Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: kenneth paul collins
Date: Mon, 25 Nov 1996 01:36:22 -0500
Ilias Kastanas wrote:
> The "rules" of "proof" have been shown to be _the_ rules of proof;
> that is the Completeness theorem. If you see something wrong there, maybe
> you could state what. As it is, breaking the rules is pointless and
> self-defeating... and irrelevant to the Incompleteness theorem.
I don't have a problem with that. What I stand against are over-generalized uses
of Godel's "incompleteness"... "Math is 'incomplete', and cannot possibly be
'completed'"... instances in which a nay sayer invokes Godel to aruge against
the possibility of this or that without even considering the thing in question.
Godel's Proof is consequential only within the realm of the rules of Godel's
Proof. When one looks, one finds that the realm of the rules of Godel's Proof is
just an island within the realm of all possible Mathematics. It just doesn't say
anything about anything that's not "on that island". And yet, it's most-often
invoked as if it says stuff about all possible Mathematics. It doesn't.
ken collins
_____________________________________________________
People hate because they fear, and they fear because
they do not understand, and they do not understand
because hating is less work than understanding.
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: kenneth paul collins
Date: Mon, 25 Nov 1996 01:50:10 -0500
Jonathan Gibbs wrote:
>
> kenneth paul collins (KPCollins@postoffice.worldnet.att.net) wrote:
> : A machine that is designed so that it can "divide & conquer"
> : can render such infinities irrelevant. Basically, such a
> : machine transforms all problems into Geometry, and, instead
> : of "algorithms", use cross-correlation among continuua to
> : arrive at solutions.
>
> [tons snipped]
>
> Sounds very facinating ken, can you point me to a good reference on
> this stuff? Perhaps a journal paper...
I've developed a unified theory of CNS function, cognition, affect,
and behavior (Neuroscientific Duality Theory). During that
development, I modeled and tested concepts pertaining to the neural
dynamics. The "continuum Geometry computer" (CGC) that I was
discussing is just a generalization of the models. It's not formally
published anywhere yet. The Neuroscience discussion is available in a
hypertext doc that runs on MSDOS machines. I can email you a copy if
you want it.
I can discuss the CGC in person, and have been looking for a place to
do so. It's a bit hard to do so online because everything has to be
converted to Geometry, diagrammed, and discussed from the perspective
of the diagrams. In person, I just have at it with a box or two of
colored chalk. ken collins
_____________________________________________________
People hate because they fear, and they fear because
they do not understand, and they do not understand
because hating is less work than understanding.
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: kenneth paul collins
Date: Mon, 25 Nov 1996 02:00:52 -0500
Ilias Kastanas wrote:
> Journal article or not, this is about analogue computation...
The CGC is envisioned as an analogue-digital hybrid.
> Which can take many forms; e.g. build a model of a graph, edges being
> pieces of string of appropriate lengths, and hold it up under the
> effect of gravity; use pegs and rubber bands around them; and so on.
> One can obtain approximate solutions to a number of problems. On the
> other hand, it is certainly a different subject.
Not really. I've been discussing computation that reduces to what's
described by 2nd Thermo (WDB2T), which is entirely analogue, and which can
be shown to be an inclusive superset of all possible digital computation.
And so such is extremely-commonplace... it's been so "familiar" that it's
been "invisible". ken collins
_____________________________________________________
People hate because they fear, and they fear because
they do not understand, and they do not understand
because hating is less work than understanding.
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: ikastan@alumnae.caltech.edu (Ilias Kastanas)
Date: 25 Nov 1996 10:13:10 GMT
In article <32993E66.25E@postoffice.worldnet.att.net>,
kenneth paul collins wrote:
>Ilias Kastanas wrote:
>
>> The "rules" of "proof" have been shown to be _the_ rules of proof;
>> that is the Completeness theorem. If you see something wrong there, maybe
>> you could state what. As it is, breaking the rules is pointless and
>> self-defeating... and irrelevant to the Incompleteness theorem.
>
>I don't have a problem with that. What I stand against are over-generalized uses
>of Godel's "incompleteness"... "Math is 'incomplete', and cannot possibly be
>'completed'"... instances in which a nay sayer invokes Godel to aruge against
>the possibility of this or that without even considering the thing in question.
I agree. G.I. is misunderstood and misused a lot.
>Godel's Proof is consequential only within the realm of the rules of Godel's
>Proof. When one looks, one finds that the realm of the rules of Godel's Proof is
>just an island within the realm of all possible Mathematics. It just doesn't say
>anything about anything that's not "on that island". And yet, it's most-often
>invoked as if it says stuff about all possible Mathematics. It doesn't.
"From P, Q follows" is explicated: in any structure where P holds,
Q also holds. It is a semantic notion, covering math. entailment as we
know it. The simple-looking formal deduction rules _do_ capture this no-
tion; every known proof can be written as such a formal deduction.
So G.I. does talk about all of Mathematics (as we presently see it,
at least): no formal system will ever "do it all"; instead, insight and
creativity are needed. A positive message, and its first proponent was
Goedel himself.
