Math Is Fun Forum

Here is the paper.  I can't find the computation you claim.

Also, be careful George.  You need to assume an infinite amount of real numbers in order to calculate that integral

What are you talking about?  I gave you what I felt was his reason, and you rejected it without criticism.  We can't go anywhere until you provide a reason for your rejection.

Because it's not in the documentary you saw, it's not evidence?  You won't believe a man when he tells you what he believes?  Or is it only Richrad Dawkins?  Whatever, you previously stated "He believes in some form of Intelligent design, just not God," which has been shown to be completely unevidenced.  All he said is that it was possible.

You got your order all backwards.  If we start with the assumption that life was planted here from a different planet, then it would be expected that the two forms of life would be very similar.  How does panspermia represent a threat to biology at all?

I have explained in numerous ways, given examples, and all you do is say "no".  That isn't an argument.  Scientists tailor what they say all the time.  That you don't accept this is simply a denial of reality.  To imagine a scientist talking at a conference the same way they do at a public lecture is quite funny, when you think about it.

Darwin's thesis, his point, in the quote was that human sacrifice is a good thing.  You think that isn't clear from the two paragraphs?

What important points?

Alright, let's try this: Imagine I go to watch the documentary.  How will I know when I've reached the point where you think there is a quote mine?

Some corrects about statements involving Newton's method:

This is not true.  Quite clearly, the function has to be differential.  But of course I assume that was implied.  However more importantly, Newton's method will only work locally.  For the function

There is only one zero, at x = 0.  For x_0 < 0.5, Newton's method will converge.  For x_0 > 0.5, it will diverge to infinity.  For x_0 = 0.5, it will oscillate between 0.5 and -0.5, never converging.

The best you can say about Newton's method is the following: Converge is guaranteed if g is a differential function with continuous derivative, and x_0 is close enough to the zero, and the derivative at that point is nonzero.

This is how I think you want to define \tilde{f}:

Now it should be clear such a limit doesn't always exist, indeed would be quite rare for most functions.  I'm not sure what A is, you introduce it without saying anything about it.  Is that a recursive definition?  An infinitely recursively defined function is not well-defined.  Then you have the differential equation involving A which you solve, and this would seem to imply that the above is not the definition of A.  So what is it?

Next you assume that A has a zero.  But if A had a zero, then your work in solving the differential equation:

Would be entirely invalid!  You can't simply assume that A has a zero when your work requires you to divide by that zero.

As for your final identity, I don't know if I am reading the symbols correctly, but it doesn't seem to work for f(x) = x at the point x=1.

Rude?  How so?  Also you go from being rude to being a persecutor by just making an error?  By just being wrong?

Kronecker saw Cantor as making mathematics become about the unconstructible.  He believed that this would make mathematics entirely useless.

I can't fathom how you thought I was relating James Anderson to George Cantor.

Yes, Dawkins believes that it is possible that other intelligent life planted life on Earth.  How could this not be a possibility?  Dawkins however does not support this view, as he clearly states.  The evidence thus far for it is nil, which is why Dawkins does not support the view.  However, it is an idea which could one day, theoretically, become evidenced.

This has absolutely nothing to do with intelligent design.  Perhaps if you pretended you were in a vacuum, it might.  But we aren't in a vacuum.  Intelligent designers have given lectures saying "we don't know who the designer is" and then went back to their church where they said the designer is god.  Intelligent designers have made it their position that evolution is false and can't happen.  Because so many intelligent designers believe in such ideas, they have become associated with intelligent design.

I don't know how you can say this.  Dawkins merely said it was possible, and then later said he does not support the view of panspermia.  Where is you evidence for the above statement?  So far, you've presented none.

You're telling me that Dawkins should speak the say way to a room full of creationists that he does to a conference of biologists?  No, clearly not.  When speaking to one who is critical of your ideas, or simply doesn't understand them, you must be careful with your language.  You must try to use the most rigor you can, and put your ideas on solid logical ground.  When speaking to someone who you know understands you and is on board, one can be way more relaxed and sloppy.

Presentation of an idea can be very important.  Knowing your audience is step one in public speaking.  If you don't, you will most certainly fail.

Ah, the good ol' "It's a big number" argument.  Bobby, more is always better.  It doesn't matter how big your number is.  No matter how big something is, if you make it smaller, you are by definition limiting it.

Yes, if the court tells you do something and you don't do it, there can be consequences.  This is persecution?

