Predicativity reading todo

 don't really want to take SRH down this road ... we don't want definitions we want to understand why but anyway:

WHAT IS PREDICATIVISM?
https://www.math.wustl.edu/~nweaver/what.pdf

https://planetmath.org/predicativism

https://en.wikipedia.org/wiki/Impredicativity

https://www3.nd.edu/~tbays/papers/burgess.pdf

Can we generate some predicative statements that we can accept?

===

Broadly there is a problem with building houses on their own roofs. In Constructivism you need foundations to build on. And that creates the need for hierarchy rules that force systems into layers.

Now no one can escape Cantor's powerful use of this to create the hierarchy of Infinities that is do vast as to defy definition. Its not that numbers of infinite, but that the number of number types are infinite and so on in an ascending hierarchy that is beyond infinity. It is boundless because any bound greater than 2^current cardinality cannot fit within the current new number and create a new type. Diagonalisation and the Power Set blows apart any set.

So "totality" in set theory is a problem as the combinations of set elements becomes a predicate that lies outside the set.

But we can also create sets not by proving the existence of new things but just filtering things without any concern for whether they exist.

Certainly all the Self-Reference proofs operate by supposing an element and then showing that if it were the exist it would create an contradiction. So we prove it does not exist.

Or perhaps we can just say that if anything were to be selected by the definition it would create a contradiction, so we  blame the definition without needing any actual existence. This was Frege's contribution. ∃x | H(x) could be a problem if x is a Horned-Rabbit. This is actually an absurdity used by Buddha in India in 500BC. What are we saying is absurd about a Horned Rabbit if it doesn't exist? When ∃x | H(x) is false we are saying that there is no x such that H(x) without anything actually existing.

Likewise we could make statement above that make definitions without getting involved in actual existence.

Could a self-referential sentence be written that does not actually imply that it exists?

We run into problems in that surely we can always implied existence in self-referential sentences. If a sentence exists, and is self-referential then it must be referring to an existence. But anyway just pushing the boat out in this Predicativity issue that always been hanging around SRH.

===

Given the set X = {1,2}

∃x ∀y| x ∈ X & y ∈ X & x <= y

So we're saying there is a smallest value. While predicative it's not a problem because 1 has other definitions like S0 the successor of 0. So we have a thing "1" which exists outside this expression. All we are saying is that in the set X which contains "1" and "2" 1 < 2. Obviously in fact "1" is beyond the scope of this definition because we're using its magnitude to select it.

In Ramsey's example of "tallest man in the room" we can argue the same that the man has a height which is defined outside the definition. Ramsey is arguing that the "man" exists beyond the definition but surely we can also say that to apply the predicate H(x) (Height of x) we are going beyond the definition.

We don't need to be constructivist, problems only occur when we are using predicates that attribute qualities to elements that are defined by the set. Any predicate that attributes qualities to elements, that is itself dependent on the set is the only way to cause a problem surely?

"Sets that do not contain themselves" is such a problem.

What is the predicate?

{ x : x ∉ x }

So the ONLY way to find out whether x belongs to the set is to look at x! Now we are in trouble.

This was visualised well in the story of the librarian who decided to catalogue the books in the library. They noticed that and while most books did not reference themselves, some book did referenced themselves. They decided to write two catalogues for these books. The Catalogue of books that do reference themselves and the much larger catalogues of books that do not. Having written the books the librarian adds them to the shelves, only then realising that they are not catalogues yet. For the Catalogue of books that do reference themselves they realise adding it to that catalogue is fine. But then adding the Catalogue of books that do not reference themselves to that catalogue causes a problem, because not it does reference itself. So the librarian moves it to the other catalogue, but not it does not reference itself. This book fits into neither catalogue, and yet a book must either reference itself or not reference itself.

You might say the problem of course is that the book is not complete until all the references are in, and so it is not referencing a finished book, or an actually existing book yet.

But if the librarian sticks to catalogues of finished books then the problem still remains. Because once finished they catalogues can then be added to themselves, which means they are not finished yet.

The actual problem is that the Predicate namely "x ∉ x" depends only on x itself. How do you know whether a book belongs in the catalogue? You must scan the book for itself. How do you know what "itself" is you must look at the book. The itself is not defined by anything "outside" the book. Once you have picked that book up the "itself" is not defined. Its like the set of all things that you are holding at the time. The scope is limited entirely to the context of the operation there is no "objectivity."

Note computer languages have "this" or "self" references that when dereferenced point to the current object. All the objects are in objective space like books in a library and have exact addresses or names. Each self variable name is then replaced with the relative address of that object at run time.

We can't escape the paradox then by binding the "self" with the name of the book. That produces a list of questions about whether each book in the library with title T contains the text T. We assume that we've already titled the two catalogues of "Books that Contain" and "Don't Contain" themselves.

That maps back into computers. Suppose we have a base class with a method PrintNotSelfReferential(). We then have a class hierarchy derived from that and a load of instantiated object in memory. Now all object in memory must either dereference themselves or not. So we make a new class derived from the base with a method to go through memory and call PrintNotSelfReferential() on every object that does not dereference itself. It gets to itself and with no reference to itself it calls its own PrintNotSelfReferential(). In so doing it references itself and so executes PrintNotSelfReferential() on a method that ends up dereferencing itself. If the method had a validation step to check the output and redo if wrong you then have a loop and it never halts. The classic "I am false."

So there's no real way out of this. Once something is defined ONLY in  terms of itself ere be dragons!

But why?

I meant to say at the top, what of fixed points in this?

Is it meaningful to ask for the fixed point of a set like :  

{ x : x ∉ x }

#TODO

Am I being stupid? Isn't SRH simple? Self-Reference

How hard is this.

So as argued in blog last year there is some use to deciding by random. So let me decide whether to start the next sentence with "Amphoteric" if the coin is heads or "Blastocyst" if it is tails:     

"Amphoteric" reached its maximum usage in 1929 according to Google NGram. Okay I actually cheated there cos I was supposed to use the word and instead I used its quotation. But then there is no agreed way in English grammar to express "use the quotation" so its actually ambivalent, a word interestingly which has the same root as "amphoteric" where "ampho" is Greek for both.

Anyway the coin could have come down as a tail:

And that is it. Apparently if you ask "Yes/No" questions what can go wrong. And since anything can be expressed as a "Yes/No" question you can decide anything this way.

But what if you extend the questioning from simply worldly things like what shall I do, to meta statements about coin flips.

Well a "near" meta statement is: shall I never use coins to decide anything again (assume Head = Yes)

Well that is okay cos the coin is deciding never to use coin flips again. And if we flip again:

That is fine we just ignore it.

But what about: Shall I obey the next coin flip?

So the decision is that I should not obey this coin flip. But if I do not obey it and ignore it then I am actually obeying it. I'm stuck.

