Greg H.

Speaking in terms of pure probability, the idea that the world will suffer some kind of natural apocalypse is, indeed, well founded. Cataclysmic events have already happened to the planet at various times in it's history, and as the years roll by, the certainty of another one happening approaches 100%. In my personal opinion, we're overdue for one.

What is very much up in the air is exactly what will happen, and when. The Yellowstone super-volcano could erupt next week. Another K-T style extinction event could occur in a thousand years. Or a million. How much you worry about these events depends on your idea of long term planning, I suppose, and your own estimation of your chance of survival.

Christianity is based on the teachings of Christ. If a religious view is not based on the teachings of Christ, then it is not Christianity (and no, this is not a no true Scotsman assertion). I have little interest in what these people or those people did that formed your view of religion, you don't sound like the kind of person who would accept anything other than the source, so I am confused by the above. Masturbating is not seen as a religious act, but I'm sure you knew that already.

The real problem is that no one can seem to agree on what the "teachings of Christ" mean, and how they are interpreted. If the truth of these teachings is as self-evident as every Christian I know states ("just read them more deeply, you'll understand") why are there literally hundreds, if not thousands of Christian denominations scattered across the globe? Seems to me if they were that self-evident, we'd only need one church because there would only be one interpretation of the discussion and texts.

But that could just be me.

The Grand Design by Stephen Hawking and Leonard Mlodinow

I'll second that one, and add in A Brief History of Time by Hawking as well.

Evolution Isn't What it Used to Be: The Augmented Animal and the Whole Wired World by Walter Truett Anderson

The Dinosaur Heresies by Richard Bakker

Edit to add

A Shortcut Through Time: The Path to the Quantum Computer by George Johnson

My wife and I met online in a role playing game chat room. We've been married 11 and a half years, and have three wonderful children between the two of us.

Funnily enough that seems to run in my family. My cousin also met her husband in a chat room, and they later discovered they lived 15 minutes from each other. They started dating and have been married for 10 years.

If you consider ~[math]A\in A[/math] as an axiom then how would you prove whether [math]A\in B[/math] and [math]B\in A[/math] is true or false?

If we accept the axiom, no proof is needed. It's automatically false, because it would require a set to be an element of a subset of itself.

Consider the following (small) practical example.

Let us say that set A is the set of all counting numbers, and set B is the set of all counting numbers less than 10.

We can easily demonstrate that set B is a subset of set A. We can also just as easily see that there's no way set A can be a subset of set B, because it not only contains all of set B, but an infinite number of other members as well. I think (and this is just me thinking out loud - I don't have the chops to prove it) that in this case, if we should find a set A and a set B so that each are subsets of the other, they'd end up being the same set.

In the interest of full disclosure, I should point out that, according the sources I checked earlier (see my previous posts) there are set theories that do not obey this axiom - obviously the practical example I gave in my initial post in this thread demonstrates one. But we can also see that these kinds of sets lead to certain problems in practical application.

See also:

Set Theory

ZF Set Theory

Axiom of Regularity

I would build something more akin to a submarine, myself. Align the decks perpendicular to the axis of acceleration and spin the whole ship for gravity.

Considering it's currently on the front page of CNN (as alink to the Time website) it's probably being inundated with traffic.

If we were designed this way, I'd have to give serious thought about using the word intelligent to describe it.

If we accept that the the axiom of regularity doe not allow that,how do we then prove that.

 

I mean how do we prove that: ~[math]A\in A[/math]

As I said, by definition, you can't prove axioms. They are commonly accepted as being true without proof. If you have to prove it, it's not an axiom.

Edit:

Grammar failure.

But that isn't true, we can observe that because of the warping of the fabric of space that that isn't true. In fact, it's never true because wherever your trying to draw a straight line, there is gravity distorting the fabric of space.

And in a curved space-time plane, the Euclidean axioms would not hold true, but there would be other axioms used in their place. An axiom is only useful (and accepted as true) in the framework it's defined in.

Some other Euclidean postulates (from Wikipedia):

• A straight line may be extended to any finite length.
• A circle may be described with any given point as its center and any distance as its radius.
• All right angles are congruent.

I'm sure some of these would also fall by the way side in a non-Euclidean space, but when you're dealing with flat surfaces they all hold true.

I've never done any in depth set mathematics, but I'm pretty sure it's an accepted definition of set theory that you can not construct a set that contains itself.

A quick google search turned up this: Axiom of Regularity

By definition, you don't prove an axiom.

And it does make a kind of sense (not that "common sense" is always a reasonable way to prove things) in that if I define a set, say Car Parts. I would expect it to contain elements like transmission, engine, steering (all of which are, in turn sets themselves containing still smaller members). I would not expect to find, tacked onto the end of that list, the very car I was describing. As a practical example, when iterating over an active directory listing, bad things happen to your application when you find groups that are members of each other (which in turn makes them members of themselves). It leads to things like infinite loops, application server failure, arguments with your security team over why they are flaming morons, and having to code around their inability to grasp the obvious.

Not that I am bitter or anything.

The point of life is living it.

My suggestion would be to keep in mind that if both objects (the ball and the player) start moving at the same time (t=0) and arrive at the same place in the same amount of time (which you found in answer c), then the velocity they travel is dependent on the distance they need to cover to reach that point.

Why 'should' we assume that the physical universe has no cause? Everything within the physical universe requires a cause, so what's the rationale for making even a vague assumption that the universe does not? It's counter-intuitive.

