Terrence Howard on Reality

[Nemra]

11 minutes ago, Salvijus said:

x^1 = x^-1

They are not equal, as defining one of them also defines the other.

[Salvijus]

2 minutes ago, Nemra said:

@Salvijus Sorry, look this one. (Please hide your post which you quote my previous arithmetic process)

If x^1 = x and x^(-1) = x,

Then,

x^1 = x^(-1),

log(x^1) = log(x^(-1)),

1*log(x) = (-1)*log(x),

1 = -1,

but 1 != -1, so you're wrong.

x^1 = x^-1 is a new model. Of course it won't fit into the old paradigm. For a new model to work. All of mathematics, rules, axioms need to be adjusted. 

[zurew]

24 minutes ago, Ero said:

Gödel’s incompleteness theorem states that any formal axiomatic system strong enough to represent arithmetic is either inconsistent (i.e one can derive incorrect statements) or incomplete (there exist statements that are true but cannot be proven).

Im surprised that Leo would make such a statement that a finite system necessarily have to contain a contradiciton, when he did make a video about Gödel's incompleteness theorem himself.

It seems that he either forgot or wasn't familiar with the "incomplete" option or he is being very vague and unprecise with his words again.

Edited June 17 by zurew

[UnbornTao]

I guess the next conversation could turn into: what is language?

[Nemra]

1 hour ago, Salvijus said:

x^1 = x^-1 is a new model. Of course it won't fit into the old paradigm. For a new model to work. All of mathematics, rules, axioms need to be adjusted. 

But you are using already-defined operations.

When you define that 1 != -1 and when you prove your mentioned expressions' equality, either accept that 1 = -1 at the beginning, which would change the whole math altogether, and you will get a different result that you now haven't even thought about, or you are wrong.

Edited June 17 by Nemra

[Salvijus]

1 minute ago, Nemra said:

But you are using already-defined operations.

When you define that 1 != -1 and when you prove those equations that they aren't equal, either you accept that 1 = -1 at the beginning, which would change the whole math altogether, and you will get a different result that you now haven't even thought about, or you are wrong

Mmm. I got confused

 

[Ero]

4 minutes ago, Salvijus said:

x^1 = x^-1 is a new model. Of course it won't fit into the old paradigm. For a new model to work. All of mathematics, rules, axioms need to be adjusted. 

You keep saying this but are yet to show us how would you readjust the axioms. If you are really that genuine about a civil debate, here you carry the burden of proof (have you not here the hebrew proverb “prove you don’t have a sister”?)

Multiple people provided you with variety of demonstrations why you are wrong. I will remove myself from the discussion with this last example.

From what I can tell your understanding of mathematics is only as far as arithmetic. So let me give you an example in geometry that you are clearly overlooking. Consider the unit circle S^1 defined in the Cartesian coordinate system through the equation x^2+y^2=1. You are aware of trigonometry, yes? You can redefine the xy coordinate systems into polar, whereas since the radius is one, you just have x =cos a and y=sin a. Now, have you heard of complex numbers? You can define that same circle using Euler’s identity e^(i pi a) = cos a + i sin a (this is the geometric meaning, there is also an algebraic one as the continuous Lie group U(1) that rests in the axioms mentioned earlier). By refusing to accept the existence of e^0=1 you are essentially saying that the circle is missing a point at (0,1). Yet i can clearly draw a circle “physically” without lifting the pen. How do you reconcile that?

 

[Salvijus]

2 minutes ago, Ero said:

Multiple people provided you with variety of demonstrations why you are wrong

I accepted your demonstrations as valid btw. And I thank you for your time. I was just suggesting an idea that it's possible to use the an alternative model and make it consistent aswell. It doesn't even have to be mine. Just alternative. 

Edited June 17 by Salvijus

[Ero]

18 minutes ago, zurew said:

Im surprised that Leo would make such a statement that a finite system necessarily have to contain a contradiciton, when he did make a video about Gödel's incompleteness theorem himself.

It seems that he either forgot or wasn't familiar with the "incomplete" option or he is being very vague and unprecise with his words again.

I think Leo is just conflating the two terms (complete and consistent) which have precise meanings. From everything I have watched and read from him, I think he understands pretty well the limitations of math, precisely because of this very real existence of self-loops and references (the proof of Gödel is itself one)

[Nemra]

@Salvijus

If 1 = -1, then what other meaning does the sign "-" have besides indicating numbers smaller than 0.

[Salvijus]

2 minutes ago, Nemra said:

@Salvijus

If 1 = -1, then what other meaning does the sign "-" have besides indicating numbers smaller than 0.

In terms of x^-3 you can make a new rule/consensus that "-" indicates division, not multiplication. So x^-3 = x/x/x. 

I mean you can start making whatever new rules you want as long as you make it consistent. 

[Salvijus]

The main questions are. 

1. Is it possible to have an alternative math system and make it consistent?

2. Is the current math system the most accurate representation of reality? 

You guys can debunk me all you want. But if the answer to the first question is yes. Then in theory my model should be able to make consistent aswell. Then you could make bunch of alternative models and debate which ones are more accurate to represent reality. 

Edited June 17 by Salvijus

[Yimpa]

I remember in middle school they were testing a new way to teach math, but the parents got so pissed off that they reverted back to the traditional way it is taught.

[Nemra]

2 hours ago, Salvijus said:

In terms of x^-3 you can make a new rule/consensus that "-" indicates division, not multiplication. So x^-3 = x/x/x. 