So its incredibly easy to cause a contradiction through self-reference. In the real world its just a system that can't get a stable answer. Suppose a Turing Machine with the following rules:

δ(q0, 0) = (q1, 1, →)

δ(q0, 1) = (q1, 0, →)

δ(q1, 0) = (q0, 0, ←)

δ(q1, 1) = (q0, 1, ←)

Or in this online TM the following program:

0 0 1 r 1

0 1 0 r 1

1 0 0 l 0

1 1 1 l 0

Recording the last move in the state means its easy to step back from the second position and loop.

So that is essentially what a contradiction is. A system that keeps contradicting itself and never stabilising. It doesn't Halt.

Now Turing was able to show that there is no Turing Machine that can decide whether another Turing machine will Halt. The problem is that it can't tell if it will Halt itself, and worse if there was such a TM you could use it to loop if it said it should not loop. That is literally isomorphic with the coin flip above or "I am false" liar paradox.

So that maps onto saying that there is no system that can tell if another system is a contradiction because it can't tell if it would be a contradiction (more accurately if it could, then you can engineer a contradiction).

So all that SRH is saying is that Self-Reference always leads to loops. Now worth exploring: do loops mean Self-Reference. Is the Turing Machine above an example of self-reference? That is, is it iso-morphic with a self-referential system? @TODO

For that consider Godel: he was able to create self-reference by listing and numbering sentences in Principia Mathematica. Once each formula had a number then a formula could operate on itself.

Now it was noted early in this blog that this "self-reference" was not "within the system", it exists in the creativity of an observer hermetically locked outside the system. Everyone knew that PM had functions that operated on elements that were understood to be numbers. But it took Godel to show that there was a diagonalisation that mapped formula to numbers thus giving sentences a self-reference meaning, and then used this to create a contradiction. But that all lay outside the system: something that viewers could decide for themselves without interacting with the system at all. Shall we call this "Extra Self-Reference". This is very different from the Self-Reference experienced by humans which appears to be "Intra Self-Reference" where the "self" knows that it is self-referential. That is not just awareness of the self, but knowledge that this actual self is the one being self aware. There is no "outside" to this situation (its also an illusion potentially as the "self" here is not a exactly "self" but rather a Universe).

Anyway must go. But how hard is this? But if SRH is going to have greater significance than this, formal systems, mechanisms and isomorphism will have to be the limit of this part of the investigation.

So really no need to get complicated. Now with such a simple formulation can you define exactly what the conditions for loop are. Are loops possible without self-reference (under any isomorphism).

And immediately we can say that were the conditions for looping possible then we have Halting Proof cos you could use these conditions to loop when you should not be looping. So that is impossible.

So the conditions under which contradictions and looping occur cannot be decided universally.

BUT and this is where SRH is interesting this proof uses self-reference. And we are saying that self-reference is the condition.

So 

(1) is self-reference the condition for looping (see above)... looping <=> self-reference

(2) can we decide whether self-reference is involved without using self-reference, i.e. can we decide whether loops happen just by looking at self-reference.

Now obviously a universal statement must apply to itself and so be self-referential. BUT what if the statement has an SRH caveat that (knowing that self-reference is a problem) excludes the case of self-reference?

===

The thing to do first is to find all the conditions of the coin flips that lead to loops. What is the structure of a loop in something as simple as the coin flips?

It is something like Tarski's Undefinability Theorem, but we are using Truth/False more abstractly to be anything "meta" within the system which is "suitably" meta to effect the outcome of the operation.

Some rules for this coin flip game:

1. The outcomes are binary Yes/No instead of True/False. But any binary outcome will do.
2. Heads maps to Yes.
3. All input must be a Yes/No question, or interpreted as such.
4. A "Program" is the chaining of Yes/No decisions, notated within {} brackets.
5. Decisions can be based upon previous answers.
6. Decisions can effect future statements (in program scope, unlimited scope)

Proposition>This system can make any decision from a countable set. Suppose we wanted to pick an N, we could just set up an infinite number of questions until we got a Yes.  

So in the first example above "ignore future coin flips?" is the greatest extent of Rule 6 and its the one that causes the problems.

We can define 3 types of questions.

Basic: eat chocolate or strawberry ice-cream

Meta1: stop playing this game.

Meta2: ignore this statement  

Meta2 have scope over the decision itself. SRH.

If we remove Rule 6 loops are loops still possible?

So 3 things to be clear on:

(1) What exactly is the condition for contradiction? Call that C.

(2) Is C the same as self-reference

(3) Is C the same as fixed point.

Now (4) is a response to the Woozle Loops post. If (3) is true then the condition for contradiction is actually a system which does not have "power" over all its elements. To phrase crudely. A Fixed Point is that element which remains unaffected by the System, like an Eigen-Vector it is unchanged, and represents a higher "meta" feature of the system. It represents the limits of the system "power." 

In fact for a Matrix to have a particular "transform" means it must be bound in a particular way and that is characterised by its Eigen-Vectors. Such meta statements interestingly are invariant under the transform. For a system to have a nature, automatically implies it has a limit. That limit defines its nature. Like a boundary on a geometric figure, that boundary defines the shape, and produces its "limit" also.

So Fixed Points actually define the limits of systems because they lie outside the systems, as does Self.

So in the post on Woozle Paths the thing being tackled is that TRUE "self-reference" itself is a contradiction. A "self" is an eigen-vector of a system and so cannot be part of the system. It is a "meta" feature of the system which lies outside it. And for a system to "be" something or have a "nature" it must have a boundary which provides the limit, which makes it what it is. But that boundary cannot be expressed "in" the system, since the system is defined in terms of the boundary!

The nature of something is what makes it what it is. It cannot then define its nature! And so a system can never actually refer to itself. This may have been the 1st version of SRH in fact that TRUE self-reference is impossible: in the sense of a system being able to encode itself, or operate on itself, or know itself. Whatever "power" or "nature" it has must be "greater" than the system. Its fixed points cannot be discovered by the system itself.

So not abandoning fixed-points after all. But rather they prove that TRUE immanent self-reference is impossible! Which was original SRH.

Derived SRH then says that Extrinsic Self-Reference like Godel Numbering (which only denotes elements within the system so that an element can refer to itself) but importantly must be done "extrinsically" by an external analyser of the system like "Godel" himself, using diagonalisation and isomorphisms, this type of SRH states that Self-Reference is the condition for contradictions.

Godel says his theorems hold for systems where self-reference is possible, but we're saying that self-reference is the problem from which his and many other paradoxes arise. We should understand the self-reference itself!

Holocaust Memorial Day

On this day its important to remember the victims of genocide, in particular the biggest genocide in history where a whole race of people was removed from North America by European colonists.  

Obviously facts on this Holocaust are extremely hard to determine because the White Americans are extremely biased and most Americans including Jews are Holocaust Deniers. But likely a population of 30 million native North Americans was annihilated to just 250,000 through disease, deliberate starvation and mass murder. Identical in fact to the Nazi Holocaust where starvation and disease were the main killers too. 

