Quantum Chaos Theory

[HawkeyeMD]

And more than 20 minutes to learn calculus...

Yes, but I suspect that he actually understood it.

 

[Yllanes]

I will see how cheep it is on amazon.
http://www.amazon.com/Mathematical-Foundations-Quantum-Mechanics-Mathematics/dp/0486435172
The Von Neumann book is too expensive, however this one looks cheep. About ten pounds.

I was not suggesting that you buy it. For one, it is much too advanced. But you can borrow it from a library. It is not a book to learn quantum mechanics, by the way.

 

[becomingagodo]

I was not suggesting that you buy it. For one, it is much too advanced. But you can borrow it from a library. It is not a book to learn quantum mechanics, by the way.

I'm not going to buy it.

 

[Complexity]

When I solve the Riemann Hypothesis, I will ba making the jokes then. The point is complexity must be doing something wrong, ten years and no proof.

Actually, BAGO, I think I'm doing something right. I've proven a theorem that is fundamental to the Riemann Hypothesis, but I'm not yet sure that this is sufficient to prove the Hypothesis.

In particular, I've proven that the probability that a square-free integer greater than 2 has an even number of prime factors is exactly 50%.

Each integer (>= 2 for our purposes) has a unique factorization into prime factors. The prime factorization of many integers contain two or more instances of the same prime factor (e.g. 8 = 2^3, 12 = 2^2 x 3). If the prime factorization of an integer does not contain more than one instance of any of its factors, it is said to be square-free.

To quote John Derbyshire, Prime Obsession - Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, paperback, p.323:

"To put it another way, it says that a square-free number is either a head or a tail [related to coin-toss analogy] - has either an even or an odd number of prime factors - with 50-50 probability. This does not seem particularly unlikely and might in fact be true. If you can prove that it is true, you will have proven the RH."

Derbyshire doesn't seem to believe that this result can be proven directly, so he states in private correspondence that the following must be proven [my rephrasing from his book]: According to Denjoy's Probablistic Interpretation of the Riemann Hypothesis, the RH is true if and only if the difference between the number of even prime factors and the number of odd prime factors in the sequence of square-free integers approximates the difference between the number of heads and tails in a sequence of fair coin tosses. By approximates, I mean that, for both sequences, the limit as N approaches infinity is the square root of ( N + epsilon ).

I've had my result for a few years - I've been letting it stew on a back burner, stirring it occasionally. I have a few choices - write it up and put it out there, understand how Denjoy's Probabilistic Interpretation hooks into the RH and determine whether what I have is enough, or carry out the proof that I've sketched out that would satisfy the requirements of the previous paragraph (potentially hellish). I'm planning on going with #2 for now, followed by #1 or #3 depending on how #2 turns out.

Also, rather exciting to me, I'm beginning to understand the structure of the M function, which is the accumulation of the Mobius mu function over the integers. This understanding would be essential for #3. [Not intended to make sense except for number theory and RH afficianados, but quite cool].

I really need to write up what I've got so far.

Ten years...

While working on the RH, I've also been working on Graph Isomorphism (almost there), k-Clique Exists (aiming at the P=?NP problem), Maximal Cliques, and Factoring. Once I nail Graph Isomorphism, I'll work in earnest on Subgraph Isomorphism.

I work on problems in turns, focusing on one until another becomes more interesting. At the moment, I want to finish up Graph Isomorphism and I want to work on the RH.

I have several years of a novel in my head that I need to get onto paper.

I've been in my first relationship and survived the death of my younger partner.

I've changed jobs several times, trying to find a good fit, been laid off twice, and financially stressed most of that time.

I've tried to be a good person, a good friend, and am learning to be somewhat kind to myself.

BAGO - Solving any of these problems would be a life's work and a life's joy. I've got more imagination than I can handle. What I lack is time.

If you think that taking years to work on the Riemann Hypothesis or any of these other problems (let alone all of them) indicates a lack of imagination or anything other than a lot of persistence, patience, and curiousity, you are an inexperienced jerk far to full of yourself to permit anything else in.

