You deserve to suffer from another pandemic.

[alterra57]

I didn't break. You are trash.

-Joseph Van Name Ph.D.

Joseph since this is your thread, can I ask you a question I'd like to know what types of research you are doing these days. I'm assuming you stopped doing math research but I'm not sure.

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

...
Cry harder. Try harder.

-alterra57 Ph.D.K.W.

You are exactly what I am talking about when I say that most people act like s@#$ most of the time.

-Joseph Van Name Ph.D.

P.S. If you see research done by a schmuck at a university, you can be confident that such research is really s@#$ty. Universities are extremely unprofessional. Universities refuse to apologize for promoting violence, so their research is s@#$ by default.

Look who's talking, the fake Ph.D, hypocrite.

Nothing that you say has any value whatsoever. Please learn virtue or die during the next 5 pandemics. But I know that you choose death. You are suicidal.

-Joseph Van Name Ph.D.

No offense to your inferior genetics but some of us are built like walking tanks.

Pride comes before death, b@#$%.

-Joseph Van Name Ph.D.

It's not pride, it's basic biology and it also makes me refuse empty eggs like yourself.

[1714874365]

1714874365

[1714874365]

1714874365

[1714874365]

1714874365

[1714874365]

1714874365

[jvanname]

I didn't break. You are trash.

-Joseph Van Name Ph.D.

Joseph since this is your thread, can I ask you a question I'd like to know what types of research you are doing these days. I'm assuming you stopped doing math research but I'm not sure.

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

...
Cry harder. Try harder.

-alterra57 Ph.D.K.W.

You are exactly what I am talking about when I say that most people act like s@#$ most of the time.

-Joseph Van Name Ph.D.

P.S. If you see research done by a schmuck at a university, you can be confident that such research is really s@#$ty. Universities are extremely unprofessional. Universities refuse to apologize for promoting violence, so their research is s@#$ by default.

Look who's talking, the fake Ph.D, hypocrite.

Nothing that you say has any value whatsoever. Please learn virtue or die during the next 5 pandemics. But I know that you choose death. You are suicidal.

-Joseph Van Name Ph.D.

No offense to your inferior genetics but some of us are built like walking tanks.

Pride comes before death, b@#$%.

-Joseph Van Name Ph.D.

It's not pride, it's basic biology and it also makes me refuse empty eggs like yourself.

Please go away. The only thing you are doing is demonstrating how much of a worthless pile of s@#$ you are.

-Joseph Van Name Ph.D.

[larry_vw_1955]

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

obviously you're a very brilliant mind. i don't think i could ever understand that type of math no matter how hard i tried but thanks for sharing. i think the world doesn't value people that do research like you. kind of sad but i guess its the truth.

what are your opinions about things like the halting problem in computer science and the stop button paradox? I'm assuming you agree with the halting problem but do you think there is a simple solution to the stop button paradox for AI?

[alterra57]

I didn't break. You are trash.

-Joseph Van Name Ph.D.

Joseph since this is your thread, can I ask you a question I'd like to know what types of research you are doing these days. I'm assuming you stopped doing math research but I'm not sure.

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

...
Cry harder. Try harder.

-alterra57 Ph.D.K.W.

You are exactly what I am talking about when I say that most people act like s@#$ most of the time.

-Joseph Van Name Ph.D.

P.S. If you see research done by a schmuck at a university, you can be confident that such research is really s@#$ty. Universities are extremely unprofessional. Universities refuse to apologize for promoting violence, so their research is s@#$ by default.

Look who's talking, the fake Ph.D, hypocrite.

Nothing that you say has any value whatsoever. Please learn virtue or die during the next 5 pandemics. But I know that you choose death. You are suicidal.

-Joseph Van Name Ph.D.

No offense to your inferior genetics but some of us are built like walking tanks.

Pride comes before death, b@#$%.

-Joseph Van Name Ph.D.

It's not pride, it's basic biology and it also makes me refuse empty eggs like yourself.

Please go away. The only thing you are doing is demonstrating how much of a worthless pile of s@#$ you are.

-Joseph Van Name Ph.D.

You're a scammer roleplaying someone you're not, a bad one at that too. Go ahead, guess who the worthless pile of shit is.

[jvanname]

I didn't break. You are trash.

-Joseph Van Name Ph.D.

