Rational Points on a Napkin

Distinction 1: Surfaces

This post is a part of an experiment for me to improve the distinctions I use in my world. I have daily conversations with interesting and well-educated people who tell me how a plane flies or how digital cookies are used in a login process. If I then try to share what I've learned with others, I'm unable to reproduce what I've learned in an eloquent and clear way. And so I decided to see if writing things down will help me refine my own stories.

Disclaimer: Don't read these posts as if I know what I'm talking about. I'm a lay person in the fields I'm writing about and you should approach these posts as such. In fact, if you know more on what I'm talking about and have something to add or correct, please do so.

So, what is a surface?

(from the perspective of math and, in particular, Algebraic Geometry)

Attributed to mint imperial of Flickr / CC BY-NC-SA 2.0

You might be wondering why I'm writing a post on what a surface is. Well, my fiancé is a mathematician who studies surfaces, and even though I have spoken to him many times about his work, I realized recently that I do not have a good lay-person distinction for the objects which he studies.

A couple weeks ago, I was speaking with a non-mathematical friend, Guillermo Wechsler, about what a surface was. He claimed that a surface was two-dimensional. I, having heard my fiancé, a mathematician in Algebraic Geometry, talk about the hundreds of different variables he was working with to describe the surface he was studying, had a different idea about what a surface was. I said...”A surface can be multi-dimensional – imagine a sphere on which you have a point with three coordinates. As there are three variables involved in describing that point, it is a three dimensional surface.”  Right?

Wrong.

A week or so ago, I recapped this conversation to my fiancé. And...I learned quickly that I didn't know what I was talking about. What I had been calling a surface was based on a common sense, non-rigorous definition. What I learned from the conversation is the following:

1. A surface is a two-dimensional object. Plain and simple. If something is three-dimensional, it is called a three-fold. If something is four-dimensional, it is called a four-fold. My first mistake was a tautological one.
2. A sphere is a surface. It is not a solid object but instead a hollow casing of a ball. But even with this made explicit to me, I had a hard time seeing a sphere as a surface. I imagined a sphere with radius 1 centered around the origin (0,0,0) of the x, y, and z-axes. In order to describe the point that intersects the y-axis, one would write (0,1,0)...three variables and so three dimensions. Tony said, “Nope. You can describe that same point on a sphere simply with longitude and latitude." The dimensions of any particular object are those that the object can be reduced to. And so a sphere is two-dimensional.
3. A surface can be produced at the intersection of multiple multi-dimensional objects. So what about the hundreds of variables Tony has to work with in order to describe his two-dimensional Del Pezzo surfaces of Degree 1? Well, a surface can live in a three-dimensional, or four-dimensional, or n-dimensional space. Imagine a one-dimensional line. It can live on a plane or in a three-dimensional world.

Now, you can also take higher dimensional objects and have them intersect to produce a lower-dimensional object. Take two planes in a three-dimensional space, with equations in the form of ax+by+cz+d=0. If these planes intersect, then you produce a line. So while a line is one-dimensional, you can produce it by equating functions of higher dimensions.

Tony, who works with functions that contain hundreds of variables, is doing something in the same vein – equating these functions in order to produce a two-dimensional object, a surface of a certain type. And this is what a lot of algebraic geometry is.  It is the process of studying geometric objects that are defined by polynomial equations. And at its most basic, it is the equating of multi-dimensional polynomials to describe a polynomial.

Bringing in 2008

Just a quick post to share a beautiful New Year's message sent to me from a dear friend:

"I wish 2008 will find you with a sharp sword in your hands and facing overwhelming insurmountable challenges that you will never overcome...unless you die and are born again."

The Story of Stuff

I was introduced to a video yesterday about our production and consumption of goods. The Story of Stuff was brilliantly done, surprisingly leaving me in an inspired mood. It tied different breakdowns I now see into one large story, the story of consumption.

Besides posting about this video, which I suggest you watch, I also wanted to take a moment for reflection and to share new declarations in my life.

As I've become more aware of "Sarah the consumer", I have changed my habits in a few ways:

1. I try to buy locally whenever I can, whether food stuff or products. My mission this holiday season was to get all my gifts from local Berkeley artisans. And I did. I bought fewer gifts, of higher quality, and I felt...joyful. It was such a better experience spending a day walking around Berkeley and Oakland shopping at small vendors than going to a large mall and crowding into stores to get “stuff” and “more stuff.”

2. I try to no longer buy cheap goods. If something costs more, it is often of higher quality, and will last longer. My ultimate goal as I settle down is to buy very few things for my house, but to invest a lot of money in them. I take better care of those things which are dearer to me. This will also mean that I will consume less “stuff” over my lifetime.