I mean you can start making whatever new rules you want as long as you make it consistent. 

Ok.

x^(-1) = x,

x^(-2) = x/x = 1,

x^(-3) = x/x/x = 1/x,

x^(-4) = x/x/x/x = 1/(x^2),

Then

x^(-1) = x, x^1 = x^(-1),

x^(-2) = 1,

x^(-3)*x = 1, x^1 = 1/x^(-3)

x^(-4)*x^2 = 1, x^2 = 1/x^(-4),

Also,

x^(-1)*x^(-1) = x^2, x^(-2) = x^2,

x^(-2)*x^(-2) = 1, x^(-4) = 1,

x^(-3)*x^(-3) = 1/(x^2), x^(-6) = 1/x^2

x^(-4)*x^(-4) = 1/(x^4), x^(-8) = 1/x^4

What the hell!

Do you see how x^(+n) becomes different?

And I haven't looked into it deeper yet. Your way doesn't describe reality the way you thought it would.

Edited June 18 by Nemra

[zurew]

59 minutes ago, Ero said:

I think Leo is just conflating the two terms (complete and consistent) which have precise meanings.

I think conflating those terms is a pretty big deal and shows a lack of understanding. Anyone who has a surface level understanding of basic logic wouldn't ever conflate incomplete with inconsistency .

How can he make a video on this and not understand the meaning of those terms is baffling to me.

[Leo Gura]

3 hours ago, zurew said:

A=2B 2A=4B

A+2B =2A

Show whats the "higher inconsistency that comes up here

As Godel showed, you can get consistency at the cost of completeness. But if you care about completeness you will lose consistency.

Your system is only consistent because it is so incomplete and feckless.

Maybe you should study the implications of his theories rather than telling me to study logic.

Any system that is capable of self-reference will contradict itself. And systems which cannot reference themselves are not really meaningful or powerful.

Edited June 18 by Leo Gura

[zurew]

5 hours ago, Leo Gura said:

Your system is only consistent because it is so incomplete and feckless.

Maybe you should study the implications of his theories rather than telling me to study logic.

Leo, you were changing your claims on the go as you realized ,your claims doesn't make sense or hold up. Starting with "all formal systems are contradictory" to "all formal systems with enough complexity are contradictory" to eventually making a difference between a contradiciton and incompleteness.

Quote

9 hours ago, Leo Gura said:

I doubt that any finite system can truly be consistent. Such systems are fudged into psusedo-consistency through mental gymnastics and unholistic ways of thinking.

9 hours ago, Leo Gura said:

They are only consistent through artificial limits. If the system is anything complex it will become self-referential and inconsistent unless you ban self-reference a d other such mental gymnastics.

I see no statement or implication of incompleteness here, I only see the assertion of inconsistency.

Edited June 18 by zurew

[Leo Gura]

14 minutes ago, zurew said:

Leo, you were changing your claims on the go as you realized ,your claims doesn't make sense or hold up. Starting with "all formal systems are contradictory" to "all formal systems with enough complexity are contradictory" to eventually making a difference between a contradiciton and incompleteness.

No, I made precise statements about the limited nature of formal systems.

Your formal system doesn't contradict itself because you made it so limited. If your formal system actually tried fo grasp any significant amount of reality it would contradict itself. It must, because you cannot formalize Infinity. All you can do is avoid Infinity. Which is what all your systems do.

Contradiction and completeness are connected.

If your mind tries to grasp Infinity it will run into contradictions. Your system simply isn't trying to do that because it is so narrow.

Edited June 18 by Leo Gura

[zurew]

3 hours ago, Leo Gura said:

All you can do is avoid Infinity. Which is what all your systems do.

Sure, but all of these limitations are directly applicable to your epistemology as well.

3 hours ago, Leo Gura said:

 If your formal system actually tried fo grasp any significant amount of reality it would contradict itself. It must, because you cannot formalize Infinity.

Contradiction and completeness are connected.

Framing it this way is misleading, because my understanding is that both incompleteness theorems are only talking about provability and not about making "is" statements - so  the system won't necessarily become inconsistent, it is just that you cannot prove within the system that the system itself is consistent (you need to go outside of the system in order to prove or disprove that system's consistency) - which is different from claiming that the system  is  inconsistent (because one is a truth claim, the other is a jusification[in this case investigating the limits of proving and proofs] and the truth value of a truth claim can be true or false regardless if I have the ability to prove it or disprove it). 

So in other words, from system's inability to prove its own consistency doesn't necessarily follow, that that system is actually inconsistent ( at least thats my understanding but I can be wrong).

Quote

https://plato.stanford.edu/Entries/goedel-incompleteness/

First incompleteness theorem
Any consistent formal system F𝐹 within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F𝐹 which can neither be proved nor disproved in F𝐹.

Second incompleteness theorem
For any consistent system F𝐹 within which a certain amount of elementary arithmetic can be carried out, the consistency of F𝐹 cannot be proved in F𝐹 itself.

 

Edited June 18 by zurew

[Salvijus]

7 hours ago, Nemra said:

Do you see how x^(+n) becomes different?

This formula is true only in the old paradigm. In the new model you'd have to remake all the formulas. Of course the new model is not going to fit in the old formulas. 

There's only one thing worth contemplating. Is there a way to make alternative math consistent? And if yes. Then there should be a way to make my model legit. 

Edited June 18 by Salvijus