Joseph since this is your thread, can I ask you a question I'd like to know what types of research you are doing these days. I'm assuming you stopped doing math research but I'm not sure.

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

...
Cry harder. Try harder.

-alterra57 Ph.D.K.W.

You are exactly what I am talking about when I say that most people act like s@#$ most of the time.

-Joseph Van Name Ph.D.

P.S. If you see research done by a schmuck at a university, you can be confident that such research is really s@#$ty. Universities are extremely unprofessional. Universities refuse to apologize for promoting violence, so their research is s@#$ by default.

Look who's talking, the fake Ph.D, hypocrite.

Nothing that you say has any value whatsoever. Please learn virtue or die during the next 5 pandemics. But I know that you choose death. You are suicidal.

-Joseph Van Name Ph.D.

No offense to your inferior genetics but some of us are built like walking tanks.

Pride comes before death, b@#$%.

-Joseph Van Name Ph.D.

It's not pride, it's basic biology and it also makes me refuse empty eggs like yourself.

Please go away. The only thing you are doing is demonstrating how much of a worthless pile of s@#$ you are.

-Joseph Van Name Ph.D.

You're a scammer roleplaying someone you're not, a bad one at that too. Go ahead, guess who the worthless pile of shit is.

-Go away. You are producing nothing of value here. The only thing you are doing is convincing me that it is not worth it at all to make any effort to prevent the next 5 pandemics.

If I stopped doing research I would get really bored. And I really do not dealing with the s@#$ from people because most people act like s@#$ as much as possible because most people are s@#$. Suppose that A_1,...,A_r are real m by m matrices and B_1,...,B_r are real n by n matrices. Define the L_2-spectral radius similarity between (A_1,...,A_r) and (B_1,...,B_r) as rho(kron(A_1,B_1)+...+kron(A_r,B_r))/(rho(kron(A_1,A_1)+...+kron(A_r,A_r))*rho(kron(B_1,B_1)+...+kron(B_r,B_r)))^(1/2). If (A_1,...,A_r) are n by n matrices, then we say that a collection of d by d matrices (X_1,...,X_r) is an L_2-spectral radius dimensionality reduction (LSRDR) if the L_2-spectral radius similarity between (A_1,...,A_r) and (X_1,...,X_r) is locally maximized. The L_2-spectral radius dimensionality reduction can be found using the typical gradient ascent, so this should be thought of as a machine learning algorithm. I promise that LSRDRs satisfy magical properties. I have been dealing with things like LSRDRs and other machine learning algorithms for AI safety since these are useful for cryptocurrency research. Imagine that. The one cryptocurrency that you don't value is the one where the developer is doing the most research. This is because the cryptocurrency sector values stupidity much more than it values intelligence. Most people value stupidity over intelligence. And that is why we all deserve more pandemics.

obviously you're a very brilliant mind. i don't think i could ever understand that type of math no matter how hard i tried but thanks for sharing. i think the world doesn't value people that do research like you. kind of sad but i guess its the truth.

what are your opinions about things like the halting problem in computer science and the stop button paradox? I'm assuming you agree with the halting problem but do you think there is a simple solution to the stop button paradox for AI?

I agree with the halting problem since it is not controversial among mathematicians and other experts and the proof is not that hard; the proof of the halting problem really simplifies Godel's incompleteness theorem. I am only familiar with the basics of the stop button problem, and I am not yet convinced that the stop button problem is what we should be focused on with AI safety. 

1. The stop button issue is only a problem when we train an AI system to optimize a fitness/loss function. But our current AI systems optimize not just for having the right outputs, but they may also be regularized and thus their L_1 and/or L_2 norms may be minimized as well. In this case, we are training an AI to minimize a quantity that is not a function of the outputs of the network. What if we keep on using more and more regularized AI that performs well in practice but which does not clearly optimize certain outputs? In this case, the stop button issue may not even be important or the solution may not work since the AIs reaction to the stop button may not even be directly optimized for.

2. The stop button issue is a problem for centralized AI systems, but what about AI systems that are distributed and where each implementation of the AI is slightly different (with fine tuning for example with LoRAs we can easily retrain an existing AI for specific purposes)? In this case, a stop button may only stop some of the AI systems, but we still need to deal with the other AI systems.

