Numb3rs

[KoshFan]

Anyone been watching this?

I think it's got definite potential, and the first two episodes have been good, but I've got my doubts. I wonder how long they can keep coming up with more plots, and it needs some more character development. Gloriously shot, though, it's extremely pretty, and it's still in its infancy. I'll give it the benefit of the doubt for a few weeks more.

And I have to admit I've been spoiled, story- and character-wise, by Whedon and JMS.

 

[Recoil]

Another crime-solving drama on CBS? The hell you say.

 

[AntonyF]

It's amazing how most of the channels are easily categorizable.

CBS - the crime drama channel.
Fox - the reality channel.
WB - the teen channel.
UPN - the black channel.

I don't have any real thought on ABC/NBC. ABC I suppose would have to be "the good channel".

 

[KoshFan]

I don't have any real thought on ABC/NBC. ABC I suppose would have to be "the good channel".

On the strength of Lost and Alias, I presume? Not much to go on -- but I'm thinking they don't have a ton of competition.

 

[2aMageing]

I watched the first episode. It took me a quarter of the show to be certain that the main character, the brother in law enforcement, was the same guy from Northern Exposure......that was kinda cool. Butwhile that of show is one of my favs, I wasn't entirely satisfied with it. Not a mainstream attitude, but for me, I wanted to rip apart the theory that you could get a starting point from only a set of ending points.......NO WAY DUDE, you need a ton of variable info......taken to the sprinkler analogy, you need velocity at impact, direction of movement upon impact, and certainly tracking the distances a human goes to commit a crime would require a whole heck of alot more info than that.


But I can and do set such concerns about propagating bad science aside to try to enjoy the show. It was highly stylized, but I don't buy into style for the sake of salesmanship.........I like a little meaning in the method.

It reminds of a movie I saw once called Snake Eyes, starring Nicholas Cage and Gary Sinise. It was Brian De Palma using lots of cuts and uncommon camera views, but the originality and undeniable talent of the stars couldn't cover the lack of depth in the story/characters, and the lack of total gound the story covers (often a "drama" will do a lot of running around with out really going any place, figuratively speaking), and the same issues seem to be present in this show.

I grant that it can be hard to get the ball moving by the end of season one, episode one. However, I have rewatched just enough season 1 of some TV shows recently that could do it right off the bat, to believe that this one may be starting thin and is destined to thin to nothing......or undergo a major retooling around midseason (if it lasts that long) and end up being a rather different show in many ways.

All in all, I'd give it a 2.5 out of 5.....but 1 out of the 2.5 is an advance upon them doing more with the premise and the characters than they have so far.

 

[PillowRock]

Not a mainstream attitude, but for me, I wanted to rip apart the theory that you could get a starting point from only a set of ending points.......NO WAY DUDE, you need a ton of variable info......taken to the sprinkler analogy, you need velocity at impact, direction of movement upon impact, and certainly tracking the distances a human goes to commit a crime would require a whole heck of alot more info than that.

But the *do* have a great deal more information than just attack locations. Most of the rest of the information that is available is tied up in the GIS (Geographic Information System) that various agencies would have for the city. Those would include mobility studies (how long it takes to get anywher from anywhere; based on road maps, speed limits, traffic light patterns, traffic density, etc. It would also include the zoning ordinances, allowing to label certain areas as not being potential "target acquistion" sites and the like.

In the sprinkler case you need all of those velocity and angle variables in order to calculate the point of origin from a single drop. If you have enough drop landing points you could do a pretty good job of nailing down the center point from which they had been scattered.

The question becomes: How many points do you nee to be able to perform a numeric regression?

I tend to suspect that the number required to get the kind of precision they were talking about probably is higher the number of victims that you are likely to see from a single serial killer.

The other problem that I had with the model they showed in the first episode was that when they went from a single origin model to a two origin model, one of the two was the same as the single origin. That doesn't necessarily follow. In fact, I would expect it not to happen.

 

[KoshFan]

Well, I can't say I follow the math but in the two-origin model, the zones they came up with weren't the same as the first. One was centered in the earlier area, but it was smaller.

Also I don't think Charlie -- the mathematician in the show -- worked from just the one serial killer. He had all the data on serial killers in general that the FBI could give him.

 

[PillowRock]

Well, I can't say I follow the math but in the two-origin model, the zones they came up with weren't the same as the first. One was centered in the earlier area, but it was smaller.