This means that 99% of the American Indian race was annihilated in this Holocaust making it the worst Holocaust in human history, and the most important to remember.

The next biggest Holocaust I know of was the Nazi Holocaust of Romani Gypsies. 85% of the world population was killed.

Strangely the most famous Holocaust was neither of these. The Jews think they experienced the worst genocide, but this isn't true. Something like 50% of the European population of Jews were annihilated, that's not even the global population. Jews also think they were enslaved in Egypt, but this is not true either.

What all this tells us is that Humans and in particular Europeans are genocidal beings. If we are to remember a race it is the race of Caucasians who are responsible for all these genocides.

I suspect, and as evidence mounts we will find out, but there were 6 species of humans at one stage including newly discovered Denisovans like in picture. And now there is just 1. Given our genocidal nature I wonder whether modern humans genocided all the other races of human.

Just as American want to deny their Genocide. I wonder whether modern humans want to deny that they are genocidal.

And one thing that is particularly nauseating is Jews pretending that they are somehow uniquely victims of Holocaust. Jews were complicit in the Holocaust. Famously George Soros admits as a child to reporting Jews to the Nazis. So what is the difference between Soros doing this and a non-Jewish German like Schmidt reporting Jews? And the Torah is one long genocide of other tribes of the Levant. And we see the Expansion of Israel into surrounding lands, even to this day, directly inspired by the German Liebestraum, and that itself inspired by the European colonisation of the "New World"-- which was never "New" it was just stolen for the original inhabitants through violence and extorsion. If you can scalp Indians for $50 a head to clear them off land then you can gas Jews to clear them off land or bulldoze Arabs off land too. But you can't reasonably do any of these. As long as Israel occupies land illegally and displaces people racially it springs from the same genocidal root as anyone else in the human race. There is no difference between Jew and Non-Jew when it comes to genocide for both victims and perpetrators. Indeed "Jews" are an irrelevant topic in the discussion of genocide. And worse the insistence of including Jews in the discourse on Genocide actually allows the true perpetrators to escape and the true nature of Holocaust to remain buried and so the Remembering of Jews actually just serves to promote Genocide and ensure it will happen again. Some non-racist honesty in all of this is essential before any progress can be made.

Gender debate

Feminism began as a reasonable reaction to the freedoms observed in men compared to women in the West. Especially after WW2 when women hired for the war effort decided to stay at work and take home a salary.

But as argued elsewhere in this blog it's all a misunderstanding. Women are kept at home because men want to be sure they do not get pregnant by other men. Unlike women who always know the child they carry is theirs, men are never sure quite who their partner slept with. For this reason women don't really care who their husbands sleep with, beyond fear they will divide their attention with another household. But for men, if they are to invest 18 years of work in a child they want to know for sure its not someone else's. That inequality is what underlies all the apparent "injustice" the feminists observe. And because feminists got this wrong the whole of feminism is wrong.

Feminists also leapt on the Black Emancipation movement. Women seeing themselves as slaves who needed freedom. But actually despite the horrors of US slavery really all this comes from Jewish ideas of Exodus. But actually all these are lies or hugely exaggerated. The Jews were never slaves as argued here, until 1930s Germany anyway. The time in Egypt was not slavery, even the Bible mentions no slavery. So all this is lies in fact and false. But anyway Exodus inspired the Black Emancipation from Capitalism. Which is ironic as Usury and Capitalism was banned in the Bible. But, while the Christians took this to mean in general the Jews took this to apply only to Jews not Gentiles. As a result the only way for Christians to borrow money in the West was from Jews. In fact this is the origin of the Jewish Ghettos. Because Jews were allowed Usury and the Christians not, the Christian Law makers asked the Jews to live outside the city so they could police Usury more accurately. The Jews agreed and so the division began that ultimately ended up in Pogroms and Jewish exclusion from society. Mammon really is not a kind god! So the growth of usury and Capitalism is actually what led to Black Slavery. Which means that Jewish culture both created the chains that enslaved the Blacks and also gave them the Exodus inspiration to break those chains! God moves in mysterious ways indeed.

But once we sweep all this nonsense aside we are left with the gender debate.

Everyone alive was born. This is the most important existential thing for anyone to deal with. And what is probably unwelcome news to those who have got stuck in the gender debate, being alive us the result of sex. There is no way to get away form this. How ever you slice and dice sexual preferences, relationships and culture it all rests on the basis of birth. You need to be born to even argue about this! It is absolutely fundamental.

SO there isn't much to add. Being born is about sex. And it involves two sexes. There is no third sex required for childbirth. Kind of end of.

But there are many types of relationship that have nothing to do with childbirth. There are prostitutes, gay relationships, rape and now trans-sexual relationships. In strict simple, plain talking these are all perversions because they pervert the basic truth of sexual relations that they are to do with birth.

However we don't need be so restrictive -- except in the case of non-consensual relations which automatically count as crime. Altho I remember a German case where a man consensually agreed to be eaten by another. His penis was eaten first suggesting a sexual motive to this rather than just being hungry! Sex can take almost any form and we agree that many forms are perversions. But as liberalism spreads we accept more and more.

Well not getting into the complexities of sexual preferences but how ever you argue this the root basis of procreation is a given from which everything else comes.

Gender is similar. In functioning sexual relationships that give rise to children there are obvious roles that people fall in to. Females for example produce milk, and gestate the child. Men do not do either. There is no real argument here. Fitting these facts into gender roles is definitely the simplest way. Indeed it would be fascism to force men and women to abandon these time honoured and logical facts. But it is true there is no reason to be heavy handed and force people into gender roles. But equally no reason to be heavy handed and force people out of them either.

So there isn't much to this debate really once you clear away the nonsense.

But now we see America yet again. The problem here is US Ego, Rights and Freedom at play. In the US you define your freedom by being an idiot and rejecting everything you are told. You appoint yourself as an expert and you decide to rewrite the rules. The problem with this is you are probably wrong. But being a loud mouthed American you won't listen and you will be the last to realise you are wrong. America and Americans have  along history of being wrong about everything.

Something the so called Cis community needs to do is claim back the sex and gender debate from the self appointed idiots who seem to think they know what they are talking about. Everything in Feminism needs review because it is obvious nonsense. And everything that derives from Feminism is on even more shaky territory. But really the main problem is if its American: then it's wrong.

Mentioned before a main problem is this false belief in "Patriarchy." There is no such thing, its an invention of Feminism. What Feminism does is invent Patriarchy and then use that to justify Feminism. But Patriarchy is part if Feminism so by SRH you can't use Patriarchy to justify Feminism. Its like a salesman or advert who creates a need and then surprisingly has the solution.

