.
Finally, after texts like this are translated into a computer-readable
form, knowledge management-style inference will become possible and
important. This can feed back into the linguistics level, e.g. for
example some author might use the property that "a universal net in a
compact space is convergent" without explicitly stating that they used
this property! The reader would have to infer that this theorem was
applied.
This reminds me of one more feature. Generally, words (like
"convergent") mean different things in different parts of mathematics.
We can have convergent sequences, series, sets, and now (apparently),
nets. Also graphs, etc. -- but you'll see that PlanetMath's
autolinking software linked the term "convergent" in this theorem to
the page "convergent series" via an alias Converges Absolutely. Point
being: there is no mention on this page of what it means for a
"universal net" to converge. An autolinking program that was enhanced
with more semantic (domain) knowledge would perhaps indicate this gap.
Certainly, if semantics matter for understanding math (e.g. we want to
know what it means for a universal net to converge, so we either have
to be told, or we have to figure it out from whatever we've been
given), an ongoing process of identifying and filling gaps in the
knowledge base will be necessary. The extent to which this process
can be bootstrapped remains to be seen. (Are easier mathematical
texts any easier to translate into a nice computer-ready form? I'm
not sure.)
I am currently on a quest to find people who are pushing the legacy of
Baudrillard, Burroughs, and others of this ilk, in a substantial way.
Often scholarly articles on these folks tend to lack a backbone -- by
contrast yours reads nice and crisp. But you're a practicing artist,
not just a theoretician. Like I said, I'll look for more of your work!
In exchange :) -- here's a link to some of my stuff, a creative
writing, recording, and performance project that is in progress:
http://planetmath.cc.vt.edu/~jcorneli/everything/novel/
Correspondence is welcome.
I visited Marnita and Carl today -- they say that Clarke is back in
town.
You might want to change your sig file. TTYS.
*
That said: one of the things I am most interested in at present is
developing an interactive website (i.e. this application doesn't have
a whole lot to do with language, at least in the usual sense) Here is
a sketch:
Right now PlanetMath is mainly a "mathematics reference work". I
envision it in the future being useful as a full-fledged math learning
environment. In other words, if I want to learn Abstract Algebra or
some other math topic, I should be able to log into PlanetMath and
reach some desired level of proficiency using resources I find there.
In order for this to work, the system will need to know which types of
problems I've solved, which topic-areas I seem to have mastered, which
things I need work on. All of this information can be stored as
triples, and some logic related to these assertions can guide the
user's interaction: "if Joe knows the First Isomorphism Theorem and
the Sylow theorems, then he should be able to solve problem A1287g."
If I can't solve the problem, the system needs some recourse: perhaps
it gives me an easier problem or a hint on how to solve the problem I
was given.
*
A linguistics goal (this has been on the back burner for a while) is
to build a semantic parser for mathematical language -- and use this
to translate standard mathematical writing into a form that the
computer can do useful things with. For example, this parser might be
used to automatically fit new problems into the network of problems
and other information described above.
A third possible application is to use the network to implement (or to
help implement) solution heuristics, to get the computer solving the
"human style" math problems. This is very far on the horizon.
*
The implementation I'm working on will run Lisp with persistent
storage via the Elephant package to Berkeley DB. Some changes to
Elephant will be needed before this will work. A "toy version" that
uses an SQL backend seems like it shouldn't be hard to finish; I may
do this today with a friend; however, Elephant plays very nice with
the Lisp object system, so I want to use that in the long run.
Part of the game plan now is to work on them -- I have had some
worthwhile exchanges with Ian Eslick and others towards making Arxana
actually work the way I want it to. The "metacommons" paper seems
more mysterious to me the more I think about it -- in particular, the
notion of a "commons" seems fishy to me; I think instead we could use
a different frame for analysis and get results that were at least as
good. The other paper may not yet be convincing vis a vis FAIF
publishing, but I don't see any reason not to start some Gonzo style
dialogs about the topics it discusses with the powers that be.
Accordingly, I'd like to set up an interview with Joseph Gallian.
