Monday, February 19, 2007

Multiplication on Multi Dimensional Arrays

Linear algebra has made our understanding of many fields of science considerably easier because it allows us to write complicated expressions in nice easy to understand forms. There have been some efforts to extend the ideas of linear algebra to higher dimensional structures. I believe tensors may be one of these fields of study.

Some applications where multi dimensional arrays could simplify mathematical expressions are the Taylor plane and distributions which have high order statistics. I have recently written some MATLAB code which seems to generalize the idea of matrix multiplication. I have tested my code for a 2x2x2 symbolic array multiplied by a vector. In normal linear algebra we can think of a lift multiply and a right multiply.

With a 3 dimensional array one could consider multiplication with respect to each of the 6 faces of the cube, and could consider every possible orientation of the operands. This is not the approach I took. Rather I made it so that you specify the inner dimensions in the multiplication of each operand. For instance you can do standard matrix multiplication with this algorithm as follows: Let:

A=

(:,:,1) =

[ a111, a121]
[ a211, a221]

(:,:,2) =

[ a112, a122]
[ a212, a222]

X=

x1
x2

If we wanted to represent the Right multiplication of A by X would write:

>> A.in(2)*X.in(1)


ans(:,:,1) =

a111*X1+a121*X2
a211*X1+a221*X2


ans(:,:,2) =

a112*X1+a122*X2
a212*X1+a222*X2

Before we discuss the other types of multiplication let:X2=permute(X,[2,1,3])=
[ x1, x2]
And
X3=permute(X,[3,2,1])=
(:,:,1) =

x1

(:,:,2) =

x2

Then the left multiplication of A by X is:X2.in(2)*A.in(1)

ans(:,:,1) =

[ a111*x1+x2*a211, x1*a121+a221*x2]


ans(:,:,2) =

[ a112*x1+x2*a212, x1*a122+a222*x2]

And one might define the rear multiplication of A by X as follows:

A.in(3)*X3.in(3)

ans =

[ a111*x1+a112*x2, x1*a121+a122*x2]
[ a211*x1+x2*a212, a221*x1+a222*x2]

The algorithm produces answers depending if X is on the left or right of the multiplication sign and which you specify as the inner dimensions. I will give a few other examples later and the readers can hopefully give feedback if the answers make sense. What is clear is that the algorithm can be used to simplify the expressions for things like high third order Taylor approximations to two dimensional quadratic surfaces. In general the algorithm should not be limited to two dimensional and third order quadratic surfaces. However, I have not tested the code yet beyond these surfaces.

With respect to higher order statistics I am interested to know if there is an easy extension of the joint Gaussian that can be expressed in terms of these high order statistics.

Some examples of non standard products:>> A.in(1)*X.in(2)

and get the expected result:

ans(:,:,1) =

[ a111*x1+a211*x1, x1*a121+a221*x1]
[ a111*x2+x2*a211, a121*x2+a221*x2]


ans(:,:,2) =

[ a112*x1+a212*x1, x1*a122+a222*x1]
[ a112*x2+x2*a212, a122*x2+a222*x2]

>> A.in(2)*X.in(2)


ans(:,:,1) =

a111*X1+a121*X1
a111*X2+a121*X2
a211*X1+a221*X1
a211*X2+a221*X2


ans(:,:,2) =

a112*X1+a122*X1
a112*X2+a122*X2
a212*X1+a222*X1
a212*X2+a222*X2

>> A.in(1)*X.in(1)


ans(:,:,1) =

[ a111*X1+a211*X2, a121*X1+a221*X2]


ans(:,:,2) =

[ a112*X1+a212*X2, a122*X1+a222*X2]


In the next case there are no inner dimensions and we get the Kronecker product:


>> A*X


ans(:,:,1) =

[ a111*X1, a121*X1]
[ a111*X2, a121*X2]
[ a211*X1, a221*X1]
[ a211*X2, a221*X2]


ans(:,:,2) =

[ a112*X1, a122*X1]
[ a112*X2, a122*X2]
[ a212*X1, a222*X1]
[ a212*X2, a222*X2]



