But G+ Doesn't Support Titles

This is cross posted from a status I posted on G+. Yes, this whole thing is one status post over there, and this is rather long even for my blog posts, because putting blog length comments out in the stream for public consumption is apparently something which one can do now. This is sort of the topic of this post, that we now have a site that behaves like a social network but offers the opportunity to blog within it's structure. Don't worry, I'm not planning on abandoning my own personal parcel of the internet to do all my blogging there, but it is an interesting thing to try. That said, if this is the sort of thing about which you worry, you may want to talk to a professional about your anxiety.

There is a saying, "form follows functionality." Apparently it means that what something, originally a building, looks like should reflect what it is supposed to do. I think it can also be interpreted as meaning that what shape something takes reflects what it is able to do. For example, there is a reason Twitter is a morass of twits, with messages limited to 140 characters and all communication broadcast to the entire community this shapes the dialogue that occurs on Twitter. Another interesting, although too detailed for me to go into here, example is Facebook. As the user base and available tools have changed there have been fundamental changes to the type of community that exists within the "Facebook" structure.

By implementing statuses unbound by pathetically small 140 or 420 (500?) character limits, Google is implicitly making a statement about the community it desires to grow in G+. Of course, how exactly this functionality will play out in the community built on top of it remains to be seen, but one interesting G+ phenomenon is Tom Anderson. Yes, this is MySpace Tom, and yes, he is a one man phenomenon.

I have mentioned before that following Tom is a quite worthwhile thing to do, because he tends to say interesting, thought provoking things. Due to the Twitter-esque asymmetric subscription mechanism (recently implemented on another large social networking site I believe), it is possible for large masses of people to follow what essentially become social networking celebrities. On twitter these people are usually meat space celebrities and we get to hear about their new sunglasses or how trashed their hotel room is. On G+ these people are Tom Anderson and, because the different functionality, we get to hear insightful thoughts (rather than one-liners) about social networking, computing, and perspective.

Unfortunately, I think that some of the same functionality that enables Tom to reach such a large audience hinders the appreciation of his posts. Inevitably Tom's posts become inundated with hundreds of comments. Although a post might provide an interesting lead in to the idea that all "reality" insofar as we can perceive it, is necessarily subjective rather than an objective presentation of some external truth. However, if such a conversation actually took off, I couldn't find it due to the low signal-to-noise ratio within the comment stream. It is wonderful that Tom has so many well wishers, but the culture of a G+ comment stream is quite different than that of a blog where, even on the more popular blogs, comments, for the most part, are a continuation of the discussion began in the original post. To borrow a nautical metaphor suggested by G+'s own nomenclature, what we have here is a stream; toss something in and it pretty quickly moves on, lost in the bustle. A blog is more of a lake, or in my case maybe a pond (puddle?), if you chuck something into it, you can still come back and revisit it a couple of times before it eventually sinks.

Of course, there is nothing inherently wrong with G+ as it is. A fun community is taking form, and if more people from my circle of friends become active on it, I'm sure I shall enjoy whatever it becomes. However, if the fine folks over at Google want to provide a platform for discussions that are simultaneously public and substantive, I would recommend providing authors some way to organize comments into multiple threads. This way substantial responses can be organized into a separate discussion, or even multiple discussions, and other encouragement could be stored separately and perused by those who find it to be of interest. That said, what extent public, substantial discourse is possible is something of an important and unresolved question among philosophers of democracy, so that's something about which we could talk ;)

A Note on Content

As I mentioned, I have many browser tabs open, storing things about which I would like to talk. However, I am not going to do that today. "Why?" you might ask. Because responding to things in a meaningful way takes a lot more time, mental energy, and effort that just making up a post whole cloth, and I am still fairly worn out.

There is the obvious reason, posts in which I respond to other things, or even develop my own idea seriously, tend to be longer, and thus take more time. They need to introduce whatever it is I am referring to, in a way so that the people who don't love hyperlinking around the Internet discovering new, interesting, and awesome things will have an idea what I am talking about without reading the source link.

It also is a more arduous process because I feel the need to give weighty consideration to what I say. In this post, after I decided what I wanted to say and why/how I would say it, I basically am just writing as it comes to me. But if I am developing an idea I think is important/interesting, or, to put it another way, about which I would really like some discussion and constructive feedback, I feel that I should take the time to structure my thought in an interesting, appealing, and accessible manner, which takes time.

Additionally, if I am responding to something thought provoking, I feel the pressure to make my response a worthy one. If I don't add meaningful thought to the discussion, then I might as well have just posted the link and let you simply read it for yourself. So, while response posts are quite interesting to write, as you might guess from the number of them I do, and pleasant in that I don't need to worry about coming up with something to talk about, they do require a lot of energy.

