Saturday, February 26, 2011

τ keeps on slipping...

Apologies: this post is somewhat more specialized than my normal fare, and probably will be boring as hell without a some mathematical knowledge.

Electrons have a negative charge. When you think about it, this really doesn't make much sense; after all, electrons are the charge carriers for electric charge, and so we would hope to assign their charge a positive value. That electrons carry a negative charge isn't a fundamental statement about reality, though, but rather an unfortunate consequence of an arbitrary decision made early on when electricity was being studied, but when electrons were still undiscovered.

Similar cases of unfortunate arbitrary conventions can be seen in other areas of mathematics and science. Recently, for instance, Michael Hartl has argued that $\pi$ is not the right constant to use in the equations governing such things as circles, frequencies and angles. Rather, Hartl argues that $\tau = 2\pi$ is a much more natural choice. Using this convention, the circumference $c$ of a circle is $c=\tau\ r$, eliminating the awkward factor of 2 in $c=2\pi r$. It may seem that we lose something when considering the area $A = \frac12 \tau\ r^2$ of a circle in this notation, but in fact this is much more natural for expressing as an integral, as those familiar with calculus will be happy to note.

Today, I'd like to show you somewhere else in physics where changing notation makes things much more natural. Concretely, I'd like to argue that using a different $\tau$ makes quite a lot of sense, when we using $\tau = it$ as a replacement for the time $t$ in equations. In fact, I take it as a lesson of quantum mechanics that we should consider time to lie along an imaginary axis and not along the real axis. This notational trick, known as Wick rotation, simplifies many physical equations, such as Schrödinger's equation. I find that \(\frac{d}{dt} \left\vert\psi\right\rangle = i \hat{H} \left\vert\psi\right\rangle\)  makes much more sense expressed in imaginary time:
\[\frac{d}{d\tau} \left\vert\psi\right\rangle = \hat{H} \left\vert\psi\right\rangle\] Adopting this convention also makes it manifestly clear why complex conjugation is intimately related to time reversal, since $\tau^* = -\tau$.

It is, in fact, quite rare for $t$ to appear in quantum mechanics without a factor of $i$ attached. Even when describing a classical object interacting with a quantum mechanical system, such as an oscillating field introducing a time-varying term to a system's Hamiltonian (that is, the operator which describes the energy of a system--- if that makes no sense, don't worry), we write something like \[\hat H(t) = \cos(\omega t)\ \hat\sigma_x + \sin(\omega t)\ \hat\sigma_y.\] But wait!, you say! There's no $it$ in that equation! As it turns out, there actually is, but we've hidden it by using trigonometric functions where an exponential function is more natural: \[ \hat{H}(\tau) = e^{-\omega\tau\hat\sigma_z/2}\hat\sigma_x e^{\omega\tau\hat\sigma_z/2} \] This form also has the advantage of making it manifest that the oscillation of the classical field can be thought of as a coordinate rotation of a time-independent field.

Other key results of quantum mechanics become much cleaner with the imaginary-time convention. For instance, this convention along with the natural units convention that $\hbar = 1$ makes Ehrenfest's theorem much less awkward to write: \[\frac{d}{d\tau}\left\langle \hat A\right\rangle = \left\langle \frac{d\hat A}{d\tau}\right\rangle + \left\langle[\hat H, \hat A]\right\rangle\]

At the end of the day, such notational choices as the sign of an electron's charge, the choice of circle constant, or the axis which we use to represent time are all arbitrary. We can do physics quite well even when a choice lacks something in mathematical beauty. My point, then, in exploring the fun of $\tau$ is to show that even though our choice of notation is an arbitrary choice made for the convenience of the humans that work with it, by making our notational choices carefully, we can coax out and make manifest deep truths.

Testing MathJax support

I have recently decided to add MathJax support using the techniques described at Dysfunctional. Unfortunately, math does not seem to be working in preview mode, and so I wrote this test post to see if formulas render when actually published. $H\left\vert\psi\right\rangle = E\left\vert\psi\right\rangle$. $x^2$ $\sqrt{x}$ \( |x^2| = x^* x\)

Sunday, February 20, 2011

Thoughts in the endgame.

