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Interestingly, Pythagoras uses squares 'internally' but still produces a one-dimensional answer.
What actually makes the most sense is to align the co-ordinate system with the tangent and then it's clear that you are only moving in one direction.
I still think that you haven't really thought through what dimensions are all about.
Although the course, represented by the string, moves through three dimensions it only has length but no width or height.
I hear (read) what you are saying but, irrespective of the coordinate system you use, there are more options for where you can move to than exist on one dimension. You cannot give another person instructions about how to get from point A to point B without using three dimensions. If you just tell them to fly 20m, they can end up anywhere inside a sphere of 20m radius. That is why we have to use 'dimensions' and coordinates and why you can't ignore them.On the other hand, you can only tell someone that you will meet them in 6hours' time. Both your clocks will be going at the same rate - in one dimension.I have a feeling that I have lost your thread. What are you actually trying to say that goes against my two statements above?
The Catholic Church adopted the theory of Big Bang as a good proof of God existing.Now we have unity between Religion and Science.
Quote from: socratus on 15/10/2008 11:35:00The Catholic Church adopted the theory of Big Bang as a good proof of God existing.Now we have unity between Religion and Science. Socratus,Your belief in a higher power, in some ways, must be a great support to you (it isn't one I can share though). One thing I would ask though is don't confuse belief with scientific evidence - even if the church chooses to muddy the waters when they make such claims about 'proof'.Maybe when mankind has found a way to find common ground between all the differing religions, we can move onto science & religion...
Nevertheless though, regardless of how many spatial dimensions you plot in, as long as there's only a single time axis, the course will always be a line.
QuoteNevertheless though, regardless of how many spatial dimensions you plot in, as long as there's only a single time axis, the course will always be a line.That's not a valid conclusion at all. You could only insist that is the case in an infinitesimal time scale. If you are going in a curve you are definitely exploring two cartesian dimensions at the very least.I still think that, when you refer to a dimension, you mean something different from what I understand it to mean. The graphs you refer to simply show how one variable changes with another. They don't refer to how someone would 'experience' a journey. The slopes and curvatures tell you about displacements, velocities and accelerations so they give you an idea of what the journey would have been like - that's all.Two independent travellers would only bump into each other if ALL the coordinates were the same, at some point in the four dimensional graph - i.e. the lines / curves intersect somewhere /somewhen. You and I have probably walked past Piccadilly Tube station but on different days - so we didn't see each other.(I even wore a carnation, specially, so you would recognise me!) I certainly didn't travel in a straight line to get there and neither did you.
Har Har.I think I misunderstood your last post. Yes your path is a line - just not a straight one - and the line can involve variations in three spatial dimensions and a steady rate of progress in the t dimension / axis.The three spatial dimensions are necessary in order that you, I and everyone does not turn up at the same place all the time.
Yes; we're smeared out along the time axis by acceleration etc..