[From Bill Powers (940725.0600 MDT)]
Bill Leach (940724c.xxx) --
I liked your replies to Bob Clark and Martin Taylor. When Martin says
"The claim is that all the information that allows the output to oppose
the disturbance is obtained through the perceptual input function that
acts on the fluctuations of the CEV induced by the disturbance. "
he is really declaring his faith that somehow the information needed for
achieving control is coming from the disturbance, which is the basic S-R
faith. He goes so far as to say that this amounts to saying that control
is a physical process and not a magical one. This is claiming far too
much, in my opinion. We explain the operation of a control system on
perfectly valid physical grounds, and in the process demonstrate that
the control system uses only information about the state of the
controlled variable; it does not require any internal computations that
deduce the state of the disturbance. The state of the controlled
variable, furthermore, is not a unique indicator of the state of the
disturbance, because it is simultaneously affected by the system's own
output, which in turn is a function of the controlled variable AND the
reference signal. As far as I am concerned, the control-system analysis
gives a complete account of how control works and why, leaving nothing
for information theory to explain. NOTHING. So there.
Your tale of a false-positive drug test is far from unusual. A great
part of the problem comes from tests for rare conditions -- that is,
conditions that hold only in a small part of the population. Let's see
if I can remember how this problem goes:
Suppose we have a test for cancer that is 98% effective both in
indicating the existence of a cancer and in indicating its absence. That
is, for people who actually have cancer, it will pick up 98% of the
cases that later prove to be real cancer, and it will reject 98% of the
cases that later prove not to have been cancer. The actual incidence of
cancer in the population in question is known, furthermore, to be 1%:
100 people of every 10000.
The question is, if the test indicates that you have cancer, what are
the chances that you actually do have cancer?
The trap here lies in the fact that 99% of the people do not have
cancer. The test has a false-positive rate of 2%. So in a population of
10000 people, it will indicate that of the 9900 who do not actually have
cancer, 198 people have it. It will also pick up 98% of those who really
do have it, meaning 98 people.
Therefore, if you test positive for cancer, the chances are 2:1 that you
do NOT have cancer. And this is using a test that can be described as
"98% accurate."
Apply this to the "second-hand smoke" problem. It is claimed (as the
news media report it) that 3000 people per year (out of 250,000,000) die
from the effects of second-hand smoke. That is an incidence of 0.000012.
A test that determines whether a given person died from this cause might
possibly, given extreme faith, be 99.9% accurate both ways, false
positives and false negatives. But a test with 0.1% false positives
would indicate 250,000 people per year dying of second-hand smoke. What
would the accuracy have to be for a test that shows only 3000 per year?
It would have to be 99.99%+, even if most of the positive results were
false positives. So the claim that 3000 people die every year from
second-hand smoke is ludicrous. No phenomenon with that low an incidence
can possibly be verified as existing with any sort of medical test that
exists now or is likely to be invented.
So how can this silly claim be made? If you read carefully, you will see
that no authority claims that second-hand smoke causes 3000 deaths per
year. What is claimed is that in 3000 deaths per year, second-hand smoke
is determined to be a contributing factor. Determinations don't make
themselves. The statement is that of all the deaths that do occur, 3000
of them are claimed by someone to have been contributed to by second-
hand smoke. It's sort of like an FBI file: the allegation becomes part
of the factual record. There is certainly no claim that if non-smokers
were totally protected against second-hand smoke for the rest of their
lives, the death rate from cancer would be measurably lower. To say that
second-hand smoke was a contributing factor is not to say that the
person wouldn't have died anyway, at the same time. The implication is
that there were _other_ contributing factors as well, such as heart
failure or bullets. You'll see this sort of weaseling all the time.
Doctors say that excess iron can cause heart problems, but they hasten
to say that there's no reason to reduce your high iron intake, because
they have no proof that reducing iron intake will help any with reducing
heart problems. So go on eating your spinach, one of them said.
All this medicostatistical mumbo-jumbo about health is simply a vehicle
for forcing one's preferences on others. Medicine has had very little
impact on increasing longevity; the primary increases have been due to
increases in cleanliness of homes, water supplies, and food, and to a
few antibiotics (which are now becoming ineffective as bacterial control
systems learn to cope with them). Most of the vast costs of medicine are
due to taking credit for cures that would have occurred without
treatment, offering false hopes to a nation of hypochondriacs, and
keeping people miserably alive for a short time against the natural
tendency to give up when all the systems are failing.
I suppose I shouldn't be so shy about saying what I really think.
···
---------------------------------------------------------------------
Best to all,
Bill P.