Ilias
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: ikastan@alumnae.caltech.edu (Ilias Kastanas)
Date: 25 Nov 1996 10:41:04 GMT
In article <32994424.136C@postoffice.worldnet.att.net>,
kenneth paul collins wrote:
>Ilias Kastanas wrote:
>
>> Journal article or not, this is about analogue computation...
>
>The CGC is envisioned as an analogue-digital hybrid.
>
>> Which can take many forms; e.g. build a model of a graph, edges being
>> pieces of string of appropriate lengths, and hold it up under the
>> effect of gravity; use pegs and rubber bands around them; and so on.
>> One can obtain approximate solutions to a number of problems. On the
>> other hand, it is certainly a different subject.
>
>Not really. I've been discussing computation that reduces to what's
>described by 2nd Thermo (WDB2T), which is entirely analogue, and which can
>be shown to be an inclusive superset of all possible digital computation.
>And so such is extremely-commonplace... it's been so "familiar" that it's
>been "invisible". ken collins
"Analogue" measures "continuous" quantities, and so yields appro-
ximate answers (which of course may be fully adequate for various prac-
tical problems). "Digital" (discrete), with exact answers, is different
(and classical computability theory applies). You can obtain it by quan-
tizing, more than 3.7 V is "1" etc; but whatever the implementation, its
properties are there.
Whenever you employ "analogue" and somehow reach an exact answer,
"digital" can reach that answer (and in effect you _are_ using the latter).
Is there a counterexample to this (inevitably vague) statement?
Ilias
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: Jim Balter
Date: Mon, 25 Nov 1996 03:53:34 -0800
Ilias Kastanas wrote:
>
> In article <32993E66.25E@postoffice.worldnet.att.net>,
> kenneth paul collins wrote:
> >Ilias Kastanas wrote:
> >
> >> The "rules" of "proof" have been shown to be _the_ rules of proof;
> >> that is the Completeness theorem. If you see something wrong there, maybe
> >> you could state what. As it is, breaking the rules is pointless and
> >> self-defeating... and irrelevant to the Incompleteness theorem.
> >
> >I don't have a problem with that. What I stand against are over-generalized uses
> >of Godel's "incompleteness"... "Math is 'incomplete', and cannot possibly be
> >'completed'"... instances in which a nay sayer invokes Godel to aruge against
> >the possibility of this or that without even considering the thing in question.
>
> I agree. G.I. is misunderstood and misused a lot.
>
> >Godel's Proof is consequential only within the realm of the rules of Godel's
> >Proof. When one looks, one finds that the realm of the rules of Godel's Proof is
> >just an island within the realm of all possible Mathematics. It just doesn't say
> >anything about anything that's not "on that island". And yet, it's most-often
> >invoked as if it says stuff about all possible Mathematics. It doesn't.
>
> "From P, Q follows" is explicated: in any structure where P holds,
> Q also holds. It is a semantic notion, covering math. entailment as we
> know it. The simple-looking formal deduction rules _do_ capture this no-
> tion; every known proof can be written as such a formal deduction.
>
> So G.I. does talk about all of Mathematics (as we presently see it,
> at least): no formal system will ever "do it all"; instead, insight and
> creativity are needed. A positive message, and its first proponent was
> Goedel himself.
a) Insight and creativity won't "do it all" either.
b) Inconsistent formal systems can "do it all".
Godel's message" is an irrelevant metaphysical flight of fancy.
--
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: patrick@gryphon.psych.ox.ac.uk (Patrick Juola)
Date: 25 Nov 1996 12:37:15 GMT
In article <57bt40$brh@gap.cco.caltech.edu> ikastan@alumnae.caltech.edu (Ilias Kastanas) writes:
>In article <32994424.136C@postoffice.worldnet.att.net>,
>kenneth paul collins wrote:
>>Ilias Kastanas wrote:
>>
>>> Journal article or not, this is about analogue computation...
>>
>>The CGC is envisioned as an analogue-digital hybrid.
>
> "Analogue" measures "continuous" quantities, and so yields appro-
> ximate answers (which of course may be fully adequate for various prac-
> tical problems). "Digital" (discrete), with exact answers, is different
> (and classical computability theory applies). You can obtain it by quan-
> tizing, more than 3.7 V is "1" etc; but whatever the implementation, its
> properties are there.
>
> Whenever you employ "analogue" and somehow reach an exact answer,
> "digital" can reach that answer (and in effect you _are_ using the latter).
> Is there a counterexample to this (inevitably vague) statement?
Not all analog data is necessarily continuous. For example, identity
is almost always discrete. So if you use an analog calculation to
get a "subject identity" result, the result will be exact but not
necessarily available to a digital calculation (within the same
complexity bounds).
The classic example of this, of course, is the O(1) argmax algorithm.
Patrick
Subject: Re: CONFIDENCE INTERVAL
From: Robert L Strawderman
Date: Mon, 25 Nov 1996 09:01:13 -0500
George Caplan wrote:
>
> I have been reading about premarketing clinical trials
> of a medication. The manufacturer says that there
> were 3 adverse reactions out ot 2796 patients. This, he
> says, yields a crude incidence of adverse reactions
> of 1.1 per thousand with a "very wide" 95% confidence
> interval of 2.2 cases per 10,000 to 3.1 cases
> per 1000.