3. Even if we have a solution to the stop button problem, we will still need to use AI interpretability to make sure that the solution is properly implemented in AI systems. This is why I consider AI interpretability to be the most fundamental aspect of AI safety.


-Joseph Van Name Ph.D.

[alterra57]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

[jvanname]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

Ok. I won't prevent the next 5 pandemics. Enjoy the 5 vaccines that you will have to get in the @$$ every 6 months for the rest of your miserable short life. And no, the vaccines won't even work.

-Joseph Van Name Ph.D.

[alterra57]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

Ok. I won't prevent the next 5 pandemics. Enjoy the 5 vaccines that you will have to get in the @$$ every 6 months for the rest of your miserable short life. And no, the vaccines won't even work.

-Joseph Van Name Ph.D.

No offense to your highness but I don't bend over like you do, didn't even get the 1st one, unlike you. Perfectly healthy but you can't comprehend that you disease ridden scammer.

[jvanname]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

Ok. I won't prevent the next 5 pandemics. Enjoy the 5 vaccines that you will have to get in the @$$ every 6 months for the rest of your miserable short life. And no, the vaccines won't even work.

-Joseph Van Name Ph.D.

No offense to your highness but I don't bend over like you do, didn't even get the 1st one, unlike you. Perfectly healthy but you can't comprehend that you disease ridden scammer.

You have been completely and totally enb@#$hed because you are a b@#$h. You will take the next vaccine because it will be in the @$$ for each pandemic every 6 months for the rest of your short miserable life. Enjoy being miserable. I tried to warn you but you are suicidal. You choose death because you are f@#$ed up.

-Joseph Van Name Ph.D.

[okorieemmanuel]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

Ok. I won't prevent the next 5 pandemics. Enjoy the 5 vaccines that you will have to get in the @$$ every 6 months for the rest of your miserable short life. And no, the vaccines won't even work.

-Joseph Van Name Ph.D.

No offense to your highness but I don't bend over like you do, didn't even get the 1st one, unlike you. Perfectly healthy but you can't comprehend that you disease ridden scammer.

You have been completely and totally enb@#$hed because you are a b@#$h. You will take the next vaccine because it will be in the @$$ for each pandemic every 6 months for the rest of your short miserable life. Enjoy being miserable. I tried to warn you but you are suicidal. You choose death because you are f@#$ed up.

-Joseph Van Name Ph.D.

Please let us stop this abuse.

NO ONE DESERVES TO SUFFER EVEN IF IT IS THE WORST CRIMINAL ON EARTH. LET'S KEEP LOVE AND UNITY, PEACE AND HARMONY WITHIN US ALL.

[larry_vw_1955]

I agree with the halting problem since it is not controversial among mathematicians and other experts and the proof is not that hard; the proof of the halting problem really simplifies Godel's incompleteness theorem.

thanks Dr. Joseph. I don't think some people here in the forum understand how lucky they are to have someone like you here. But I do. I'm really enjoying your insights. About the incompleteness theorem, does it bother you that there's statements that are true but can't be proven but I'm not even sure we know an example of such a statement. But that would be kind of bad to spend ones life trying to solve a problem that actually is true but can't be proven but you don't know that. so you waste your life working on something like the twin prime conjecture. no mathematician would consider it wasted but maybe non productive to a degree.

I am only familiar with the basics of the stop button problem, and I am not yet convinced that the stop button problem is what we should be focused on with AI safety.

i kind of understand where you're coming from. if we can have self driving ubers such as waymo then clearly that problem has been solved to some degree of acceptability even though sometimes they get stuck in traffic or impede an ambulance...

you're the man! appreciate you.

oh another question hope it's not too off topic but what's your whole stance on the JWST? do you think it was a waste of money or is it actually accomplishing something useful? or do we already know there is life outside of the solar system, intelligent life even? are we the only "intelligent" life in the universe or is there something smarter than us out there somewhere? and what is god or does god even exist? as a scientist i don't know how someone would approach investigating those types of questions but i would love to hear what you have to say about them.

[jvanname]

Lmao, please don't prevent the other "5" pandemics, I'd like to go through this pain you're rambling about.

Ok. I won't prevent the next 5 pandemics. Enjoy the 5 vaccines that you will have to get in the @$$ every 6 months for the rest of your miserable short life. And no, the vaccines won't even work.

