correlations and integrators.

CSGnet Archive CSG2007
21

[From Bill Powers (2007.01.11.1203 MST)]

Rick Marken (2007.01.11.1040) --

Now can we switch to something more interesting, like what to do when you are living in a country full of people who thought it was a good idea to impeach a competent, articulate and generally successful President like Bill Clinton but who will not even consider impeaching a couple miserable incompetents like Bush and Cheney.

Clinton was up for impeachment because he was accused (incorrectedly, as Starr finally admitted) of an actual crime involving Whitewater. He did lie, but it's hard to find anyone in Washington who sees anything wrong with that. Being superstitous, gullible, and incompetent, which is very bad for those who depend on you, is not a crime or misdemeanor. By the way, the committee who wrote the Constitution and Bill of Rights were pretty bad at spotting ambiguities in their language -- just look at the second amendment. So what does "high crimes and misdemeanors" mean? Does it mean

(high crimes) and misdemeanors,

or does it mean

high (crimes and misdemeanors)?

Of course they didn't say how to measure height, so it's still a Rohrschach test whichever way you take it.

Actually, I think we should run the government like a business, at least in the regard that you simply fire incompetent managers.

Best,

Bill P.

22

[Martin Taylor 2007.01.11.14.16]

[From Rick Marken (2007.01.11.1040)]

Bill Powers (2007.01.10.0930 MST)

Martin Taylor 2007.01.09.17.34 --

I'm a bit overwhelmed by all the mathematicizing that's being showered on me, so maybe my most prudent move would be to retire to the balcony and watch.

I don't understand why we're even having this discussion.

Because there was a discussion of correlation between signals in the control system, and I thought that the vector-based analysis on my Web page might be helpful, since it showed the limits on some of the correlations in what I thought was a particularly clear way.

Bill didn't understand the vector representation and I thought that I could help him to do so. But the discussion diverged, as these things tend to do, into all sorts of byways, such as difficulties in understanding the need to get rid of the idea that correlation necessarily had some connection with randomness, and stuff like that.

I'm not at all sure that I managed to get across the marvellous transparency that representing signals as vectors can give you. It doesn't really matter, I suppose. If a carpenter wants to use a screwdrive to drill holes, there's really no point in demonstrating an electric drill. But then I wouldn't want to use an electric drill to emplace screws, unless I had appropriate transforming attachments :slight_smile:

I'll just get back to dealing with the issue of variable reference values, when I get a moment from the ever-present immediate stuff.

Martin

23

[From Bill Powers (2007.01.11.1300 MST)]

Martin Taylor 2007.01.11.14.16 --

I'm not at all sure that I managed to get across the marvellous transparency that representing signals as vectors can give you. It doesn't really matter, I suppose. If a carpenter wants to use a screwdrive to drill holes, there's really no point in demonstrating an electric drill. But then I wouldn't want to use an electric drill to emplace screws, unless I had appropriate transforming attachments :slight_smile:

"Marvellous transparency?" Too bad it can't be communicated in words. Anyway, I have several kinds of screwdriver bits that I use in my electric drill, so I believe I can catch up with the work one way or another.

Representing signals as vectors is fine as long as you retain the ability to distinguish the nitty-gritty details of practical problems. Reducing everything to OM is not necessarily an advancement of learning.

But I carp at shadows, out of general disgruntlement. I'm supposed to be packing to go the Hilton Head tomorrow, and I'm sure I will forget everything vital. Yet here I sit typing. I suppose I must quit.

Best.

Bill P.

24

[From Rick Marken (2007.01.11.1520)]

Martin Taylor (2007.01.11.14.16) --

Rick Marken (2007.01.11.1040)

I don't understand why we're even having this discussion.

Bill didn't understand the vector representation and I thought that I could help him to do so. But the discussion diverged, as these things tend to do, into all sorts of byways, such as difficulties in understanding the need to get rid of the idea that correlation necessarily had some connection with randomness, and stuff like that.

It doesn't? I thought the correlation coefficient is completely connected to randomness (and linearity). The correlation is the square root of the coefficient of determination (r squared) which is a measure of the proportion of variance in one variable that can be accounted for by a least squares linear prediction of that variable from another. Lack of fit is presumably due to random contributions to the values of each variable. So the degree of randomness (unexplained variation) is just 1 - r squared. That's true whether you take r to be the cosine of the angle between two unit vectors or whatever.