When you get basic PM sponsorship data to me -- I'll initiate the
rendezvous. I'm also of course quite willing to meet that other local
guy you've mentioned to me when he becomes available.
I'd really like to figure out a way to get some income, since at least
two of my three possible plans involve costly extended stays away from
home (in Cambridge, Massachusetts, or Bloomington, Indiana).
The idea of going back to grad school seems to me to be a bit of an
improbability, but nevertheless worth exploring; and these two places
seem to represent two different possible but improbable paths, in CS
and social science respectively. The third path is to make PlanetMath
into a viable career option. There is no real reason that there
couldn't be some overlap between these three things -- like on a
simplex, the three can be blended.
Thinking about it, two "exogenous" options present themselves to me.
(1) To sell some writing, which is another improbable thing, but given
that I've been producing some quantities of it, not impossible; (2) to
check out of the Free-o-sphere for a while and get some sort of paying
job that uses my waking energy. Of course, it can't all be expended
when everyone else is asleep or that won't work out very well.
(Maybe I'll take up actually studying math during my wakeful hours;
that would be a bit of a change of pace for me, and somewhat
productive -- I talked to a local professor here about his
mathematical logic course, which is some stuff I should really know
well, but don't at present; he loaned me a copy of the text book and
said I should visit again.)
*
On a rather different note, here is a neat example I sent to Ian
indicating why I think the scholium system is "cool":
Example: Building, maintaining, and interacting with learning
resources.
Right now PlanetMath is mainly a "reference work". I envision it in
the future being useful as a full-fledged learning resource. In other
words, if I want to learn Abstract Algebra or some other math topic, I
should be able to log into PlanetMath and reach some desired level of
proficiency using resources I find there.
In order for this to work, the system will need to know which types of
problems I've solved, which things I have "mastered", which things I
need work on. Obviously all of this can be stored as triples. The
assertions about assertions come in with things like: "if Joe knows
the First Isomorphism Theorem and the Sylow theorems, then he should
be able to solve problem A1287g." So they throw me this problem and I
can't solve it, and a new fact is added to the database: Joe bombed
another problem. The system needs some recourse: perhaps give me an
easier problem or give me a hint on how to solve the problem I was
given.)
*killer app* ;)
Keeping things unique by the data itself is an interesting
minimalistic proposal... apparently even if OIDs are changing,
compound objects like Triples are stored will still be stored
"safely"? E.g. if I store the triple
[ThingA, ThingB, ThingC]
this will always be (de)serialized so that it points at the right
Things (even if the OID of ThingC, say, happens to change)?
If this works, that would be neat. (If not, I could easily enough
maintain some persistent index and use it to create handles for
Things.)
Your statement of what I hope to accomplish in filtering-by-theory is
correct. Having Theories just be subsets of Things would be fine for
a prototype. Eventually it could be nice to be able to label the
elements of a subset and store such labelings; Pseudo-SQL-wise,
presumably all that amounts to is another column that is ignored
before the "member" function is applied a la your example.
http://gathatoulie.blogspot.com/2007/09/re-semantic-hypertext.html
By doing some research after phrasing my questions, I learned more
about what was going on... and if you read that link, you'll see, you
and I seem to agree on just about every point...!
I do kind of wonder why I was so clueless about relative ubiquity of
meta-statements. Perhaps because these really are not a big part of
the standard "semantic network" theories one learns about in school?
One idea for a somewhat complicated application is in the note above
("Building, maintaining, and interacting with learning resources");
something simpler and immediately fun would definitely be cool.
The business of coding things up for Arxana is still a matter of
figuring out what backend to use to store the triples. Maybe tomorrow
we'll work out some SQL backend -- my favorite is still the Elephant
front-end to Berkeley DB for Lisp, but some details in the interface
are still missing.
http://www.w3.org/TR/rdf-primer/#reification
(Although, based on this primer, I can note that while reification is
not "quoting", my set-up for triples in Arxana is quoting; so the two
systems are not identical. Some further critique of RDF focusing on
its lack of quoting are here: [1]. Must say, I haven't quite grokked
the details of the critique.)