-Joseph Van Name Ph.D.

No offense to your highness but I don't bend over like you do, didn't even get the 1st one, unlike you. Perfectly healthy but you can't comprehend that you disease ridden scammer.

You have been completely and totally enb@#$hed because you are a b@#$h. You will take the next vaccine because it will be in the @$$ for each pandemic every 6 months for the rest of your short miserable life. Enjoy being miserable. I tried to warn you but you are suicidal. You choose death because you are f@#$ed up.

-Joseph Van Name Ph.D.

Please let us stop this abuse.

NO ONE DESERVES TO SUFFER EVEN IF IT IS THE WORST CRIMINAL ON EARTH. LET'S KEEP LOVE AND UNITY, PEACE AND HARMONY WITHIN US ALL.

Instead of talking in all caps, why don't you make an effort to support those who have been trying to make a difference. I have given up on helping people because nearly everyone is insufferable.

I agree with the halting problem since it is not controversial among mathematicians and other experts and the proof is not that hard; the proof of the halting problem really simplifies Godel's incompleteness theorem.

thanks Dr. Joseph. I don't think some people here in the forum understand how lucky they are to have someone like you here. But I do. I'm really enjoying your insights. About the incompleteness theorem, does it bother you that there's statements that are true but can't be proven but I'm not even sure we know an example of such a statement. But that would be kind of bad to spend ones life trying to solve a problem that actually is true but can't be proven but you don't know that. so you waste your life working on something like the twin prime conjecture. no mathematician would consider it wasted but maybe non productive to a degree.

I am only familiar with the basics of the stop button problem, and I am not yet convinced that the stop button problem is what we should be focused on with AI safety.

i kind of understand where you're coming from. if we can have self driving ubers such as waymo then clearly that problem has been solved to some degree of acceptability even though sometimes they get stuck in traffic or impede an ambulance...

you're the man! appreciate you.

oh another question hope it's not too off topic but what's your whole stance on the JWST? do you think it was a waste of money or is it actually accomplishing something useful? or do we already know there is life outside of the solar system, intelligent life even? are we the only "intelligent" life in the universe or is there something smarter than us out there somewhere? and what is god or does god even exist? as a scientist i don't know how someone would approach investigating those types of questions but i would love to hear what you have to say about them.

I am not bothered by Godel's incompleteness theorem. First of all, it is better to have an incompleteness theorem where we know that our axiomatic system cannot prove everything than to not have an incompleteness theorem and not know whether our axiomatic system can prove everything or not. The correct response to Godel's incompleteness theorem is to look at Godel's second incompleteness theorem to tell us how to strength  our axiomatic systems so that we will be able to prove more results. Godel's second incompleteness theorem states that no axiomatic system stronger than Peano arithmetic is allowed to prove its own consistency. Godel's incompleteness theorem is good because it gives us a direction to go to strength our axiomatic systems. If we want to strength an axiomatic system A, then a natural thing to do would be to work in the system A+Con(A) which states that A is consistent. We can iterate this process to obtain A+Con(A)+Con(A+Con(A)), and so on and so forth. While iterating this process does yield stronger axiomatic systems, this process of iterating the consistency is rather inefficient and cumbersome. First of all, if we iterate the process that gives us A+Con(A)+Con(A+Con(A)) finitely many times, we won't get very far, so we will need to iterate this process transfinitely. But we can do much better than this. Godel's completeness theorem states that an axiomatic theory is consistent if and only if it has a model. Therefore, by combining Godel's second incompleteness theorem with his completeness theorem, we conclude that a strong axiomatic theory cannot prove that it contains a model of itself. Therefore, in order to strengthen an axiomatic theory, we can add an axiom from which we can obtain a model of that theory. And by adding axioms about models, we can get better strengthenings of our axiomatic theory. For example, if we add an axiom stating that there exists a well-founded model of ZFC to the ZFC axioms, then this new axiomatic theory is stronger than what we would obtain by iterating the process of ZFC+Con(ZFC) transfinitely. We can do even better than this though. Large cardinal axioms are much stronger strengthenings of the standard ZFC axioms that easily encapsulate the process of transfinitely iterating the consistency hierarchy A,A+Con(A),A+Con(A)+Con(A+Con(A)) and much more. Not only do large cardinal axioms provide strengthenings of ZFC, but one can prove interesting theorems from these large cardinal axioms including theorems about finite structures. The only catch is that if we go too far with large cardinal axioms, then we will end up with an inconsistency (such as Kunen's inconsistency). I am personally confident that all large cardinal axioms up to rank-into-rank cardinals are consistent. If anyone is able to prove that the existence of n-huge cardinals for all n is inconsistent, then I will forfeit all of my cryptocurrency.