Welcome to the endgame of a long political play for electoral dominance in the United States. What do I mean by that? I mean that groups like The Family and Koch Enterprises, amongst others, have been playing the long game in American politics, and that they have nearly reached the culmination of their strategy. As Rachel Maddow brilliantly explained, the unrest in Wisconsin can only be understood in the context of a struggle for the survival of the Democratic Party. After all, unions are the last bastion of the left in terms of fundraising, and so cutting off unions means cutting fiscal support for the Democratic Party. Especially post-Citizens United, elections are won with money, and so marginalizing unions means disenfranchising voters from all walks of life.

What would it mean, though, for the Republicans to have won so thoroughly? To answer that, it helps to understand what the Republican Party (under all its guises) is and what they stand for. As much as the Democrats are beholden to the forces of irrationality, the Republicans mark themselves as being still less rational. As much as the Democrats are subservient to unbounded corporatism, the Republicans distinguish themselves as being still more enamored of model of the corporation as state. While the Democrats are weak on issues of human rights, the Republicans are plain monstrous.

This last point deserves some elaboration: witness the unabashed war on women, going so far as to seriously propose that it be legal to kill doctors for providing medical care to women that includes abortion. Faced with economic crisis, they would callously eat the future, all the while saying "so be it." Given the pro-democracy movements in many parts of the world, the Republican taking heads are by and large siding with the dictators and using the movements to inflame Islamophobia. What other word than "monstrous" can describe these kinds of actions and positions?

We must ask ourselves, then, whether we want future challengers in the political arena to be obliged to play by rules written by the current crop of Republicans; rules that increasingly leave no room for reasoned debate, or indeed, for any thought more complex than a sound-bite. Do we want to solve our problems, or are we content to let a small few make them much worse as they pursue their own self-interest? Those that have brought us to this endgame know full well that they will not reap what they have sown, for the consequences are still longer-term than their callous and wicked plays at power. Thus it falls to us, those who care about the world that we inherit and that we pass on to the next generation, to decide what the nature of politics will be.

It's not all so bleak, of course. Given that there's about 90,000 people protesting in Wisconsin against the latest round of union-busting, the Republican endgame may yet be averted or at least postponed. Let us not waste the opportunity given to us by this uprising, but instead use it to remind people of what the stakes really are.

Saturday, February 19, 2011

Project Umbra Update for 19 Feb

Just thought I'd let you know what I've been working on with Project Umbra for the past two weeks.


The biggest change in Shadowtable has been the addition of a new Combatant Details pane that provides more details about a selected combatant. In the future, this pane will also let the game master quickly change initiative scores and other details.
This pane will also be used for managing players connected to a given combatant via Shadowcloud.


Speaking of Shadowcloud, the mobile-web component of Project Umbra has been updated with several new mocked-up pages which in the future will allow for users to create characters and view their statuses.

The biggest update, however, has been that Shadowcloud is now available for use at Many parts of this app are still non-functional, and those that are are quite alpha-ish, so please be gentle!

Some of the more interesting parts of Shadowcloud that can be viewed now are the character creation page and the character status page.


That's it for this update! I hope you enjoy following Project Umbra, and that as it matures, that you will find it useful.

(Speaking of useful, I could still really use some help from those amongst you more experienced at mobile web development than I am. Please let me know if you would like to join the Project!)

Sunday, February 13, 2011

Scorching the common ground

Only the most ardently Luddite amongst us deny that technological advances change our lives in myriad, dramatic and often unexpected ways. Western approaches to city planning post-automobile, for instance, differ in marked ways from before the introduction of cheap medium-range transportation. Likewise, the introduction of telecommunications technology like the telegraph and the telephone changed how people relate to each other, making distance that much less of an impediment to human interaction. Broadcast media such as radio or TV changed nearly completely the primary modes by which information and culture diffuse in Western societies.