Anyway, lack of originality doesn't necessarily mean make an idea any
worse! However, it does seem to mean that if Arxana is to wins in
anything, it would probably be in applications, not in terms of basic
theory, because the basic is apparently all developed (whether or not
there is a viable implementation).
All that said: in plain language, everyone agrees that the "reified
triple model" will be valuable whenever it is valuable to make
assertions about assertions. (The example in the RDF primer talks
mainly about recording the "provenance" of assertions. I'll just
mention that of course there are other things one might want to say
about assertions.)
(Note: One place where some additional theory may to be needed is in
describing "side-effects" of making an assertion or taking other
actions. It is one thing to be able to talk about an assertion once
it exists -- but it is certainly also good to be able to make
assertions about ACTIONS. I don't know if RDF talks or "thinks" about
actions at all -- but since they are already "semantic" in the sense
of having a "physical meaning" I think it would be very helpful to be
able to modify semantics; e.g. notify me if the price of this stock
falls or rises more than 3 points.)
Application-wise, just because a model exists for RDF does not mean
that there is necessarily any good way to compute using that model at
present...
Here are some other perhaps more interesting examples, again related
to PlanetMath.
Example 1: Evolution of metadata as basic objects evolve.
Currently, objects are owned by one person. (E.g. the object "Group"
is owned by user Drini.[2])
This is very different from the model used by Wikipedia, where anyone
can edit any object and the changes are applied directly to the object
in question.
I've been considering the idea of allowing anyone to edit an object on
PlanetMath, but splitting these versions off as "variants" until they
are either approved by the original owner (in which case they
supercede the original object) or adopted by a new owner. A third
party might choose between different objects that define or discuss
the same term based on metadata like:
"Group" hasEducationalLevel "Undergraduate"
"Group" hasLevelofDetail "Low"
Suppose that these metadata carry over to new variants and suppose
that someone comes up with a much more detailed and advanced
definition. (Such definitions can exist; cf. the Encyclopedic
Dictionary of Mathematics.) The triples above are no longer accurate,
but the metadata is owned by the new owner of the object. So, it
would be good for a third party to be able to annotate the bogus
metadata. (Currently, such annotations would just go into text
fields: "dear owner please change your 'level of detail' metadata
field, its wrong!!", but more specific/directed commentary would
probably be helpful for everyone involved.)
The details here may be a bit complex -- but the basic principle is:
when objects change, their metadata may sometimes change too; so, we
need some language for talking about changing metadata.
Example 2: Building, maintaining, and interacting with learning
resources.
Right now PlanetMath is mainly a "reference work". I envision it in
the future being useful as a full-fledged learning resource. In other
words, if I want to learn Abstract Algebra or some other math topic, I
should be able to log into PlanetMath and reach some desired level of
proficiency using resources I find there.
In order for this to work, the system will need to know which types of
problems I've solved, which things I have "mastered", which things I
need work on. Obviously all of this can be stored as triples. The
assertions about assertions come in with things like: "if Joe knows
the First Isomorphism Theorem and the Sylow theorems, then he should
be able to solve problem A1287g." So they throw me this problem and I
can't solve it, and a new fact is added to the database: Joe bombed
another problem. The system needs some recourse: perhaps give me an
easier problem or give me a hint on how to solve the problem I was
given.)
*killer app* ;)
Some User Interface Considerations
Well, I have thought about this some, maybe not in much depth.
Rendering as hypertext is what I was focusing on in an earlier
prototype -- links that attach to certain pieces of text are of course
overlayed on top of the text itself; markup with different attributes
may appear with different colors; overlapping links (the most basic
case being multiple targets for the same words) could be switched out
either by switching the whole rendering (e.g. by using a scroll wheel)
or by choosing between multiple targets after "right-clicking". My
prototype stuff has been in Emacs.
