Datheron

I'm no math wizard, but this seems like rudimentary calculus; that is, of course, that 0/0 is a big no-no. On the other hand, what would happen if we put limits on both sides?

And BTW, I believe the other equation is invalid simply because sqrt(1) = +/-1.

FarSeeker

Ok, let's go over this again. Bill Snedden asked:
Soooo, I was using what SHOULD BE familiar physic's concepts to provide an analogy. Since you don't seem to be catching on, I'll just use my Sunday School analogy: the Triangle. The name means "three objects" (angles), but a triangle is a single object. Is that understandable?

Otherwise you have to get into higher dimensional math. And yes, it is a transformation, but so what? Dimensional transformations are what I am talking about You'll have to go back over the past couple of years of Discover magazines, but one issue covers knots and higher dimensional solutions to untying them. Find it and read it; then come back and we'll discuss it.

On the other hand, perhaps you simply didn't read my original post:
"2. How can a circle be a square?
3. How can a triangle be a circle?"
Not "how is", but "How can it be." The word game is what you are playing. But if you misunderstood, let me clairify.
2. How can a circle and a square be the same object?
3. How can a triangle and a circle be the same object?

When you project or "bring' a cone into a 2 dimensional realm, it can be either a circle or a triangle. A similar transformation occurs with a cylinder
(want to crash your mind? take a look at a hypersquare:
<a href="http://www.tux.org/~bagleyd/4d/TesseractDOC.html)." target="_blank">http://www.tux.org/~bagleyd/4d/TesseractDOC.html).</a> The Flatland story (it's on the web) can help you understand. The residence of Flatland could never see a circle, they would only perceive a circle of varying diameters. They would see cones as circles that could also be triangles, and cylinders would be squares that could also be circles.

1=2 because one object of higher dimension can be multiple objects in a lower number of dimensions. a 3D cylinder can be both a square and circle in a 2D realm.

1.) Electrons exist, that is not my assumption.
If you want to argue that QM is invalid, go the "Science & Skepticism" forum.

2.) A quantum particle is a discrete object. Consult linguistics and physics.

3.) A wave is a diffuse object. Drop a stone into a puddle. Look at a waveform on an oscilloscope.

If "it is obvious that it is certainly possible for a particle to be a wave," Please do so and solve one of the great QM mysteries of the =&gt;20th centuries.

Tercel

Way too long from the sounds of it!

I thought to understand what it isn't might help. After all you're not supposed to understand what it is - didn't you read the part about incomprehensibles?
Someone brought up things like particle-wave duality as an analogy and I agree. The trinity is simply a doctrine that we have because the evidence points to it. It isn't easy/is impossible to understand and I'd far prefer to be defending something simpler from an apologetics standpoint: but like particle-wave duality - stupid as the idea may sound it's what the evidence points to and no other theory sufficiently explains the evidence.

I didn't post it all! Only a bit more than half of it was relevant... the rest was mostly busy condemning to hell anyone who didn't agree with the thing. (Gotta love that age-old religious intolerence! )

Good idea! Only problem is that the Athanasian creed predates the inquisition by about 7 centuries. It is certainly a lot more boring than the Nicene and Apostles creeds: At least they've got content.
You know, when I first saw the Athanasian creed I thought it was heretical. Somehow my Sunday School teachers had managed to completely avoid the doctrine of the Trinity and supporting verses (Probably because no one taught it to them and they didn't understand it): I'd ended up an Arian by default and had thought that's what everyone was! Is it any wonder that there are so many people at this site who went to Sunday School and came out Atheists?

I'm not familiar with that example. I can guess though: 3 leaves on one clover?

I don't think you even need a context of "faith". Skepticism in our ability to determine complete truths is only reasonable... but unfortunately rather lacking - especially in fundamentalists and their so-called "skeptical" counterparts.
I think I would get on really well with the agnostics if I didn't happen to believe in God...

I think Christianity tends to come as a bundle. Say you convince someone with evidence - a good argument about the ressurection, or miracles in the Christian tradition, or testimonys of changed lives etc. As well as deducing something -say that the Christian God seems to exist- it's going to count as further evidence to support the entire truth of Christianity as a whole, and so the thing's going to snowball.