Of course, too, many of the features of society which we take completely for granted now are the products of advances in technology as well. We use signage to indicate all manner of information, as it is reasonable to expect that the vast majority of adults are literate and thus will be able to understand such signage. Though nearly invisible in its prevalence, then, the use of signage is a feature of a society that has truly adopted the printing press technology to the point where literacy is a requirement for societal participation.

It thus behooves us to understand how technology reshapes society. We do this in many ways, not the least of which is by exploring technological impacts in fiction. Betraying my own literary interests, I feel compelled to point to science-fiction as being one of the primary vehicles for exploring how society--- even humanity itself--- change in the face of technological advances. To choose an example that has truly permeated into the culture-at-large, consider the technologically-driven optimism of Star Trek: the United Federation of Planets represents humanity at its best, thriving in a true post-scarcity economy enabled by fictional technologies such as the replicator. Whether or not we ever make a replicator, or whether such a thing is even physically reasonable, setting a show against the backdrop of a world in which replicator technology has banished scarcity helps us understand something very real and very timely today: rapid prototyping. Sites such as MakerBot, Shapeways and Thingiverse reflect that there are some kinds of scarcity being made obsolete by technological progress. Primarily, scarcity deriving from access to manufacturing equipment is becoming less and less pronounced, shifting scarcity onto raw materials. This obsolescence of scarcity was explored first in fictional worlds such as that depicted in Star Trek, and so we are at least somewhat prepared for its impacts.

Where, then, do we turn to understand how the line between human and machine becomes less obvious by the year? Where, then, do we turn to understand the changing of such concepts as "gender" from immutable to transient? Where, then, do we turn to understand the impacts of an ever increasing longevity? We turn to many things, including turning again to fictional realms. We turn to stories like Tomorrow and Tomorrow and Tomorrow, to stories like Accelerando (free e-book, CC licensed), to stories like Ghost in the Shell. There are, of course, many many others that could and should be mentioned in such a list--- it is beyond my intent to provide such a list here, though. Rather, I wish to emphasize that the usefulness of a story to discussion need not hinge on its direct physical reasonableness. Indeed, fanciful tales help us understand quite a bit about the relentless advance of technology and of scientific knowledge.

Many issues of transhumanism and of a society transformed by access to information can be understood under that most controversial of umbrellas, the Singularity. There, we find stories and arguments abound to help us understand what it means to be human when our biology is a platform as fungible as any other. In discussing and understanding the arguments and stories that go along with the Singularity, we find new perspectives on the human condition, at least some of which shall hopefully be useful in the decades and centuries to come.

Here, I note that those defending the irrationality of religion make arguments that are, on the surface, quite similar. It doesn't matter if there exists any literal gods, so long as the stories help us understand ourselves. The primary difference in my argument, however, is that I do not advocate rejecting the application rationality and skepticism on the basis that temporarily suspending it can be a useful exercise. Indeed, it is well argued that the rejection of skepticism is a highly dangerous position to take, even at its best. Thus, I reject the "rapture of the nerds" approach to the Singularity as completely as I reject the whole thesis of religion.

The conflating of useful hypotheticals and of artistic endeavors with a religion-like dedication to a set of claims, even in absence of evidence, is why I take issue with the Kurzweil approach to the Singularity so rightfully mocked by PZ Myers today. By turning the Singularity from a discussion into a religion, Kurzweil and others like him obstruct the usefulness of Singularity thought. Rational and skeptical people, reacting to Kurzweilian nonsense like "immortality in 35 years," are inclined to sometimes also reject the usefulness of hypothetical thinking about posthumanism, transhumanism, artificial intelligence, and of pervasive information networking.

My humble proposal, then, is to reject the scorched ground of religion-infused Singularity thinking and to instead find common ground well-supported by the rigors of evidence and yet informed by hypotheticals. We can have it both ways insofar as we are willing to refrain from magical thinking about technology that passes Clarkian thresholds.

