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God Paradoxes

2

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  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    robindch wrote:
    Well, there are an endless list of things like cube-shaped spheres, blue-colored yellows and rational fundamentalists which are contradictions in terms, which is a poor man's logical impossibility. It's more fun to derive contradications from deity's stated attributes instead! Um, let me see...

    Omniscience: Is it impossible for him to know something which he does not know?

    Or, indeed:

    Can God know uncertainty?


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    robindch wrote:
    > Can God create a creature with free will, and yet still know in advance all
    > the choices they will ever make and things they will ever do?


    No. Even a mythic god must submit to logic occasionally. Either god is omniscient and knows what people will do (in which case free-will is an illusion and god is just playing a cruel joke with people's fate) or else god is not omniscient and free-will exists as advertized.

    Calvin came up with that one, as far as I remember, and had to create his own Reformed Church (one of the earlier ones) to manage the theological fallout.

    If I were to predict correctly, from my knowledge of a friend, where they were likely to be on a Friday night, do I thereby constrain their free will? No, and nor would perfect knowledge, which enabled perfect prediction, constrain free will.
    bonkey wrote:
    You can't have both. Its that simple. Either the knowledge pre-exists or it doesn't. If it pre-exists, then the decision is already made - its predetermined. If it doesn't exist, then by definition complete knowledge of everything is impossible.

    So either you can freely make a decision, or your choice can be known.

    Hmm. If we take a position outside time, so that all events can be viewed as if they were in the past, then the paradox disappears. From God's position outside time (no, I don't know where that is!), all your decisions have already been made - he has not constrained them by 'knowing them in advance'.

    It does make the idea of being punished by the "creator" for the free will actions he was perfectly capable of predicting at the moment of Creation rather a sick idea, though.

    cordially,
    Scofflaw


  • Closed Accounts Posts: 997 ✭✭✭Sapien


    An intelligence cannot have omnipotence and omniscience and free will. It can have any two, but not the third.

    This stands for omnipotence constrained by God's "nature".


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Scofflaw wrote:
    If I were to predict correctly, from my knowledge of a friend, where they were likely to be on a Friday night, do I thereby constrain their free will?

    No, because you are still capable of predicting incorrectly. You might be wrong, and you won't know for certain whether you are right or wrong until Friday night (at the earliest) when you find out if you were right.

    If, however, you were infallible, you could say this with certainty in advance . If you had omniscience, same deal.

    As it is, you can't. You can take a best guess, but thats it. I never said there's a paradox between God taking a best guess and us havnig free will. I said there's a paradox between God knowing in a non-fallible, 100% correct 100% of the time ominiscient sort of way where my friend will be Friday night.
    Hmm. If we take a position outside time, so that all events can be viewed as if they were in the past, then the paradox disappears.
    Except that once you do so, you accept that free will is only an illusion and all future events are already, in fact, pre-determined. It is only that they appear to be determined by free will because of the limited perspective of people within time.

    So, if you can take a position outside time and view these things, then free will is an illusion.
    From God's position outside time (no, I don't know where that is!), all your decisions have already been made - he has not constrained them by 'knowing them in advance'.
    Then from God's position outside time, I cannot freely choose to do something. There is no choice for me to make. The decision is already made.

    jc


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Sapien wrote:
    An intelligence cannot have omnipotence and omniscience and free will. It can have any two, but not the third.

    I disagree that omniscience and free will can co-exist. They are logical antitheses. The latter requires the outcome of a decision cannot be pre-determied with certainty in every case, and the former requires that it can.

    jc


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  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    bonkey wrote:
    Yes, thats the idea of free will. The idea of knownig everything says that God knows what our decision will be, even before we've made it.

    But as Scofflaw points out there is a difference between knowing the outcome of an event and effecting the outcome of an event.

    God knows if the coin toss is going to be heads or tails, but his knowing this doesn't make the coin land either heads or tails. The coin is still free to make what ever random (in a chaos theory sense) outcome it would do if God didn't know the outcome, or even if God didn't exist.

