Monthly Archives: November 2007

"Big comma" operator for multidimensional indexing?

I’m running into an annoying problem on my dissertation. Since it’s on tensors, I’m doing a lot of multidimensional indexing, and I find myself doing a lot of this:

Xi1,i2,…,in.

Now, Einstein notation lets me avoid writing sums (again, though, I’m not a fan of it, since there already exists a very nice Σ operator for sums), but it doesn’t do a thing for sequences like this one. In fact, I can’t find any operators that can represent this more concisely.

Now, I can probably treat i as a vector rather than a sequence of scalars, but that might confuse people.

If all else fails, I can probably define something like this:
X,j=1n

, with a big comma in that phrase similar to the huge sigma you use in a sum, but that’s difficult to represent, as the fact that I need to explain what I was writing demonstrates.

I’m leaning towards the vector solution, but if someone knows a good notation for this, please let me know.

"The Capacity for Compassion Divides the Value of the Soul"

I was reading the first page of Hofstadter’s new book, “I am a Strange Loop”, and, as usual, Hofstadter got me thinking. He begins by attempting to draw a dividing line between what has a soul and what does not, using an analogy to what animals may be ethically killed for food to demonstrate the inconsistencies and paradoxes that result when attempting to define that boundary. His own solution is essentially a compromise – he will eat certain animals, but abstain from eating others. His reasoning for choosing certain animals is not precisely made clear.

Well, I tend to view eating as an expression of a natural order, so I don’t feel precisely the same qualms he does about it, but regarding the intrinsic “presence” of a soul, I believe that the dividing line is determined by the soul’s capacity for compassion – that is, to ensure a positive outcome for all, not just itself. In essence, then, the “magnitude” of a particular organism’s soul becomes a function of its behavior rather than an intrinsic property. We can then discard the word “soul” altogether and speak from strictly utilitarian terms:

In an everyone-for-themselves world, the law is kill or be killed. No one will shed any tears for any loss of life, because everyone is only looking out for his own well being. This represents the absolutely degenerate case.

In an entirely compassionate and altruistic world, everyone looks out for everyone else. Presumably, no one starves because everyone gathers food for the good of the community (of course, how this is done without killing is a major missing detail, but an irrelevant one). This is what communism in its purest form promised, but it is of course absolutely unattainable, as the entire world has witnessed over the past century.

So let’s set these situations at opposites and speak about the area in the middle. Specifically, we’re interested in the reciprocity of the situations.

The less compassion one shows, the more likely one is to harm others to benefit himself. However, this creates a scenario (prisoner’s dilemma where the prisoner is guaranteed to proclaim you guilty) in which the only good response is opposition (i.e. you proclaim him guilty as well so you don’t get locked up). The exigencies of the situation then demand a particular type of response, and, because it’s a simple requirement, the moral opposition to this should dwindle.

Therefore, I can set my own dividing line based on the compassion of the creature.

The only remaining question now is that if I eat animals, am I demonstrating the same sort of reprehensible behavior that I spoke of before? That’s a tricky question which many people are going to answer differently, but ultimately, I believe that the amount of good one’s continued existence can engender is a counterbalance against the amount of life one is responsible for taking in the name of sustenance.

Implementation of Media Similarity Search

Similarity search technology in images, music, and other multimedia content has been researched to death. This idea is not about research in any of those areas (I save that for work at Temple). The idea is simply an implementation of these techniques. Something like Google images that allows you to upload images and query based on similarity to the given image. Small-scale systems exist, but I have yet to find any that are as large as mainstream keyword-based image searches, such as Google Image Search. I’ve suggested this to Google when I was in their NYC office (I even gave them my BACH paper to suggest how they could do it for music!), but as far as I know, they still lack this feature (though they are joined by all of the other large search engines).

Large-scale query-by-humming systems already exist, so the lack of those isn’t a problem, but video could also benefit from such an approach (find video with this sound, find video with this frame, etc.). Images could be broken down using MPEG7 descriptors, time series analysis after linearization by a Hilbert curve, or vector quantization, among other techniques. Music could be broken down by a Fourier transform/power spectrum analysis; even the mood of the piece can be accurately predicted by this technique (according to the literature). Video search can be treated as a simple array of images and music (frames) and solved by the bagging the previous two methods.

Focus precludes creativity?

Now that I am narrowly focusing on my dissertation, I have noticed that my tendency to generate ideas has slowed. While this is useful both in my current situation (I don’t need distractions while working on the paper that ultimately forms the basis for the beginning of my career as a scholar) and from an evolutionary perspective (if you’re in a situation that requires focus, such as gathering food, unrelated ideas probably don’t serve as well as focusing on the solitary task at hand), it represents a fundamental divide (which is temporarily bridged) between my primary breadth-first mode of thought and the rest of depth-driven society. What is more interesting is that it says something about the operation of society as a whole if the majority of its thinkers are depth-first.

Philosophy and Novelty

I’ve come up with many philosophical ideas that I’ve later discovered to be unoriginal, but I don’t really read much philosophical literature. What, then, is the message? Is it that my thoughts would be original if I had been born a century earlier? Or does the legacy of past philosophers suffuse society to such an extent that the ideas are easily rediscovered, even by one who has never gone out of the way to study them?

Why must novelty be so hard? Must I study previous works every time I discover an idea to ensure that the idea was not written down? I couldn’t; I have far too many ideas and it would take far too long. Neither can I simply throw ideas away, as one particular lesson that I’ve learned from the scientific community is that people simply cannot estimate the potential value of any idea. Paradoxically, an exhaustive study of the field would additionally seem pointless if I am capable of synthesizing others’ philosophies intellectually; the only distinction lies in knowing that an idea is unoriginal. I’m not sure there’s a particularly good answer, except perhaps to ignore it, write as if all of my ideas are original (thanks Descartes), and let society sift through them later if it chooses (and if it doesn’t, there’s no point in writing them down in the first place because they’ll simply be ignored).

Dissertation – Week 2

Tensor theory is deep. It’s one of those areas that’s much more complicated than it needs to be. The good news is that I can still pick the fundamentals up within an hour and it’s going to enable me to write a lot of background if I want to (I’m thinking around a 35 page background section is sufficient, leaving me around 80 or 90 for methodology and the remainder for other sections and appendices). I’m done talking about SVD and its equivalents, but now I get to mention PCA, ICA, and LSI! 🙂

I wanted to perform an actual experiment this week and get started on the methodology, but unfortunately, I don’t understand how our data is formatted and the only one who can explain it to me isn’t around when I am until next Tuesday, so that is going to have to wait.

I’ve written 4.5 pages so far; 6 left to meet the weekly goal. It may all be background, but I can do it if I take tomorrow and maybe Saturday to write.

And Einstein notation? I admire Einstein as much as the next guy, but that’s a pretty stupid idea, honestly, whether Einstein introduced it or not. Think about it: not only are you summing without using a + or summation symbol, but you’re now using both subscripts and superscripts to describe things that are not true indices or exponents. I certainly don’t think I’ll be using it in my dissertation.