I don't have a lot of energy, so you got this today ;)

Administrivia

A couple of quick notes. I remain firmly committed to keeping my updates to the at most one per day rule. Since I would like it if people read and thought about every one of them, it seems that one a day may actually be too fast a tempo. However, you may notice I make exceptions, this happens when I post something I don't particularly care if people think about, although I still like being read ;). These administrative posts are one example, nothing much deep happening here. Another was the poem yesterday, I like it and all, but, in my opinion, it really isn't deep thought provoking. So, that's just a heads up as to where I'm at in regards to update schedule.

Like I said, I like to believe that I am being read. The main way I achieve that is through your feed back. Sure, when I have time off I obsessively stalk the stats page, gazing longingly at the page view count, but since my cynical side assumes most of those are bots or other automatic processes sizing up my turf, I don't put a ton of stock in it. So, if you are not commenting out of some mistaken belief that what you have to say is not relevant or worthwhile, please feel free to comment, I love comments. If you don't want to take the time, please do not feel obligated too! But, if there is something you feel like saying but you aren't sure, as long as it is polite (and I don't mean you have to agree with me, in fact, I kind of prefer when people don't), go ahead and post it.

On a related note, I love feed back where ever it comes from, I especially like it when it is on the post itself. The reason for this is that, ideally, other people will respond not only to my post, but to the comments already on it, and we can get a discussion going, and discussions are some of my favorite things in the whole world; deep conversations and dancing, my two favorite activities. Of course, I understand that in the past there have been issues with posting comments for some reason, or maybe you just don't feel comfortable doing so, or just don't want to. This is, of course, fine. If you want to post a comment, but find yourself unable to, if you get it to me in another way and tell me that you want it posted, I will post it under your first name, or whatever moniker you prefer.

Finally, although I'm whittling down my backlog of blog topics, I still have a selection available. So, I was going to see if people have any preference which they see first. However, I will describe them in my own vague style, where a post about value, commercialization, and Monsanto is actually about a call to my Grandma. So, the choices you have are my third post on music videos about the song Dead and Gone, my third post on Kant's categorical imperative about homeless people, a post about football, or a post about public transit. I may do a post about Facebook next, because it is timely (I was going to do it tonight, but this is actually turning into a substantial post, so probably tomorrow), but, if people express a preference, it will be the first of the four options that I get to. That should be enough for today, have a good night!

Poker Face and the Problem of Other Minds

A week ago, the estimable Mr. Karplus of Sounds Like Japan fame posted a rather addicting "mashup" of the top 25 pop songs of 2009. In a successful attempt to procrastinate reading some math, I embarked to watch the music videos for each of these songs. Through this process I came to two realizations; firstly, as addicting as some pop music is, some is either musically or substantially (ie relating to its content) unpalatable; secondly, there are some interesting concepts to be explored.

Music tends to evocative, rather than expository, communication, by which I mean songs tend to communicate by inspiring the listener, rather than rationally detailing their message as a philosophical or mathematical argument would. Due to this, I will be giving myself license to interpret the song as it relates to me, instead of claiming to explain something inherent to the music. If you appreciate music qua music, that is, the musicality of music, you should check out Sounds Like Japan, Tim knows his stuff!

As you might imagine from the title, I am going to begin by examining Lady Gaga's song "Poker Face." Let me make clear from the beginning that I do NOT wholeheartedly endorse the message of this song! That said, what is the essential message of this song?

I find that choruses are a good place to begin the search for the overall purpose of a song. Because it is repeated throughout the song, the message in the chorus ties the various parts of the song together. In "Poker Face," the chorus is as follows:

"Can't read my,
Can't read my
No he can't read-a my poker face
(she’s got to love nobody)"

My interpretation is that this song is narrated by a woman who avoids emotional investment in her romantic relationship because her partner cannot discern her true detachment behind her "poker face." However, I do not think that this is a very satisfied woman.

The line of the song that I find most objectionable is, "And baby when it's love if its not rough it isn't fun." My main problem with this message is that it normalizes force in the context of a romantic relationship, something I find abhorrent. While, rationally, I recognize that each couple defines their manner of interrelation within the context of their personal relationship, our society has such deep issues with domestic and relationship violence that it hardly seems necessary to glorify it in song.

The reason that I mention that line is that I find it indicative of the self-destructive behavior the unhappy narrator is displaying. Further supporting this interpretation is the previous line, "Russian Roulette is not the same without a gun." If that doesn't seem self destructive, I don't know what would. The question then becomes why is the narrator, despite the freedom implied by, "she has got to love nobody," so despondent?

My interpretation is that the depression results from being unloved, despite being in a romantic relationship. The chorus makes clear that she considers some essential part of herself unknown to her partner. In such a situation, one must doubt whether he really loves her, because she believes that he doesn't really know her, because he cannot read her poker face, that is, know her most private reflections.