I do not know much about the JWST, but I have no reason to believe that it is a waste of money.

-Joseph Van Name Ph.D.

[alterra57]

Why are you begging for money? Get a job scammer.

[jvanname]

Why are you begging for money? Get a job scammer.

Everything you say is f@#$ing stupid.

-Joseph Van Name Ph.D.

[larry_vw_1955]

I am not bothered by Godel's incompleteness theorem. First of all, it is better to have an incompleteness theorem where we know that our axiomatic system cannot prove everything than to not have an incompleteness theorem and not know whether our axiomatic system can prove everything or not. The correct response to Godel's incompleteness theorem is to look at Godel's second incompleteness theorem to tell us how to strength  our axiomatic systems so that we will be able to prove more results. Godel's second incompleteness theorem states that no axiomatic system stronger than Peano arithmetic is allowed to prove its own consistency. Godel's incompleteness theorem is good because it gives us a direction to go to strength our axiomatic systems. If we want to strength an axiomatic system A, then a natural thing to do would be to work in the system A+Con(A) which states that A is consistent. We can iterate this process to obtain A+Con(A)+Con(A+Con(A)), and so on and so forth. While iterating this process does yield stronger axiomatic systems, this process of iterating the consistency is rather inefficient and cumbersome. First of all, if we iterate the process that gives us A+Con(A)+Con(A+Con(A)) finitely many times, we won't get very far, so we will need to iterate this process transfinitely. But we can do much better than this. Godel's completeness theorem states that an axiomatic theory is consistent if and only if it has a model. Therefore, by combining Godel's second incompleteness theorem with his completeness theorem, we conclude that a strong axiomatic theory cannot prove that it contains a model of itself. Therefore, in order to strengthen an axiomatic theory, we can add an axiom from which we can obtain a model of that theory. And by adding axioms about models, we can get better strengthenings of our axiomatic theory. For example, if we add an axiom stating that there exists a well-founded model of ZFC to the ZFC axioms, then this new axiomatic theory is stronger than what we would obtain by iterating the process of ZFC+Con(ZFC) transfinitely. We can do even better than this though. Large cardinal axioms are much stronger strengthenings of the standard ZFC axioms that easily encapsulate the process of transfinitely iterating the consistency hierarchy A,A+Con(A),A+Con(A)+Con(A+Con(A)) and much more. Not only do large cardinal axioms provide strengthenings of ZFC, but one can prove interesting theorems from these large cardinal axioms including theorems about finite structures. The only catch is that if we go too far with large cardinal axioms, then we will end up with an inconsistency (such as Kunen's inconsistency). I am personally confident that all large cardinal axioms up to rank-into-rank cardinals are consistent. If anyone is able to prove that the existence of n-huge cardinals for all n is inconsistent, then I will forfeit all of my cryptocurrency.

I do not know much about the JWST, but I have no reason to believe that it is a waste of money.

-Joseph Van Name Ph.D.

You truly are a brilliant mathematician Dr. Joseph. I would imagine there's very few mathematicians that would understand all of what you just discussed. Of course, I'm woefully inadequate to understand it but I'll be googling some of the things you talked about to try and get a better understanding but wow. You are one amazing mind and thanks for your 2 cents (200 more cents more like it!). If foundations of mathematics is not your specialty research area then I would be flabbergasted since you sound so authoritative in your knowledge of it. Thanks so much for your lengthy response, I really do appreciate it.

All I can say about the incompleteness theorems in my limited understanding of them is I just don't understand how there could ever be a concrete example of a statement that is true but cannot be proven. Because from what it appears, all that "true" means is "cannot be proven with the set of axioms in the system". So you could either add the statement itself or its negation to your axiom system and I guess it would still be consistent. I don't see how that could work with something like the Twin Prime Conjecture or The Collatz Conjecture. The Twin Prime Conjecture is either true or false. That truth exists we may just not know what it is. So because of that issue, the statement that there are infinitely many twin primes doesn't seem like a feasible candidate to add as a new axiom of arithmetic since we don't know if it is true but the truth exists one way or the other about it so if we choose the wrong version of the statement we are going down a wrong path.