    Likewise God knows what we are about to do. But he doesn't influence what we are about to do. We still have to ability to make our own decisions, but God knows what decisions they will be. You can't surprise God (despite what the Bible may claim :p ) but that doesn't mean we don't have free will.

    Well that is how religious people have explained it to me, i don't believe in God, natch :cool:


  • Moderators, Society & Culture Moderators Posts: 24,420 Mod ✭✭✭✭robindch


    > If I were to predict correctly, from my knowledge of a friend, where they
    > were likely to be on a Friday night, do I thereby constrain their free will?


    Good point -- you're not. But then again, you're only guessing from past form that your friend will be there, and you don't know for sure whether (s)he will. If your friend will, without doubt, be there, then it's certainly arguable that your friend is not exercising free will and has become predictable!

    The problem with deity-based omniscience is that, in this case, the deity knows with absolute certainity where your friend will be. This limits the courses of action of your friend to one line, and one line only, which means that your friend has no choice but to do what's been pre-programmed. This is the opposite of free-will.

    The religious assertion that the deity "lives outside of space or time" is untenable in the absense of a proper definition of the phrase. As it stands, it makes no sense and seems to be used mostly as a handy escape hatch when intractable problems with religious logic arise. A bit like the "deity works in mysterious ways" statement :)


  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    bonkey wrote:
    Then from God's position outside time, I cannot freely choose to do something. There is no choice for me to make. The decision is already made.

    Oh ok, I got it now. I wasn't getting the decision is already made bit.

    You have to go all the way back to the start of the universe, and realise that if God sets everything off, and knows where everything will go, then the decisions we appear to make are wholly dependent on the choices God makes at the moment of creation, since everything leads from everything else in a completely predictable (to God at least) fashion.

    While we may believe we have free will, the decisions we make are simply a by product of the instant of creation. God sets the ball rolling, and knows exactly where the ball will roll.

    God knows the outcome of the coin toss, but his knowing doesn't effect if the coin falls heads or falls tails. BUT his decisions at the moment of creation do, because every point in time relates back to every other point in time, and God knows the linkage and its outcome since he made it. So the decisions God made at the moment of creation decide if the coin falls heads or tails, and it cannot do something other than what God know and decided it would do when he created the universe.

    You can have an onimpedent god and a being of freewill, but only if the being of freewill is independent of the god. If the god made the environment then how he made the environment will constrain the being.


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Wicknight wrote:
    But as Scofflaw points out there is a difference between knowing the outcome of an event and effecting the outcome of an event.
    Is there? God created everything that goes into said event, knows everything that will ever happen to each of those constituent factors, etc.

    What, exactly, other than God, has effected the event?
    God knows if the coin toss is going to be heads or tails, but his knowing this doesn't make the coin land either heads or tails.
    I never suggested it did.

    Lets leave aside that I was talking about what you call, nto what the coin lands on, and still consider the thing. If God knows what side teh coin will land on, then there is no decision to be made by anyone anywhere. The coin will land that side.

    What the coin thinks (were a coin capable of thought) cannot influence the outcome one whit. The outcome is predetermined. The coin will land heads because God knows the coin will land heads.
    The coin is still free to make what ever random (in a chaos theory sense) outcome it would do if God didn't know the outcome, or even if God didn't exist.
    It can't be random if someone knows the outcome!!! Thats the entire point! You can't have both - you cannot have a random event which can be predicted. Its a straight-up contradiction in terms.
    But he doesn't influence what we are about to do.
    He doesn't need to. I never said he did.

    What we are going to do is predetermined. There is no chance whatsoever that what we will do is not what an omniscient God already knows is going to be done.

    No chance whatsoever.



    You can't surprise God (despite what the Bible may claim :p ) but that doesn't mean we don't have free will.
    Unfortunately, it does mean that. We can believe we have free will, but its just an illusion because the decisions are pre-determined.

    We can believe that any event isn't pre-determined because we don't have access to the pre-determination...but that's not the same.

    Consider this....

    A guy builds what he believed was a game of chance. From every test he could think of, the results were random. From this guy's perspective the outcome is not predetermined.

