Who is an atheist?

Full story: The Sydney Morning Herald

In my last blog there was a moderately spectacular blue between various parties .

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“Think&Care”

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#9534
Aug 23, 2013
 
Bob of Quantum-Faith wrote:
Not according to my math gurus it ain't.
As it turns out? In math, it's possible to show that certain types of infinity are "more" than other types-- provably so (within math, of course).
So, at least according to math, an infinity of infinities is a greater infinity than just a singular infinity.
If that makes sense to you? No? Me neither, but my math superiors assure me that it does-- in **math**.
<grin>
First, let's look at what it means for two sets to the 'same size' as sets. One way (the standard way, in fact) to define this is that two sets have the same size if they can be paired off with each other: each element of one set corresponding to one element of the other set. We say the two sets have the same 'cardinality'.

So, for example, the set {1,2,3,4,5} can be paired off with the set {2,4,6,8,10} by pairing 1<->2, 2<->4, 3<->6, 4<->8, and 5<->10, so they have the same size as sets (five elemts each).

But when we apply thise definition to infinite sets, we can get some counter-intuitive results. For example, the set of positive integers {1,2,3,4,5,...} and the set of even integers {2,4,6,8,10,...} can be paired off in this way (as above), even though the second has 'more' things in it than the first. So these sets have the same cardinality even though the second is a proper subset of the first. This can only happen for infinite sets and is even sometimes used as the *definition* of infinite for sets.

Now, sets that can be paired with the set of positive integers {1,2,3,4,5,..} are called 'countably infinite'. But it turns out there are sets that are infinite and not countably infinite. The set of all decimal numbers is such a set. This set is an infinite set *larger* than the infinite set of positive integers. In fact, it turns out that there is an infinite heierarchy of 'sizes' of infinite sets.

Now, the collection of decimal numbers between 0 and 1 is infinite: examples are .1,.01,.001,.0001, etc. But the set is bounded. What is happening is a playoff between two different ideas of size: cardinality as above, and length. The interval between 0 and 1 is infinite in cardinality and finite in length. Because of things like this, it is crucial to be clear which of many different ideas of size are used in any given context.

Now, when we define addition and multiplication of infinite sizes, we generalize off the finite definitions. So, to add two infinite sizes, we take sets of those sizes that do not overlap and put them together. The sum of the sizes is the size of the resulting set. For multiplication, we have a copy of one of the sets for each element of the other, etc. I tturns out that addition and multiplcation of cardinalities is easy: the sum or product of two infinite cardinalities is just the larger of the two (so it will be infinite also).

“Think&Care”

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#9535
Aug 23, 2013
 
one cube parsec wrote:
<quoted text>
LOL
<quoted text>
<quoted text>
I thought infinity was defined as 'a concept of endless', so if you add endless number of entities to another endless number of entities, you still have endless number of entities.
So infinity + infinity = infinity
and infinity x infinity = infinity (adding repetitively)
So of course one set of endless objects may be more than another.(which is why infinity -infinity = UNDEFINED; and not 0)
But still always add up to endless yet again.
You have to be very careful about the concept of 'endless'. For example, the collection of decimal numbers between 0 and 1 inclusive has an infinite number of things, but has two ends and is of finite length.
Only space(3D) has infinite dimension ie endless like also a line(1D) or a plane(2D).
So one infinity can be more than the other, but still many universes will add up to one universe,(making many universes impossible)
[I take the position tentatively]
Well, technically, the dimension of 3D space is, well, 3. The *volume* is infinite. Again it is crucial to be very precise because there are different notions of size that can disagree. The length of a line is infinite, but the volume is zero (so is finite).

“Quantum Junctn: Use Both Lanes”

Since: Dec 06

Tulsa, Oklahoma USofA

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#9537
Aug 23, 2013
 
polymath257 wrote:
<quoted text>
First, let's look at what it means for two sets to the 'same size' as sets.
Thanks, Poly!

Fascinating, as always. And you manage to bring it down to normal earthling levels of comprehension.

Brilliant!

:)
spider

Ely, UK

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#9538
Aug 23, 2013
 
Bob of Quantum-Faith wrote:
<quoted text>
It can also address the deeply-rooted fear of **not** existing.
That's the deep-down **ape** gibbering at the idea that eventually everyone ceases to be.
So some soothing (if fake) balm for this condition in the form of empty promises of "life after death".
That's a lure that has wide appeal.
One I can well understand, even as I realize it's not a sustainable plea.
I hadn't considered the gibbering ape angle,, but it's a good point . Truth is they have nothing to worry about, all that lives and breaths has done so before in one form or another. Ashes to ashes, dust to dust , does have some merit as we are all recycled.