Given some arbitrary statement that one does not know how to prove and seems challenging to prove, how do they go about proving it is not provable in their axiomatic system? I would think that's impossible. For example the Riemann Hypothesis.

One other quick question, have you ever heard of Dr. Norman Wildberger I think that's his name. He has made alot of videos criticizing the "real numbers" as though they really don't exist and he doesn't think there is a valid construction of them, just handwaving. Do you think the real numbers have a solid foundation? or do they have issues. he maintains that things like dedekind cuts and cauchy sequences as ways of constructing the real numbers are flawed. to me that's kind of troubling since higher math is all based on you guessed it, the real numbers! 

[alterra57]

Why are you begging for money? Get a job scammer.

Everything you say is f@#$ing stupid.

-Joseph Van Name Ph.D.

Says the guy who's using ChatGPT to formulate his topics  .

[jvanname]

I am not bothered by Godel's incompleteness theorem. First of all, it is better to have an incompleteness theorem where we know that our axiomatic system cannot prove everything than to not have an incompleteness theorem and not know whether our axiomatic system can prove everything or not. The correct response to Godel's incompleteness theorem is to look at Godel's second incompleteness theorem to tell us how to strength  our axiomatic systems so that we will be able to prove more results. Godel's second incompleteness theorem states that no axiomatic system stronger than Peano arithmetic is allowed to prove its own consistency. Godel's incompleteness theorem is good because it gives us a direction to go to strength our axiomatic systems. If we want to strength an axiomatic system A, then a natural thing to do would be to work in the system A+Con(A) which states that A is consistent. We can iterate this process to obtain A+Con(A)+Con(A+Con(A)), and so on and so forth. While iterating this process does yield stronger axiomatic systems, this process of iterating the consistency is rather inefficient and cumbersome. First of all, if we iterate the process that gives us A+Con(A)+Con(A+Con(A)) finitely many times, we won't get very far, so we will need to iterate this process transfinitely. But we can do much better than this. Godel's completeness theorem states that an axiomatic theory is consistent if and only if it has a model. Therefore, by combining Godel's second incompleteness theorem with his completeness theorem, we conclude that a strong axiomatic theory cannot prove that it contains a model of itself. Therefore, in order to strengthen an axiomatic theory, we can add an axiom from which we can obtain a model of that theory. And by adding axioms about models, we can get better strengthenings of our axiomatic theory. For example, if we add an axiom stating that there exists a well-founded model of ZFC to the ZFC axioms, then this new axiomatic theory is stronger than what we would obtain by iterating the process of ZFC+Con(ZFC) transfinitely. We can do even better than this though. Large cardinal axioms are much stronger strengthenings of the standard ZFC axioms that easily encapsulate the process of transfinitely iterating the consistency hierarchy A,A+Con(A),A+Con(A)+Con(A+Con(A)) and much more. Not only do large cardinal axioms provide strengthenings of ZFC, but one can prove interesting theorems from these large cardinal axioms including theorems about finite structures. The only catch is that if we go too far with large cardinal axioms, then we will end up with an inconsistency (such as Kunen's inconsistency). I am personally confident that all large cardinal axioms up to rank-into-rank cardinals are consistent. If anyone is able to prove that the existence of n-huge cardinals for all n is inconsistent, then I will forfeit all of my cryptocurrency.

I do not know much about the JWST, but I have no reason to believe that it is a waste of money.

-Joseph Van Name Ph.D.

You truly are a brilliant mathematician Dr. Joseph. I would imagine there's very few mathematicians that would understand all of what you just discussed. Of course, I'm woefully inadequate to understand it but I'll be googling some of the things you talked about to try and get a better understanding but wow. You are one amazing mind and thanks for your 2 cents (200 more cents more like it!). If foundations of mathematics is not your specialty research area then I would be flabbergasted since you sound so authoritative in your knowledge of it. Thanks so much for your lengthy response, I really do appreciate it.

