Construction technics over time and 12000 miles apart.

There is great insight to be gained in why the paradox is a paradox and how the paradox works. Seeing why that particular paradox is a paradox, and what extra detail is needed to unravel that, is very significant for understanding your reality.

Ok lets think again, this is my take upon it, which is a slightly different to Aristotle but intrinsically the same.

The man & the tortoise and the man & the bus are two similar paradoxes, that use the same conjecture, i.e. that before you can travel the whole distance you must first have travelled halfway. Then before you can travel the rest of the distance you must next have travelled half way of the remainder to travel. This is represented by the series X=1/2+1/4+1/8+1/16+1/32 ...... etc. Each term being half of the preceding term. By simple inspection it can be seen that the series is infinite, and will never end.

There is a difference between them though in that one has two moving objects, and one has a fixed and a moving object. Lets examine the tortoise one first.

The tortoise starts off first and some time later the man starts off behind it. He sees where the tortoise is and travels half way to THAT point. When he gets there, he sees where the tortoise is NOW, which is a bit further on than he saw before. So he again travels half way of the distance. Using that logic he could get to within a millionth of an inch of the tortoise but never catch it. Of course in practice once he is that close, one stride and he is in front.

Now the bus. He sees where the bus is and travels half way to it. When he gets there, he then travels halfway of the remaining distance. and so on. Using that same logic he could get to within a millionth of an inch of the bus but not reach it. Of course in practice once he is that close, he just hops on the bus.

It all depends upon which question you ask! If you ask can the man ever reach the tortoise or bus, then the answer is no. If you were to ask

1. Could the man ever get close enough to the tortoise so that he could jump over it, then the answer is yes. At that point the infinite series stops, and a new event takes place.

2. Could the man ever get close enough to the bus that he could hop on it, the answer is yes. At that point the infinite series stops, and a new event takes place.

So how did Zeno manage to confuse us? Zeno's argument is based on the assumption that you can infinitely divide space (the race track) and time (how long it takes to run). By dividing the race track into an infinite number of pieces, Zeno's argument turned the race into an infinite number of steps that seemed as if they would never end. However, each step is decreasing, and so dividing space and therefore time into smaller and smaller pieces implies that the passage of time is 'slowing down' and can never reach the moment where Achilles passes the Tortoise. We know that time doesn't slow down in this way. The assumption that space (and time) is infinitely divisible is wrong.

Happy now? You owe me a beer :-)

There is great insight to be gained in why the paradox is a paradox and how the paradox works. Seeing why that particular paradox is a paradox, and what extra detail is needed to unravel that, is very significant for understanding your reality.

Ok lets think again, this is my take upon it, which is a slightly different to Aristotle but intrinsically the same.

The man & the tortoise and the man & the bus are two similar paradoxes, that use the same conjecture, i.e. that before you can travel the whole distance you must first have travelled halfway. Then before you can travel the rest of the distance you must next have travelled half way of the remainder to travel. This is represented by the series X=1/2+1/4+1/8+1/16+1/32 ...... etc. Each term being half of the preceding term. By simple inspection it can be seen that the series is infinite, and will never end.

There is a difference between them though in that one has two moving objects, and one has a fixed and a moving object. Lets examine the tortoise one first.

The tortoise starts off first and some time later the man starts off behind it. He sees where the tortoise is and travels half way to THAT point. When he gets there, he sees where the tortoise is NOW, which is a bit further on than he saw before. So he again travels half way of the distance. Using that logic he could get to within a millionth of an inch of the tortoise but never catch it. Of course in practice once he is that close, one stride and he is in front.

Now the bus. He sees where the bus is and travels half way to it. When he gets there, he then travels halfway of the remaining distance. and so on. Using that same logic he could get to within a millionth of an inch of the bus but not reach it. Of course in practice once he is that close, he just hops on the bus.

It all depends upon which question you ask! If you ask can the man ever reach the tortoise or bus, then the answer is no. If you were to ask

1. Could the man ever get close enough to the tortoise so that he could jump over it, then the answer is yes. At that point the infinite series stops, and a new event takes place.

2. Could the man ever get close enough to the bus that he could hop on it, the answer is yes. At that point the infinite series stops, and a new event takes place.

So how did Zeno manage to confuse us? Zeno's argument is based on the assumption that you can infinitely divide space (the race track) and time (how long it takes to run). By dividing the race track into an infinite number of pieces, Zeno's argument turned the race into an infinite number of steps that seemed as if they would never end. However, each step is decreasing, and so dividing space and therefore time into smaller and smaller pieces implies that the passage of time is 'slowing down' and can never reach the moment where Achilles passes the Tortoise. We know that time doesn't slow down in this way. The assumption that space (and time) is infinitely divisible is wrong.

