I absolutely love xkcd!

]]>Yes, random number generators are faced with problems such as repetition, predictability and so on. But I have a theory that is because if you can write it down it becomes static and true random is dynamic. Just a theory.

]]>krassi_holmz

I just heard that the Genius "Michael Faraday (1791-1867)"

Never hardly used any Math!

A.R.B

]]>Maths is not "invented" by a human.

It's somthing abstract, you can't feel it, touch it, but still "it's there"!

The signs and the equations are just one picture of the math, which the human created.

Mathematics is some kind of invariant. It's unchanged over the universe, it's abstract, and doesn't depend, for example of the length of plank (as in phisycs). It's a mental ocean of knowledges.

But I've ever asked some kind of weird questions : how far can math go? which are the boundaries of the abstraction? Can we do everything with it?

And the other question - what is the structure of mathematics? So far we're proving beautiful theorems in different fields of maths, but no one (with little exeptions) has fully understood a field - that is, to form some kind of intuition to answer some questions whitout proving them.

And another - what is the mathematics made from? And who controls it?

There are weird mathematical paradoxes too, which ;ie in the foundamentals. For example the Goedel's incompleteness theorem - that we can't have math that proves or disproves everything - that maths has limits.

Another interesting contemporary structures are so strange, that nothing can be proven about them at all.

I'll give you an exampe: the infinite random sequence.

Many paradoxes are connected with it. It's proven, that the mantissas of *almost every* real numbers are such random sequences. But in fact, such sequence is unconstructible! There's no example of truly random infinite sequence!

Another example, which is more fascinating, is the halting probability : the probability arbitary computer program to halt.

It is shown that this probability exist, and is between 0 and 1, but is *algoritmically unpreictible* - that is, we'll can never know what is, for example, its 100th digit!

Is the mathematics inconsistent? Nobody (with little exeptions) knows. And we can't be sure until we find a crack in it.

But after 30000 years evolution, we've still not understood the "mattery" of the mathematics - the language of the universe we live in.

If someone clearly states their assumptions/beliefs/axioms and then carries on from there to explain their new ideas, then there is no argument.

If, for example, you build up a theory that excludes zero, we are all keen to listen. But then someone may say "ah, but what happens when you subtract 1 from 1?", and you need to provide an answer that works within your new framework.

In fact, let us build up such a theory. In this theory I say that a number is the set {x,u} where x is a real number and u is an always unique infinitesimally small number. I could then say that it is impossible to subtract any two such numbers and achieve zero. But then you may discover some flaw in my theory that makes it impossible (which is likely). But if we discuss this back and forth we may end up creating a new and wonderful branch of mathematics! In fact ...

]]>That is very interesting, Ricky. Can I call maths is based upon several beliefs???

Yes, math is based upon a belief, or rather a series of beliefs. George, we have no other option, I certainly wish we did. If we start with nothing, then we can't do anything. Prove that an even plus an even number is even without using anything which comes from a belief.

What if I have a different belief-I don't shrine the maths religion?

That's the most wonderful thing about math! You *can* have entirely different beliefs. And if these beliefs turn out to work in solving problems which other mathematicians (or just people in general) are interested in, whether they be real or theoretical, you're beliefs will be accepted into math. If your beliefs yield no useful results, they probably won't.

Strangely enough though, I don't know from when the premises of maths has become irrefutable, unchangable of the maths system.

It isn't unchangeable, George. You can change it very easily. Simply come up with a new system which yields positive results, as math has done over the centuries.

Good luck!

]]>You're mixing math and physics/chemestry in a way which isn't defendable - please don't. Mathematics is, deliberately, a system which isn't based on the 'world'. The ancient Greeks invented the system with axioms, proofs, etc, because of the view on the world they had - greatly influenced by thinkers like Plato. Physics and chemistry are greatly dependable on math, but they're based on observations of the 'world'. Since math is not based on how the 'world' works, you can't prove something wrong in mathematics by using science.

On geology:

Geology is originated from the measuring trick of Egyptian officials-They need to remeasure and determin the segment line of farms after annual flood of the River Niles.