    Someone playing this game of chance was able to spot something the designer didn't and was able to win every time. From this person's perspective, the outcome is predetermined.

    Now...is the outcome pre-determined or not? Even if the creator believes that its entirely random, is he right?

    Now swap that around....so that the creator knows the game is fixed, but he's the only one who knows. Everyone playing it is fooled into believing its a game of chance, where he knows that it isn't. Is it a game of chance?

    The notion of free will only exists when you look at the problem from teh perspective of one of the participants. We believe we have free will because we can't predict the outcome.

    Thats not objective. Objectively, we only have free will if the outcome cannot be predicted. A non-predictable outcome is incompatible with omniscience.
    Well that is how religious people have explained it to me,
    It doesn't make them right.

    Indeed, if you don't believe in a god, then you must already accept that their methods of reasoning are flawed...so why would you put weight behind their explanation when it relies on the same lines of reasoning?


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Wicknight wrote:
    Oh ok, I got it now. I wasn't getting the decision is already made bit.

    :)
    You have to go all the way back to the start of the universe, and realise that if God sets everything off, and knows where everything will go, then the decisions we appear to make are wholly dependent on the choices God makes at the moment of creation, since everything leads from everything else in a completely predictable (to God at least) fashion.

    Exactly.

    A deterministic system is only dependant on its initial parameters.
    A non-deterministic system precludes pre-determination and fore-knowledge.


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  • Closed Accounts Posts: 879 ✭✭✭UU


    Well, I think the whole concept of Supreme Being like in the Bible is quite an archaic and scary idea. He contradicts himself on numerous occasions. Surely, if there is a god, wouldn't he be perfect? After all, he gives humans 'free will' so that they can have a moral conscience to make choices - right or wrong. Yet, he punishes people for doing "bad" things he doesn't approve of! Why bother to give us 'free will' then if he isn't happy with our choices? Surely, God would embrace our choices and be happy that we are following the 'free will' he gave us regardless of the outcome?! :rolleyes:

    Also, I think that the idea of "God made man in his image" is false. Perhaps, it'd be more acceptable to claim that "Man made God is his image"? After all, the god of the Old Testament has got to be the most unpleasant character in all fiction - he's jealous and proud of it, petty, vindictive, unjust, unforgiving, racist, an ethnic cleanser urging his people on to acts of genocide. In many respects, he reminds me greatly of, dare I say, Hitler, Stalin, Sadam Hussain...... :(


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    UU wrote:
    Well, I think the whole concept of Supreme Being like in the Bible is quite an archaic and scary idea. He contradicts himself on numerous occasions. Surely, if there is a god, wouldn't he be perfect? After all, he gives humans 'free will' so that they can have a moral conscience to make choices - right or wrong. Yet, he punishes people for doing "bad" things he doesn't approve of! Why bother to give us 'free will' then if he isn't happy with our choices? Surely, God would embrace our choices and be happy that we are following the 'free will' he gave us regardless of the outcome?! :rolleyes:

    Yeah. It almost as if someone attributed some great powers to a believed-in deity, and since then has been "cobbling" answers together to cover over the inevitable cracks that their initial attrributions have led to.
    After all, the god of the Old Testament has got to be the most unpleasant character in all fiction - he's jealous and proud of it, petty, vindictive, unjust, unforgiving, racist, an ethnic cleanser urging his people on to acts of genocide.

    Reminds me a lot of Zeus. Looks like him too.

    jc


  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    bonkey wrote:
    Reminds me a lot of Zeus. Looks like him too.

    Bonkey you aren't implying that monotheist religions developed organically from older polytheist religions are you :eek:


  • Closed Accounts Posts: 879 ✭✭✭UU


    bonkey wrote:
    Reminds me a lot of Zeus. Looks like him too.

    jc
    Oh, yeah. Didn't you ever hear of the whole link between Roman paganism and Christianity? Let me explain.

