Hitler against Godel's Theorem

[John Clark]

Hitler against Godel's Theorem

John K Clark   See what's on my new list at  Extropolis

[Lawrence Crowell]

Der Untergang used again in a parody. 

Godel's theorems are our friend. It is even a friend in physics. With physics I think it is a "sieve" that conforms physical principle to have horizon conditions, whether uncertainty principles or event horizons in GR, that conform physical reality to fit within the Church-Turing thesis.

LC

[John Clark]

On Tue, Jun 1, 2021 at 8:38 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Godel's theorems are our friend. It is even a friend in physics. With physics I think it is a "sieve" that conforms physical principle to have horizon conditions, whether uncertainty principles or event horizons in GR, that conform physical reality to fit within the Church-Turing thesis.

Some claim Godel proved that the human mind is more than just a Turing Machine, but I disagree. Godel found a way to use numbers to write a sentence that talks about itself, it says "I am not provable in this formal system", and the operations of a particular Turing Machine are analogous to a formal system; however a human being can look at that sentence and see that it is true even though the machine itself could never produce it, therefore the human mind can do something the Turing machine can't. However, what Godel proved is that an operating system powerful enough to perform arithmetic THAT IS CONSISTENT cannot be complete, and he says no operating system can prove its own consistency. But when human beings are not doing formal logic exercises but just living everyday lives their operating system is most certainly not consistent, they can have two logically contradictory opinions at the same time, a brief glance at politics shows it is very common. And humans can be absolutely positively 100% certain about something, (that is to say they have proven it to their own satisfaction), and still be dead wrong. Godel's biography illustrates this point, he refused to eat and died of starvation because he was absolutely positively 100% certain that his food was being poisoned.

So we are inconsistent Turing machines.  And even today we could easily make a machine that could answer any question, provided you don't mind if it sometimes gave an answer that was wrong or even idiotic.

John K Clark

 

[Lawrence Crowell]

It is Penrose's thesis that consciousness is a sort of Godel trick. Back in the 1980s as an undergraduate I would have agreed with this, when I started reading about this. I read Hofstadter's book "Godel, Escher, Bach" and began pondering these things. I have however come to think there were problems with this. It is clear humans are not consistent Turing machines or computers. Computers are infernally consistent, and can compute numerical sequences, but they do not make an inductive leap in saying the set of natural numbers has infinite cardinality. Humans can rather easily see the set is infinite and however make mistakes. 

LC

[spudb...@aol.com]

I loved Kurt Godel work because he went deep in the weeds for answers, existential answers, (the universe rotates) and he was neurotic as me, but a 1000 levels of magnitude smarter. Excellent! Don't see much hope for confirmation of s spinning universe, but this may have to wait for some other age to uncover? He was a great guy.

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[Bruno Marchal]

On 3 Jun 2021, at 13:28, Lawrence Crowell <goldenfield...@gmail.com> wrote:

It is Penrose's thesis that consciousness is a sort of Godel trick.

?

Penrose on the contrary use Gödel’s theorem, like Lucas, erroneously, to claim that we are not machine.

Basically he says that the correct machine cannot see []p -> p, but that we can see it, even for us.

But he just confused G and G*. In other place they confuse G and S4Grz. 

Back in the 1980s as an undergraduate I would have agreed with this, when I started reading about this. I read Hofstadter's book "Godel, Escher, Bach" and began pondering these things. I have however come to think there were problems with this. It is clear humans are not consistent Turing machines or computers.

That is a consequence of mechanism. To be consistent at some level, the “variable” machine have to develop a non monotonically layer, and yes, you are taking risk when saying “yes” to quick to the charlatan-doctor...

Computers are infernally consistent,

Before you install windows, I guess :)

A computer is just a relative universal number, it can imitate (and sometimes even become) all other digital machines, both the consistent and the inconsistent one.

To be precise: consistency apply to theories, that is set of beliefs, or assertable or provable propositions. 

Computability is an absolute notion. Provability is a relative notions. 