 

[fishkr]

Knowing very little about something is a very weak platform for formulating ideas about it.

But don't let that stop you, Mr. BAGO.

 

[Complexity]

You can learn calculus in twenty minautes, so what is possible in a week. Only god knows

Actually, you can't learn calculus in twenty minutes.

For the purposes of this discussion, let's assume that you've already learned algebra and trigonometry well.

The three-course sequence in calculus that I took in college used a text, Calculus and Analytic Geometry by Purcell (2nd), that contains 901 pages of text and hundreds of problems. That's 12 months of calculus classes meeting, if I recall, around 4 hours per week. I wasn't the best student during some of them, but I should have worked most if not all of those hundreds of problems. The best and, for most, the only way of learning calculus is to work problems until your fingers bleed.

Then there was the course in advanced calculus, in which we used Kaplan's Advanced Calculus (2nd). That book's about 700 pages long, though I know we didn't finish it. Many, many problems. Fingers must bleed.

Listing the topics for these courses would take me more than 20 minutes.

Once you make it through these courses, there are courses in real analysis, complex analysis, differential equations, linear algebra, ...

That still doesn't make you ready to study physics seriously. You'd also need courses in probability, statistics, and several more advanced math classes (e.g. tensors, differential geometry, topology, number theory).

So, in 20 minutes, you can learn that the instantaneous rate of change is called the derivative, the area under a curve is called an integral, and Calculus is Good (please forgive my oversimplification of an oversimplification).

How many problems did you work in that 20 minutes?

Paraphrasing Euclid, there is no royal road to mathematics.

If you want to become skilled at some aspect of mathematics, let alone become a mathematician, you're going to have to work your ass off like the rest of us. It will take years, not minutes.

 

[HawkeyeMD]

Actually, you can't learn calculus in twenty minutes.

Paraphrasing Euclid, there is no royal road to mathematics.

If you want to become skilled at some aspect of mathematics, let alone become a mathematician, you're going to have to work your ass off like the rest of us. It will take years, not minutes.

There, there. We know.

I am in no way a mathematician or a physicist. I took one semester of pre-calculus, one semester of calculus and one year of physics because it was required for my application to medical school. I took the non-calculus-based version of physics over the summer and made it through by the grace of unbelievably hard work, my electrical engineer dad and a PhD friend of my husband's who didn't mind getting emotional phone calls at two in the morning when I couldn't work out magnetism problems.

All I know is that I don't know much, but I do think it's all fascinating and I so appreciate people here who are patient enough to try and explain things to me in terms I might understand. If I try. Just a little.

What is really a shame about this guy is that with all the resources available to him, the best that he seems to be able to do is to reduce the goodwill of those who have really studied and worked at what he claims to want to know about, and who might otherwise help him.

Don't let it bother you.

 

[becomingagodo]

In particular, I've proven that the probability that a square-free integer greater than 2 has an even number of prime factors is exactly 50%.

I'm really skeptical, when are you planning to publish you're proof. As you must have made some errors in you're proof.
It seems everybody who is working on the Riemann Hypothesis thinks their near proving it.

 

[Complexity]

I'm really skeptical, when are you planning to publish you're proof. As you must have made some errors in you're proof.
It seems everybody who is working on the Riemann Hypothesis thinks their near proving it.

As I said, first I need to understand how Denjoy's Probabilistic Interpretation of the RH works, then determine whether proving the 50-50 result is the goal and proving the similarity to a sequence of coin tosses is merely a means to that goal. If so, I'm done; if not, I've got years of work left and the outcome is uncertain.

Good! You should be skeptical. I need to back up my assertions with proof.

It doesn't follow, however, that there must be some error in the proof of the result that I've claimed. It is straightforward and I've been able to persuade some mathematically inclined friends in a short time. I think it is correct. We'll only know when I publish it and it gets scrutinized.