I'll just get back to dealing with the issue of variable reference values, when I get a moment from the ever-present immediate stuff.

Don't worry about it. I think the problem doesn't really exist, at least in my mind reading demo. The main solution is to use orthogonal (in the sense of uncorrelated) disturbances.

Best

Rick

···

----

Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

25

[Martin Taylor 2007.01.11.21.46]

[From Rick Marken (2007.01.11.1520)]

Martin Taylor (2007.01.11.14.16) --

Rick Marken (2007.01.11.1040)

I don't understand why we're even having this discussion.

Bill didn't understand the vector representation and I thought that I could help him to do so. But the discussion diverged, as these things tend to do, into all sorts of byways, such as difficulties in understanding the need to get rid of the idea that correlation necessarily had some connection with randomness, and stuff like that.

It doesn't? I thought the correlation coefficient is completely connected to randomness (and linearity). The correlation is the square root of the coefficient of determination (r squared) which is a measure of the proportion of variance in one variable that can be accounted for by a least squares linear prediction of that variable from another. Lack of fit is presumably due to random contributions to the values of each variable. So the degree of randomness (unexplained variation) is just 1 - r squared. That's true whether you take r to be the cosine of the angle between two unit vectors or whatever.

All pigeons are birds. I suppose you would deduce from that that all birds are pigeons?

Everything you say is correct, but it's just one application of correlation. Of course it's where the idea came from historically, and what kids are taught in school because they need to know of ways to deal with randomness in experimental data. If the only birds you knew were the homing pigeons you kept, you might think that an entity had to be a pigeon if it was a bird. When you've seen a few other varieties, you realize that not all birds are pigeons. Not all applications of correlation involve randomness.

I'll just get back to dealing with the issue of variable reference values, when I get a moment from the ever-present immediate stuff.

Don't worry about it. I think the problem doesn't really exist, at least in my mind reading demo. The main solution is to use orthogonal (in the sense of uncorrelated) disturbances.

OK, I won't worry about it in the context of your problem, but it's still an interesting enquiry, which I intend to pursue.

Martin

26

[Martin Taylor 2007.01.11.21.55]

[From Bill Powers (2007.01.11.1300 MST)]

Martin Taylor 2007.01.11.14.16 --

I'm not at all sure that I managed to get across the marvellous transparency that representing signals as vectors can give you. It doesn't really matter, I suppose. If a carpenter wants to use a screwdrive to drill holes, there's really no point in demonstrating an electric drill. But then I wouldn't want to use an electric drill to emplace screws, unless I had appropriate transforming attachments :slight_smile:

"Marvellous transparency?" Too bad it can't be communicated in words.

I'm wondering why. I've tried to use very simple words, and the concepts themselves are very simple. I think there must be a language problem, a bit like the problem I encounter with wine experts who try to get across the wonderful experience of wine by using words like "raspberry, gasoline, leather, long nose" and so forth. Or maybe it's like getting across the beauty of a Raphael painting in words. Perhaps you have to have the basics thoroughly in your bones before the beauty is apparent.

Representing signals as vectors is fine as long as you retain the ability to distinguish the nitty-gritty details of practical problems.

You do, and then some. For example, being able to SEE that the vectors for two signals don't change when you take their Fourier transforms gives you a good handle on working in the time domain, the frequency domain, or something in between. They don't change, because all the Fourier transform is is a rotation of the basis space. So, if you have a situation in which you can see the answer in the frequency domain, you then have it in the time domain, too. Sometimes one is easier, sometimes the other.

Reducing everything to OM is not necessarily an advancement of learning.

I've no idea what OM means, but in any case I was suggesting that more tools give you more chances to solve problems. The idea of offering you a hammer is not to suggest you should join everything using nails.

I'm supposed to be packing to go the Hilton Head tomorrow, and I'm sure I will forget everything vital. Yet here I sit typing. I suppose I must quit.

It's one of the rules of packing for a trip that you remember you forgot something vital only when you have just gone past the point of no return. I do, however, have one counter-example: my taxi to the airport for a trip to Europe had only gone two blocks when I realized I'd forgotten my passport.

Enjoy the trip!

Martin