Take a current UK advert which introduces the idea of "nose blind." This is the feature of the smell you get when cooking that during cooking you lose the ability to smell what you are cooking. Well some marketing exec realised they could use this to sell unnecessary air fresheners. No one really uses them, but you can make people paranoid and feel they do need them. Like all bullshit you can turn to the salesman and say well if you can get nose-blind then so can your guests so you don't need it. All swords are doubled edged. All salesmen defeat themselves. Feminism has all the tools of its own ruin/ It is nonsense.

What remains is the "way things are" and like all good scientists and Buddhists you must start with the value of the way things are upon which to base your thoughts and actions. You can't dismiss the way things are like Feminists do. You can't hate the way things are because they are the world that you live in and from which everything you say and do comes.

So caveat to myself. America is the way the world currently is. But its important to understand America for what it is, not what it says it us! And they are almost completely opposite. America comes with its own ultra-massive sales department (which includes the whole of the NEWS and Hollywood) and I think most people don't realise this.

US Dictatorship

 Just follow up the previous post on the disaster that America is both for its own people and the world the Ukraine War is the last US war and has tipped the world once more into instability.

No sooner did 20 years of US war in Iraq, Afghanistan and Syria end than they began war in Ukraine.

"The United States Armed Forces completed their withdrawal from Afghanistan on 30 August 2021" [Wikipedia].

The Ukraine War actually began on 6th April 2014 [wikipedia]. And has received support from the America (and its coalition) on one side and  Russia (and its coalition) on the other.

But America withdraws all its troops on 30th August 2021. And Russia invades almost exactly 6 months later on 24 February 2022.

US Press argues that it withdrew troops because it knew that Russia was going to mount an offensive. But this doesn't make sense. If Russia wanted to take Ukraine it would have invaded at the start of the Donbass war in 2014 while America was still pre-occupied in the disastrous Afghan, Syrian and Iraq wars. No-one would wait until their arch enemy was ready for war to actually start an invasion.

Clearly the Russians invaded Ukraine BECAUSE the US was increasing its support of Kiev. And this fits with global US military activity anyway.

But its far worse because the Euro-Maidan was highly suspicious anyway. It fits the pattern of both MI6 and CIA military operations where a small political protest is used to publicise the Wests political interests. This then turns violent, is suppressed by the incumbent government and that is used as propaganda to invalidate the incumbent and promote the Wests puppets. This has been done literally a hundred times around the globe over the last 70 years. Most famously in Iran in the Western campaign to crush democracy and reinstall the Western leaning dictator the Shah Mohammad Reza Pahlavi whose corruption opened the door to Western oil and enabled the stealing of billions of dollars from Iran. This is such an established pattern it is unthinkable that the Euro Maidan was anything else. And when we discover that Russia is the country being targeted -- that is the Empire the West has been trying to suppress for over a century -- it makes all the more sense.

And a quick paragraph on the Cold War is needed there. The original plan for WW2 was to use Russia to defeat Germany (the central European Empire that the West wanted to destroy) and the turn on Russia. But Germany proved harder to defeat than expected and the West was forced to agree to a truce in central Europe. The US turned this truce into the Cold War and began a nuclear arms race. In addition the US also suppressed the Japanese Empire to its West in WW2 another goal that is often ignored by Europeans. Any suggestion that Peral Harbour was an accident is nonsense. US was reading Japanese Enigma by then and they knew the attack was coming.

The absurdity of the lies spread by the US over the Cold War is best revealed by this graph of nuclear weapons. Just like WMDs and Iraq the US just lied about the weapons capability of the countries it wanted to destroy and put under its dictatorship. Russia was never a nuclear threat. For the first 10 years they had just 3 nuclear weapons while the US amassed a huge arsenal. When the Russians eventually started to make weapons in self-defence it took then 30 years to catch up with the US. Only after the US had lied its way into an arms race and destabilised the whole world was Russia an actual threat. Only the US would threaten all life on earth to gain the political upper hand! Everything about the US is about lies and pure evil. Quite the opposite of the image it likes to portray.

And a mention of WW1 is needed there. Cui Bono. WW1 ended with the suppression of Ottoman Empire (a 1000 years empire that the West had been brutally attacking since the Crusades), Austro-Hungarian and German Empire (the remnants of the Roman Empire through the Holy Roman Empire).

It is all just a game of Empires! And Ukraine is just the latest round of attacks and instability by the rampant US Empire.

And so we have the absurd news that the US joins Germany in sending tanks. US joins Germany in sending battle tanks to Ukraine. One slight problem with this being that Germany was defeated by the Americans and Berlin has no freedom any more. In losing a war you lose your independence. All the talk of Nazism is nonsense as the West was fighting to destroy Germany long before any Nazis had even been born. And that makes the Holocaust and interesting thing. If War against Germany precedes Nazism by decades then Nazism was not the reason for WW2. And that means the whole smokescreen of Holocaust is also irrelevant in the reasons for war. Churchill is well known for having added documents to the British records office to justify things after the event. The whole Holocaust thing is irrelevant in understanding WW1 and WW2. And this blog has argued at length that the absence of records of the humanitarian crisis that faced Europe after the war, and the fact that over half of all Holocaust victims died after liberation from starvation they experience only in the last few months of the war points more to the war itself being the cause of death more than Nazis policy. This has nothing to do with "Holocaust Denial" which is another smokescreen. The point is that quite possibility the main reason for the huge deaths tolls in Germany after D-Day was actually the Allied invasion (as you would expect - war causes, indeed its a central strategy, to cause infrastructure collapse and starvation anyway). So we are left with aggressive expansion of the Western empire to explain the whole of WW1 and WW2.

So in fact like all the "allies" the support for the Ukraine war is not a free choice and all of Europe is being forced yet again to support the US Imperial expansion and to take on Russia.

But what is most worrying is that this obvious fact is not represented in the media. The Media tries absurdly to pretend and hide the fact that the US is the driving force behind ALL these wars in headlines like "US joins."

Now how can a "free" press tell such lies so consistently? IT IS NOT FREE. WE ARE NOT FREE.

And that is interesting. The people who think they are free are actually the ones who are not. Places like Russia decide on their own military campaigns. They do not have to obey the orders of a foreign Imperial power like Washington. Britain on the other hand is a vassal state of the US Empire. We lost WW2 and had to let the US take over and have remains an occupied country ever since with a military that is under the control of Washington. Since 1942 Britons have not been free. And our press is not free and must obey Washington press releases without question.

Its all very ironic.

But life outside the US Empire is hard. Were Britons to fight for our freedom again like we did with Brexit against Brussels dictatorship we would immediately be put under strict US sanctions and the country would quickly fall into poverty like Russia, North Korea, Iran or any other country that rejects US dictatorship. It all depends how much we value our freedom, and how easily we are bought and corrupted. You just need to see UK governments to see how completely corrupt and sold out the US they are. We live as subject of an Empire like we did under the Romans. But almost no one realises cos the press is so completely corrupted itself that we keep been told we are free even in the face of absurdity like economic collapse as we pay trillions to fill economic holes created by the US sub-prime collapse. If any other country had destroyed the UK like this it would be all over the press and we would be at war. Even COVID ultimately goes back to US research being conducted in China.