Quantum mechanics is counter intuitive a lot of the time, but that doesn't mean it's wrong.

To quote one mentioned on this thread(by an atheist), "atheists just assert that a universe might be able to exist without a real causal agent."

 

That's not an atheist explanation of the universe - it's a vague generalization that says we cannot (or at least should not) make the assumption that a causal agent necessarily exists or is even necessary for the universe to exist. That statement, in and of itself, makes no attempt to explain how the universe came into being. The key word you seem to be overlooking, or ignoring, is might, implying that the question is still unanswered and awaiting evidence.

Actually, the other thing was the area of the quadrilateral being exactly equal to one-half the area of the triangle. Joat already answered it for me.

I like math, so I tend to nibble at ideas that seem interesting to me. This one came to me one afternoon when I was doodling during a conference call. I think I vaguely remember the term circumcentre from my geometry classes, but they were more years ago than I care to count. I may have to re-familiarize myself with the concept.

As a further exercise, supposing I once again have a right triangle, ABC, whose sides are of known lengths a & b.

Given the pythagorean theorem, it is possible that I can compute the area and circumference of the circumcircle (I went and read a bit on them) in the following manner:

[math]A = \pi r^2[/math]

[math]C = \pi d[/math]

Since we know that [math]a^2 + b^2 = c^2[/math] and for a right triangle, we know that the radius of the circumcircle equals exactly [math]\frac{1}{2} c[/math], we can say

[math]A = \pi\left(\frac{1}{2}\sqrt{a^2 + b^2} \right)^2 [/math]

and

[math]C = \pi\left(\sqrt{a^2 + b^2} \right)[/math]

Or am I talking out of my butt here?

It's not that they "should", it's that otherwise they don't have any real meaning otherwise, they have no real ground or actual basis to be acted upon.

I don't know that that is necessarily true.

For instance, I can very easily say "I won't steal because when people steal from me, I feel bad." The argument may appear logical, but it's based solidly on how I feel about the matter. I feel bad about being stolen from, and since I don't want to make other people feel bad I won't steal from them. There's certainly a logical order to that statement, but the premise (I feel bad) is an emotional reaction to a situation, not a logical one.

Since you declared the correction of your (apparent) spelling error to be not on topic, I can only assume you actually meant to discuss public trails.

On the topic of public trails by jury, I believe that local planning commissions are probably more appropriate in determining the routes and obtaining the necessary land grants for the establishment of public trails. That said, the greenbelt space dedicated to these public trails can increase property values since that area (presumably) won't be developed and offers a view of some kind. That may not always be true though.

And contrary to your statements in the OP, the point of a public trail is mostly just to have a nice place to go walk or bike.

Just because something is logical doesn't mean it's objective. If you make an ethical statement, it should have logic to back it up otherwise it is meaningless. Without logic, ethics is just a random spout of words that were the result of interpretations of the feelings perceived by the release of chemicals and nothing more.

I'll concede that ethical statements should have some logical premise. Unfortunately, "should" does not necessarily carry over into "does".

Logically, why does something have to be done just because of your emotions?

What does logic have to do with emotions? Emotions aren't logical. Logic can be used to override emotions (such as calming yourself down in a dangerous situation so you can make rational decisions), and emotions can certainly override logic. What makes you think they are connected in any way?

Thanks Joat. That more or less confirms the back of the napkins drawings I have been puzzling at for a few years. I was never more than a passing student of geometry (my brain, it seems, is not a fan of Euclid ), so I never had the knowledge needed to prove what seemed logical to me.

I appreciate the confirmation.

Yes it will. In fact they will fall on the mid point of AC. If you call the mid point of AC "O" then lines OA OB and OC are radii of a circle. You can work from there to prove your statement.

That's what I was hoping, actually. Following that line of reasons, the area of the quadrilateral bounded by AB, BC, and the two bisecting lines should be exactly half the area of the triangle ABC.

If we assign the values of a and b to AB and BC, then:

Area_ABC = 1/2ab

So the area of the quadrilateral would be

Area_quad = 1/2a * 1/2b = 1/4ab

Is this true for any triangle, or is it another of those special cases for right triangles?

This is a question that has been perplexing me for a number of years. Unfortunately, I don't have the experience with geometry to answer it myself, so I am hoping someone here can help.

Note: No this is not homework help - It's the basis for another idea that's been percolating around in my brain, which I may add to the end of the thread, assuming this turns out the way I expect.

Let us suppose we have a right triangle, ABC, with sides AB and BC, and hypotenuse AC.

If we draw one line that bisects and is perpendicular to AB and another that bisects and is perpendicular to BC, will the intersection of those lines fall exactly on AC?

I dont know how to indentify an irrational number except to say it is not a product of an integer fraction - including re-occurring such as 1/3

That's exactly what an irrational number is.

Your initial premise may be flawed.

You're assuming that there is some logical process that drives ethics, when the two conclusions may not even be related. If a man enters my home and points a gun at me, I can logically conclude that he means to do me harm. Now there may be other considerations to take into account, but we'll use the simplistic example for now. Ethically, it may be wrong to kill this man, but logically, if I intend to preserve my health and well being, I may have to, ethics or not.

If mosquitoes killed humans every time they bit one of us, then the logical course of action is to kill off the mosquitoes before we all die - it's an "us or them" kind of proposition. But it doesn't necessarily follow that what is logical is also ethical. Ethics has nothing (or at least very little) to do with survival.