As with many problems, the RH is like a mirage in the desert - its solution always seems to be just over the next hill.

 

[drkitten]

All I wanted to know is "Is the Riemann hypothesis going to be proven in the next few years using quantum chaos theory?"

Then why didn't you ask that?

What you actually asked was :

What the hell is even quantum chaos theory?
How does matrix machanics and non linear equation go together?
Isn't their serious problems with quantum mathematics?
Where will becomingagodo get his million dollars now?
Isn't quantum mechanics that stupid theory with the dead and alive cat?
Don't the idea of chaos, quantum mechanics and numbers contradict each other?
How can a number be chaotic or quantum, it makes no sense. Can someone explain?

It is a simple question.

it is indeed. But you didn't ask it. And from the tone of your posting, it's fairly clear that you wouldn't understand an answer (characteristing QM as "stupid," for example).

How does babies vision have anything to do with mathematics?

I assume that this is another "reasonable" question in disguise -- what you really want to ask is something like "what's the address of Wembley Stadium," or "do these trousers make me look fat," but you phrased it badly?

 

[drkitten]

Here's another example. Part of why you don't understand the implications of what you read is that you demonstrably don't understand what you read.

Here are two of your quotations:

In the book calculus made easy by Martin Gardner he said that they change the name from differential coefficent to derivative. I'm not saying your incorrect, as your not, however I under the impression from the calculus made easy book that they change derivative into differential coefficient and made differential coefficient mean something else.

Proberly, however doesn't having a cool name make mathematics better. Like how they change the differential coefficient to derivative.

Well... which is it? Did they change "differential coefficient" to "derivative," or did they change "derivative" to "differential coefficient"? That's not a minor detail -- that's the difference between turning bread into toast (which any fool can do) and turning toast into bread (which is impossible). You are describing two incompatible states of the world -- without even noticing the incompatibility. Clearly, what you read (in Martin Gardner or elsewhere), you didn't understand.

And now you're trying to extend your lack-of-understanding to new heights and new areas of speculation.

I suspect that if I bothered to pick up the relevant Gardner book, he would in fact have written nothing of the sort -- but you misinterpreted him. (Actually, I'd place a small side bet that you misremembered Gardner as the source, but that's largely irrelevant.) But in order to understand the implications of a theory, you first need to understand the theory itself. If you start out with the unshakable belief that whales are fish, then you're not going to understand why and how people are trying to fit them into mammalian taxonomy....

 

[Complexity]

All I wanted to know is "Is the Riemann hypothesis going to be proven in the next few years using quantum chaos theory?"

By the way, BAGO, how could you expect anyone to answer this question?

 

[Myriad]

God doesn't play dice.

Serious question: what makes people so sure of this?

Imagine that you're looking at an enormous machine, the size of a large building, full of intricate moving parts. Some parts look familiar, like gears and rotating shafts and wires and digital displays; others look strange, like floating blobs of jelly that spin and change color in unpredictable ways as smaller blobs bounce off them. You can tell that it would take years of study to understand the overall organization of the machine, and years more to understand any particular part of it in detail. Your tour guide then points out that what you're looking at isn't the whole machine, because it extends for miles underground; in fact, it's not even known how far underground it extends.

And over and over again, people look at this machine, and say: "I don't understand this machine, but one thing I know for sure, it doesn't ever go 'ping!'"

Note that in this analogy, the machine which could not possibly go 'ping' could represent God, or the physics of the universe, or both. In either case, the conclusion that it does not go 'ping' seems absurdly unjustified. The only difference is that if the machine is God, then it also has a big sign on it that says, "It is absolutely not possible for you to fully understand this machine." Which would seem to make it even more absurd to make sweeping statements about what it does and does not do.

But perhaps I'm missing something, and seeing an absurd conclusion where others perceive a simple observable fact. So, I'll ask the question: How do you know that God does not play dice?