    You see, when Emporer Constantine decided to christianise the Roman Empire, he needed to suit the needs of Pagans too. So basically, he turns the whole concept of a single deity into a "mental idol". And what would be a more perfect figure to use than Zeus? That is why, God has been regulary portrayed as an elderly man with a white beard and quite a powerful temper. That never reminded me of a "loving God" at all! Actually that was quite well explained in "Angles & Demons" by Dan Brown. Here:
    'Um . . . hold on,' Hitzrot ventured, sounding awake now. 'I know something Christian that's original. How about our image of God? Christian art never portrays God as a hawk sun god, or as an Aztec, or as anything weird. It always shows God as an old man with a white beard. So our image of God is original, right?'

    Langdon smiled. 'When the early Christians converts abandoned their former deities - pagan gods, Roman gods, Greek, sun, Mithraic, whatever - they asked the church what their new Christian God looked like. Wisely, the church chose the most feared, powerful . . . and familiar face in all of recorded history.'

    Hitzrot looked sceptical. 'An old man with a white, flowing beard?'

    Langdon pointed to a heirachy of ancient gods on the wall. At the top sat an old man with a white, flowing beard. 'Does Zeus look familiar?'

    The class ended right on cue.


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    bonkey wrote:
    The coin will land heads because God knows the coin will land heads.

    Hmm. No - the reverse - God knows the coin will land heads because the coin will land heads. God's knowledge is contingent on the actual outcome, not the reverse.

    God does not need the universe to be deterministic to know the outcome of the random events "in advance", because to God they are not "in advance" or in the past - they are all "now". He is neither predicting nor recording - he is experiencing, presently, all events ever.

    The same applies to free will. Every decision you have ever taken or ever will take is being experienced by God now, all at the same time. He does not know your decisions in advance, nor are your decisions made in advance, he only knows them as you make them - but to him, that is now. He is a panopticon, if you like.

    Anyway, that's enough of talking on behalf of a concept whose likelihood I consider vanishingly small...

    gnomically,
    Scofflaw


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Scofflaw wrote:
    The same applies to free will. Every decision you have ever taken or ever will take is being experienced by God now, all at the same time. He does not know your decisions in advance, nor are your decisions made in advance, he only knows them as you make them - but to him, that is now.
    So you're no longer saying that all events are in the past, you're saying all events are in the present. I had framed a lot of what I said based on your previous assertion that when we step outside time everything is effectively in the past.

    Allow me to readjust....

    Relative to God's perspective, there is no uncertainty. From God's perspective, our universe is devoid of time. There is nothing to seperate all events from each other. There is no before, during, or after. Its no different to us looking at a static image - there is nothing happening from our perspective, because for something to happen requires time to elapse and change to occur.

    From God's perspective, nothing is changing, and there is no time elapsing. Everything just is.

    So where, within all of this, is free will? There is no when in which we can make a choice. There is no scope for it relative to God's perspective. There is no before, during and after. There can be no choice.

    We may see ourselves as having free will, but God can't. There is nowhen for us to excercise it in. relative to his perspective.


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    bonkey wrote:
    So you're no longer saying that all events are in the past, you're saying all events are in the present. I had framed a lot of what I said based on your previous assertion that when we step outside time everything is effectively in the past.

    Allow me to readjust....

    Yes, my apologies - it was badly put, since, as you pointed out, it makes everything look predetermined. It was intended only as a way of visualising God's viewpoint.
    bonkey wrote:
    Relative to God's perspective, there is no uncertainty. From God's perspective, our universe is devoid of time. There is nothing to seperate all events from each other. There is no before, during, or after. Its no different to us looking at a static image - there is nothing happening from our perspective, because for something to happen requires time to elapse and change to occur.

    From God's perspective, nothing is changing, and there is no time elapsing. Everything just is.

    So where, within all of this, is free will? There is no when in which we can make a choice. There is no scope for it relative to God's perspective. There is no before, during and after. There can be no choice.

    We may see ourselves as having free will, but God can't. There is nowhen for us to excercise it in. relative to his perspective.

    Yes. I would agree with that.

    From God's perspective, free will is meaningless - the mechanism by which we take decisions is irrelevant. God knows what we are doing in every now at the same moment, and choice is effectively non-existent.