function y=mtimes(A,B)
%maxdim=1;
size1=size(A.A);
size2=size(B.A);
L=max(length(size1),length(size2));
size1A=[size1 ones(1,L-length(size1))];
size1B=[size2 ones(1,L-length(size2))];
size2A=size1A;
size2B=size1B;
size2A(A.in)=1;
size2B(B.in)=1;
size_ans=size2A.*size2B;
y=zeros(size_ans);
if isa(A.A,'sym')isa(B.A,'sym')
y=sym(y);
end
pSizeAns=[1 cumprod(size_ans(1:end-1))];
%p1size1B=cumbprod(size1B);
%p2size2B=[1 p1size1B(1:end-1)];
for i=1:prod(size_ans)
K_Ans=mod(floor((i-1)./pSizeAns),size_ans)+1;
getA=cell(size(K_Ans));
getB=cell(size(K_Ans));
for j=1:length(K_Ans)
if (size2A(j)==1)
getA{j}=':';
else
getA{j}=floor((K_Ans(j)-1)/size2B(j))+1;
end
if (size2B(j)==1)
getB{j}=':';
else
getB{j}=mod(K_Ans(j)-1,size2B(j))+1;
end
end
sliceA=A.A(getA{:});
sliceB=B.A(getB{:});
Ap=1:length(size1A);
Bp=1:length(size1B);
Ap(A.in)=[];Ap=[A.in Ap];
Bp(B.in)=[];Bp=[B.in Bp];
sliceA=permute(sliceA,Ap);
sliceB=permute(sliceB,Bp);
myProd=sliceA.*sliceB;
y(i)=sum(myProd(:),1);
end

Saturday, February 17, 2007

Linear Systems, State Space and Geometric Series

Consider the linear system:

X(n+1)=A X(n) + B U(n)
Y(n)=C X(n) + D

Where:A is the state transition matrix
B is the state input matrix

A can be derived from the continuous state space equations via the matrix exponential:
http://en.wikipedia.org/wiki/Matrix_exponential

I was recently thinking about the best way to evaluate the state input matrix B for a time step which is k times as large as the value used to obtain the known value of the state input matrix B. This method assumes we know the state transition matrix A for any time step.

Notice that by actively applying the linear system of equations above recursively:

X(n+k)=A^k X(n)+ A^(k-1) B U(n+k-1)+ … A^(0) B U(n)

Let B(k) = A^(k-1) B(1) U(n+k-1)+ … A^(0) B(1) U(n)

Where B(k) is the state input matrix for a time step equal to k times the time step for the known state input matrix B(1)

as is done in the case of the geometric series:
http://en.wikipedia.org/wiki/Geometric_progression

B(k) – A B(k)=I B(1) - A^(k) B(1)

And

B(k) = inv(I – A) * (I – A^(k) ) B(k)


Now this solution is only useful if A does not have eignvalues too close to one and your input is a natural response to a linear differential equation. The trick if the input is not constant is to augment the state space matrices:
AA=
[A1 I]
[0 A2]

XX=
[X1]
[X2]

Where:
A2 is the state transition matrix describing the input dynamics
X1 in the initial state of the system
X2 is the initial state of the system describing the input dynamics.

Now B(k) becomes:
B(k)X2 = A1^(k-1) A2^(k-1) X2 + … A1^(0) A2^(0) X2

Where X2 is the initial value of the input state dynamics.

We have to be careful here because A1 and A2 don’t necessarily commute. As a consequence:
(A1*A2)^(k-1) is not necessarily equal to A1^(k-1) A2^(k-1)

Let:

W(n)= A1^(k-1) A2^(k-1) + . . . +A1^(0) A2^(0)

Then

W(n)-A1*W(n)*A2=I- A1^(k) A2^(k)

Unfortunately the only way I can see how to solve this is by solving the system of equations that one gets is by comparing equal elements in the matrices on both sides of the matrix equation. This mean a matrix inversion for a vector of size n^2 where n is the number of states. This may or may not be a time saving. It will depend on the size of n and k. For small values of n and large values of k it should work really well.

As for choosing A2 if we wanted a damped sinusoidal input with angular frequency wo and with a magnitude multiplier of rho we would write:

A2=
[rho*cos(wo) rho*sin(wo)]
[-rho*sin(wo) rho*cos(wo)]

High Order Statistics and Gaussian Distributions

I happened to be thinking about the problem today and the easiest mathematical technique I could come up with is to multiply the distribution by a polynomial. That way information about the higher order statistics can be used to tweak the most important part of the distribution while the tail properties stay unchanged.

For instance say we had something like a Gaussian distribution but with a bit of skew we might use a distribution of this form:

P(x)=d*(1+a x) exp(-x^2)



Now consider trying to evaluate the maximum likelihood. Setting of P(x) with respect to b equal to zero:

0 = d*a*exp(-x^2)
- 2*d*(1+a x)*x* exp(-x^2)

which can be rewritten as:

0 = a- 2*(1+a x)*x

or

0= a x^2 + 2*x - a

Notice when a goes to zero the mean goes to zero which is the case for the standard normal distribution. In the case of maximum likelihood x is a measurement. For independent distributions the likelihood function is of the form:

P(x1,...,xn)=d*(1+a1 x1) exp(-x1^2)*...* d*(1+an xn) exp(-xn^2)

By applying a linear transformation from x1 to xn you can form distributions with correlated statistics and non zero means. I am not sure if by choosing the correct linear transformation of the independent variables x1 though xn and choosing the constants a1 to an if one can generate n random variables with any valid desired second and third order statistics. I leave that as an exercise to the reader. lol