Respectfully,
Myriad

 

[Jimbo07]

How do you know that God does not play dice?

Respectfully,
Myriad

becomingagodo seems to like to pick phrases from Einstein wall-posters. Given the experimentally verified probabilistic nature of QM (and assuming that God exists), God almost certainly plays dice with the universe...

 

[drkitten]

Serious question: what makes people so sure of this?

Elementary mathematics.

Ignorance plus stupidity yields confidence.

 

[Jimbo07]

Elementary mathematics.

Ignorance plus stupidity yields confidence.

Yer post be confusing to me... didst the 'elementary mathematics' quote mean to support the opposite position... or did you mean they be usin' numerology and arithmetic?

 

[drkitten]

Yer post be confusing to me... didst the 'elementary mathematics' quote mean to support the opposite position... or did you mean they be usin' numerology and arithmetic?

No, the "elementary mathematics" is the equation I presented

Let A be BAGO's ignorance.
Let B be BAGO's stupidity.
Let C be BAGO's confidence.

It really is as simple as A+B = C.

 

[Jimbo07]

No, the "elementary mathematics" is the equation I presented

Let A be BAGO's ignorance.
Let B be BAGO's stupidity.
Let C be BAGO's confidence.

It really is as simple as A+B = C.

Nurtz.

That means I misread your post. It can't be my fault. IT CAN'T!

can it?

 

[becomingagodo]

Well... which is it? Did they change "differential coefficient" to "derivative," or did they change "derivative" to "differential coefficient"? That's not a minor detail -- that's the difference between turning bread into toast (which any fool can do) and turning toast into bread (which is impossible). You are describing two incompatible states of the world -- without even noticing the incompatibility. Clearly, what you read (in Martin Gardner or elsewhere), you didn't understand.

2. I have let stand here Thompson's justified criticism of the term "differential coefficient," a term in use when he wrote this book. The term was later replaced by simpler word "derivative." Henceforth in this book it will be called a derivative.-M.G.

Page 49 of Calculus Made Easy by Silvanus P.Thompson and Martin Garner
Well, according to Martin Garner they did change the word. You should check you're facts. The moto of the book is "What one fool can do, another can."

So, I'll ask the question: How do you know that God does not play dice?

It was a joke, I don't believe in god.

If you want to become skilled at some aspect of mathematics, let alone become a mathematician, you're going to have to work your ass off like the rest of us. It will take years, not minutes.

It was a joke, I don't like calculus, however according to a book I have most calculus problems can be solved without calculus like how the fly train problem can be solved by a trick. Plus in the age of calculus computer programs do you really need to be that good at calculus as it looks like any one with a T4 calculator can solve calculus problems. A book by Ivan Niven's basically shows how you can solve calculus problems without calculus.

As with many problems, the RH is like a mirage in the desert - its solution always seems to be just over the next hill.

Their must be hundreds of mathematician working on the RH problem. They all can't be idiots.

Let A be BAGO's ignorance.
Let B be BAGO's stupidity.
Let C be BAGO's confidence.

It really is as simple as A+B = C.

Shouldn't it really be
A+B implies C
and C doesn't imply A+B
Because if that was true
C-A=B which would mean Confidence takeaway Ignorance eqauls Stupidity
How would taking away the ignorance out of a person make them stupid?

 

[Yllanes]

It was a joke, I don't like calculus, however according to a book I have most calculus problems can be solved without calculus like how the fly train problem can be solved by a trick. Plus in the age of calculus computer programs do you really need to be that good at calculus as it looks like any one with a T4 calculator can solve calculus problems. A book by Ivan Niven's basically shows how you can solve calculus problems without calculus.

Calculus problems go far beyond the fly and the trains (in fact, that one isn't even a calculus problem because you don't need calculus to solve it, as you say).

Calculus is elementary mathematics, don't you think it is some advanced, arcane technique that you can do without. Open any textbook at random (the best first year books are Spivak's and Apostol's) and tell me how to do the problems there without calculus.