Thursday, February 10, 2011

Announcing Project Umbra: Mixing metaphors (in a good way).

It's no secret that I am a gamer. I play board games, card games, video games, tabletop games... pretty much every kind of game this side of LARPs (I do have limits). As a gamer, I see games changing in response to technological advances, along with everything else in society. Video games, for instance, have transformed immensely into one of the richest new art forms available. At the same time, advances in small-run printing coupled with online fora for game reviews have allowed for many more unique board and card games ranging in complexity from stunningly simple (such as Zombie Dice) to mind-mindbogglingly complex (such as Arkham Horror or Battlestar Galactica).

What remains, however, is the conception that tabletop, board and card games are based on physical objects (dice, cards, boards, papers, tokens, figurines, maps, etc.) whilst video games are based on information processing. This divide means that the more complex games, like those mentioned above, require an awful lot of bookkeeping to play, dissuading all but the more passionate gamers such as myself. This is seen in extremes with many roleplaying game systems. The rulebooks for HERO System 6th Edition, for instance, cost $80 and weigh in at about 1,000 full-color pages. Players must keep track of endurance, body and stun damage, mental and physical defences, skill level allotments, initiative, position, etc., while the game master (GM) must keep track of all of this and more for each of the antagonists.

My question, then, is what power can be gained by mixing the physical and informational models. Let the computers do what they do best, keeping track of rules and statistics, while the humans do what humans do best: spin stories and build worlds. Of course, many tools exist that nudge in this direction, but very few embrace the fusion of information processing with physical metaphor and human creativity.

Enter Project Umbra: a suite of web-based tools for keeping track of stats and states in Shadowrun 4e. Players will be able to log in to a game hosted by a GM from their smartphones, and will be shown their damage levels, wound modifiers, initiative orders and other vital information. The GM, for his/her part, will be able to use an Android tablet (Honeycomb or later) to view and manipulate entire combats quickly and unobtrusively. Games won't have to be interrupted to ask for initiative rolls from each player in turn; they can simply tap a button on their phones to make that information available to the GM, keeping table talk focused on the characters rather than the rules.
A player can quickly see what games are available to them from their mobile phones using the web-based Shadowcloud client.
In the future, I plan on expanding Project Umbra to other roleplaying systems, but for now, focusing on Shadowrun 4e allows for the project to be developed organically--- that is, without having to understand the full scope before writing each line of code. The potential here is rather unexplored, after all, and so it's far from clear what the right approach will be to each problem.
A game master can quickly view and manipulate an entire combat by using an unobtrusive tablet, instead of a laptop whose screen blocks their view of players.
Like any truly community-minded project, Project Umbra is an open-source project based on open specifications and open platforms. The tablet-facing part of Umbra is based on the Android platform, and as such, can be run on any of the many forthcoming Honeycomb-powered devices. The web-based portion uses Google App Engine for Java (itself a derivative of the open-specification J2EE platform) to serve standards-compliant HTML5 content powered by the open-source jQuery and jQuery Mobile libraries. Communications between components are handled by JSON serialized data, generated by the Gson library. All Umbra-specific code is licensed under either the GPL or AGPL, as appropriate, and as such, is freely available to interested developers for reuse.

I think the potential for Project Umbra is quite exciting, frankly, and am looking forward to playing more with it and making the most I can of the technology. If you would like to be a part of the project and help in any way, please let me know. Just like any good game, Umbra isn't limited to just one mind.

Happy gaming!

Monday, February 07, 2011

An opportunity for self-improvement.

The abstract is often easier to understand by way of concrete examples. It is all well and good to speak of a pattern, but without showing an anecdote that illustrates that pattern, it's difficult at best to understand the significance of that pattern. It is thus that I'd like to briefly revisit last night's post on moral blind spots, taking the time to point out one specific community that could benefit from some self-reflection about such blind spots.