Sunday, January 14, 2007

The Difference between a Set and an Element

I on Usenet asked a very simple question. I asked, “what is the difference between me and the set containing me". I got a multitude of responses. G. Frege generalized the idea nicely and called it heap theory. I am not sure if the name but it allows a nice theory of collections:

From G. Frege's Post:

From: G. Frege - view profile

Date: Tues, Jan 9 2007 10:50 am

Email: G. Frege

Groups: sci.logic

- Hide quoted text -

On Tue, 09 Jan 2007 00:09:16 +0100, G. Frege wrote:

> [...] Hence it seems that for heaps there's no difference between "e"
> and "c".

> So let's stick with "c" (and forget about "e") for heaps:

> a c A

> "a is a constituent of the heap A"

> You wrote: "David Lewis wrote a famous book a few years back called
> "Parts of classes" (which argues in effect that standard set theory is
> what you get by combining the mysterious operation of forming
> singleton sets from their members with mereology -- the study of the
> part/whole relation -- for the subset relation (he argues) is a
> part/whole relation."

> It seems that there is a relation between my little "theory of heaps"
> and those part/whole-theories.

> Indeed, in contrast to a set there are no elements _in_ a heap. A heap
> just consists of its constituents. As a consequence heaps "merge":

> Let d = [a,b], then [d,c] = [a,b,c].

> For example, if Q would be the heap consisting of all rational
> numbers, and I would be the heap of all irrational numbers, then
> R := [Q,I] would be the heap of all real numbers.

> With other words, the heap [Q,I] does not just have two elements Q and
> I, but consists of all real numbers.

Some additional considerations:

If A and B are heaps, we have:
A = B <-> Ax(x c A <-> x c B).

We may define:

The /union/ of heaps:

A u B =df [x : x c A v x c B]

The /intersection/ of heaps/:

If Ex(x c A & x c B) we set
A n B =df [x : x c A & x c B]

The heaps A and B are called
/disjunct/ iff ~Ex(x c A & x c B).

Theorem 1:

If two heaps A and B are not disjunct,
then A n B = [x : x e A & x c B].

A "model" for the theory of heaps: a plain of points.
--> Venn diagrams!

.-------------------------------.
| |
| .-----. .-----. |
| | A | | B | |
| '-----' '-----' |
| |
|_______________________________'

If two heaps A and B are disjunct (have no constituent in common) then
the intersection of A and B is _not_ just empty (like in set theory),
but there simply _is no_ intersection.

Another fundamental definition:

A heap a is /atomic/ (or an /urelement/) if
Ax(x c a -> x = a).

(The heap a just consists of itself in this
case. It does not have other constituents.)

A constituent a of a heap H is
an /atom/ of H if a is atomic.

Non-atomic heaps might be called /molecular/.

Finally one might consider the /number of atoms/ of a heap H:

|| H || =df |{x : x c H & x is atomic}|.

(Here I make use of combined heap and set theory.)

Axiom (Urelements):

For every n, if n is a natural number,
then n is atomic.

Then we would have, for example:

|| [1,2,3] || = 3.

Let IN = [x : x is a natural number], the heap of natural numbers,
then

|| IN || = aleph_0.

etc, etc.

Imho, the theory of heaps forms a very "natural" theory of
"collections".

One might even, paraphrase Cantors informal "definition" of sets, and
state:

"By a heap we mean any collection H of definite, distinguishable
objects h of our intuition or of our thinking (which we call the
'constituent' of H) to be conceived as a whole."

F.

Later the discussion turned to an interesting discussion about some of the technical aspects of forming a set theory:

G. Frege
As you are of course well aware, the
axiom is usually formalized in the context of pure set theory where
everything in the domain of the quantifiers is assumed to be a set.
Under that assumption you can just formalize the axiom without any
qualification:

(x)(y)[(z)(z in x <-> z in y) -> x = y] .

But, as you note, this axiom is false if there are non-sets in the
domain of the quantifiers.




Thursday, January 11, 2007

Meign Kampf, Hitlar and Zionism

There seems to be a conspiracy going around that Hitler loved the Zionist. Acording to DogOnPourch there are only two places in Hitler’s book in which the Zionist was mentioned. Those places are quoted by DogOnPorch bellow. I will leave it to the reader to decide weither Hitlar’s comments are flattering or not.




Oh the irony, that Hitler loved the Zionists, but despised the ordinary Jewish people.

So much so, that the Zionists, got positive reviews in Mein kempf.


Hardly...'Zionist' is mentioned only in two chapters in "Mein Kampf". Both times in passing...Zionists as unclean traitors to even their own people or devious types that would use their own country as a method to further their world-wide Jewish criminal conspiracy. 'Zionism', oddly enough, is never mentioned.

