Sonia Sotomayor’s Neural Hierarchy


When you hold a soccer ball in your hands, you can identify its left half as being the one under your left hand. But if you were to spin the ball around, the left half would still be under your left hand, even though the ball’s position had changed. This is because in and of themselves a sphere does not have a right and left side.

Left and right are concepts that can only apply to objects that have a front and a back, and an up and a down.  Like people. My left side is always left, no matter whether standing on my head or lying in bed. I suppose if you made a mark on what is currently the left side, I could easily rotate the malt ball so that the mark was on the right side.  Now what can you do? I suppose claim that at 10:21 it was the left side, but now, at 10:22 it’s the right side. But you get the idea.   Your designation of the half-sphere with the mark at it’s apexas the ‘left side’ even when it was sometimes pointing down, or up, or to the right – depending on how you spun the ball – would be arbitrary.

Something only slightly more subtle happens when you try to map a categorical concept onto the brain.

America’s Supreme Court illustrated this nicely in oral argument two days ago (October 6, 2009), as described in a lively article in the New York Times, from which I quote below:

“Mr. Katyal reminded the justices that the case before them concerned videos of dogfights and that the law itself was mainly prompted by so-called crush videos, which cater to a sexual fetish. Those videos show women in high heels stepping on small animals.But the 1999 law by its terms applies to audio and video depictions of all sorts of activities in which “a living animal is intentionally maimed, mutilated, tortured, wounded or killed” if that conduct was illegal where the depiction was sold.The case before the court, United States v. Stevens, No. 08-769, arose from the conviction of a Virginia man for selling videos of dogfights. The man, Robert J. Stevens, was sentenced to 37 months in prison. The federal appeals court in Philadelphia last year overturned Mr. Stevens’s conviction and struck down the law on First Amendment grounds. Patricia A. Millett, a lawyer for Mr. Stevens, urged the justices to follow suit, saying the law could not be rendered constitutional by narrowing it through judicial interpretation.“There is interpreting and then there is alchemy,” Ms. Millett said, “ and I think this statute requires alchemy.”  The law does exempt materials with “serious religious, political, scientific, educational, journalistic, historical, or artistic value.”  But several justices indicated a discomfort with the vagueness of that standard and with entrusting the question of a work’s “serious value” to prosecutors and juries. “Could you tell me what the difference is between these videos and David Roma’s documentary on pit bulls?” Justice Sonia Sotomayor asked Mr. Katyal, referring to “Off the Chain,” an exposé of dogfighting. “David Roma’s documentary had much, much more footage on the actual animal cruelty than the films at issue here.”  Mr. Katyal responded that “the line will sometimes be difficult to draw.”

Neurolaw is just taking off as a field; and someday it is going to have a field day with this type of questioning session.  Because from the standpoint of neural network theory, the justices (and everyone involved in the case, more or less) are engaged in the legal equivalent of trying to figure out which is the left side of a malt ball.  They are trying to map a categorical model of decision making (something is or is not of serious value, images of fighting dogs are or are not exploitative or meta-criticisms of exploitation; or in questioning by Scalia not reprinted in this post, bullfighting is or is not fun or moral to watch) onto the brain, which is absolutely not set up to make such high-level categorizations.

The simplest way to think of this is to imagine what a neural network does. Which is, in a nutshell, what a business does – it funnels information up from a large number of people (say, the cashiers at the checkout in Walmart) up to a small number of people (say the CEO).  This information is  refined as it moves up the chain of command, to the point where the CEO may have no idea how to scan a blouse or charge a credit card, but can easily name the total profit of the company; the checkout cashier, on the other hand, has no idea how the company is doing.

Even more importantly, as information about, say, sales climbs the hierarchy, other sorts of information – say about costs – something the cashiers have no information on – also climbs up another hierarchy, say accounting hierarchy.  At some point sales and costs information gets integrated in a single division, or for the sake of argument, in the mind of a single Vice President.  Multiple VPs may then get together – some with cost-benefit information, some with exptertise on home furnishings, others with knowledge about popular fashion, others who track demographic trends – and they feed their information to the Executive VPs who integrate that information to decide what to sell when in which stores.

So where am I going with this? Well, the same thing happens in a neural network that is watching, say, a dogfighting video.  While low-level neurons in the eye may be seeing the same images, high-level neurons receiving highly processed information from multiple sources combine a variety of streams of information to conclude that they are watching a crush video or a video exposing the moral hazard of crush videos.  But this conclusion only exists at a very high level – a level far, far above the one in which neurons are determining that they are seeing animals being harmed.

Therefore doomed to failure, from the very outset, is any effort to define a crush video in terms of whether animals are being harmed in a movie – that information is necessary, but not sufficient, to define that type of video.

There’s a lot more to say about this issue, of course.  But the point here is that unless the way neural information is processed and refined in neural networks, which is to say hierarchically, is taken into account, is seems unlikely that the Supreme Court or Congress is going to be able to verbally define the difference between decent or indecent material – they are aiming their language and their definitions way too low.

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