Computation, translate into provability, is sigma_1 provability, already entirely obtained by the jewel Q:

Classical First Order Logic + Equality, +:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

Which, BTW, is among my favorite theory of everything (ontology).

I insist that theology, and thus physics, does not depend on the choice on the ontology, as long as we avoid induction axioms, and the axiom of infinity (in that sense, Mechanism is quite atheistic no creator, no creation, just the dream of number entailed by the Turing universal/complete theory Q.

My second favourite theory of everything is the theory of combinator CL (I explained it up to its Turing universality some years ago):

Axioms:
KAB = A
SABC = AC(BC)

Inference rules:
If A = B and A = C, then B = C
If A = B then AC = BC
If A = B then CA = CB

The laws of physics can be said to emerge, in an Emmy-Notherian generalised way, from the invariance of the observable for all universal numbers.

and can compute numerical sequences, but they do not make an inductive leap in saying the set of natural numbers has infinite cardinality.

The Löbian universal machine known as ZF does that all the time.

You might mean that she does not learn to do that? Wait for alpha-go learning a bit of set theory. They might make an inductive leap that the humans will take some times to understand, at some point. And only God will know if such machines are consistent or not.

Are you telling me that you would always say “no” to the doctor (for the artificial brain?).

I don’t know the truth, but when you listen to the machines, through Gödel, Löb … Solovay, you understand that the universal machine are born in arithmetic, are right at the start confronted to an hesitation between Security (totality, control) and Insecurity, like searching for some numbers which might, or notion exists, going from surprise to surprise… They are never completely satisfy and want always more, until they wake up, to fall asleep again...

Humans can rather easily see the set is infinite and however make mistakes. 

When machine do inductive inference, or pattern recognition, or play chess, or whatever, they do mistakes.

They don’t do mistake at the level of their implementation, but you don’t do that either; you just don’t mess with the physical laws, nor machine mess with the arithmetical laws which implements them. Hofstadter (the only physicist who get Gödel’s right) got this right, and sum it well up with the image of a lot if 1+1=2 building a picture I-of 1+1=3.

You can put Gödel’s theorem in this form: (note that <>t is the same as ~[]f, consistency)

<>t -> ~[]<>t

That is; a consistent machine/entity cannot prove its consistency.

But that is equivalent to

<>t -> <>[]f

For a consistent machine, it is consistent to be(come) inconsistent.

And indeed, PA + ~con(PA) is consistent, and that is already a sort of axiom of infinity making that unsound, but still consistent, machine, far more powerful than PA.

Arithmetic is full of life, but you get  the many liars as an uncomfortable but unavoidable gifts…

Bruno

LC

On Wednesday, June 2, 2021 at 11:47:26 AM UTC-5 johnk...@gmail.com wrote:

On Tue, Jun 1, 2021 at 8:38 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Godel's theorems are our friend. It is even a friend in physics. With physics I think it is a "sieve" that conforms physical principle to have horizon conditions, whether uncertainty principles or event horizons in GR, that conform physical reality to fit within the Church-Turing thesis.

Some claim Godel proved that the human mind is more than just a Turing Machine, but I disagree. Godel found a way to use numbers to write a sentence that talks about itself, it says "I am not provable in this formal system", and the operations of a particular Turing Machine are analogous to a formal system; however a human being can look at that sentence and see that it is true even though the machine itself could never produce it, therefore the human mind can do something the Turing machine can't. However, what Godel proved is that an operating system powerful enough to perform arithmetic THAT IS CONSISTENT cannot be complete, and he says no operating system can prove its own consistency. But when human beings are not doing formal logic exercises but just living everyday lives their operating system is most certainly not consistent, they can have two logically contradictory opinions at the same time, a brief glance at politics shows it is very common. And humans can be absolutely positively 100% certain about something, (that is to say they have proven it to their own satisfaction), and still be dead wrong. Godel's biography illustrates this point, he refused to eat and died of starvation because he was absolutely positively 100% certain that his food was being poisoned.