I speak of the problem of sexism within the atheist community. To put my example in context, consider some of the reasons an individual might adopt atheism: a skepticism towards unsubstantiated claims made by religions, an understanding of and respect for science as a method of learning, and (perhaps most importantly) a dedication to the use of reason as a problem-solving and decision-making tool. Note that all three of these reasons by necessity involve some level of introspection, observation and rational thinking--- all tools essential to making good moral decisions. Moreover, by definition, atheism is absent the intense homeostatic motives of religion, enabling a greater responsiveness to advances in moral thinking.

One would thus be justified in suspecting that the atheist community would be, on the whole, less susceptible to the all-too-human biases, preconceptions and discriminatory divisiveness found in so many other human communities. Alas, however, there exist some stunning counterexamples, from which I wish to highlight a particular counterexample. Jen McCreight has taken a fair amount of her time lately to document examples of sexism in the atheist community, including accepting a guest post on the subject and documenting the deplorable behavior found at r/atheism (see here, here and here).

As I have said before and will likely say again, one of the quintessential features of scientific thinking and of rational thinking is the capacity to self-improve by recognizing errors. Here, we see a notable blind spot that many (but not all!) of my peers in the atheist community seem to share. If we are as truly dedicated to the cause of rationality as I would hope that we are, then this is a wonderful opportunity to demonstrate that we need not be burdened by such irrational biases. We can make manifest our willingness to be wrong and to make amends by recognizing that our behavior is not as respectful of those women in our community that offer such potential to enrich and broaden our views. We can make positive changes to grow our community into a healthier and more diverse group, starting by eschewing sexism.

It is no secret that our culture is not always kind to women, girls and others that check the "female" box when filling out forms. If, however, we are to truly take the principle of self-correction seriously, then we must rise above the nonsense that is sexism. Please, don't squander this opportunity to do the right thing.

Sunday, February 06, 2011

On weak points and blind spots.

It's been a long time since I've written here, I know. I'd like to break the silence with some long, epic post composed of sheer brilliance, but I don't see that happening. Instead, I'd like to expound briefly on some themes that are by now familiar to readers of this blog.

In particular, I've been thinking a lot lately about how and why intelligent, well-meaning people can still do horrible things, or at the least, turn a blind eye to them. Even the most thoughtful of people can be seen to ignore the role, for example, that the Catholic Church plays in perpetuating the AIDS epidemic. Those that otherwise serve as prime examples of humanistic morals can still ignore or deem unimportant the moral issues associated with modern communication, such as censorship, DRM, or net neutrality. Passionate feminists can still take a sex-negative attitude (though many, thankfully, do not). So too can passionate advocates of science and education be misogynistic creeps.

In my experience, everybody, regardless of intelligence or compassion, is afflicted by moral blind spots and weak spots. It is important to remember this as we make decisions in life, as none of us is infallible, and as none of us have privileged access to the facts and logic that must direct our compassion. Indeed, there have been many times where I have been wrong in my thinking about ethics and morals, and where I have been happy to have been shown the errors in my previous modes of thought. (This is a theme that I hope to get around to revisiting soon!) To my mind, then, the most important part of moral thinking must be a willingness to be wrong, paired with a dedication to discovering and correcting such wrongs.

Of course, I have been a bit glib until now in using words like "wrong" to describe moral hypotheses, so allow me to rectify that. When I discover that my attitudes and morals imply a course of action that would unduly harm another sentient by infringing upon their ability to exercise their freedoms as they see fit, I call such attitudes "wrong." Just as surely, if I harm someone by unfairly restricting their opportunities, then that is also "wrong." If I base my moral thinking on suppositions which are found to be false, then that thinking is "wrong." Thus, self-correction takes the form of education: to avoid such wrong-headed approaches to life, I must be educated sufficiently to empathize with as many points of view as possible, and I must be educated such that I can well predict and understand the consequences of my actions.

Invariably, however, I will not achieve omniscience, and thus must by necessity commit to wrong modes of thought where ethics and morals are concerned. The drive to improve oneself is essential in coming to terms with this reality; if I cannot eliminate blind spots, can I not make them smaller?