>
> How does one make a confidence interval estimate in
> this case? The number of reactions is so small that
> I don't think I can approximate the s.d. by
> sqrt(((p(1-p))/n); and when I do, I don't get the result
> given.
The formula for the sd is appropriate regardless of sample
size - it is the formula for a binomial proportion.
However, the method of forming the CI (ie using the normal
approximation to the binomial) may not be. Using the usual
normal approximation, the 95% CI is (-.00014, .00228). This
procedure is inappropriate, but also does not match their
quoted answer.
Using the binomial distribution, I obtain (0.00039,0.00313)
as the 95% CI, which is "exact" - the exact sampling distribution
is used in this calculation. It also does not match what they
report, but is closer.
There are other possible methods (e.g., Poisson,
or arcsin transformation) which may have been used to
obtain their results.
--
***************************************************************************
Robert Strawderman, Sc.D. Email: strawder@umich.edu
Department of Biostatistics Office: (313) 936 - 1002
University of Michigan Fax: (313) 763 - 2215
1420 Washington Heights
Ann Arbor, MI 48109-2029 Web: http://www.sph.umich.edu/~strawder/
***************************************************************************
Subject: Re: Bootstrap algorithm
From: Rodney Sparapani
Date: Mon, 25 Nov 1996 10:18:13 -0500
This is a multi-part message in MIME format.
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Eric Saczuk wrote:
>
> I am wondering if anyone out there knows where and/or if I can get my
> hands on software which would allow me to carry out the Bootstrap
> algorithm? I have about 7,000 reiteration to perform and I don't look
> forward to programming my own macro in Fortran. If anyone has any
> usefull info on this, please let me know, it would be greatly
> appreciated, thanks!
>
> Cheers, Eric S
Eric:
Attached is a SAS macro that does bootstrapping, but it does so
by creating large files. Judicous use of keeps or drops is
warranted and by variables are out of the question.
Rodney
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Content-Type: text/plain; charset=us-ascii; name="boot.txt"
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Content-Disposition: inline; filename="boot.txt"
%global _iter_;
%macro boot(iter=1000, data=&syslast;, out=_null_, seed=int(time()), class=, by=&class;);
%*
MACRO: BOOT
INPUT PARAMETERS
BY: The stratification variable that the dataset is sorted by (not required, default=&CLASS;).
CLASS: The stratification variable (not required, no default).
DATA: The input dataset (not required, default=&SYSLAST;).
ITER: The number of iterations to perform (not required, default=1000).
OUT: The output dataset that you would like to create (required, default=_NULL_).
SEED: The seed to use for the RANUNI() function (not required, default=INT(TIME())).
OUTPUT DATASET VARIABLES
BOOT: Zero for input data, one for re-sampled data.
OBS: The observation number of the input data corresponding to the re-sample.
SEED: The seed used for the RANUNI() function.
STRAP: Zero for input data, the current re-sample iteration otherwise.
INTERMEDIATE OUTPUT DATASET VARIABLES
END: A flag set to true on the last record of the input dataset.
OFFSET: Pointer to the beginning of the current stratification block.
I: Counter that loops NOBS times for the current STRAP re-sample.
NOBS: The number of observations in the current stratification block.
P: Pointer to the observation to be selected from the current stratification block.
GLOBAL MACRO VARIABLES CREATED
_ITER_: Set to the input parameter value &ITER.;
_STRATA_:Set to the stratification input parameter &BY;, (if any).
LOCAL MACRO VARIABLES CREATED
LAST: Set to the last stratification variable from the &BY; list, (if any).
I: Steps through the &BY; list, to find the &LAST; variable, (if any).
;
%local last i;
%let _iter_=&iter;
%if %length(&class;) %then %do;
proc sort data=&data; out=&out;
%end;
%else %do;
data &out;
set &data;
%end;
by &by;
run;
%if %length(&by;) %then %do;
%global _strata_;
%let _strata_=%upcase(&by;);
%let i=1;
%do %while(%length(%scan(&by;, &i;, %str( ))));
%let last=%scan(&by;, &i;, %str( ));
%let i=%eval(&i;+1);
%end;
%end;
data &out;
set &out; end=end;
by &by;
drop i nobs offset;
retain offset boot strap 0;
seed=&seed;
obs=_n_;
output;
if end then do;
link boot;
stop;
end;
%if %length(&by;) %then %do;
else if last.&last; then do;
link boot;
end;
%end;
return;
boot:
boot=1;
nobs=_n_-offset;
do strap=1 to &iter;
do i=1 to nobs;
p=ranuni(seed);
p=ceil(nobs*p)+offset;
set &out; point=p;
obs=p;
output;
end;
end;
boot=0;
strap=0;
offset=_n_;
return;
run;
%if %length(&by;) %then %do;
proc sort data=&out;
by boot strap &by; obs;
run;
%end;
%mend boot;
--------------46554F45EAC--