So we are inconsistent Turing machines.  And even today we could easily make a machine that could answer any question, provided you don't mind if it sometimes gave an answer that was wrong or even idiotic.

John K Clark

 

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[Bruno Marchal]

I let you know that I have some mail account problem, as my university is making change. I send this from the net directly. That problem might perdure up to September. The Covid does not help... Apology for inconvenience. You might contact me on FACEBOOK if something is urgent https://www.facebook.com/Bruno.Marchal24

I would not say that we are inconsistent machine. We are more like consistent (even arithmetically sound) machine, with some layer of non-monotonic logic to handle local belief revision.

[Bruno Marchal]

I have answered this, but I don't find my answer. Penrose use Gödel's theorem to argue that we are not machine, by a reasoning similar to one already found, and refuted, by Emil Post, and later developed (wrongly) by Lucas and Penrose. Eventually Penrose got it right, and that kind of argument does not show that Gödel's incompleteness is a problem for Mechanism, but it does show that a machine cannot know which machine she is, nor which computations support it in arithmetic, which is indeed a step in the reduction of the laws of physics to the statistics on all relative computations in arithmetic. That explains why, after deriving the phenomenology of the wave collapse from the Schroedinger equation, like Everett did, it is still necessary to derive the wave equation from the statistics on all computations (as seen from inside, which is the hard part to define, except that it becomes easy once we get the theology of the machine.

The propositional machine theology G1* has been given here. It is the modal logic with all theorem of G as axioms, + []A ->A, + p -> []p (for p propositional letter), and importantly without the Necessitation rule. And G is the (normal modal logic) with axiom []([]A -> A) -> []A (the Löb formula). A normal modal theory has [](A->B) -> ([]A -> []B) as axioms, and is closed for the Modus ponens and the necessitation rule.

Then the logic of the observable is given by the modal logic of the intensional variant, defined in G1(*) by the logic of []A & <>t & A, and some related.

That gives a quantum logic for the observable by universal numbers in arithmetic, naturally related to the many computations structure implied by elementary arithmetic or Turing equivalent.

More on this later. I am also testing the mail system, and if the google-group still recognise my old adresses. 

Bruno

[spudb...@aol.com]

Just for confirmation, Bruno, you message has been received if not completely comprehended by myself, but just as a saying "received" by your email provider. My only thought might be is "Do we have a choice in what we are observing?" Moreover, "if we somehow do, can we make better by observing." Many would say this is quantum woo, and that is fine by me. The follow up would be, mayhaps if we form a 'better node' say, of millions of observer's we could fix things better? As in Quantum Woo style-all focus upon the same thing? 

Probably not, so it's back to work for scientists and engineers....

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From: Bruno Marchal <mar...@ulb.ac.be>
To: Everything List <everyth...@googlegroups.com>

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[Bruno Marchal]

Hmm... I just reply from the new mail address, but of course, I don't have (yet) the permission. Some difficulties to change the setting. I copy my answer directly on the webpage of this list.

Hi spudboy100,

Thanks! 

Do we have the choice in what we are observing? 

Yes and No. To take the paradigmatic exemple, imagine that you are in Helsinki, and you will be scanned, copy, destroyed, and reconstitute in Washington and Moscow. For a third person observer looking at this, you are in W and in M. From your (multiple) first person view, you feel that a choice or a selection has been made, but that cannot possibly be "your choice". Indeed in Helsinki you might desire to become the one in Moscow, but the guy in Washington will illustrate that indeed it was not a question of choice, unless he suicides himself immediately somehow. You could, when still in Helsinki, write a letter, or a mail, to the people in Washington, asking them to NOT make the reconstitution, making Moscow into a "probability 1 by default", though, and this illustrates that making a choice is a form of suicide. If you are in love with Alice and Eve, and decide to marry Eve, it is somehow equivalent with killing the "you" who would have lived with Alice.

In that sense, I answer "yes". We do have partial choice in observing or moving in our life, and it is a sort of preselection among our (infinitely many) futures.

Can we make better? I guess so. At least relatively to what you might consider as better, for example by selection the option which maximize this or that things that you might prefer, for you or for other you care about.