Having laws about what can and can't be taught in public schools is persecution?  Please, show me how.

Such as?  Why do you continue to put forward assertions you know I will question without any evidence?

This isn't important at all, but your first sentence shows that you are misreading Dawin's quote.

He is separating out three people different types of people, the first being those who have a mental handicap (for which, "imbecile" is the proper word).  He is not calling the later two the first term.  But again, this isn't really important.  And I'm not sure what you mean by "The two paragraphs are not what they seem", since you don't seem like you want to explain that.  But I'm also not sure how that is relevant to the point being discussed: Ben Stein's honesty.  I'll try to state it plainly:

Ben Stein ended the quote prematurely, making it sound like Darwin thought humans shouldn't help one another.  A full reading of the quote shows that Darwin really thought the exact opposite: that our sacrifice for one another is noble.

Again, that's dishonest.

Check out number 4 in this link.  Yet another example of the dishonesty.

Think about dividing the square [0,1] x [0,1] into n^2 little blocks.  Then you want to only include those little blocks which contain some piece of delta.  Which are those going to be?  Now do this as n goes to infinity by taking an intersection.

Your quotes on Cantor were all about his ideas.  Is it wrong to call a charlatan a charlatan?  If your answer to this is no, then you are only upset at Kronecker because he turned out to be wrong.  Perhaps he was harsher than you thought he needed to be, but this is just a question of degree; i.e. shades of gray.

Yes, Dawkins thinks panspermia is a likely candidate for the origin of life on Earth.  But this does not make him believe in an "intelligent designer".  Surely you see the large gap.  By the way, your bias shows through here by putting, "intelligent" in front of panspermia.  Google only has 93 hits for such a term, and while it may make it seem like panspermia is close to intelligent design, in reality those concepts are in no way related (other than they both deal with origin of life).

The man was tried for the teaching of evolution, not believing it.  When you teach something you've been told you're not allowed to teach, you do deserve to be fired.

Accept others opinions?  Who the heck said I ever did that?  No, I read the facts.  The fact that they lied to the people who they interviewed.  The fact that I've seen Ben Stein talk about his movie, making the connection of evolution and Hitler when it's well known there isn't one.

You shouldn't make assumptions, bobby.

Are you trying to say something?

Two mathematicians does not make a persecution.  Besides, Cantor is a wonderful example of the exact opposite of your point.  While Cantor's idea were harshly criticized, in the end they were the right ideas and they won out.  Today they are regarded by most mathematicians as one of the most beautiful discoveries.  All ideas need to be criticized, the ones that survive are worth knowing.

I also challenge the claim that he was denied fame.  He was a well known and quite popular mathematician in his lifetime.  Perhaps one could argue he would have been more famous, but that's not what you claimed above.

Is this rhetorical?  The answer is well known, and it has nothing to do with him going "against the party line".

The "persecution" in Expelled is about scientists being fired for not achieving the minimum level of scientific research at their institutions. You keep claiming there is persecution, but refuse to give an example of anyone being fired because they believe in intelligent design.

The doc?

Which is?

I did some computational biology research for a summer, but it was working for a physicist/computer scientist.  Anyhow, I'm still not entirely sure what is making you upset at the article.  At first it seemed like people being forced out of science for going against the accepted theories, and now it seems to be because they think math may not be as useful as it once seemed.

They also seem to have a complete misunderstanding what math is.  To boil it down, it's any system of rules.  I find it impossible to imagine a science (or a universe!) that didn't rely on rules.

What is "that"?

Who has lost a job?

Anyone not using mathematics for technological developments will be left behind.  The problem will take care of itself.

You want to use Schwarz's lemma.

For T_0, you want to find an open set that contains a but does not contain b, where a is not equal to b.  Are you having problems with this?

For T_1, remember that the sets you wish to separate two points with need not be open.  In fact, because the cocountable topology is not Hausdorff, it is actually required that they are not open.  With T_1, all that is required is that their closures not intersect.  With this is mind, your life is made much easier if you choose closed sets.

Consider the function on the disk.  That R^2 is uncountable means that for some n, there is a limit point in the set {p : a_n = 0 in the power series about p}.  The nth derivative of f is therefore zero an each of these points.  Since there is an infinite amount of points in a compact set, there is a limit point.  This implies that the nth derivative of f is zero on the entire disk.  Therefore the nth derivative of f is zero everywhere giving that f is a polynomial.