Also, in German, the word for 'great' is the same as 'large'...große...which is the word Hitler uses. Revisionists however seem to think that this word means 'great' as in wonderful/wundervoll
...lol. The phrase B_Cat's article uses is wrongly worded to boot.

...'great movement out of Vienna'...

...actually reads...

'Among them there was a great movement, quite extensive in Vienna...'

Adolf Hitler, Mein Kampf, Vol. 1, Chapt. 2.

Yet I could no longer very well doubt that the objects of my study were not Germans of a special religion, but a people in themselves; for since I had begun to concern myself with this question and to take cognizance of the Jews, Vienna appeared to me in a different light than before. Wherever I went, I began to see Jews, and the more I saw, the more sharply they became distinguished in my eyes from the rest of humanity. Particularly the Inner City and the districts north of the Danube Canal swarmed with a people which even outwardly had lost all resemblance to Germans.
And whatever doubts I may still have nourished were finally dispelled by the attitude of a portion of the Jews themselves.
Among them there was a great movement, quite extensive in Vienna, which came out sharply in confirmation of the national character of the Jews: this was the Zionists.
It looked to be sure, as though only a part of the Jews approved this viewpoint, while the great majority condemned and inwardly rejected such a formulation. But when examined more closely, this appearance dissolved itself into an unsavory vapor of pretexts advanced for mere reasons of expedience, not to say lies. For the so-called liberal Jews did not reject the Zionists as non-Jews, but only as Jews with an impractical, perhaps even dangerous, way of publicly avowing their Jewishness.
Intrinsically they remained unalterably of one piece.
In a short time this apparent struggle between Zionistic and liberal Jews disgusted me; for it was false through and through, founded on lies and scarcely in keeping with the moral elevation and purity always claimed by this people.
The cleanliness of this people, moral and otherwise, I must say, is a point in itself. By their very exterior you could tell that these were no lovers of water, and, to your distress, you often knew it with your eyes closed. Later I often grew sick to my stomach from the smell of these caftan-wearers. Added to this, there was their unclean dress and their generally unheroic appearance.
All this could scarcely be called very attractive; but it became positively repulsive when, in addition to their physical uncleanliness, you discovered the moral stains on this 'chosen people.'


and...

Adolf Hitler, Mein Kampf, Vol. 1, Chapt. 11.

The Jew's domination in the state seems so assured that now not only can he call himself a Jew again, but he ruthlessly admits his ultimate national and political designs. A section of his race openly owns itself to be a foreign people, yet even here they lie. For while the Zionists try to make the rest of the world believe that the national consciousness of the Jew finds its satisfaction in the creation of a Palestinian state, the Jews again slyly dupe the dumb Goyim. It doesn't even enter their heads to build up a Jewish state in Palestine for the purpose of living there; all they want is a central organization for their international world swindle, endowed with its own sovereign rights and removed from the intervention of other states: a haven for convicted scoundrels and a university for budding crooks.


I'm sure that will prove interesting to the anti-Zionists here.
;)
The above quote was taken from:
Zionism and Anti-Semitism ,s243a at:
http://www.canadawebpages.com/pc-forum/topic.asp?TOPIC_ID=8512

The reader my also find the following discussions interesting:
Zionism, anti-Zionism is anti-Semitism , Jeffusa
Einstein and Zionism ,s243a



Collective Quilt, & British Imperialism, by Sean


I posted DogOnPorch’s comments here because I find he has a perspective well grounded in history. I thought there was no basis for the deletion of his post from Politics Canada. Rather then have such valuable insight disappear I reposted it here. I got one rather long reply from Sean which tries to show the absurdity of collective guilt by historical references of British imperialism.

I do not agree with Sean’s concussion. I am not a historian. I appreciate other historical perspectives. My feelings are the British empire was not as destructive as suggested by Sean but it is certainly an interesting historical question. His post was clearly substantial enough to be a headline topic on this blog.


"'On the German home front, a collective guilt settled onto the German population who'

The problem with the collective guilt argument, s243A, is that it can be used against a *lot of* other European countries, and hit a few others much harder than Germany when you take the past couple centuries into account.

My family is Irish, for example. When we look at our family tree there's... oh, a couple surviving branches, whereas most families have a rich tapestry going back generations. Why? In the early 1800's, the British decided that we pesky Irish then resident in Corcaigh-- better known as Cork, to those on the outside-- were too much of a troublesome nuisance to the Crown to be given the same rights, even to basic survival, as the British themselves. So over a century, in a collection of military operations, hypertaxation, arrogant and brutal repression, deliberately murderous economic policies (aka pumping out Irish foodstuffs other than the potato when the potato itself was known to be hit by blight), and horridly bloody attacks on Irish civilians-- after the 1916 Easter Rebellion for example-- millions of Irish were killed, and much of my family was thereby deliberately wiped out.

