That is a good example of evaluating the situation. In the same way that matter and energy interchange properties, time can be turned into space and space into time. We measure time by dividing the space into sections of events that make sense to us. Numbers, and their consequent fractions, help us to comprehend that the composition of time, as we know it, is based on a linear rate of change even that this could cause confusion on a large scale.
The mean lifetime is thus seen to be a simple “scaling time” if it decreases at a rate proportional to its value.
But, the problem involves the fact that the arrow’s flight is not necessarily a constant process of halve spaces, but and undetermined distance of midpoints in which time may or may not have a constant value of decay. On the other hand, Zeno’s paradox states that for motion to occur, an object must change the position which it occupies, and in an instant there is no motion or time.
So in order to solve the problem, the notion of infinity must be determined prior to any conclusion.
Quite right hence we us the mathematical notion of infinity that is a number that is unbounded and cannot be added multiplied or divided. Really it doesn’t exist, but as an abstract it is useful in placing limits on reality.
Well this thread wouldn’t exist if there wasn’t I’m all in favour of producing novel solutions, that’s what the language of philosophy and maths is for. Extraordinary philosopher he worked out how to derive the volume of a sphere by using the principles of integral calculus, had he been able to formalise it into general rules he would of been 2000 years before his time.
we can apply πr^2 (the area of a circle) to integral calculus rules 3 times and when we take account of the extension of dimensions into 3 we get the solution 4/3πr^2. any real shape can therefore be modelled by the use of integrals, and indeed even imaginary shapes that may or may nor exist but that are extended into a 4th axial dimension, can be modelled and so on. A sphere is also infinitely divisible into ever thinner slithers where at the limit of infinite its size is defined by π’s exact value. Although of course the result is an ever more accurate approximation as we more accurately define π’s solution. We have to admit that at the limit of infinity the sphere can be perfectly modelled as the error is increasingly small as it approaches the limit, there is no such thing as a perfect mathematical sphere, but it can be abstractly realised.
Interesting I suppose. But back to the subject: I’d like to ask - because I admit ignorance - what the original solution to Zeno’s paradox was (and who devised it)?
i posted a proof on the first page that even though you’re going half of the remaining distance infinitely many times, you’re still only going a finite distance.
Say,two celestial bodies are moving in the same linear direction through space. They are unhindered, the distance is infinite. Of the two stars [meteors, whatever] one is slightly ahead, but the one trailing overtakes half the distance between them every minute. Does it ever pass the leading star, by your model – or, rather, do you think it would never pass the other in/if reality?
the way you phrased the question, i think, does make it a bit different from the original paradox. the question it really brings up is is there a smallest unit of space? if space is infinitely divisible, then every minute he gets half the distance closer, and he could to that infinitely many times. if there is a smallest unit of space (which there may be - i don’t want any amateur ass holes coming in here saying they know for sure that space is continuous and infinitely divisible, because i’m 100% sure that you don’t know that), then there will be a time when the ships are only 1 unit apart. after 1 more minute…well, they can’t be half a unit apart if we’re already at the smallest unit.
Infinitesimally divisible, but again that would be a limit not a realised form. 1/infinity. You and by you I mean me and most people can’t even imagine dividing something into infinite parts, but you sure can grasp the implications of doing so.
Aristotle, yeah Aristotle was the dude with the first solution as far as is known, bless. Archimedes was the first rigorous mathematical solution so I suppose for a logically rigorous solution both of them got it right although I’d say Archimedes would of got extra points for formalising the maths.
You certainly did Kudos. It’s a more rigorously laid out method of the basic rules of calculus, dividing up graphs ad infinitum to realise a finite solution.
That’s what I meant by following in ‘logical order’ – at what point does th logical order of mathematics cease to express the logical order of reality?
I’m talking strictly about math representing reality, not theoretics.
Good question, at what point? At the point it fails to reflect reality. Then it’s not science it’s just abstraction, and it remains philosophy. A lot of science can fall afoul of the imagination, that’s no bad thing, it’s only bad when we start forgoing science and exploring maths in lieu of it, conjecture upon conjecture may serve the imagination well but does it reflect anything we can rigidly interpret?
I’m a great believer in maths being subservient to reality and experiment not the other way around. What sort of scientist would I be if I wasn’t, a string theorist?
what came first the maths or our ability to describe the world in terms of it, I’d argue against it being real and only being related by linguistic logic to it. It’s quite simple if it doesn’t reflect something we can actually perceive in our limited scope then it is not logical it is merely imaginary magic until it does, no matter how limited or advanced our scope, we have to accept that some things are beyond our comprehension at that time when they defy actual perception, to analogise we have to accept that a photon is both a wave and a particle, because we cannot directly measure it without upsetting its intrinsic nature. Like Bohr or Kant whom Bohr based much of his philosophy, that makes me an instrumental realist. If a tree falls in the woods and no one is around to hear it, does it make a sound? No, because sound needs an instrument to measure it, a sound is merely an interpretation based on our senses not indicative of the actual acoustic wave form, if you follow the analogy.
Well there’s Vodon and Voodoo science, sometimes its hard to tell the difference between the two religions without the scientific method slapping both of them.
