[hanzoganz]

Originally Posted by David Maes Nature sometimes seem to behave mathematically. I don't know if it's true, but somewhere I heared some kind of group of animals would use kind of a prime number, which would mean that mathematics could be a part of nature. On the other hand we have Gödels incompleteness theorem; if you want to prove all basic propositions of mathematics in a mathematical way, then you get impossible solutions.

Gödel didn´t prove for impossible solutions. He proves that in a closed system there are always propositions that can´t be proven true or false without recurring to other propositions -axioms- from outside the system. This way, this propositions are called indecidible.

Originally Posted by David Maes But if it would be true... Nature kind of 'uses' mathematics, but on the other hand we somehow cannot prove the basic propositions. What does it mean?? Also mathematicians sometimes use software to prove their maths. The only problem is that some proofs are getting so complex that they just cannot get proven anymore. I mean the computer program proved it, but if some experts want to check out the prove, sometimes (even after years) they just cannot prove it because of the complexity of it. It may have an advantage also, making it more natural; if mathematician experts have intuitions, they might be more motivated to show their logics without computer proof.

Nature like math or math like nature? An eternal debate.
About computers: there are a lot of different kinds of math. The classical math, the analysis and other branches has to deal directly with proofs of theorems. this is done by hand. Now, there is simulation, where the computers come handy, specially to visualize the possibilities of a lot of calculations. But the computer doesn´t give the answers. It gives graphs that need to be interpreted. Bot ways, we need to use intuition.

[David Maes]

Originally Posted by hanzoganz Gödel didn´t prove for impossible solutions. He proves that in a closed system there are always propositions that can´t be proven true or false without recurring to other propositions -axioms- from outside the system. This way, this propositions are called indecidible.

Yep, seems a bit like complementarity and subjectivity; it makes me thinking about Gestaltpsychology also (think of 'two faces or one vase'; You can't perceive both of them at the same time.).

Can a logical system be a perceptive system?

[hanzoganz]

In the aristotelian sense, a statement can only be true or false, valid or invalid. In the modern sense of fuzzy logic, there are a lot of stages between cero and one. So yes, new logic systems can be thought as perceptive systems. This is what made possible the development of AI.

[harmonygirl]

I agree with you. sometimes the same facts give rise to entirely different notions of true/false, right/wrong. Interesting that AI should be birthed through a more perceptive system!

[baudrunner]

I see. Why didn't you say so?

The way to this knowledge is through the imbuence of extrallectual victual of the liquidic nature where you will find a new kind of math that will have you reeling, veritably staggering in the scope of its influence in which you will find that the ins and outs, not to mention the wheres and whyes of inductive reasoning and the muddle in the puddle where there is rain and reason and a new awakening to the conscious realization that the expression of the equation is not always equal to the pain of enlightenment, that space is the welcoming dearth of knowledge that you will then crave. Only then will you find the light at the end of the tunnel, where there is nothing but the fabric of evermore that neverwas, the backdrop of photonic enlightenment that represents the nothing that you will appreciate so much more for ever having been.

Then, you will wake up with a headache.

All you had to do was ask.

[hanzoganz]

The day you stop asking, you start dying.

And math doesn´t come by enlightenment but by a constant effort.
Anyways, I like the à la Isidore Ducase writting.
but this is math not poetry.
cheers

[Guille]

Originally Posted by hanzoganz The day you stop asking, you start dying. And math doesn´t come by enlightenment but by a constant effort.

I agree completelly with what you say here. Curioisity is the essence of human beings. And math is perseverance, not luck.