Not genocidal? Oh yes, very genocidal. And if you have any doubts about Ireland, then check out British "civilization" as brought to Tasmania and Australia, where the British government gave settlers cash payments and land for hunting down and massacring the aboriginals there. Or India, where the toll stands at up to 50 million dead Indians-- a number that dwarfs Hitler and Stalin-- due to British policies of confiscating Indian croplands, brutally taxing the peasantry, manipulating prices in Indian markets and taking out desperately needed food from Indian markets, as had been done in Ireland. http://tinyurl.com/yxwr8g

Now, the British themselves were busy getting flattened like pancakes themselves (and pansies, which they were) in Afghanistan on 3 different occasions as well as in several unsuccessful battles in South America, where a bunch of militias in Uruguay and the Plata somehow defeated the British and blocked them from the region: http://tinyurl.com/y7hxgb

Yet it was precisely this British fecklessness and incompetence that led them to be so cruel in their colonies. Maybe it was partly just a matter of taking out their frustrations on the Irish, aboriginals and Indians, but a lot of it was also the desperate need to acquire resources to launch their failed wars. One could go on-- British terror bombing in eastern Africa or around Basra in the early 1900's, British slavery in Jamaica (which was especially cruel), no shortage of examples here.

Why bring this up? Because in Germany, the people and the nation's government have clearly and openly apologized for what happened during the 1930's and 1940's and made reparations. Whereas Britain in particular-- and other colonial powers to a lesser degree-- have not apologized to anywhere near the same degree for their own colonial atrocities lasting for much longer, doing much more damage, and being abetted by governments which were wealthy and didn't have the excuse of hyperinflation or revanchism (as Germany during the late Weimar years did-- and the Nazis never, ever won a majority either, despite confused claims to the contrary).

If you truly feel ashamed of your own German heritage, then I feel very sorry for you. Many Germans in the 20th century did horrible things which we justifiably condemn. The Germans also produced people like Bach, Kant, Beethoven, Brahms, Daimler, Benz, Diesel, Goethe, Siemens and who knows how many other people whose work in science, medicine, chemistry, art and music have if anything shaped the world we live in. We owe a good deal of the comforts of the modern developed world to the hard work and moral character of Germans in prior centuries-- the very computer you're writing on is a direct descendant of the information revolution that was launched with the Gutenberg printing press.

All this is to say that countries in glass houses shouldn't be throwing stones. When Western Europe's major colonial countries-- and Britain in particular, which was by far the worst colonialist in the 19th century with an atrocious record even worse than the 20th century dictators-- come clean about their own crimes, and when they return what they themselves looted from their colonies, then maybe I'll be a little more sympathetic to the moral indignation about the WWII Axis countries. But until such consistency is demonstrated, I see little more than propaganda and hypocrisy at work on this topic.

5:39 PM

Delete
Sean said...

Another point to add here, s243A, that may help to give a sense of the scale of the British ruin in India-- prior to British military operations both of the East India Company and the main army itself, India was the second-richest country in the world, with a civilization almost three times as old as Britain and more ancient even than the great cultures of ancient Greece.

Likewise, Britain only actually took control of around 53% of what is now India on the map-- the rest of the country stayed independent of British rule, with Indian rulers who did business equally with Russians to the north and British to the (mainly) northeast. Yet even in the subset of the Subcontinent under their control, the British did terrible damage to kill so many millions of people and cause such economic destruction. India had advanced industries before the East India came along, by 1948, eastern India (the seat of British power) was devastated, while the unconquered regions of India relatively prospered.

Even today, it is the regions in India not under British control that are the most thriving economically and culturally, while those under British imperial rule are in the worst shape. This much applies to other colonies as well. Notice also that the common claim of a "humane British decolonization"-- compared to France-- is also BS: British operations in Kenya were very brutal, read for example "Britain's Gulag" by Caroline Elkins to get a sense of the deliberate massacres, many with a genocidal tinge, that took place there. (And compare also Australia, North America-- the deliberate spreading of smallpox-- and Ireland for other examples.) The British were defeated in the Suez, Israel and southern Yemen among other places after WWII, but often in the wake of a very ugly war against the civilian population, for example.

One other example to bring up-- the Opium Wars, where the British started a war to force an addictive drug onto the Chinese population, in return for products of actual value from China. Hard to think of a more disgusting basis for launching a war, and there aren't much in the way of parallels in the 19th century-- except admittedly for France, which joined with Britain during the Second Opium War in 1860 and, along with Britain, burned down the almost incomparable cultural treasure of the Imperial Summer Gardens in their vandalism (for which the British and their partners in crime in the Second Opium War will be forever cursed, until the Brits make apologies and pay full reparations with interest for it).