For an AI-style view, you could have a node rendered with slot
relationshps running down the screen, links to known entities provided
where suitable, annotations lined up in a second column --
JoeCorneli
[ResidesAt]: [421 Cedar Avenue] (became true in Feb 2004)
Again for "hypertext": Note that typesetters have been dealing with
"scholia" for centuries. Marginalia, inline annotations, different
fonts... all kinds of great ideas can be found in historical
manuscripts. So, for textual views, a LaTeX renderer that could pull
of some of these old-fashioned tricks would be great.
The simplest "graphical" systems would just be adaptations of typical
link-node semantic net frontends. 3D and color would be cool of
course.
Finally, in some of my best day-dreams, I imagine a graphical system
that specifically deals with partitions of space. Why? Because
categorizing assertions move objects from partition to partition.
(Generally there are many different ways to partition up a space.)
This is where my old interests in Riemann geometry start to come back
to light... but I haven't worked out (m)any details.
[1]: http://www.mulberrytech.com/Extreme/Proceedings/html/2004/Stickler01/EML2004Stickler01.html
[2]: http://planetmath.org/encyclopedia/Group.html
I've been talking with Elephant's developer Ian Eslick about "what
makes Arxana special?" -- or, as he put it, "what makes it kick ass
over existing approaches?".
The one thing I have been able to come up with is that in Arxana you
can make assertions about assertions. I don't know of other systems
that let you do this. (OK, there are systems like this in Logic, but
I am talking about hypertext systems.)
Suppose I say:
a lizard is a mammal
In Arxana, this would get saved as
assertion_alpha = (a lizard, is a, mammal)
or something like that.
You can come along and say:
assertion_beta = (assertion_alpha, has truth value, false)
Now it is your word against mine. (Which could be taken to imply:
when triples are created, certain data about the creator will be
uploaded automatically. If I am the proverbial zit-faced
thirteen-year-old and you are the proverbial Nobel Prize Winning
biologist, then most people will take your side. Some people may
still be interested in knowing that I made a bunk assertion and trying
to understand why or what they can do about it.)
I am specifically thinking about this system opposed to the systems
developed for the Semantic Web. I am pretty sure that while the
Semantic Web allows you to make all kinds of frame-like systems:
JoeCorneli isa Human
JoeCorneli hasGender Male
JoeCorneli isWearingGarment Kilt
etc., it does not let you make assertions about specific filled slots.
The fact that I can make assertions not just about the statement
JoeCorneli isWearingGarment Kilt
*in the abstract* but the unique "assertion_gamma" that represents
"is" this assertion seems like a special and very useful feature of
the Arxana system.
I could be wrong -- this may not be a special feature -- it may not be
an exceptionally useful feature. But in any event, it seems to be the
feature that sets Arxana apart from other semantic network style
systems that I know of.
As for how assertions about assertions could be a kick-ass feature, my
guess is that one way is that it can be used to override leaky
abstractions. If someone makes a frame with slots like:
A: a car has four wheels
B: a car runs on gasoline
I can go in and rip this to shreds with commentary.
Comments? (Please!)
END NOTE
In Arxana we can (and do) make assertion about assertions in the
abstract, but perhaps such statements are only "evaluatable" with
respect to Theories. For example: perhaps the assertion
JoeCorneli isWearingGarment Kilt
is true in the theory I'll call "Joe's Day Today". It may be false in
the theory "Joe's Day Tomorrow". In any event, the words are the
same; but we may want to take the two versions as "different
statements" when they appear in different Theories.
http://planetmath.org/~jcorneli/everything/music/session-A-rap.ogg
http://planetmath.org/~jcorneli/everything/music/sessionA-jam1.ogg
http://planetmath.org/~jcorneli/everything/music/sessionA-jam2.ogg
http://planetmath.org/~jcorneli/everything/music/sessionA-jam3.ogg
http://planetmath.org/~jcorneli/everything/music/sessionA-jam4.ogg
http://planetmath.org/~jcorneli/everything/music/sessionA-jam5.ogg
words cut, pasted, and otherwise munged by joe corneli otherwise known as arided.