    From our perspective, however, we have free will - and within that perspective this is genuinely free will, because we move through time sequentially, and for us there is an after and before to every decision. We do not know what we will do until we have done it, and from our perspective what would have happened changes when we make decisions.

    As far as I am concerned, this resolves the apparent paradox, but makes it impossible for his creations to deserve punishment at his hands. The moment of creation, the moment of sin, and the moment of punishment are simultaneous from God's perspective - he creates, watches, and condemns each mortal at exactly the same "moment".

    cordially,
    Scofflaw


  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    Scofflaw wrote:
    From our perspective, however, we have free will - and within that perspective this is genuinely free will, because we move through time sequentially, and for us there is an after and before to every decision. We do not know what we will do until we have done it, and from our perspective what would have happened changes when we make decisions.

    There is until you realise that God set everything off in the first place.

    So while God might not influence directly your decision right now, your decision right now was already determined in the instant of creation, since everything from that point is predictable given the variables God set up in that instant. God decide what you will do, and everything you will ever do, 10 billion years ago.

    Scientists still ponder this idea even without God in it. Since everything started with the big bang, if you were able to simulate the big bang could you predict everything from the moment to the end of time?

    Is there really any true randomness in the universe, or is everything a result of predictable cause and effect going back to the inital varibles of the big bang?


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    Wicknight wrote:
    There is until you realise that God set everything off in the first place.

    So while God might not influence directly your decision right now, your decision right now was already determined in the instant of creation, since everything from that point is predictable given the variables God set up in that instant. God decide what you will do, and everything you will ever do, 10 billion years ago.

    Scientists still ponder this idea even without God in it. Since everything started with the big bang, if you were able to simulate the big bang could you predict everything from the moment to the end of time?

    Is there really any true randomness in the universe, or is everything a result of predictable cause and effect going back to the inital varibles of the big bang?

    Well, that's actually a separate question - whether the universe is deterministic or conatins any true (rather than apparent) randomness.

    In a deterministic universe, then all is determined, and there is no room for free will. That is the case whether or not we bring God into the question.

    However, the mechanism I have outlined, putting God outside time, allows God a perspective on even a completely random universe that still allows omniscience.

    cordially,
    Scofflaw


  • Registered Users, Registered Users 2 Posts: 15,443 ✭✭✭✭bonkey


    Wicknight wrote:
    Is there really any true randomness in the universe, or is everything a result of predictable cause and effect going back to the inital varibles of the big bang?

    Totally off-topic I know, but...

    Current thinking says quantum effects are non-deterministic.

    but...

    it is possibly that what we believe to be non-deterministic is, in actual fact, merely very, very complex and in accordance with well-defined rules we are as yet unaware of.

    In other words, the universe may be deterministic, but we don't know that it is. And even if it was, we almost certainly could never wield the computing power to determine it.
    squaddy wrote:
    As far as I am concerned, this resolves the apparent paradox,
    Maybe. Free will exists only from certain perspectives using this resolution. In other words, its not really free will...not objectively speaking...just something thats good enough to fool the necessary people into believing it is.

    So it doesn't remove the paradox, it says that the paradox ceases to exist as long as we refrain from looking at the problem objectively and limit ourselves to (the right) subjective points of view.

    Imagine if science ever declares that the universe is deterministic but that its complex enough that we can't ever carry out the determination. Do you believe the church would have no problem with this? Or would it not see it as being in conflict with our concept of free will....despite it being no different to how you've just removed the apparent contradiction!


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  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    Scofflaw wrote:
    Well, that's actually a separate question - whether the universe is deterministic or conatins any true (rather than apparent) randomness.

    In a deterministic universe, then all is determined, and there is no room for free will. That is the case whether or not we bring God into the question.

    No but if God exists the universe would have to be deterministic by its very nature of being created by God.

    Although I suppose that is another God paradox. Can God create a non-deterministic universe while still knowing everything that will happen and still being responsible for everything.

    This God idea seems awful silly.


  • Registered Users, Registered Users 2 Posts: 17,371 ✭✭✭✭Zillah


    Wicknight wrote:
    Although I suppose that is another God paradox. Can God create a non-deterministic universe while still knowing everything that will happen and still being responsible for everything.