Thankfully for our modern world, China was still strong enough, despite its corrupt government, to stay independent, such that China was never colonized by Britain or any other Western power in the 18th-20th centuries. (There were in fact some smaller encounters after the Second Opium War when Chinese forces, with improved weapons, were managed to thwart attacks and beat back not only the British but also the French, Dutch, the Russians, even Americans. The rest-- the Chinese managed to fend off with some well-placed bribery.)

Still, on the record, I'd say that if we're considering atrocities against civilians, genocides, war crimes and other brutality, the British and other 19th-century colonial powers have a lot to answer for and a lot of loot to return. Some Irish people I've met even cheer not only the Zeppelin attacks and the Blitz (and the Luftwaffe bombings of British factories during WWII, the V-2 and V-1 bombings) but also the brutal Irish Republican Army attacks against Britain from the 1920's onward, especially the very terrible attacks on British pubs, malls and shopping facilities from 1970 to the present. A few are so full of rage that they even cheer the more recent terrorist attacks against the British homeland (like 7/7), as justifiable retribution.

I find this to be preposterous-- British civilians today are not responsible for what their ancestors did. What Britain needs to do is to acknowledge this past fully and stop acting like a hypocritical moral authority, and pay reparations and return loot where it was stolen-- not suffer attacks against its homeland for what prior generations did. Today's Britons cannot be blamed for this, and attacks against them are terrorist atrocities, not "acts of vengeance." Yet this is the problem with collective guilt arguments-- dragged out enough, collective guilt is used to justify such modern attacks for past atrocities by prior British governments, as some of my own friends have declared. Pointing the finger of collective guilt can have deadly consequences for innocent people."

DogOnPorch's On Stalin, the SS and Holocaust Minimization

DogOnPorch's Deleted Reply in this thread:
http://www.canadawebpages.com/pc-forum/topic.asp?TOPIC_ID=8648

"For one...the SS was a volunteer army. You joined up...they decided if you fit the coat after that. (see link for a recruitment poster http://www.calvin.edu/academic/cas/gpa/posters/waffenss.jpg )
The Wehrmacht, Luftwaffe and Kriegsmarine had conscription as well as volunteers. Being that the German army was the best in the world not only for equipment, but for leadership and individual motivation, it can't be described as an army of slaves. The average German field NCO could even make tactical decisions without consultation of the higher-ups (ie air strikes...artillery support...reinforcements et al). The Red Army pre-1943 is closer to an army of slaves. After 1943 the commissars lost much of their power and regular ranks were brought back...sergent...captain...major, etc.Hitler far outweighs Stalin in terms of killing people if we take WW2 into account rather than just the Holocaust. About 20 million Soviet civilians alone were wiped out by the Nazis/Germans. Soviet military casualties amounted to 8-10 million dead with another 5-6 million taken prisoner (most never to be seen again). Then if you add the rest of the Allies and their civilians...well you get the idea. Lots of bodies. Stalin also didn't have any 'Final Solution' going on. He just worked you to death. But if he did want to kill you, he had the costs down to about 38 cents or so per body...the cost of the bullet and clean-up.
As a Canadian with Volga German roots, I have a unique perspective of WW2 as I had relatives who fought with the British, Canadians, Americans, Germans...including in the Waffen-SS in Yugoslavia with an all Muslim unit (a hot topic if you recall)...and Soviets as Volga Germany is/was located in the Saratov region of southern Russia.
Conversly, I had an aunt who was a well known Holocaust survivor (SS St Louis) as well as several (all women and their children) who died in the Minsk Ghetto when it was liquidated. Not to mention other relatives I'll never get to meet as they perished at the hands of Stalin when he Gulaged all the Volga Germans who didn't join the Red Army. So you don't need to describe the situation to me...my family lived it.
After hearing my uncle's old Yugoslavia and Nuremberg Trial stories (he was a translator after being captured by the British), I'm very, very, very, anti-Nazi. That revisionists are now trying to play down the evil commited by Hitler makes me furious to say the least. As far as some Germans being Nazis and others not...it is a misleading statement. Though regular army (Wehrmacht) units didn't participate directly in things such as the Holocaust...they were certainly working hand in hand with their Waffen-SS counterparts in fighting the actual war. On the German home front, a collective guilt settled onto the German population who even if they weren't dyed in the wool Nazis were all too aware that their actions and decisions in the early 1930s led to the reality of Germany being flattened like a pancake.
This banning...of Jeff and I...seems more the result of B_Cat just plain not liking what we had to say rather than any real outrage about the dead of WW2 or any other given reason. That other obviously rabid posters are allowed to splooge out their Anti-American, Anti-Jewish, Anti-Israeli clap-trap without 'the Editor' blinking an eye just confirms it to me. The ironic part is that in a way, B_Cat's postings 'summoned me' here as her comments turned up on several occasions during an internet search on Zionism.
So why don't you just stop all this BS and write 'the Editor' for us saying you made a mistake. It just looks like you were trying to quietly get rid of us without good cause...hoping nobody would notice the empty chairs. As some said...they just thought we stopped posting here suddenly.
Cheers to all."
http://www.youtube.com/watch?v=RAwU10XBICg[/i] by DogOnPorch