3. I have moved off of “toxic” household cleaners and toiletries and on to natural products. We live in a society that dumps toxins into our world, without thought or care to what we are doing. As I've become an observer of this and called it a waste, continuing along this path is no longer an option for me.

I'm hoping that where previous generations have had the notion of “the American Dream” and the “white picket fence,” my generation will question this and come up with new answers. Most Americans do not have the white picket fence; that number continues to decrease as the middle class shrinks. We have numerous breakdowns caused by the way our society lives. I would love to be involved in a generation that resolves many of these breakdowns, creating a sustainable, less materialistic, and happier life for us.

Creative Commons 5th Birthday in San Francisco

Last night, I went to Creative Commons' 5th birthday party in San Francisco. Once the event was announced, I jumped right on to the RSVP list. It had been a year since I attended my first CC event and had grown to love this free culture crowd.

Upon entering the Terra Art Gallery, the light wood floors, white walls dotted with unique canvasses, and side lighting created a classy yet welcoming atmosphere. Tony and I fell into a guessing game of remixed songs by DJ Spooky (Glass Onion, anyone?) and watched as old footage of a Brazilian (?) dancer ebbed and flowed with the music.

Lessig spoke about where Creative Commons has been over the last year. It is becoming less of a marginal entity for digital copyright, and moving into the realm of the mainstream. Lessig announced that 5 groups (one including the CC Board committing as the 5th organization dropped out at the last minute) have committed to fund Creative Commons $500K per year for the next five years. As Lessig's rhythmic speech and slide show ended, leaving me in a semi-euphoric state, he announced the star performer for the night.

Gilberto Gil and his son, Ben Gil, came on stage. Now, I guess I really wasn't paying attention to the CC announcement, because I had missed that this would be happening. We crowded towards the stage, eventually to sit on the floor as if we were all circling a camp fire listening to an incredible folk storyteller. And really, that's what it was like. Dressed up in a large urbanish art gallery, we sat on the floor, staring wide-eyed and agape, at one of the century's most influential culturists.

In short, it was a beautiful night - celebrating free culture over the last five years.

If you want to read more about the night, Lessig has posted key points of his speech on blog.

Finally, this post is under a Creative Commons Attiribution-Noncommercial-Share Alike 3.0 License due to the Share-Alike license of the wonderful photo above.

Neighbors Project

I had a lunch on Friday with Kit Hodge, a friend from college that I hadn't talked to for years. It was wonderful to see her and to catch up. Since 2000, she's done a lot of grassroots work in neighborhood issues in New York (and, I think, Chicago).

We spoke a while about Neighbors Project, the organization she is now President and CEO of. It is grassroots movement of young people (20-30 years old) living in cities, working to improve the quality of public life in our urban neighborhoods. The organization was started in 2006 by people worried about "both the increasing polarization of our country due to expanding suburban sprawl and the polarization in our city neighborhoods due to increasing gentrification."

What struck me about Neighbors Project as I searched the website and in my conversation with Kit, was its relevance to one of my recent concerns. I am interested in enriching our communal spaces -- environmentally, culturally, our language and media. Neighbors Project showed me that many of these things could be done by all of us, by the caring of our neighborhoods. By supporting local merchants and farmer's markets, your money stays in the community, and out of large chains' hands. By having birthday parties in local parks or biking more, we care about the urban environment and safety around us. By saying hello to neighbors or organizing neighborhood watch communities, we begin to care for the individuals in our community. Planning and engaging in local film festivals, we support our arts and culture.

The Neighbors Project brings simple checklists for people: sitting and reading on your front stoop, getting to know all your elected officials in person, or repairing your bike on the sidewalk. The lists are simple actions that people can pick up, one at a time, as they learn to improve their relationship to their community and their community's relationship to them. Very practical... and very appealing.

The Wikimedia Foundation Announces Compatibility with Creative Commons licenses

After IOC's concert last night, I headed down 3rd St in San Francisco to a party hosted by the Wikipedia and Creative Commons crowd.  Talking to various people in the crowd, I was impressed by all the work that each individual has done for the Free Culture Movement.  To boot, there were some talented karaoke singers and back-up dancers there.

At the event, Jimmy Wales, founder of Wikipedia, announced that Wikipedia would be making their content, currently licensed under the GFDL, compatible with the CC-BY-SA license.  You can find the video of it on jamendo's blog.

There is also a discussion of what this means happening on Lessig's blog.

A Clip From the IOC Concert

Durufle's Ubi Caritas from my choir's concert yesterday. Great piece for altos.

The text and translation are below.

Ubi caritas et amor
Deus ibi est.
Congregavit nos in unum Christi amor.
Exsultemus et in ipso jucundemur.
Timeamus et amemus Deum vivum.
Et ex corde diligamus nos sincero.
Ubi caritas et amor
Deus ibi est.
Amen.