With the "many-worlds", or "many-histories" or the non quantum (a priori) "many-computations" in arithmetic, the quantum woo is minimized, in fact the whole quantum is explained through the common "amoeba" first person indeterminacy in arithmetic

 You can see (Indexical, Digital) Mechanism as the hypothesis using the less magic, in fact only the magic of mathematical logic or computer science. No need of a magical personal-god, or impersonal-god, just elementary arithmetic which execute all computations in the bloc-universe, or better bloc-mindscape manner. Something we know, or should know, since the 1930s.

Bruno

[spudb...@aol.com]

Your theory strikes me of a related theory by Canadian philosopher, John Leslie (Emeritus, Guelph University) who did the logic  of "ethical requiredness," for the universe, Plus he employs some of your Neo-Platonism.* He also has employed the Bloc Universe in his writings, using sort of Einstein's letter to the family of Michel Besso as a condolence. Frame reference and all that.  Leslie has termed himself an atheist in the sense of no personal deity as you have stated below. 

https://www.researchgate.net/publication/337952476_Infinite_Minds_A_Philosophical_Cosmology

*For that matter so does Swiss digital philosopher, Juergen Schmidhuber.

https://people.idsia.ch/~juergen/

Hope everyone whose system can take (I'd avoid the very young) gets vaxed? Good luck. 

https://groups.google.com/d/msgid/everything-list/743e16ec-9358-4aa2-8461-eb048e3f24dfn%40googlegroups.com

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[Bruno Marchal]

There are some relations. Note that "my theory" is just Descartes theory, and it can be found in old Indian text too, or Chinese text. It probably exists since an ape use a piece of wood to extend its arm, and it is the "simplest" theory of mind and matter since long. now, its digital version comes from the discovery of the universal machine in arithmetic (Turing, Kleene, Post, ...) and it entails the reversal physics/theology, or physics/theology (using the original sense of the greek). So, I don't want this to look as if I was bragging, but the key is that I have no theory, just a theorem, with a constructive proof making Digital and Indexical Mechanism testable (Digital means we use the Church-Thesis, and Indexical means that the assumption is personal "*I* say "yes" for the digital body/brain transplant). Schmidhuber has participated to this list, and the problem for him was that all finite sequence is predictable leading to some doubt on the first person indeterminacy, a bit like Clark and Bruce Kellet today). That problem is not serious, as the point is that in Helsinki (if you remember) you cannot write in the prediction diary, neither W, nor M, but only (W v M) if you want the prediction validated by the two reconstituted person. Than that first person indeterminacy extends to the infinitely many computations in arithmetic, leading to a many-histories interpretation (Brough by all universal numbers) of arithmetic.

This result is shocking for the dogmatic believer in Aristotle theology, with a materialist ontological commitment.  There are many, as we are lied on this since 1492 years, and when you see that cannabis is still schedule one, despite the lies are recent and easily debunked, you can imagine that materialism will remain with thus for sometime, but it will be abandoned by lack of evidences, like vitalism has been abandoned in biology.

When you understand that all computations are run in arithmetic, you understand that the burden of proof is in the hand of those who claim to have evidences for their material ontological commitment. Nevertheless, Mechanism makes the dream argument rigorous, and eventually, Materialism is shown to require some magic to make some computations more "real" than others. The careful observations of Nature confirms mechanism, up to now. My work shows how to test this, and why quantum physics confirmed the most striking feature of digital mechanism. I dont know the truth, and my meta-goal is to show that we can do theology with the scientific attitude, including physical experimentation. This helps also to distinguish clearly physics (the science of the observable and prediction) and theology/metaphysics: the science questioning the nature of the fundamental reality.

