Things you always wanted to know the answer to [Vol. 5]

[basherX]

AstonZagato said:

I don't think you've grasped the proof.
Do you agree that, starting from 2 the first move is 1 and the next move is ½ and the next is ¼?
If you halve each value, it looks like the next value along (i.e. ½ and ¼). It is only ever missing the 1. So if you take half the total away, it always cancels out the exact same fraction in the series above leaving just the 1.

1 + ½ + ¼ + ? 
  - ½ - ¼ - ? 

I think I understand the proof. However doesn’t it rely upon infinity? And, in a time series rather than a mathematical proof I (genuinely) don’t know whether scientists work on the premise that time is infinite. Maybe that’s as much a philosophical question as a mathematical one. I was never very good at physics.

[Dr Jekyll]

basherX said:

AstonZagato said:

I don't think you've grasped the proof.
Do you agree that, starting from 2 the first move is 1 and the next move is ½ and the next is ¼?
If you halve each value, it looks like the next value along (i.e. ½ and ¼). It is only ever missing the 1. So if you take half the total away, it always cancels out the exact same fraction in the series above leaving just the 1.

1 + ½ + ¼ + ? 
  - ½ - ¼ - ? 

I think I understand the proof. However doesn’t it rely upon infinity? And, in a time series rather than a mathematical proof I (genuinely) don’t know whether scientists work on the premise that time is infinite. Maybe that’s as much a philosophical question as a mathematical one. I was never very good at physics.

I don't even understand the proof.
i appreciate that an infinite series can add up to a finite number, as in Achilles chasing the tortoise. What I don't see is how covering just half the distance to something can cause you to reach it. How far apart are they before the last move?

[Clockwork Cupcake]

Dr Jekyll said:

How far apart are they before the last move?

At what point are the two objects touching? When you can no longer get a razor blade between them? When you can no longer see a gap? When the electrons of the outermost atoms begin to repel? When the outermost atoms perturb each other? When deformation starts to occur?

It's all very silly really, as we know what the real world answer is.

As I previously mentioned, at what point is 1.999999999999' pints indistinguishable from 2 pints when measured to pub tolerances?

[AstonZagato]

basherX said:

AstonZagato said:

I don't think you've grasped the proof.
Do you agree that, starting from 2 the first move is 1 and the next move is ½ and the next is ¼?
If you halve each value, it looks like the next value along (i.e. ½ and ¼). It is only ever missing the 1. So if you take half the total away, it always cancels out the exact same fraction in the series above leaving just the 1.

1 + ½ + ¼ + ? 
  - ½ - ¼ - ? 

I think I understand the proof. However doesn’t it rely upon infinity? And, in a time series rather than a mathematical proof I (genuinely) don’t know whether scientists work on the premise that time is infinite. Maybe that’s as much a philosophical question as a mathematical one. I was never very good at physics.

Yes, it absolutely relies on infinity. If you can name a fraction that fits in either series, the the exact same fraction will exist in the infinite series. In a finite series, the same would not be true - you'd be short of one tiny fraction.

Also, it depends on the time taken for each step. If it the same time for each step (say 1 second per step), or is the speed constant (say 1m/sec)? If the former, then it takes an infinite time, if the latter then it would take two seconds to cover two meters. In the case of the former, then the universe would decay, etc.

Edited by AstonZagato on Friday 25th June 18:59

[glazbagun]

Say you were an Iraqi living in Iraq when the US invaded. If you had shares in Boeing, Lockheed Martin or General Electric, etc, could you still collect your dividend? What about Germans during WWII? Does the government you're at war with still honour gilts/bonds you've bought from them?

[Abbott]

LeadFarmer said:

Here's something I've pondered over for some time..

If two objects moved closer to each other by 50% say every 5 seconds (time isn't relevant) would they ever touch?

So if they were say 1m apart, then moved to 50 cm apart, then 25cm etc etc. Surely they would never touch, and would keep moving towards each other for ever?

Zeno's Dichotomy Paradox

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#A...

[Clockwork Cupcake]

Abbott said:

Zeno's Dichotomy Paradox

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#A...

Blimey, is there an echo in here?

[FiF]

gobuddygo said:

ambuletz said:

Do couriers hate this? I feel bad. but I think its quite ridiculous that you can't cancel something before it's been sent out, or even packed.

No they love it, we have a Hermes local lady courier, she loves the fact that my wife and step daughter order loads of clothing from Next and then return them, she gets paid twice.

I would suggest they only hate it under certain circumstances. Some years back my Mrs helped out one of her friends who was a courier and was going on a long holiday to USA, but had been let down at last minute by the arranged backup. My word, that was an eye opener.