All I can say about the incompleteness theorems in my limited understanding of them is I just don't understand how there could ever be a concrete example of a statement that is true but cannot be proven. Because from what it appears, all that "true" means is "cannot be proven with the set of axioms in the system". So you could either add the statement itself or its negation to your axiom system and I guess it would still be consistent. I don't see how that could work with something like the Twin Prime Conjecture or The Collatz Conjecture. The Twin Prime Conjecture is either true or false. That truth exists we may just not know what it is. So because of that issue, the statement that there are infinitely many twin primes doesn't seem like a feasible candidate to add as a new axiom of arithmetic since we don't know if it is true but the truth exists one way or the other about it so if we choose the wrong version of the statement we are going down a wrong path.

Given some arbitrary statement that one does not know how to prove and seems challenging to prove, how do they go about proving it is not provable in their axiomatic system? I would think that's impossible. For example the Riemann Hypothesis.

One other quick question, have you ever heard of Dr. Norman Wildberger I think that's his name. He has made alot of videos criticizing the "real numbers" as though they really don't exist and he doesn't think there is a valid construction of them, just handwaving. Do you think the real numbers have a solid foundation? or do they have issues. he maintains that things like dedekind cuts and cauchy sequences as ways of constructing the real numbers are flawed. to me that's kind of troubling since higher math is all based on you guessed it, the real numbers!  

I have not heard of Norman Wildberger, but there are some mathematicians who criticize basic structures like the real numbers or even the natural numbers. And they do not have much of a reason to do so. We cannot even find an inconsistency with extremely large cardinals, so these extremely large cardinals probably exist. So since extremely large cardinals work just fine in practice, we should accept that there is probably some legitimacy to them and to the real numbers as well. One can say that the real numbers and large cardinals may exist but only in a countable model (this is guaranteed by the Lowenhein Skolem theorem), but that unnecessarily complicates the issue. I do not see any reason why large cardinals would evade all attempts at finding an inconsistency while they only exist in a countable model and cannot extend to larger models.

So far, large cardinal axioms have not helped with problems like the Twin prime conjecture, but I have used rank-into-rank cardinals to produce some falsifiable statements about finite algebraic structures, and I have ran the computations trying to falsify these statements myself, but I have not been able to find any inconsistency even after about a million attempts on a computer. Large cardinal axioms may not allow us to prove everything like the twin prime conjecture, and we may not be able to keep on adding stronger large cardinal axioms since mathematicians have not been able to formulate large cardinal axioms much higher than rank-into-rank; there are some cardinals axioms that are much stronger since they imply models of rank-into-rank, but these stronger axioms are not consistent with the axiom-of-choice. If we do not abandon the axiom of choice, then the only way that I know to make larger cardinals is to take something like limits of cardinals, but this idea does not seem to go very far since we do not know how to get them to be as strong as the axioms that are inconsistent with the axiom of choice.

Why are you begging for money? Get a job scammer.

Everything you say is f@#$ing stupid.

-Joseph Van Name Ph.D.

Says the guy who's using ChatGPT to formulate his topics  .

You are worthless. The Lord Jesus Christ hates your soul and will send you to Hell after the next 5 pandemics kill you.

-Joseph Van Name Ph.D.

[alterra57]

Your "help" is not needed, get a job and stop trying lowlife scumbag scams.

[jvanname]

Your "help" is not needed, get a job and stop trying lowlife scumbag scams.

F@#$ off. I already said that I will no longer make an effort to prevent the next 5 pandemics because people need an @$$ whooping more than anything else. What the f@#$ are you going on and on about? Oh wait. You are completely incapable of thinking or communicating anything that remotely makes any sense because you are extremely mentally ill just like most Bitcoiners are.

-Joseph Van Name Ph.D.

[alterra57]

Your "help" is not needed, get a job and stop trying lowlife scumbag scams.

F@#$ off. I already said that I will no longer make an effort to prevent the next 5 pandemics because people need an @$$ whooping more than anything else. What the f@#$ are you going on and on about? Oh wait. You are completely incapable of thinking or communicating anything that remotely makes any sense because you are extremely mentally ill just like most Bitcoiners are.

-Joseph Van Name Ph.D.

You are angry because you couldn't scam anyone, if mental illness = too smart for you to get money out of us then I'm the most retarded one here. Please don't be angry mister scammer, there will be plenty of missed opportunities for you.