Bruno

[spudb...@aol.com]

My only concern about cannabis is the study that it did impair mathematical abilities. That is about it for me. In a few areas of the US, legal cannabis has been permitted. Which doesn't stop the thugsters from selling it illegally, under price. That is a social issue and not a medical one. On whether consciousness requires a material substrate, I have no preference, because honestly it is not up to me. It's the universe, I just work here.  On the other hand I do hold with the idea of taking whatever advantage, even neuro-chemical, of the knowledge of anything the facts provides? The Beyond 1492 project likely needs funding, and I suspect that computer science, eventually, will provide for such a adaptation. My feeling is we don't need more religions to benefit us, but instead mental apps based on whatever facts we can uncover, be it flesh or spirit? 

https://groups.google.com/d/msgid/everything-list/084b375d-c5bb-4cbc-8540-4c37e32e122bn%40googlegroups.com

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[Bruno Marchal]

It is the first time I hear that cannabis impairs the mathematical abilities. You might give reference, and I hope it contains a comparison with chocolate, alcohol, etc. Without such comparison, anyone can find that anything impair mathematical (or whatever) studies, but usually such studies are not quite serious, or just pretext to not study. If you like mathematics, there is some chance that cannabis will help, and if you don't like mathematics, there is a lot of chance cannabis will *not* help.

The question if consciousness requires material substrate is not a question of liking this or not. If Indexical Digital Mechanism is assumed, there is simply no choice: the material appearances must be explained without invoking any ontological commitment. 

We need to separate truth from what we want. It usually does not match easily. It is the separation of theology from science which makes people believe that the religious truth is a matter of choice. This is eventually used by people who want to freeze the field for their special interest. The god/non-god debate is a trick by materialist (believer in some fundamental substance) to make us forget that the original questions in theology was about the existence of a primary physical universe. To simplify, the question was should we invest in mathematics or in physics when we search the simplest ontology capable of explains all facts, or as much as possible facts?

Bruno

[Henrik Ohrstrom]

Cannabis impares all cognitive functions. (And have a painkiller effect comparable to paracetamol. )

https://www.newser.com/story/205310/studying-math-dont-smoke-marijuana.html

You can download the article as pdf from the newser article.

There is no problems finding more examples. Interestingly, or maybe not, experienced users are less affected from an acute dose (spliff) than untrained users.

So if you are using, you don't get stupider than you are already.

https://www.nature.com/articles/1395716

Appart from getting rather slow you also have a serious chance of triggering a psychosis, especially if you get the good strong stuff.

https://www.thelancet.com/journals/lanpsy/article/PIIS2215-0366(19)30048-3/fulltext

If you doubt academic evidence, try writing an exam after a spliff and see for your self. Don't do it for any important exam though. A demanding cognitive computer game can serve the same function.

Alcohol impares cognitive functions.

Methylxantines, theobromine (chocolate) teofylline (tea) coffeine (coffee) all improve cognitive functions. 
Adrenaline improve, sugar improve.

Low dose amfetamines are probably good but high dose not so much and low to high is razorthin when you need math. If you only have to run around with a machine gun, you have a much better dose interval. So amfetamines are popular in the army, not so much in the university world. Can have a place if you have ADHD tendency.

/Henrik

[Bruno Marchal]

Nobody says that cannabis is not harmful, but it remains far less harmful than alcohol, especially during a pandemic. And cannabis is a *very* efficacious medication for a large spectrum if disease, which does not mean that it has not some secondary indesirable effects. 

Then the worst is prohibition, as it multiply a lot the danger of any medication having a potential danger. 

I am not convinced by the Lancet papers, as it contradicts all the examples I have seen as a teacher of mathematics, where I have thought myself that student smoking cannabis get bad results in mathematics until I change my own attitude toward them. The problem is that cannabis is used by some as a way to explain away their difficulties at school, but when we stop playing that game with them, I arrive at the opposite conclusion: it helps the student. I wrote a paper on this for a newspaper, a long time ago (1980s) which, of course, refuses to publish it as it could be seen as apology for drugs, which is illegal in my country. The very illegality of a substance damages all the information we can have on that substance.

[spudb...@aol.com]

Hey, if cannabis helped me in understanding and remembering mathematical patterns and operators, I would have rocked the ganj, years ago. Your observation is that ganja doesn't impair mathematical capabilities. I wonder if one is a mathematical talent such as yourself, are instead impervious to THC's effects? On the other hand, if ganja was efficacious in promoting math skills should not have Bob Marley excelled at math references in his music?