So its all lies and always has been. From WW1 looking forward and probably backwards too the country America that has been at war for its whole existence is all about violence, lies and extortion. People wonder why the dollar is the reserve currency? It was a fraud committed by the US at Bretton Woods. They simply cheated and stole the reserve currency from the rest of the world. It is important to understand what you are dealing with when discussion the US. It is all lies, all bright lights, all fast talking and all criminality.

A friend was shocked to discover that McMafia is entirely fictional. I have no doubt it was funded the CIA to spread propaganda about Russia.

With anything American you can be sure it is a lie, a dream, a fabrication, a dishonesty. No surprise it is called the American Dream. It simply isn't true! In the UK a cowboy is someone who does a bad job and takes the money anyway. This is exactly what the US always was and still is: just Cow Boys. The same people who murdered a whole race of Indians as well and enslaved millions in hard labour from which few survived even a few years. A country of pure evil. It roots are rotten, its history corrupt and it will always be evil.

Sad days for the West and for human freedom indeed. and Ukraine is just the last of a century of lies and nonsense and as usual US policy just leads to death and slavery. Poor Ukrainians. It looks like lots of them believe the hype and the lies.

US Gun Crime & Capitalism

There is so much nonsense in this world its a miracle that humans ever survive. In fact the inability of humans to make any sense is proof that the world works all by itself. Westerners say of India that what seems like chaos somehow producing a functioning country is proof of God. But we only need to observe that without humans the world somehow produced humans. So following the previous anti-recursion argument whatever produced humans must be of greater expressiveness than humans.

Just to revise that: humans cannot be explained in terms of humans. So there must be stuff out there which is not human which goes together to make humans. Not getting into the nature of emergence and sunyata but any Turing machine can be replaced by a non recursive function. You just make a set of rules so vast that it can click along a step at a time and make the correct replacement. I've not studied this its more of a hypothesis to be tested at this stage. Recursion is not needed. You can create any fractal a step at a time, indeed my first fractal tree did this in a left-turn algorithm drawing all the way down each path and just using binary for the L/R decisions. Only after that did I do it recursively with a branch function which had position and scale! You can find all the fixed points of the Mandelbrot set by traditional root methods, but admittedly the functions are built by recursive replacement, but there must be a way to directly find the equation to root for the nth degree of the Mandelbrot: Z = Z² + C without recursion. So recursion is a red herring. It can always be replaced by a canonical function. It is just appealing from a computing perspective because a small amount of code can create much more impressive results. In fact recursion is the slowest way to code it is just theoretically pretty. Never use it in time critical code! Its like modern AI, in fact the astronomical amount of data that goes into GPT etc makes the results not that impressive. They are just impressive at managing such vast amounts of data, that is the true power of neural nets. SO if we put the "magic" of recursion aside we simply have stuff coming together and humans being the result. That is the miracle and it is beyond humans how this happens. ** Okay one caveat. Systems with input coming from output do have fixed points and do evolve towards or away from those constraints (in fact experiment to find a system which ignores a fixed point: i.e. not attracted, repelled or chaotic in the region of the FP ???). So over history humans have changed the path of their own evolution, and so you can say that current humans are built upon "humans." But again this is catastrophic cos it means that whatever we are today is part attributed to what we were yesterday, and whatever we think of ourselves today depends upon yesterday. We can never escape the legacy of the Past--there being a modern tendency to think we are "improved" in some way, but actually we are more constrained.

Anyway massive digression. US Gun Crime debates are all nonsense.

Graph shows US States ordered by strictness of gun laws against murder rate. There is no correlation. That means no matter what laws you apply to gun control it does not change the murder rate. Where people are confused is that in states where guns are easier to come by murderers use guns more which makes it look like the guns lead to more murders. But they don't. Americans kill other Americans regardless the methods (well actually the whole world, they drop 46 bombs a day on foreigners).

So why the gun debate. Well its the 5th Amendment and the US obsession with liberation from the British Empire which despite happening 250 years ago they don't seem to have got over. Which is all very ironic cos they executed the biggest genocide in Human history in America and had the World's biggest slave trade so Americans are actually the people least interested in freedom. An attitude they continue with through endless wars, bombing and extortion on a global scale.

So why do Americans like killing everyone so much?

Well you can look at any number of factors but globally the thing which correlates best with murder rates is inequality.

Not on the graph but the R2 = 19% which is huge for 168 countries. Had an argument with a friend who was sceptical about the trend. If you plot just 100 random points the R2 is 0.1%. Without any advanced stats an R2 of 19% is huge. Economic things like income, GDP, growth--all the usual factors associated with welfare-- do not correlate anything like as well.

This is true for lots of things like violent crime, rape, mental illness. They all correlate with inequality best.

So why might this be?

Well this blog has speculated the answer all along. Wealth is relative.

You only know how much you have or do not have by looking at other people. 40 years ago people did not feel poor because they did not have mobile phone cos such things did not exist yet! If other people they have little then you need little. If they have a lot you feel you need a lot. This is why Frankl observed status in Auschwitz. Even in the depths of abject poverty people still had a hierarchy of fortunate and unfortunate. And this misunderstanding (typically American that more is more is why the planet is facing destruction - how serious is that America!).

So in countries like America where there is an economic "free for all"--especially given Capitalism where the wealthy can develop further income from "investing" to make them even richer, and the poor have the opposite effect of borrowing and so giving hard earned money to the already rich lenders-- in a liberal capitalist market you have increasing inequality. And in a world of inequality many people come to feel poor because they see such extreme wealth in the hands of a few rich. This injustice leads to stress, mental illness and criminality.

Now Capitalists are right in a way. In a country with equal rights where everyone has equal opportunity to work and become wealthy then this softens the blow of poverty. But it doesn't make poverty go away. The only way to make poverty go away is to have equality of wealth. When everyone has the same amount then no one feels rich and no one feels poor. This is the only solution to poverty. But in Capitalism poverty is the driving force that makes the poor work, this is why it is so productive. People who are not actually poor, never-the-less feeling poor and feeling they have to work and get more. It is a perfect treadmill. But it is an illusion. Under Capitalism the rich will only get richer through investment, not through work. So the poor are already disadvantaged. While poor are busy working, the rich investors in their companies are getting dividends and wealth simply through parking some of their money in the company. That is all they need to do to get an income! And their is no loyalty as soon as another company starts making profits they will withdraw that money and potentially crash your company through no fault of yours. The poor workers spend their lives struggling to attract the wealth of the super rich, and they pay them for this service. Its a profoundly unfair system in its very heart. And this unfairness underpins the creation of "poverty" in Capitalist economics. There is no such thing as poverty in any other system. You don't get native Indians living in poverty, or Australian aboriginals. They just take what is on offer and are thankful for it. There is no struggle, there is no unfairness or inequality beyond what Nature and God dishes out.