Child Civilization

Sunday, December 31, 2006

Political Grab Bag

I originally created this blog to try to cut though the confusion of the news but lately I have gotten interested in artificial intelligence. So what I am going to do is create kind of a free for all thread where you can respond to one of the threads I started on another form. When I have time to put together a more focused topic, I will. The purpose of this thread is to keep track of some discussions I found interesting and see what political topics readers here might be interested in. Hopefully this thread will act as raw material for a better researched thesis.

Taxation World Wide , s243a

Zionism and Anti-Semitism ,s243a

Ethiopia declares war against Somali militants ,s243a

Wars Are Won in the Media ,s243a

Yes, Oil from Venezuela , B_cat

Einstein and Zionism ,s243a

Oh Glories After life [8-)] ,s243a

Zionism, anti-Zionism is anti-Semitism , Jeffusa

Religion and Control , s243a

Mahmoud Abbas , s243a

US prison population largest in the world!! , kuzadd

Fact Checking Glen Beck ,s243a

The Party Line, Lenin & Political Correctness , s243a

"Give me Liberty or Give Me Death", Patrick Henry , s243a

Biblical Violence ,s243a

Biblical Justification to fight Tyranny , s243a

Chavez Buys Himself An Election , s243a

First Muslim congressman elected , s243a

Perpetuating The Belief Woman are Victims, s243a

Liberals get Free Pass on Environment , keepitsimple

Fuzzy Logic and Data Mining , s243a

Global Warming - How Science Should Work , keepitsimple

Global Warming - Best News Yet , sneaky

Smoking is More Dangerous then Afghanistan , s243a

Pride Vs Political Correctness , s243a

Excommunication ,s243a

Is the CBC Sexist? , s243a

CPC Will Table Bill to Control Dangerous Chemicals , s243a

Science vs the way products are sold , keepitsimple

Crossing the Floor , DarthHarper

global warming, big oil and Christmas! , biopiracy

Cdn University To Ban Pro Life Groups , jjfoxy

The Biggest Divider , s243a

Kyoto: 20 Billion , sneaky

Anti-Harper Bias , OakvillePC

France Vs Canada (CO2, Economy, population) , s243a

Clean Air Act, Have you read it? , s243a

If Belinda leaves politics... , kwlafayette

Are many Environmentalist Sexist? , s243a

alph Klein: Just another chauvinist Conservative , tbud

Solar Forcing of Climate , sneaky

Alberta Oil Industry doing its part , sneaky

The Cost of Being GREEN , DFCaper

Clean Air Act - A good Start , keepitsimple

who wants to get chipped ? , PollyNewbie

CIA Mind control , s243a

PollyNewby's Anti-American Post , s243a

Pray 5 Times a Day or Lose your Head, scribblet

Multi Agent Systems: A Nutrition Problem

I don’t think multi agent systems are the answer to artificial intelligence but I see them as a useful tool for prioritizing problem solving so an AI system can return quick answers quickly and in the background use more sophisticated techniques to solve the problem. We can think of this background processing as a thinking or pondering process even though some of it could be step by stem machine instructions. Bellow is what I pasted to the new mars message board on this issue.


Minsky talks a bit about this in _Society of Mind_

He blackboxes the decision with a _More_ agent (i.e., decides "is greater than") that is located in a network of agents (the whole network of agents is the society of mind, agents can be complex or single-neuron simple). There might be just one _More_ agent but there are probably many of them - maybe no single agent can compare apples and oranges, maybe it can. The comparison agent _More_ may be different from, but linked to, the language agent _More_ (observe each of listening, speaking, reading and writing seem to eventually connect to the same language agent). Each individual mind may structure the network differently.


I’ve heard about multi agents before. A student that had the same supervisor as me was doing his thesis on multi agent systems. He was building a system for an oil company to combine multiple fault detection techniques. I don’t think human’s work in this fashion because personally I can’t concentrate on very many things at once. Although the human mind has a highly parallel architecture.

Today I was thinking about how AI could be applied to a diet program. I was thinking how on packaging they list the ingredients in food but they don’t tell you how much of each ingredient. However they give the composition of the food in terms of vitamins and if you assume the composition of the food in terms of vitamins is made up of a linear combination of the ingredients you should be able to estimate how much of each ingredient there is.