"Markov Chains,

We Gonna Be all right!

Triple Integrals,

We be Jamm'in in the name of Plato!

Irae Mon!

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From: Bruno Marchal <mar...@ulb.ac.be>
To: Everything List <everyth...@googlegroups.com>
Sent: Thu, Aug 12, 2021 7:47 am
Subject: Re: Hitler against Godel's Theorem

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[Bruno Marchal]

One case is not a statistics. Many studies have been done. During the high (which last about 4h) the impairment is obvious, and people are much slow, although some show more patience for some task. That is my experience too, I have never succeed to program in machine-language without cannabis. Actually, I needed a long treatment to come back to mathematics after some events which disputed me from the whole subject. This means also that the role of cannabis is very dependent of the mindset of the consumer. I have needed it also to pay my taxes (you needed a lot of patience to accomplish that task some years ago, but it is coller now). You can find some video where scientists confess to have made their discovery "under influence" (mostly cannabis, but also LSD, mushrooms, etc.). 

The studies are less clear for the car driving. I have seen two studies which shows that the use of cannabis diminishes the number of accidents. the explanation was that young driver-smoker did not even dare to drive their car, when they succeed opening the door, and that is the quite opposite phenomenon than with alcohol, which gives a wrong feeling of self-assurance where cannabis rather induce some paranoïa, and old smoker-driver seems to succeed much better complex car and truck testing, but I found some studies which do not corroborate this, so more studies are needed. Here the main problem is that the "schedule 1" classification does not even allow the research unless it can be use to add to the demonisation.  It is a scandal that the discovery that cannabis shrink mice brain tumour has been hide from 1974, until a team in Spain rediscovered it, and show it works in vitro for human cells too. Since then there are thousand of papers, but the schedule one makes still hard to publish the paper. We know also that some drug, like heroin, becomes the best medication to quit them, once they are legal and medically prescribed with low price.

Anyway, prohibition is nonsensical, except for stealing money (and health in passing). my position on this is well sum up by ... the founders of USA:

"Prohibition... goes beyond the bound of reason in that it attempts to control a man's appetite by legislation and makes a crime out of things that are not crimes. A prohibition law strikes a blow at the very principles upon which our government was founded" -Abraham Lincoln.

"If the people let government decide what foods they eat and what medicines they take, their bodies will soon be in as sorry a state as are the souls of those who lives under Tyranny." -- Thomas Jefferson

The deeper problem is our tolerance of BS in the whole "human domain", which comes from the separation of theology from science, allowing its (mis)use in "politics". This trains people in believing in argument per authority, and obeying to tyrants. We will leave the Middle-Age when theology is back in science, i.e. back to doubt, theories and experimentation (like I illustrate directly with the canonical theology of the universal+ (Löbian) machine (the universal machine which is aware of its Turing universality, like PA or ZF, ...). Unfortunately, we continue to regress on this, and I am rather worry how it has been possible to let someone like Trump banalising racism and nazism so much. In my country, despite it is illegal to go in public with a nazi flag, or to harbour the swastika, some carnival have shown how much antisemitism is banalised and tolerated. That stinks, and show we have not learned the lesson of WWII (which is not finished in the Middle-East, also).

And then the climate change, which might be a consequence of prohibition, as the first industrial car producers asked right at the start why to use petrol, which change irreversibly the atmosphere instead of Hemp (and other plants) which do not. Prohibition is a trick used by racists (to imprison foreigners arbitrarily, or black people) and those who destroy capitalism by making the free-market into a market driven by crime (and confused then with capitalism).

Let us hope we manage to avoid genocides, but after Rwanda I have some doubt we will succeed. 

Hard period for the good willing truth researchers... 

Also, math and music are very well related. Some consider mathematics as silent music. Maybe Bob Marley's music would not be that cool without the ganga. How could we know that :)

Bruno