This is why Capitalist countries have the greatest inequality and the greatest mental health problems, murder problems, rape problems: it is because they are unfair.

Now the thing everyone wants to know is which economic systems create the greatest happiness.

Unfortunately happiness measures actually measure income. So the richer you are the higher your happiness. This means that you cannot use happiness statistics to look at whether wealth makes you happy. Which is unfortunate cos it means we cannot test at the moment whether Capitalism really makes you happy!

But if murder, rape, mental illness and crime are all made worse through Capitalism it rather suggests that happiness is also reduced by Capitalism.

And that is a rather shocking result because the US has been bombing the world and holding the world in a constant state of warfare in order to promote Capitalism. But if Capitalism actually makes you unhappy then the US has been killing millions of people around the world to spread unhappiness!

This actually seems rather obvious. You don't make people happy by killing them. Iraq, Afghanistan, Europe, Japan, Philippines, Israel are all profoundly unhappy because of US involvement. And places like Iran, North Korea, Russia are equally unhappy through endless unfounded hostility and sanctions. In everyway the US is an aggressive ignorant behemoth much like its own people, and does nothing better than kill.

That just sound ridiculous cos the movies and the media always sell US a exceptional and advanced country with only good intentions. That is except the anomalies like the vast number of bombs they drop, the high murder, suicide, rape and crime stats. In fact everything the media says about the US doesn't make sense in the data. In the data it is a failed state lagging behind the whole world in basic civilised benchmarks like literacy. You might think how a country looks after its ill might be a measure of its civilisation yet US scores bottom in healthcare outcomes in the developed world. Despite spending 2x that of any other country its health care is a total failure. The country is a disaster, and yet the media never says any of this. The only conclusion to face here is that the US has bought and control the Western media and journalists are silenced from criticising the US. That makes its atrocities even worse. The US must then be the leader in global propaganda and brainwashing! That makes everything far worse!

Anyway reliable data on happiness would be the ultimate decider in this, but unfortunately all happiness data is currently skewed towards economic performance.

What we can say for sure though is regardless where the human race has got to in the 21st Century the human race before us has prospered sufficiently well to have got us here, so we certainly can't criticise that.

===

One hot debate is whether gov should spend more money. One thing that tends to come out is no.

This is murder rate against per capital government spending. R2 only 5%. However per capital government spending is essentially GDP so this is just a graph that GDP does not really affect murder rate. Altho the trend is down so it does help. 

Fixed Points, Loops, Chaos, Woozle Searching vs Owl.

Just formally extending interest in Fixed Points to loops, and noting they have nothing to do with self-reference by themselves.

Given a function with a range that is a subset of the domain we can evaluate it recursively. A fixed point is the value with a loop of 0. That is f(a) = a. But actually it need not be achieved in one iteration. f(f(f(a))) = a: this will do for a fixed point. And the key thing is once a fixed point is found further iterations cannot change this. A loop is thus defined as one we find our way back to the start we are no longer able to leave the already traced path and are bound by our previous behaviour. To deviate would be to contradict our own definition and so the only solution must be to trace the existing path. The decision of what shall I do becomes what did I do. 

This could be called Woozle Searching. While a woozle is a kind of "weazle like" creature, in fact a far more interesting definition would be the path traced until you rejoin your steps. On a Woozle Search once you rejoining your steps you are fixed into a loop and the path is defined. The system cannot now change the path, or to put another way the "nature" or "eigen" (to use the German) is now expressed. In the Pooh books a woozle search gives different results for every run. Essentially its a random walk that follows itself once re-encountered.

The interesting thing here, and which captured my childhood imagination, was that the "thing" you were searching for turns out to be yourself. Yet, and this is of interest regarding Anatta, you had yourself at the start: you were the one doing the search so you have uncovered nothing new. Yet realising that you are searching for yourself is something new. "You" change "value" from being the one doing the search to being the one being searched. You the subject becomes you the object; you experience a change in grammatical tense. This is brilliantly exploited in film "Angel Heart" where the detective pursuing a murderer finds out it is himself. Finding yourself changing tense and meaning is quite an interesting thing if you have a fixed "atta" concept of yourself.

This "woozle" following what turns out to be "your" footprints leads to the idea that recursive functions are a kind of self-reference where the function responds to "itself."

But actually this is WRONG. Owl is needed to see the Woozle Path! A Woozle Search is only expressive enough to trace a path. You need Owl at the centre to apply a meta function that gives the self-reference! In the case of Woozles: to point out that the footprints are your own.

This means actually that Fixed Points are not expressiveness enough to code self-reference. This is actually obvious. A Fixed Point is just a value of the domain which is not changed by the function. It is interesting in that recursion also makes no difference. The presence of Fixed Points proves only one thing that the range of a function must intersect the domain it says nothing about "self" reference. You need a Godel mapping of functions into the domain for that to happen. It happens at a whole different "meta", isomorphic level.

So these kinds of fractal patterns with space being contorted around fixed points, do not have anything to do with "self" reference. Yes they include loops of recursive functions, and once a value executes a "Woozle Path" through the function it cannot escape to infinity and is bound into the set, but the Mandelbrot set does not itself know anything about this. It is just billions of Poohs and Piglets searching for Woozles.

An Owl on the other hand can look at all these paths being traced and see the spirals and "Applemen."

This was noted before in the Blog but being reversioned here. A fixed Point does not "know" it is a fixed point. A Woozle Path likewise. They needs an Owl to become fixed points or Woozle Paths.

This is another version of SRH, indeed the original 1996 insight.

Now if we were to encode Owl into a system we have something interesting.

But we can also note the recent Normative observation. An Owl cannot be subject to an Owl themselves. For a Woozle Path to exist requires an Owl sitting in the tree to see it. But an Owl does not need another Owl to see it!

We enter Plato's Third Man Fallacy here. If Owl needs another Owl in order to function then there is no such thing as an Owl.

Owl(x) must be sufficient to do what Owl does to x.

If Owl(x) is of the form 

value Owl(x) {

    ...

    Owl(x)

    ...

}

Then we are saying that Owl(x) is not sufficient to perform the operation of Owl. In which case applying more Owl(x) to the process cannot help!

This links with the previous post and the idea of "expressiveness." If Owl does not already have the power to do what Owl does then adding more owl cannot help.

Its an devastating interpretation of recursion. The presence of recursion actually reduces the power of the function. It is saying that the function does not have the power by itself.

Yet Recursion is appealing here. Applying a function recursively can provide hugely broader expressiveness: 

Thing to note here is that--like with all fractals--the application of simple function recursively to a simple seed creates an infinitely complex form which is really just copies of the same seed on infinite levels. Its been noted that Nature uses this a lot as DNA is a limited store of information and so recursion is almost always used by nature to expand it "expressiveness."