“Quantum Junctn: Use Both Lanes”

Since: Dec 06

Tulsa, Oklahoma USofA

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#9539
Aug 23, 2013
 
spider wrote:
<quoted text>
I hadn't considered the gibbering ape angle,, but it's a good point . Truth is they have nothing to worry about, all that lives and breaths has done so before in one form or another. Ashes to ashes, dust to dust , does have some merit as we are all recycled.
As one observer quipped?

We are made of star ashes, after all.

:)
spider

Ely, UK

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#9540
Aug 24, 2013
 
Bob of Quantum-Faith wrote:
<quoted text>
As one observer quipped?
We are made of star ashes, after all.
:)
Simple logical observations such as this, help to clarify the feelings of Deja vu as suffered by many folk. ;-) I have allways been around one way or anothert, no one will ever be truly rid of me, lol.
spider

Ely, UK

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#9541
Aug 24, 2013
 
Immortality in one form or another,,, kind of gives me a cosy glow :-)
one cube parsec

New Delhi, India

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#9542
Aug 24, 2013
 
polymath257 wrote:
<quoted text>
You have to be very careful about the concept of 'endless'. For example, the collection of decimal numbers between 0 and 1 inclusive has an infinite number of things, but has two ends and is of finite length.
Was I wrong somewhere?

Yes agree we got to be careful. What is important is WHAT is endless, lest we start confusing apples with oranges. Like the the numbers of different fractional no. between 0 and 1 would be endless, even as they have a lower and upper bound. Same as the infinite number of points on a line segment.

Also, a line segment 1 meter long has bounded finite length, but infinite number of points on it, length is finite, number of points is infinite.

Further, another line segment 2 meter long will also have infinite no. of points on it. But possiblly the longer line segment has more points on it, hence one infinity can be larger than the other.
Well, technically, the dimension of 3D space is, well, 3. The *volume* is infinite. Again it is crucial to be very precise because there are different notions of size that can disagree. The length of a line is infinite, but the volume is zero (so is finite).
Oops, did not mean number of dimensions is infinite, by infinite dimension I meant the lengths along the three axis are endless. My bad. 3D means 3 dimensions.

In apriori math, number of Dimensions CAN be infinite, all we got to doing is keep integrating from one onto the other. But in the universe as we know it, that is very meaningless beyond 3.(But I have some ideas on what the fourth dimension is (((hushhh, but it is not quite physical as we understand physical)))).

Hope I got things right?
one cube parsec

New Delhi, India

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#9543
Aug 24, 2013
 
Bob of Quantum-Faith wrote:
<quoted text>
As one observer quipped?
We are made of star ashes, after all.
:)
We are all stardust - Carl Sagan.
one cube parsec

New Delhi, India

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#9544
Aug 24, 2013
 
I just might have found the illusive quadruple integral!

“Quantum Junctn: Use Both Lanes”

Since: Dec 06

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#9546
Aug 24, 2013
 
spider wrote:
<quoted text>
Simple logical observations such as this, help to clarify the feelings of Deja vu as suffered by many folk. ;-) I have allways been around one way or anothert, no one will ever be truly rid of me, lol.
Indeed-- I just yawned (I so need some coffee), and there is a very good chance that some of the air molecules I exhaled once went in and out of Shakespeare's lungs...

:D

“Quantum Junctn: Use Both Lanes”

Since: Dec 06

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#9547
Aug 24, 2013
 
spider wrote:
Immortality in one form or another,,, kind of gives me a cosy glow :-)
We are stardust...

;)

“Quantum Junctn: Use Both Lanes”

Since: Dec 06

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#9548
Aug 24, 2013
 
one cube parsec wrote:
<quoted text>
We are all stardust - Carl Sagan.
:)

Yes... yes we are.
spider

Ely, UK

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#9549
Aug 24, 2013
 
Bob of Quantum-Faith wrote:
<quoted text>
Indeed-- I just yawned (I so need some coffee), and there is a very good chance that some of the air molecules I exhaled once went in and out of Shakespeare's lungs...
:D
Ohhh,,, not just shakespears lungs,, but many lungs, how about, anything that has ever lived or breathed .
As an aside,,, as I understand things the Bard never had the oppourtunity to sample coffee or tea, tut tut.
There is level of evidence to suggest that the man suffered from a degreee of plaguerism, not that it really matters,,, as people are often so easily taken in on other levels, which have far more importance on everyday life where truth is concerned.