Ancient Greeks took over this trick and made further development, they derived premises and conclusions. But the premises were sure to be the right reflection of the nature at that time. Lines, triangles, and circles, to name a few. It was not until Euclid that all premises of geology was reduced to 4 axioms, leaving the other premises natural deductions of these four.

However, these four premises are intuitional, along with other hidden premises called defination.

At that time, due to lack of knowledge about the nature, the Ancient Greeks believed their premises are true reflection of the Nature, and they thus held it.

Several ancient Greek Philosophers (Including Zeno and Aristotle), did, seriously debated over the issue involving the defination of line, infinity, or other premises of geology.

Aristotle use several real world examples such as annual Olympic games, space, and "infinitely" divisible gold to support his "potential infinity" belief. He obviously assumed geology should be in accordance to the nature.

And in general, Ancient Greeks didn't give geology the privilage to enjoy some premises unnatural or irrational. In their view of academy, philosophy governs any other academics, and is the ultimate and correct understanding of the universe. This view is clearly illustrated by Aristotle's organization of his works.

Ancient Greeks, did, make a false assumption in another academy. They used to believe the thought was from the heart, but they altered to that from the brain after they gained enough knowledge of the human body.

I, therefore, have strong confidence in the Ancient Greeks in changing their premises in geology if they had got the chances to examine whether those premises are correct in nature.

Strangely enough though, I don't know from when the premises of maths has become irrefutable, unchangable of the maths system. Can I call the maths, the most logical and most rational major so far we human have, has an irrational and religious starting-point?

]]>If you have no axioms, then you can't do anything.

-That is very interesting, Ricky. Can I call maths is based upon several beliefs???

-What if I have a different belief-I don't shrine the maths religion?

George,Y wrote:Ricky wrote:What I have recently found increasing interesting is that you can prove that numbers exist. Once one accepts ZF set theory, and then defines the natural numbers, you can prove that the natural numbers do in fact exist. Then once you define addition, you can prove that addition exists. You can do exactly the same with multiplication and exponents. And then the same with the integers, rationals, and reals.

That could be circular logic, Ricky. For example, the premise is the set exists, after some certain deduction the number exists. The logic in the middle may be sound, but you should accept the premise first.

Not at all. That's exactly what an axiom is, George. Something taken to be true without proof.

If you have no axioms, then you can't do anything.

And this is why I like mathematics so much. It's a system, nothing more, nothing less. A system, albeit very advanced, based on some basic ideas - which we prefer to call axioms. If you met a person with no knowledge of mathematics at all, you could explain even the most complex things - by traceing them all the way back to the axioms of mathematics.

]]>Ricky wrote:What I have recently found increasing interesting is that you can prove that numbers exist. Once one accepts ZF set theory, and then defines the natural numbers, you can prove that the natural numbers do in fact exist. Then once you define addition, you can prove that addition exists. You can do exactly the same with multiplication and exponents. And then the same with the integers, rationals, and reals.

That could be circular logic, Ricky. For example, the premise is the set exists, after some certain deduction the number exists. The logic in the middle may be sound, but you should accept the premise first.

Not at all. That's exactly what an axiom is, George. Something taken to be true without proof.

If you have no axioms, then you can't do anything.

]]>pi man wrote:Anthony.R.Brown wrote:Another important point is!

Is it possible to fill a Glass with water 100% I think not! because water droplets are larger than air pockets,that Glass contains! so the answer must always be Only 99.99999....% possible!

But everyone knows 99.99999...% = 100%

Not me.

So far as I know, there is not a single material that is 99.999...% pure:

24K gold is 99.999999% pure,

Diamond can be even purer, but not with infinite 9's.And that is how my chemistry teacher told me:" strictly there is no material pure up to now".

You're mixing math and physics/chemestry in a way which isn't defendable - please don't. Mathematics is, deliberately, a system which isn't based on the 'world'. The ancient Greeks invented the system with axioms, proofs, etc, because of the view on the world they had - greatly influenced by thinkers like Plato. Physics and chemistry are greatly dependable on math, but they're based on observations of the 'world'. Since math is not based on how the 'world' works, you can't prove something wrong in mathematics by using science.

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