You might say Ah ha we have an Owl being defined in terms of lots of little Owls.

But no. The seed is given. The result is just the result of transforming infinite copies of this. There is nothing "new" here. So its not "full recursion." A trivial example is this recursion for the factorial:

Factorial (n) {

    if (n == 0)

        return 1;

    else

        return n * Factorial(n-1)

}

The point is that there is a clause which stops the recursion and returns an absolute non-recursive "seed" in this case the value 1.

So for n=4 we have doing replacement:

Factorial (4) = 4 * Factorial(3) = 4 * 3 * Factorial(2) = 4 * 3 * 2 * Factorial(1) = 4*3*2*1*Factorial(0) 4*3*2*1*1 = 24.

The last term is an absolute expression with no recursion and an absolute result.

Now this is a tricky thing because it suggest that all things are based upon an absolute "seed." And this is true, sort of.

Within a domain this is true. This Factorial is only defined over the domain of Positive Integers. But if we were to apply it to -1 then we get an unexpected result:

 Factorial (-1) = -1 * Factorial(-2) = -1 * -2 * Factorial(-3) = -1 * -2 * -3 * Factorial(-4) ...

As can be seen this never delivers a result and the recursion continues forever. This function never Halts! And if we inspect the partial results it looks like it approaches positive or negative infinity, a very unsatisfactory result indeed!

By different methods the Gamma function can be found which gives results for the Real Domain (and Complex Domain) as well.

So this Factorial function above only works for a specific domain. When we say Absolute we also need to define the Domain. In this sense it is not "Absolute" it is relative to the Domain.

I used to say "All things are Relative" and the Platonic criticism of this is to make the point above that "relativity" demands recursion.

Likewise we were arguing that Owl cannot be relative. If Owl depends upon Owl then Owl has no power. A recursion that is without limit has no power.

But if we do define a limit to a recursion then we also limit that recursion to the domain of the limit.

The Ultimate Domain to which all other Domains belong cannot be arrived at through recursion, because it cannot be the "seed" of a recursion, and a recursion which never returns a seed is infinite and does not Halt.

So "All things are Relative" is true in that a Domain is needed. Nothing exists for definite outside a given Domain, which is the set from which the "seed" is taken.

Owl cannot be saved by recursion. If Owl is insuffient then no compounding Owl can help.

This puts a limit on "emergence" too. Buddha says in Diamond Sutra that since everything is made of components that are not itself then everything is an illusion. This actually says that Owl is made from components that are not Owl. And if Owl is one of the components then nothing emerges from the other components. If you put a cake into the ingredients list then you can just bin all the other ingredients and keep the cake.. obviously.

SRH is saying that Owl cannot be made from components that include Owl.

Or we can say that were a function that defined Owl contained Owl we can say that the rest of the function serves no purpose.

If a function contains itself it must be the case that the rest of the function serves no purpose and is extraneous.

This is all very obvious.

One small thing missed. A Fixed Point is a value that maps to itself from domain to range. Now if the functions are countable and the domain is ordered and countable then functions map to the domain. (Time run out) but I believe there is no connection between the fixed point of this function and self-reference. That ends the blogs interest in fixed points.

===

Wanted to add the odd feature of recursion that it tends to lead to fixed points. For Cos(x) = x it very rapidly homes in on x = 0.739085133 which is the fixed point. It is a "locally stable" fixed point as values around it reduce to it under recursion.

This is the general feature of many recursions and self-reference that it seems to limit a function and force it towards some constraint.

Even a function like x = x^2 which diverges is forced towards a limit of a kind in this case infinity.

Some limits are loops or cycles like most of the values in the Mandelbrot set, and by forming loops the actual number of unique solutions must be considerably limited like in the 100 Prisoners puzzle. I wonder if that is an exponential level of restriction to shift cardinality from Reals to Countably infinite? Pure random speculations.

And then some "loops" are chaotic and while not going to infinity or zero also never cross their own path. This seems impossible but these functions are not continuous and move in steps so can jump around in Real space and never run out of new places to fall.  

Which looks like this:

The fixed point is around 1.16573 but starting at 0.6 the Woozle Search never intersects itself and never loops. For reasons I don't understand yet the region around this fixed point diverges... something to do with its differential absolutely no doubt.

Starting at 1.16573 with a precision of 5 dps the result is still not stable. This fixed point is not stable at all and regions around it diverge into Woozle Searches:

Which can be used to make a fun never repeating chaotic orbit in any dimensions e.g. 2D with a0 = 0.6, b0 = 0.7

So in this instance recursion is creating apparently infinite complexity, and appears to increase the expression of the system. I know this has had quite an allure with infinite complexity apparently being reducible to just a few parameters like in this example. And many like Stephen Wolfram believe that the complexity of Nature likely being recursive can be reduced to much simpler chaotic parameters. Never-the-less at root there must still be absolute forms which cannot be reduced further. So the question remaining here is what is the difference between  the outcome of a recursion and the absolute form upon which the recursion operates. In other words is the fractal owl created from repeated operations on a seed Owl actually any different?

But just flagging this way in which "energy" of a system seems to be usually limited by recursion, and analogously self-reference.

This idea of an "energy" of a system that grows weaker around stable attractors, but fuelled in systems with unstable attractors that are never able to stabilise. And then the 3rd type of those that explode to infinity. In chaotic systems these fixed points are even called "Strange Attractors" even suggesting a kind of force or attraction/repulsion within the system.

Equally there is a kind of analogous "force" in logical systems that sets statements like "I am false" into instability. There is no fixed point here, no solution that remains untouched by the statement for it to be stable. This is true of all statements that negate themselves in some way. Particularly problematic with "∀" statements that include a Not as there is no way to "escape" the statement if the statement falls into its own scope.

Anyway rambling now. Point made.

===

Tho I should be careful:

general self-referential lemma,^[6] which says that for any formula F in a theory T satisfying certain conditions, there exists a formula ψ such that ψ ↔ F(°#(ψ)) is provable in T [ref]

That is the existence of fixed-points IS the existence of self-reference. And yet what the above is interested in is that such expressions only exist because the system is not operating on the "self." Self-Referential statements are actually those statements which are independent of the system.

Perhaps that is interesting. "Self" even in humans is ironically our way out of the system. We think of self as being separate and cut off from the world. It appears to be independent of the world. It is unaffected by the world. In deep meditation states the self reveals itself without reference to the phenomena of the world. It is like a "fixed point" that is not operated on by the world. But we don't normally realise that this "self" is the same for all people, it is the true nature of reality, the "value" unaffected by the system that is the world.

So its not "self-reference" in that the system cannot express itself. Rather it can only fail to operate on certain elements of its domain - the fixed points - which also make the "selves."

This needs formalisation, just brainstorming.