The comment about being paid twice is correct, and it not being an issue is also correct, except when the state of the place you are collecting from is such that you really don't want anything from there in your vehicle and just touching the parcel makes you feel grubby. Some people are animals.

[The Mad Monk]

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

[FiF]

Clockwork Cupcake said:

Dr Jekyll said:

How far apart are they before the last move?

At what point are the two objects touching? When you can no longer get a razor blade between them? When you can no longer see a gap? When the electrons of the outermost atoms begin to repel? When the outermost atoms perturb each other? When deformation starts to occur?

It's all very silly really, as we know what the real world answer is.

As I previously mentioned, at what point is 1.999999999999' pints indistinguishable from 2 pints when measured to pub tolerances?

You can also get to the point where the electrons of the outermost atoms begin to mingle or share their orbits, thus you get two materials bonding together. You can get two dissimilar metals to form a true metallurgical bond.

In fact I've done it to solve issues where the service conditions are such that there is no one mono material which will serve the purpose, but two materials bonded together can make a product which has a good life. An example is composite boiler tube, the inside of the tube contains a water / steam mix which contains some chlorine, a suitable material is a terrific carbon alloy steel, economical to produce and fabricate. The outside environment are very high temperature corrosive combustion gases and ash which corrodes the tubes from the outside. You can't use mono stainless tubes as thry would fail rapidly due to stress corrosion cracking from the chlorides. Composite tubes with a carbon steel inner layer and high alloy stainless outer layer, metallurgically bonded so the through wall thermal transfer is still good provides long term solution. That's just one example, there are other more complicated applications.

[Abbott]

Clockwork Cupcake said:

Abbott said:

Zeno's Dichotomy Paradox

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#A...

Blimey, is there an echo in here?

apologies, note to self, dont post late at night after a couple of glasses.

[StevieBee]

The Mad Monk said:

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

Sort of.

Edgeware Road is the terminus so the trains stop there rather continue in a loop all day.

[Clockwork Cupcake]

Abbott said:

apologies, note to self, dont post late at night after a couple of glasses.

[talksthetorque]

Clockwork Cupcake said:

Abbott said:

apologies, note to self, dont post late at night after a couple of glasses.

Do you mean 1.99999… glasses?

[Lily the Pink]

The Mad Monk said:

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

I'm sure you used to be able to do that - am I imagining that or if not, when did it change ?

[Speed 3]

Lily the Pink said:

The Mad Monk said:

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

I'm sure you used to be able to do that - am I imagining that or if not, when did it change ?

2009 the circle was broken:

https://www.ltmuseum.co.uk/collections/stories/tra...

IIIRC it was when they upgraded the Overground and fully connected it to the Tube network

[nonsequitur]

The Mad Monk said:

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

You can but it is imperative to avoid Mornington Crescent. This includes the double back change at Bank ruling.

[The Mad Monk]

Speed 3 said:

Lily the Pink said:

The Mad Monk said:

London Underground Railway. The Circle line.

Can I get on a train on the Circle line and go round and round?

If not, why not?

I'm sure you used to be able to do that - am I imagining that or if not, when did it change ?

2009 the circle was broken:

https://www.ltmuseum.co.uk/collections/stories/tra...

IIIRC it was when they upgraded the Overground and fully connected it to the Tube network

If I get on at Edgware Road and go clockwise, what happens when I get back to Edgware Road?

I can see - I think - htat if I go anti-clockwise, when it gets back to Edgware Road it scuttles down the line to Hammersmith.

Is that right?

http://news.bbc.co.uk/1/hi/england/london/7926242....

[glazbagun]

Abbott said:

apologies, note to self, dont post late at night after a couple of glasses.

I wish my friends wanted to talk about Zeno's paradoxes when drunk!

[Dr Jekyll]

Abbott said:

LeadFarmer said:

Here's something I've pondered over for some time..

If two objects moved closer to each other by 50% say every 5 seconds (time isn't relevant) would they ever touch?

So if they were say 1m apart, then moved to 50 cm apart, then 25cm etc etc. Surely they would never touch, and would keep moving towards each other for ever?

Zeno's Dichotomy Paradox

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#A...

That's a slightly different situation. It's just saying that objects can eventually touch even though the distance to be covered can be expressed as as infinite sequence of 1/2 + 1/4 + 1/8 ..........

The question is about what happens if every 5 seconds (or whatever) half the remaining distance was covered, so the rate of approach keeps halving. How can there be a final 5 second move which brings the two into contact when every 5 second move explicitly doesn't cover the distance? Exactly how you define contact is irrelevant providing you are consistent.