Hmm, I don't think a detailed explanation of the Trinity is at all necessary in explaining the Gospel:
"We all have turned away from God and done wrong things. We are not obedient to God and have gone our own way; God is Good and is one day going to destroy all evil completely; Since we do evil that would involve destroying us; But God LOVES US (Gotta have the caps there ); So God put part of himself into a human and became a man named Jesus Christ; Jesus lived his life in complete obedience to God, even accepting without a word of complaint, despite his innocence, a painful and humiliating death by Crucifixion at the hands of those he had come to help; Christ's perfectly obedient life puts humankind back into a right relation with God and undoes our rebellion; Thus anyone who will accept Christ's sacrifice for us and will allow themselves to be put right with God will be saved and avoiding destruction they will receive eternal life; As a proof of this promise God raised Christ from the dead two days latter to be seen by many; The risen Christ then ascended into heaven to begin to establish his rule over all the spiritual powers and authorities whom he will also return to faithfulness in God; To aid us he sent his Spirit to dwell in our hearts and to guide us in to truth and faithfulness to him."

See: the doctrine of the Trinity can be all but completely ignored. I would imagine there are plenty of dedicated Christians who have lived saintly lives but wouldn't have a clue about many doctrines: To a great extent discussing doctrine is merely an academic and intellectual exercise - and probably a hopeless and devisive one at that... just look at the Arminianism/Calvanism debate for example!

Tercel

Tercel

Foxhole Atheist,
So you realised that my maths was wrong? Really?

How strange... and here I was thinking that I'd finally proved that 1=3.

Tercel <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" /> <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />

Tercel

I would feel better if I could work out whether or not you meant that sarcastically...

Most probably in the 6th Century sometime.

Yeah there was a bit of debate over whether Jesus was half-man half-God or whether he was fully man and fully God. If memory serves me correctly I think the Church finally decided on the latter at one of the Ecumenical Church Councils in the 4th Century (Christianity being illegal prior to that made having large Church Councils rather difficult). However there is some argument that the decision owes something to political pressure from the Emperor Constantine. Just how much pressure is debateable - It certainly seems to me unlikely that people who are prepared to die for their beliefs (before Constantine became Emperor many Christians were killed for their beliefs - indeed apparently Constantine witnessed at least one such death in his childhood and was greatly impressed by the Christians faith) would be prepared to change very far no matter what the pressure.
I for one am inclined to wonder whether the decision actually matters: Although I suppose it provides a useful distinction between demigods like Hercules who are really no more than a unusually powerful human and Jesus actually "has the full content of the divine nature"...

Tercel

daemon

Triangle means three angles, not objects, and said angles are properties of the triangle. This is in no way the same as saying a circle is a square, and one of these must fail as an analogy.

Actually, what you asked was
At no time did you indicate transformation was any part of the question; you asked how two different geometric objects could be identical, and the answer is that they cannot. Is my left hand my spleen simply because both are part of me?

I see no relevance to higher dimensional mathematics to the questions you posed. You asked questions about 2-dimensional objects, and you got answers about 2-dimensional objects. If you had intended on referring to higher dimensional geometries, perhaps you should have stated that, but you did not.

Do you really think I didn't realize this? I understand perfectly about geometric cutsections, but this is not what you have asked.

I've seen (approximate ) tesseracts, and, yes, of course I've read Flatland. Have a copy at home, and read it years ago.

At no time is the cylinder a square or a circle; the 2-dimensional shapes are simply cross-sections of the 3-dimensional object. And, no, 1 does not equal 2.

Nope, not gonna bother, I observed far too many electron interactions in my engineering courses.
I find it amazing that you can ask such a bizarre question, and think this is such a great mystery, when you have already claimed to have solved it yourself! Is not an electron both particle and wave? I saw you say so yourself! Then, to continue and claim that it is an impossibility is laughably ludicrous! It quite obviously is the case that an electron exhibits both wave-like and particle-like behaviors, so just as obviously it is possible. If it were impossible, it would not be so, ne?

The more relevant question here is how it is, and that I cannot tell you.

[ January 30, 2002: Message edited by: daemon23 ]</p>

HRGruemm

This "mystery" ceased to be one over 40 years ago.

Only the concepts of "classical particle" and "classical wave" are mutually inconsistent. A quantum state is neither; but there are some situations where specific quantum states*) behave approximately like classical particles, and others where other quantum states+) behave approximately like a classical wave.

*) one-particle states
+) coherent states, e.g. photons in a laser

Regards,
HRG.

Photocrat

Yeah, that's what I figured you meant :]

Not that we couldn't bore a few people to tears... ;]

Foxhole Atheist

Well Tercel, when it comes to the trinity, you know, we have to be as exacting as we can be, don’t we? Other wise, it may spin off into 4, 5, 6, or who knows how many gods we may end up with?

HRG

And truer words were seldom spoken!

Just for the record: Cauchy sequences, Dedekind cuts *) etc. may be more elegant, but defining reals as infinite decimals (i.e. formal sequences of decimal digits) is perfectly OK. You just have to exclude those which have only a finite number of digits differing from 9.

What a real number is, should be left to everyone's private conjectures .....


Regards,
HRG.

*) i.e. topological resp. order completion of the rationals ..