Armando de la Torre 2

Nature of mathematics: mathematics does not say anything, but with mathematics you can say everything.

All of mathematics can de reduced to mathematical principles.

Why is mathematics so important? 


Elements in math:

• Egypt / Babylon created the concept of number. (old world)
• Greeks added the concept of proof. (classical world)
• (Modern world) added the concept of duration / experiment. 
• (20th century) added the concept of probability. 

Tautology: the predicate means the same as the subject.
All of mathematics is tautological, because the core of mathematics are equations (both sides are the same)

Through mathematics we use experiments in order to come up with more theorems, By experiments we prove the truth of our statements. But we cant have experiments without mathematics. Mathematics helps us explain the result of experiments.

Meta-Dialogue: mar 7

Is beauty objective or subjective?
Nature is not always symmetric, then could beauty be asymmetric?

Complete: you could enter or add anything and it would still work.

Consistent: doesn't have contradictions.

Gödel thought that mathematics is a system, which is incomplete but consistent. The reason for this is that we cant prove mathematics with mathematics. We would need another robust system to explain this system. This cant be done.

Mathematics is like religion because it believes in certain truths that cant be proved. (Fire in the Equations, leap of faith).

The ptolomaic system was complete but inconsistent.

Can there exist a mind without the universe? Could the universe exist without a mind?



We should be more metacognitive and try to understand people more. We should listen to other points of view, in order to improve our difficult conversations. Both sides have to agree to try to work things out. If only one person is committed to improving the situation, then you cant have an easy conversation.

Humans seek to express themselves. Maybe this is because we are naturally selfish, maybe its because we need someone else's approval, maybe its because we are afraid we might get hurt or maybe its because if the human emotion and necessity to follow people.

One talks in a dialogue to try to contribute a piece to the puzzle. A persons input can also be useful for the rest of the people, as long as one is not trying to impose ideas.

Having a conversations means to remodel something, not to construct it.

Gödel, Escher, Bach #7

Proof: something that humans need to prove a derivation.

could propositional calculus be the pure rules of logic?

The rules are what makes a system work. If it weren't for the rules, we wouldn't have a system.
Rules can be seen as something isomorphic.
Although rules don't have to be isomorphic to reality.

Aleatory: outside the system.

A complete system should respond to everything. It should be universal. According to Gödel this doesn't exits.

Meta-Dialogue: feb 28

The following things this week talk about the importance of interpretation:

• Fire in the Equations
• Empathy process
• 12 angry men
• Language (Armando de la Torre)
• The world is a formal system
• Patterns

How do we know that we know?

What can we rely on in the universe in order to give us facts and truth?
If everyone has their own interpretation how can the world ever agree on anything?

Maybe we can demonstrate it in allopoiesis, showing mastery. But this still doesnt solve the question of how can we know that we know.
In 12 angry men, we can see that one is never sure that you really know.

We can take Poppers side. He said that we can only know when something is not true, but we can never know if something is 100% sure of something true. Like in 12 angry men, there is always a possibility for doubting. (reasonable doubt).

Episteme: knowledge that is certain. What is objective truth outside the impression you have on it.

Interpretation: kind of like what happened with the chair. Everyone has different perspectives.

Should we have a reasonable doubt on reality?
Always have in mind that there are perceptions and an objective truth.

What would happen if we doubt everything?
We always need a leap of faith (Fire in the Equations).
We have to at least believe in these leaps of faith:

• you exist
• you are sane
• knowledge can be acquired

We are in this reality, in which we can never know an objective truth. We can't pop-out (GEB) of the system in order to get a bigger view of the whole truth detail. Its outside our reality. 

The seeking of the truth is not a dead end, in which there is no point in trying. It is a road/goal that we will never reach but in the process of reaching it, we will acquire certain things that will make us or help us comprehend the world better. 

Even though we don't have the complete truth, we have a better understanding.

"Truth is not a democracy."

Crito

Socrates, trying to prove Crito that it was wrong to run away, answers that if he would run away he would destroy the city's justice. He would just end up proving that the courts have no power. They would do harm to the city and destroy the rules.

If the city gave you education, gave you nurture and then treated you badly, you should still obey it, even more than your parents. He believes he should obey and put the city before anything else, even oneself.

By staying in a city, you agree with the laws. Its like having a contract. Socrates mentions we should not break an agreement.

Gödel, Escher, Bach #6

connections:

Things come with meaning or we either give meaning to things. (Fire in the Equations). People look for pattern and things in nature that might not be there. (Fire in the Equations).

Mathematics can work as a universal language. (Philosopher Looks at Science).
Physics and geometry can not be universal languages.

Gödel says that there is nothing complete and consistent. Then this means that there really cant be a universal language, right?

The Fire in the Equations # 2

Can we be certain of anything? or do we just make theories and assumptions in order to try to explain things?

Observation.
it is one of the ways by which we learn.
The only way we percieve the world is through our senses.
But how can we ever reach an objective truth, when everyone might sense things differently and interpret them differently?

THE WORLD IS A FORMAL SYSTEM, we give our own interpretations to different things. Could it be that the world is just a system waiting for us to put our own variables?


The mind of a 17th century person:

• The universe is rational. 

If it is not rational, there would be no predictability. So it would be futile to study it (like reading a book with scrambled letters).
"It is difficult to see how all pattern could be merely our fabrication. But could it be that human beings have come to attribute more importance to the pattern found in nature than nature does herself?".
Is rationality pattern, symmetry and predictability? We can see patterns because of our beliefs (Thinking Fast and Slow)

• Accessible universe

If God understands it, so do we.

• Contingency

"One cannot learn about the universe by thought and logic alone. Knowledge comes by observing and testing it."