Where there is charity and love,
God is there.
The love of Christ has gathered us together.
Let us rejoice and be glad in it.
Let us revere and love the living God.
And from a sincere heart let us love one another.
Where there is charity and love,
God is there.
Amen.

Palabras at CC Salon

I finally made it back to post about another presenter at this month's Creative Common Salon. *Phew*

Sharon Daniel, from UC Santa Cruz, spoke on her project, Palabras, a participatory video and media project for communities that are not connected to technology. Instead of individuals being bloggers or podcasters and representing a network, communities would be the collective voice for their local region. Currently, they have projects set up in several Buenos Aires shantytowns, San Francisco, and Darfur.

They introduce these communities to Palabras with simple tools -- an altered single-use digital video camera and a simple web application similar to that they use in gaming and chat -- and training in those tools. Videos are recorded and put into a database; users can tag their works, creating their own folksonomies. Currently, there are 5,000 clips. Communties can reference these videos through the tags, begin to make connections between various stories, and create a shared language. A bio of Sharon describes the project as "designed to facilitate Collective self-representation by employing folksonomies (folk + taxonomy) to generate sequences of original video clips based on the semantic associations given to clips by their authors."

I look forward to seeing where Palabras goes and if it can become a valuable space for empowering the voices of collectives and citizen journalists in impoverished areas.

Strayform at San Francisco CC Salon

So I finally made it out across the Bay to another Creative Commons Salon. I haven't been for several months and so it was great to get back to Shine, see familiar faces, and learn what people are doing with copyright in our new digital world. I'm going to highlight a few of the speakers in the next couple of posts.

It seems everywhere I'm turning these days, someone is talking about distributing the investment or sale of information works...Radiohead's newest album being a well-known example. I was introduced to another by Brandt Cannici last night. Strayform is a site that operates both as a means of funding artists, scientists, authors, or other producers of digital goods in a distributive way. An artist can work without restrictive contracts, and the viewers of the site can use and share that content for free.

By cutting out the middle man, Strayform also reduces the cost of music, art, and word production and distribution by 90%, reducing the needed investment cost and increasing profits to artists. Strayform takes care of the life cycle of producing a piece of art. Let's take a CD as an example.

The Investment

Currently, large media companies are needed to fund the life cycle of a CD, from production to distribution and advertising. With Strayform, a musician can post a project on Strayform, setting a fundraising goal if he would like. Anyone can then contribute as much as she would like to that project. Strayform gets a percentage of the final transaction for a successful project to run their operations. If a project doesn't meet the needed funding, Strayform eats the cost.

The Production

Strayform allows the artist to upload images or tracks as he makes his project. Contributors can follow the making of that project over time, becoming involved not just in the consumption of the final product, but also in the creation of the art.

The Marketing and Distribution

The finished project is licensed on Strayform under a Creative Commons license. Currently the only license available on this site is a non-commercial, non-derivate CC license. However, as CC licenses are non-exclusive, the artist will be able to go elsewhere and license his work differently. The artist will also keep all commercial rights to the work.

Commercial Uses

Strayform currently presents the means to move the works to YouTube or iTunes where the works can be monetized. The artist also has the ability to set their own rules for people wishing to use the work for commercial purposes. The artist can specify how much a person must pay if, for example, his piece were to be used in soundtrack for a film with a $10 million budget.

What's Next?

Strayform launched in August. Currently there are over 100 artists, and 300 pieces of content on the site. In a future version of Strayform, there will also be ticketing and sales options. The artist will be in charge of their work here as well. Based on sales of tickets, the venues will contact the artist. You can find more about Strayform and what future updates will bring on their site.

I'm excited to see how this service progresses and if it is an answer...with the community taking care of their artists and the artists giving back to their communities.

I Recently Joined Wikispaces

This is just a quick heads-up to let you know about a great change in my life. I recently began my new position as Marketing Manager at Wikispaces, a wiki-hosting company based in San Francisco. Wikispaces provides simple wiki tools, along with excellent customer support, to be used by your organization or community. We also offer a free upgrade to our Plus plan for teachers who will be using their wikis solely for K-12 educational purposes. You can find out more about what our customers are saying on our Quotes page, with more great feedback coming in every day.

Not only does Wikispaces offer great tools, but the people and the style of the company are gems of the business world. I have been getting to know Adam, Dom, and James in our office, and find them to be great, fun, intelligent people with a huge focus on how to provide the best product and service to our customers. (As for Bisma, I've unfortunately only really been able to communicate with her via e-mail and IM as she is currently back in classes at Berkeley. And while I've enjoyed the short chats we've had, I'll have to arrange a meet up over on our home turf, somewhere close to the University.)

Finally, I wanted to let you know you can also find me blogging regularly now at Wikispaces Blog on topics from how wikis are being used in education, business, or other areas to Wikispaces' features and services.