“Think&Care”

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#9550
Aug 24, 2013
 

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Bob of Quantum-Faith wrote:
<quoted text>
As one observer quipped?
We are made of star ashes, after all.
:)
We are star dust,
We are golden,
We are billion year old carbon,
.....

“Think&Care”

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#9551
Aug 24, 2013
 
one cube parsec wrote:
<quoted text>
Was I wrong somewhere?
Yes agree we got to be careful. What is important is WHAT is endless, lest we start confusing apples with oranges. Like the the numbers of different fractional no. between 0 and 1 would be endless, even as they have a lower and upper bound. Same as the infinite number of points on a line segment.
Also, a line segment 1 meter long has bounded finite length, but infinite number of points on it, length is finite, number of points is infinite.
Further, another line segment 2 meter long will also have infinite no. of points on it. But possiblly the longer line segment has more points on it, hence one infinity can be larger than the other.
In actuality, the longer interval has the same cardinality as the shorter one, even thought they are of different lengths.
Oops, did not mean number of dimensions is infinite, by infinite dimension I meant the lengths along the three axis are endless. My bad. 3D means 3 dimensions.
Exactly. Different notions of 'size'.
In apriori math, number of Dimensions CAN be infinite, all we got to doing is keep integrating from one onto the other. But in the universe as we know it, that is very meaningless beyond 3.(But I have some ideas on what the fourth dimension is (((hushhh, but it is not quite physical as we understand physical)))).
It is now classic to let time be another dimension (whether it is the fourth or the first is a metter of convention). The problem comes in when doing general relativity when spacetime (the four dimensional geometry) is curved (like the two dimensional sphere is curved).
Hope I got things right?
Mostly.

“Think&Care”

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#9552
Aug 24, 2013
 
one cube parsec wrote:
I just might have found the illusive quadruple integral!
Nothing particularly elusive about it. It is just the integral in four dimensions. You can even do 'cylindrical' coordinates, where three coordinates are linear, a version of 'spherical' where two are linear, and another version of 'spherical' where only one is linear. There is even a double version of polar, two radii and two angles.

As you go up dimensions, it gets even more interesting!
spider

Ely, UK

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#9553
Aug 24, 2013
 
polymath257 wrote:
<quoted text>
Nothing particularly elusive about it. It is just the integral in four dimensions. You can even do 'cylindrical' coordinates, where three coordinates are linear, a version of 'spherical' where two are linear, and another version of 'spherical' where only one is linear. There is even a double version of polar, two radii and two angles.
As you go up dimensions, it gets even more interesting!
What would happen if you ran this through a Black hole??????????
one cube parsec

Delhi, India

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#9555
Aug 24, 2013
 
polymath257 wrote:
<quoted text>
In actuality, the longer interval has the same cardinality as the shorter one, even thought they are of different lengths.
Are you telling me that the set of points in a one meter line segment, and the set of points in a two meter line segment both have the same cardinality?

I don't think one can even say that about the sets of points in two different line segments BOTH one meter long! I do not think you can compare infinities like you can compare numbers. Can you?
It is now classic to let time be another dimension (whether it is the fourth or the first is a metter of convention). The problem comes in when doing general relativity when spacetime (the four dimensional geometry) is curved (like the two dimensional sphere is curved).
Agree one Dimension is not higher or lower than another.

I think integrating an 'n' dimension space is like sweeping it through the (n+1)th dimension. You can do it in math assuming the (n+1)th dimension exists, but in reality if that dimension does not exist, such math is just fiction. That is, you can only sweep a 2D plane thru 3D space, IF AND ONLY IF 3D space exists already, to get your 3D shape. Or you can sweep a point (0D) along any single (EXISTING) dimension (1D space) to get a line.

ALSO if you integrate a 2D object/shape along time, do you get Cinema!
AND if you integrate a 3D shape/object/matter thru time, do we get movement and 'real' physical EVENTS?

Do you think TIME is a pure physical entity? Or a purely logical one? That is:-exists only in our mind?, born from our sense of before and after, a side effect of our ability to store information and compare?

Finally, if a fourth spatial dimension exists, and there are beings that live in it, are we to them what a character in a movie is to us!
one cube parsec

Delhi, India

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#9556
Aug 24, 2013
 
polymath257 wrote:
<quoted text>
Nothing particularly elusive about it. It is just the integral in four dimensions. You can even do 'cylindrical' coordinates, where three coordinates are linear, a version of 'spherical' where two are linear, and another version of 'spherical' where only one is linear. There is even a double version of polar, two radii and two angles.
As you go up dimensions, it gets even more interesting!
I think the coordinate systems only help us study the various dimensions, and locate points in them, express shapes in them etc.

Unless I am wrong?

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