Nietzsche slave conscious and Romance

So Capitalism lead to the worldly sphere controlling capital, and the domestic and family sphere becoming marginalised.

With women assigned to the marginalised family sphere, women became marginalised and their whole existence limited to the property of their fathers or their husbands.

As a result women were forced to justify the family sphere and their relationships with father and husband.

It is no surprise that in Capitalist countries women created the Romantic novel and the exaltation of Romance to a level where it really could fill a whole life and be justification in itself for life.

This is identical to Nietzsche's account for how Jewish slaves came to justify the restraint and poverty of slavery, turning it from limited life to a reason for existence itself.

Now in the case of "poverty" this does not follow empirically because in India austerity was from time immemorial a way to wrestle ourselves free from desires and seek a higher level of freedom, something even Princes like Siddhartha followed turning their back on worldly wealth and satisfaction. But there is no such joy for Romance which seems to genuinely have arisen from Capitalist slavery.

One must note the importance of Romance in India. I do not speak Hindi but understand the romantic language available exceeds that of English in which Romance novels were first written. And Arabic is well known as a Romantic language also. But both these cultures of North India and Arabia are deeply Capitalist if not before then certainly after the Mogul Empire. So one can hypothesise more generally that cultures where ownership of the world falls into private hands (Capitalism) and which assign women to the domestic sphere (which is a natural assignment given that women make milk and are needed to feed babies, and also carry the child during gestation, and I believe are inclined to a stronger bond to babies following the hormones released during gestation and childbirth -- obviously not always); those cultures, are also more likely to develop a Romantic culture to justify the bondage of women.

This has obvious been through many reflections and ironies. The traditional Pre-Roman culture of the Western Celts placed equal power between men and women hence the famed disaster when Romans encountered Boudicca. She could not understand the lack of respect they paid her, and they could not understand the power she assumed. So as Roman's did they raped her daughters and flogger her naked in public. Nice people those "civilised" Romans... yeah "what did the Roman's do for us?" other than slavery, genocide and imposing unequal social relations that gave rise to the Right-Wing and destroyed Britain for 2000 years. So when the Troubadours of Mediaeval France elevated the position of women in what became Chivalry this ancient sense of sexual equality was rebranded within Capitalism and ironically men subordinated themselves to idealised women. But its all just reflections of Capitalism placing unequal power into the hands of worldly and domestic sphere. Quite how any children were born without mental illness after the destruction of the domestic sphere by Capitalism is a mystery... or perhaps this is the whole psychosis that Capitalism and ownership created? It is no surprise that at the height of Empire the Victorians returned to chivalry and idealised women.

Worth noting that prior to the Ironage Celts it was actually Women that held the power. Fertility and the Earth were the main thing observed in the world. The ability of plants, land and women to produce new offspring was the most important power of the world... then and now. While Capitalism has rather obscured this as the layer of business and industry has obscured the true working of the world, even a quick look outside to see the Sun light reminds us that the true source of the world lies in Nature. Capitalism is just a thin layer that mankind has laid over the top. Vaccines was a funny version of this. All vaccines do is give the natural immune system a heads up on a pathogen so that it is better prepared when it meets it. Mankind adds almost nothing, the power all exists in the natural immune system we are born with and which women nurture in the womb. And to add to this SARS2 naturally evolved into Omicron and a less lethal version anyway. Mankind had almost nothing to do with all of this, part from arguably creating SARS2 in a laboratory in the first place. So the world has changed very little since the days when female fertility was considered the core force of the universe. Yet there was no Romance here. Romance remains a modern creation that comes as a reaction to domestic slavery brought about by the decline of the domestic through ownership and Capitalism.

100 Prisoners problem, Hash, SRH

https://en.wikipedia.org/wiki/100_prisoners_problem

So the best known strategy is to start with your number, and then go to the number in the box. This will always lead into a loop because eventually you will open a box with your number and that will send you back to the start.

So this strategy in this context will always end up with self reference. And self -reference means a loop.

So that is isomorphic with halting problem (for a finite program to never stop it must end up executing the same commands again and again), the liar paradox where the state keeps alternating forever, and all paradoxes because they end up applying to themselves recursively.

Now is the case of this puzzle the loops have a very interesting property. 30% of loops are less than 51 steps in length.

Now SRH is normally noted as limiting the power of systems where we are looking for the greatest expressive power. But in this case Self-Reference limits the system in a favourable way (for the prisoners) by a huge amount improving their changes of escape from 1/10^30 to 1/3. This is a demonstration of the extraordinary power of Self-Reference to constrain systems.

I guess the challenge now is to find a way in Self-Reference works to increase the expression of a system. Or prove that were it do so would end up in contradiction.

===

Crudely/Informally suppose a system S were able to determine expressive power with a function E(x). That means something like the size of the domain. Godel kind of says this when he says his theorems are true for any system sufficiently expressive to "allow" for self reference, that is the domain includes itself (maybe not directly but via isomorphism and mapping of one domain to another - so for example any ordered countable domain becomes a domain for anything that operates on Natural Numbers).

So E belongs to S. E(S) must be greater or equal to E(E). That is whatever expressive power E gives itself cannot be less than the whole system for which E belongs. S must be able to express E for example. Scrap this.

Take two systems S0 and S1 where S1 can express itself and S0 cannot then E(S0) < E(S1). SRH actually says that self-reference leads to reduced expressivity. That seems to be absurd. Surely being able to reference oneself is greater expressivity. But you don't have Godel limitations without self-reference. So very crudely are we saying that including self-reference is 1 step forward and 2 steps back?

Firstly you need a mega system U which is capable of ex[pressing S0 and S1 so you can have a function E that can apply to them both. The very existence of E(S0) and E(S1) statements implies a mega system U that can express both S0, S1 and E. So really we are just talking about subsets of U. S0 is a subset that excludes self-reference and S1 enough to reference itself.

So E(U) > E(S1) > E(S0) is the common sense. and SRH says that E(U) > E(S0) > E(S1) because self-reference actually acts to limit the system.

Now it might seems that U can be S1. You take any self-referential system as S1 and take a subset that excludes self-reference as S0. But SRH says that E(S1) < E(S0) so if SRH is true then S1 is not sufficient to express an E which can determine the expressive power of itself and a subset.

Does this make any sense at all????

S1 is sufficient to reference itself so why can't it determine its own expressive power? SRH would say it can't!

Is there a contradiction in determining your own expressive power? This is going very Godel and provability. Can't you create a "I am false" type statement which says it can't express itself. Tarski also that True/False cannot be expressed within a system without contradiction. Once you give a self-referential system the ability to determine expressability then you open up the possibility of it saying legitimate things that are impossible.

A subset of E would be L(x).. and been here before. L(x) looks at statement x and determines whether it can refer to itself. L(L) is a tautology then as to give any result is to apply self-reference as so much be true.

... run out of time ...