Happy now? You owe me a beer :-)

Heck, once the man reaches less than the Heisenberg uncertainty distance for his wave function from the object, he is there. In this case he can and will reach each object.

And to get back onto some old real world constructions:


Stonehenge WASN'T built by ALIENS - Boffins' shock claim

Actually symbol of complex farm-subsidy deal

... "When Stonehenge was built, there was a growing island-wide culture - the same styles of houses, pottery and other material forms were used from Orkney to the south coast. This was very different to the regionalism of previous centuries," Prof Mike Parker Pearson from Sheffield Uni explained.

"Stonehenge itself was a massive undertaking, requiring the labour of thousands to move stones from as far away as west Wales, shaping them and erecting them. Just the work itself, requiring everyone literally to pull together, would have been an act of unification.”

The boffins reckon the eight stones stand for different groups of Britain's earliest farming communities, with some of them coming from southern England and some from west Wales. ...


Keep searchin',
Martin

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Stonehenge WASN'T built by ALIENS - Boffins' shock claim

Keep searchin',
Martin

That is indeed a good effort worthy of a beer, even if you didn't quite get there... :-(

Heck, once the man reaches less than the Heisenberg uncertainty distance for his wave function from the object, he is there. In this case he can and will reach each object.

So that one definitely gains a bonus beer!

In short, integration divides a calculation into infinitely thin steps, but you equally get infinitely many of them, so that you get an infinitely accurate addition of all the area under a plotted graph of whatever function.

That must be worth sharing some beer!

The boffins rejected popular theories that it was inspired by the Egyptians, built or inspired by aliens or the site of a druidic temple in favour of the warring farmer theory.

Stonehenge WASN'T built by ALIENS - Boffins' shock claim

Martin,
I'm just curious.

1. What do YOU think Stonehenge was built for?

2. Do YOU believe the interpretation of mainstream archaeology and Prof Mike Parker Pearson in that news article?

3. Do YOU think Aliens built Stonehenge? Or do you think it was built by primitive stone-age farmers?

4. Martin are the people who built Stonehenge YOUR ancestors? (I assume your British)

I want to know YOUR thoughts Martin, not what someone else said in some book. I don't want to hear quotes from academics. Tell me what your instinct tells you!

... Stonehenge

Still a bit confused here!!

Can the tortoise catch the bus?

The boffins rejected popular theories that it was inspired by the Egyptians, built or inspired by aliens or the site of a druidic temple in favour of the warring farmer theory.

Oh fer gawds sake, too many people are making too much fuss out of this continuing saga.

Fact 1 - Stonehenge was not built by, or inspired by aliens.

Fact 2 - No one knows for certain how it was built, or what it was built for, and probably never ever will do. There may be a link to the Druids and the Solstice, who knows.

Fact 3 - No one really cares one way or the other anyway. It is simply there for all to enjoy and to conjecture about. Keeps Wiltshire tourism going.

Fact 4 - Too many academics are chasing esoteric subjects to get their PhD's, and others trying to justify their academic positions.

Stonehenge

Keep searchin',
Martin

I've been to Stonehenge several times, the last time being about three years
ago. You do get the feeling that it was constructed purely for pagan/religious
reason. Buy my current thinking leans towards Stonehenge having been constructed
to mark an event. The event being that a small meteorite crashed into the ground here,
witnessed by the local people. They saw this as a sign coming from their
pagan God. So built this contraption, we call Stonehenge, around the meteorites
landing site to act as a place of homage.

I like the meteorite theory, its a good one! Nick i would consider your theory to be 100 times more plausable than what Prof Mike Parker Pearson says. Its a very reasonable theory Nick.

You were building my hopes up that my IQ had suddenly risen to 200.

But its wrong.

Oh well, perhaps I'ts sunk down to below 100 now...I must try harder!!

Sorry you're disappointed in me Johnney, I also must do better. I'm fairly happy that I know most likely how stonehenge was built i.e. upending stones into holes for the pillars with the tops flush with the ground, and then dragging the lintel stone over the top, then excavating around them. That theory works for me given it is dated to about 3000 BC. As to why it was built I'm open to suggestion. Pagan rites of some sort are the most likely, Druids and the solstice, are possible, as is also an ancient burial ground.

I visited it as a young lad in the 1960's before it was fenced off to the public, and did stand by them and touch the stones. Sorry to say I didn't get a sense of wonderment or awe from that. I drive past it regularly on the A303 to the West Country, perhaps I should stop one day and have another look.

Actually I find the Egyptian pyramids and their angled shafts aiming at certain star systems much more fascinating, but that's for another thread.