    Y'know, I think thats the Christian answer... I can see one of them nodding and solemnly saying "...Yes."
    This God idea seems awful silly.

    It'll never catch on.


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    bonkey wrote:
    Totally off-topic I know, but...

    Current thinking says quantum effects are non-deterministic.

    but...

    it is possibly that what we believe to be non-deterministic is, in actual fact, merely very, very complex and in accordance with well-defined rules we are as yet unaware of.

    In other words, the universe may be deterministic, but we don't know that it is. And even if it was, we almost certainly could never wield the computing power to determine it.


    Maybe. Free will exists only from certain perspectives using this resolution. In other words, its not really free will...not objectively speaking...just something thats good enough to fool the necessary people into believing it is.

    So it doesn't remove the paradox, it says that the paradox ceases to exist as long as we refrain from looking at the problem objectively and limit ourselves to (the right) subjective points of view.

    Well, you could substitute "frame of reference" there for "perspective", which makes it sound a whole lot more respectable - admittedly without changing anything really...

    Is free will within your own frame of reference really free will when it does not appear so from another frame of reference? Hmm. Are you six foot tall when viewed from the frame of reference of someone travelling close to light speed? If not (Lorenz contraction), are you really six foot tall? Is it your own frame of reference that is important, or other people's?
    bonkey wrote:
    Imagine if science ever declares that the universe is deterministic but that its complex enough that we can't ever carry out the determination. Do you believe the church would have no problem with this? Or would it not see it as being in conflict with our concept of free will....despite it being no different to how you've just removed the apparent contradiction!

    Well, again that argues for an actually deterministic Universe, which, as I said, is not addressed by my resolution.

    It is perfectly possible (leaving aside God) that the Universe is sufficiently complex that it would be impossible to describe it in sufficient detail to predict it for any useful length of time - and it seem quite likely that this is so.

    In the absence of an omniscient deity, this would seem to me to be practically the same as a non-deterministic universe...

    cordially,
    Scofflaw


  • Registered Users, Registered Users 2 Posts: 23,283 ✭✭✭✭Scofflaw


    Wicknight wrote:
    No but if God exists the universe would have to be deterministic by its very nature of being created by God.

    Although I suppose that is another God paradox. Can God create a non-deterministic universe while still knowing everything that will happen and still being responsible for everything.

    Yes - or at least that's what I've been putting forward.
    Wicknight wrote:
    This God idea seems awful silly.

    And yes.

    cordially,
    Scofflaw


  • Registered Users, Registered Users 2 Posts: 3,579 ✭✭✭BopNiblets


    Oooh, I got one:
    What's gods motivation?


  • Registered Users, Registered Users 2 Posts: 17,371 ✭✭✭✭Zillah


    BopNiblets wrote:
    Oooh, I got one:
    What's gods motivation?

    Get his ego stroked.

    And thats not a paradox, its a question.


  • Moderators, Arts Moderators Posts: 10,518 Mod ✭✭✭✭5uspect


    All this talk of god being outside time and everything being deterministic reminds me of the whole 10 dimensional space string theory thing. I found this link good for trying to explain the idea to me. (Click the helix on the right to start).

    So is god a 10 dimensional being playing with us in this lab (or kindergarten)?


  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    5uspect wrote:
    All this talk of god being outside time and everything being deterministic reminds me of the whole 10 dimensional space string theory thing. I found this link good for trying to explain the idea to me. (Click the helix on the right to start).

    Wow, that is be far (by a long long way) the best introduction tutorial for 10 dimensional space I've ever seen

    Great link, must bookmark that.


  • Moderators, Arts Moderators Posts: 10,518 Mod ✭✭✭✭5uspect


    Yeah I stumbled on it a few days ago.
    ("stumble upon" it is perhaps the greatest way known to man to waste a day in front of your computer)


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  • Registered Users, Registered Users 2 Posts: 37,303 ✭✭✭✭the_syco


    pH wrote:
    Can he make a Euclidean triangle with all its internal angles not adding to 180?
    If he did, it'd be proberly called something other than a Euclidean triangle:p


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