Exactly. That's the problem. If you take a distribution that ideally ought to have two foci and do regression designed to give a single center, that center will generally be in between the two foci, not at the position of one of them.

I realize that whatever fictional math they were doing was to have been more complicated than center-or-a-circle vs. two-foci-of-an-ellipse, but the basic princinpal behind this idea still bugged me a bit when I saw that one of his final two areas was still in basically the same place as his original single area.

Also I don't think Charlie -- the mathematician in the show -- worked from just the one serial killer. He had all the data on serial killers in general that the FBI could give him.

You're talking about when he was deriving the model. I was happy that they showed them testing his model with multiple "truth" data sets. That was good.

I was talking about whether they had enough data points to do the final analysis to locate a single killer.

Think of it this way:

Suppose you have a distribution in two dimensions that is generated by the equation for a straight line, but with some random error added in to in each location. You can calculate a line that fits two points. However, the odds are very high that the line you get will be wrong (in the sense that won't match originating equation). The random variability isn't sufficiently averaged away across your data set. You need more data points to be able to do an emperic regression in which you would have any confidence. If the distribution should really be a parabola (second order), then you need more points. If it is third order (basically an S curve shape) then you will need still more.

It's just not clear to me that 12 victims is enough to narrow things down as much as they showed. Of course, it wasn't really 12 independent data points either. They showed during the episode that one of the victims was a "target of opportunity" that the rapist/killer came across while staking out another victim. So we have, at most, 11 independent points from which to do our regression. Maybe that's enough data points, and maybe it's not. I remain somewhat skeptical of the idea that they had suffcient data points to use that basic method (an almost purely numeric regression, without much of any phenomenology that you can pin down with any precision).

 

[2aMageing]

In the sprinkler case you need all of those velocity and angle variables in order to calculate the point of origin from a single drop. If you have enough drop landing points you could do a pretty good job of nailing down the center point from which they had been scattered.

My question is......doesn't this have built into it a fundamental assumption that the sprinkler is casting it's drops equidistant from itself??? Without trajectory information couldn't the sprinkler be anywhere within the distribution area, or even out side of it if you don't assume that it has to spray 360 degrees? I know I'm breaking down the sprinkler a great deal, but I think what I'm looking at identifies an inherent issue of unreliability in directly connecting resulting points with a source

(what was his stated rate of certainty after correction, 90 something percent??? I STRONGLY doubt that kind of percentage is attainable when workig in real life with such a large set of roughly defined variables)

If I'm wrong I'd love someone to show me my error of reasoning, as I am not a statistical specialist.....just a few classes on sampling and standard deviation. I just got my instincts saying the system being analyzed for such a premise is far beyond any mathimatics we have, and may well be beyond pure math entirely.

It would take sociologist, psychologist, geographer, and probably close to another half dozen specialists combined into one person with genius capability for creative and efficient synthesis into a single inclusive system. It might be possible, but at the outer realm of possibility, and I don't think calling someone a genius mathematician gets the job done..........

But like I said, it is more my prefered kind of premise than a sexist husband, his wife, and kids and their weekly hijinks.........

 

[PillowRock]

In the sprinkler case you need all of those velocity and angle variables in order to calculate the point of origin from a single drop. If you have enough drop landing points you could do a pretty good job of nailing down the center point from which they had been scattered.

My question is......doesn't this have built into it a fundamental assumption that the sprinkler is casting it's drops equidistant from itself??? Without trajectory information couldn't the sprinkler be anywhere within the distribution area, or even out side of it if you don't assume that it has to spray 360 degrees?

It's assuming that you know basically what kind of sprinkler that you are talking about (rotating like they had vs. back-and-forth vs. flat-hose-with-holes vs. whatever). Actually, if you don't just have the locations of the drop landings, but also have the time associated with each drop landing, then you can probably figure that out on the fly from the data as well.

Of course, the math is much simpler and cleaner if you get to assume negligible wind effects (or, at least, relative consistant wind). Even that can be worked through with some effort, though.


However, that (the sprinkler) is a nice simple case. Plus it's one where a complete data set would be *lots* of individual points.

I already agreed that I don't think they had enough data points to do what they did with the killer's location. Not with that kind of precision (size of area) or confidence (his percentages of certainty, especially for a human behavioral problem, seemed *really* high) at any rate. They might have been able to build a emperic numeric model that worked that well based on the input of a few hundred data points (which sounds like a small sample space compared to what I udually deal with) ..... but with 11 or 12? That's rough.