This leads us to the problem of other minds. While each of us has uniquely privileged access to our own minds, we can neither access the mind of another on such an effortlessly deep level, nor easily share our own inner workings. Thus, one of the greatest wonders and joys of living is the continual sharing of ourself with others and being trusted by others who attempt to share themselves with us.

One of my favorite YA authors, John Green, coined the term, "imagining each other complexly," to describe this process. Imagining is an appropriate term, given that our impression of someone else is forever trapped within our own mind, but the joy and hope of the phrase comes from the word complexly. We seek to know our partner not as they exist-for-us, by which I mean as we want them to be, but as they exist-for-them-self, to borrow a distinction from my man Emmanuel Kant. To quote John Green in this video, where he is quoting Ze Frank, "we want to feel what it's like to be other people, and let other people feel what it's like to be us." While this was said specifically in relation to why YouTube users make videos, I think it applies to why we write blogs, write music, risk ourselves in the hope of love, and why we walk out into society each day in spite of the often alienating nature of the world in which we live.

To finish with "Poker Face," while the narrator "has got to love nobody," she also has got nobody to love, nor is she loved in return, at least not in a complex notion of the word. While the song starts out in an ominous tone, by the end the chorus sounds distinctly like a lament. I believe the narrator would welcome exchanging the risks of basing a relationship on emotional deception for the true risks involved in an emotionally vulnerable relationship based in open honesty.

Let me conclude by noting that this is a good example of the value that philosophical reflection has to the "layperson." Personally I think "Poker Face" is a wonderful and catchy song, but consumption of its message without critical reflection seems, in some sense, dangerous. With reflection one can both enjoy a driving, compelling, mournful song and attempt to come to grips with some of the problems that seem essential to being a human.

Mathematics, A Eulogy?

Did you know that the area of a circle is Pi times its radius squared? Did you know the area of a triangle is one half of its base times its height? Did you know for a right triangle (a triangle with one angle of 90 degrees or pi/2 radians) the sum of the squares of the two sides adjacent to the right angle is the same as the square of the side opposite the right angle, the hypotenuse (did you know that I, a mathematician, still cannot spell hypotenuse?)? More importantly, do you know why?

Earlier today I posted a Facebook blasting the mainstream method of mathematics education. This was out of various frustrations, including my frequent interactions with people in the late stages of chronic math apathy, and conversations with colleagues on the state of our students. I have colleagues, how weird is that! Much of my despair boils down to our dogmatic adherence to a system which is fairly seriously flawed. I don't claim to have THE solution, I have thoughts that I would like to see tried out, but mostly, I want to see us have the courage and vibrancy to experiment boldly with our curriculum, changing it to try to get out of this malaise.

I believe I was unduly harsh, as math is not the only subject that suffers from some deep problems endemic to our education system. One horribly harmful practice is the passing along of students who have not sufficiently mastered current materials to higher level courses. Because math is such a rich and useful subject, attempting to understand a subject without a thorough grasp of the prerequisite courses is akin to the canonical fool attempting to build a sturdy foundation upon ground made of sand. Although factoring polynomials (mostly quadratics) and negative numbers are two fine examples of things one ought master before proceeding, as they end up in fairly frequent use, by biggest concern is fractions.

I cannot understand what part of our system so scars students that they stay scared of fractions long through their math careers. If one simply wishes to work with fractions, two simple rules suffice, common denominators to add, multiply straight across. This will not convey an understanding of the nature of fractions, but it will provide you with all the "special" tools that you need to manipulate them, they won't be things of beauty, but at least they ought no longer be feared. However, as I indicate at the end of the first paragraph, the essential point of math is NOT an isolated scattering of lifeless, lonely facts, but an intricate, intertwined network of collaborating reasons why things are true.

Were I to be given an island on which to implement my social experiments, my math curriculum would, broadly, look as follows (and mothers could keep their children...). An introduction to the positive integers, addition, and the number one. These topics are deeply connected, as you can think of one, the unit, as the starting place for all mathematics, without it there is only nothing, then addition miraculously conjures the rest of the whole numbers, as one is joined by one for two, and so forth. Here we introduce the miracle of zero, which leaves numbers unaltered Should we ever experience diminishing, as happens when one departs, we become familiar with negative numbers (not subtraction, which is a misleading myth). Now, one might find it useful to repeatedly add a number to itself, such as if students arrive on buses each carrying 32 children, 32 children after the first, 32+32 after the second, 32+32+32 after the third, and thus is multiplication formed from addition.