One might try to solve this problem with matrix inversion but some ingredients with virtually no nutritional value will lead to an ill conditioned matrix inversion. Say you have access to visual basic, MATLAB and not a lot of money to by extra packages for visual basic. You might write a short script in visual basic to solve the problem based on ridge regression because it keeps you having to worry about numerical issues like pivoting.

You might write one or more complex techniques in MATLAB to deal with the problem because it has built in algorithms created by experts in their field. Now the visual basic algorithm you can probably run as a thread in the background or maybe it will be fast enough that you won’t even to bother to run it as a thread. It will give you a crude quick answer and let you proceed.

MATLAB is a large process and you might want to access it via a server on another computer. It can only handle one process at a time and two instances of MATLAB running on one computer don’t share resources well. IF the algorithm in MATLAB is sufficiently more complex it might take a while and even if it runs quick, the MATLAB resource could be tied up solving a more difficult problem that you previously requested it solve.

As a consequence you might have to wait for the answer. The main program can do two things. It can create an ID representing the problem and each answer can be uniquely stored and linked to the question so it can be used when needed. With this kind of architecture you can use the crude answers to provide early solutions to problems and will have access to better answers latter to improve the solution. Thus in my diet example as you enter in new food information, you can get a quick answer of what you ingested and later in the day if you are curious you can check to see if more sophisticated techniques changed that answer much.

Another point is have the program set up to use several techniques will allow people to utilized what packages they have available. Not everyone may have access to complex software packages running on other computers so if these auxiliary systems aren’t configured the software will still be able to function and return an answer.

Friday, December 22, 2006

Words as Functions

I have lately been interested in the structure of language. I thought I would combine this interest with my desire to learn more about the database software Microsoft Access. I will provide a link to the database later when I am further along but for now I would like to consider how to represent the relationships between words.

The data base structure I will describe in another thread. This thread focuses on how to represent the definitions of these relationships. The definitions are represented in a similar form as you might see in a program language for reasons of brevity. Currently I have non intent to parse these definitions.

For example one relationship between words I define with a function called is_a

z::noun=

is_a(x::((noun::instance)::singular),

y::((noun:class):::singular)

);

The function ""Is_a"" assigns the noun x to the set y resulting in the noun z.


In English we may say a cat is an animal. In mathematics or logic we may say a cat is a member of the set of animals or a cat has type animal. The difference right now is not important but hopefully I will have time to learn more about things like, type theory, set theory and category theory so I can better define these meaning. If a poster wants to start a thread about one of these topics please email me and I will consider it for posting.

In functional form instead of saying the cat is an animal we could right is_a(cat,aminimal). You will notice from the above definition the function returns a value of type noun. The motivation for this is so we can describe sentences in terms of compositions (expression trees or graphs) of these functions. For instance the big cat is an animal might be written something like is_a(big(cat),animal) or is_a(intersection(big_things,cats),animal).

The form big(cat) must return a noun which is a big cat in order for us to apply the is_a function. Thus for reasons of data homogeneity we try to have all functions return a noun which is a thing or a group of things.

Notice that we wrote the expression in two different mathematical ways. In the first form we consider big an adjective. An additive is like a function on sets. We take the set of cats and return the set of only big cats. In the second form we realize that the concept of an adjective is not necessary and can be represented with more fundamental mathematical operations. For instance if we consider the two sets. The set of big things and the set of cats. The intersection operations forms a new set of all things that are both big and are cats.

Consequently the adjective big can be represented in terms of set operations on nouns. More precisely:

big=(x)@intersection(big_things,x)

z::noun=

are(x::(noun::plural),

y::(noun::plural)

);

The function ""are"" assigns a group of nouns x to the set y resulting in the noun z."

z::noun=The(x::noun);

The function ""The"" designates z as an instance of the set x."

z::noun=

Has(x::noun,

y::noun

);

The function ""Has"" assigns the property or a possession y to the noun x resulting in the noun z."

z::noun=

Have(x::(noun::plural),

y::noun

);

The function ""Have"" assigns the property or possession y to the noun x resulting in the noun z."

Adjectives and Ambiguity

I was thinking about adjectives like big. When we say something is big is it inherently big or big with respect to some set. Like if I say a big cat, do I mean a lion or a cat that is bigger then the average house cat? Is this ambiguity a strength or a weakness in languages? What challenge do such ambiguities present for computers dealing with languages. What kind of solutions do people foresee?

http://www.newmars.com/forums/viewtopic.php?t=5179

Sunday, September 17, 2006

Welcome to My Blog

Hello,

Welcome to my BLOG. My name is John and I have a vast interest in topics. I called my BLOG child civilization because we are still young and learning. The goal of this BLOG is to try to articulate my attempts to sort though the Chaos of information we are inundated with to understand where we are and where we are going. I am concerned about the preservation of liberty and civilization and strongly interested in science and math.