Now things become a little tricky, but I have faith in our citizenry to persevere. Just as zero played a special role for addition, leaving things unaltered, our unit plays the same role for multiplication. And just as the addition of -n undoes addition by n, because together they add to 0 which leaves things untouched, multiplication by 1/n undoes multiplication by n, because they multiply together to zero. Thus we run into the first fractions as reciprocals to the whole numbers, and we noticed that division too is an illusion. Consider 0*n, which we know to be n added to itself zero times, when no buses have arrived, there are no students, no matter how many are on each bus, so 0*n=0. Now suppose you are discovering this for the first time, what must you suspect about 1/0? Well, one expects multiplying by 1/0 to undo multiplication by 0, because that is the role of 1/n to undo n. So, 1/0 times 0*n should be n, no matter what n is. However, no matter what n is, 0*n always arrives at 0, so 1/0*0 needs take on more than one value to satisfy our system, since it cannot, and indeed must be 0 since anything times 0 is zero, we discover that 1/0 cannot be included in our system without breaking the patterns that we have established. Because there is no division, and n/0 is instead n*(1/0), we must conclude that, should zero occupy a denominator, we have left our reasonable system of numbers, so this is to be avoided. This has gone on long enough, but we may quickly build exponentiation from multiplication the same way we build multiplication from addition, and roots now are un-exponents, the same way negatives are un-addition and fractions are un-multiplication.

Of course, this is a bit of a mess when skated through in 2 paragraphs, rather than over the course of a year or two, but the point is that it is all interrelated. This is where the beauty of mathematics comes from, it is a mosaic, and a puzzle, and a fractal laden, dew adorned spiderweb on a cool morning. Addition and multiplication are different, not separate, and subtraction and division no longer exist, much simplifying the order of operations. Recall that these operations have the counter intuitive property that they do not commute (that is, 3-2 is not 2-3, and 2/3 is not 3/2). Since these operations no longer exist, this strange fact, an artifact of a formulaic approach to math, need no longer be considered. Now 3+(-2) and (-2)+3, as well as 2*(1/3) and (1/3)*2 can be swapped as much as is desired.

The WHY is beautiful, without it math is just an exercise in memorization and rote manipulation, two things that are fairly boring and easily done by computer. With why, math becomes a rich environment for exploring, every new piece of information not a fact, but a new piece of the puzzle which must be slotted into an awaiting rough edge. The easiest method to determine the area of a circle requires calculus, but I can prove the Pythagorean theorem on a napkin in under 5 minutes (if we are in the same place, feel free to ask me to do so, it is a beautiful proof). How amazing is that, these two facts, that we casually teach side by side in an introduction to geometry, have vastly different backgrounds and stories. Personally, I think the area of a triangle is the easiest of the three, and accordingly, I leave it as an exercise for the reader, should you be in the mood to explore. It may help to take right triangles as your point of departure, but remember that not all triangles are right triangles.

As I posted on Facebook, learning math the traditional way is akin to learning to write poetry by taking lines from the poems of the greats and sticking them next to each other in varying orders. Or, to be less absurd, it is learning about history by rote memorization of dates and events, with no thought paid to the overall correlation and causality, the beautiful, interconnected, vastness of human experience. It is learning a foreign language sentence by sentence, hardly paying heed to individual words in the phrases blindly committed to memory, let alone the system of syntax and grammar. Overall, I have to say that what is a very important question to answer, but only because you need to establish the what before you can sail off into the sunset after your elusive why's...

Feedback Appreciated

Well, today is the last day of August, and as things end other things begin. When things begin, I often wonder how they should go. So, today I thought the question should be, how do you want this blog to go? I have some specifics that I have been considering, so I thought that I would run them by you.

The current format is a post with content I find interesting on Fridays (Philosophical Friday), and questions on Tuesdays (Response Tuesday). How is that working for you? I have trimmed out my more frequent updates in hopes of not giving readers content shock, but there are some things I have been considering adding. If I do add some stuff, I could add it here, and you could read it at your own discretion, or I could create a separate blog to segregate posts by topic.

Some of the topics I have considered giving voice are my daily life and religion. Also, I enjoyed having a theme in July, but when August's theme flopped *nasty glare at people who didn't suggest topics* I found I had fun making a post on a topic of my choice, like Find Your Song. So, I have considered putting one day in for topical thought provoking posts and one for a post of my whimsy.

So, if I did all of these and did them on my Blog my schedule might look something like the following. My Life Monday, Topical Tuesday, Response Wednesday, Theological Thursday, Free Choice Friday. Of course, that might be a lot of content to churn out, especially during the school year, but I could adjust things so I wrote on MWF one week and TTh the next.

So, my question to you is twofold. First, what content sounds interesting? Secondly, should I add it to this blog, or segregate it by topic?

Oh, if you happen to be stuck in a training meeting all day, here's a more open ended question to chew on. This occurred to me while driving past a log-truck filled with lumber. Specifically, are dead trees still trees? More generally, consider the boundaries of nouns, how do you tell when one "leaves" the category a noun describes? Are cats still "cats" after they die, are lions "cats", are stuffed animal cats "cats"?