Maths question of the day

[northsomersetblade]

I've got 5 minutes, so go on then smart arse.

Where will the ball land?

Here:



The motion is in two dimensions into x and y components, and gravity acts only in the y component




.

 

[northsomersetblade]

I've got 5 minutes, so go on then smart arse.

Where will the ball land?

Or I could have just said

 

[Greasy Chap Butty]

I've got 5 minutes, so go on then smart arse.

Where will the ball land?

On top of a cloud?

 

[Greasy Chap Butty]

The "balls" will not be uniformly spherical, or the same weight. The fact that different numbers are carved into them will impact on weight & sphericalicity (made up word). It's negligible, but not exactly random. Go to extremes - one is a pea, one a golf ball, one a tennis ball, one a football, one a medicine ball & one is the moon. No way is that draw random....

The key being 'negligible' of course. I'd hazard a guess it affects it by one part in hundreds of millions.
To all intent and measurable purposes, random.

 

[Ball_Sup (Phil)]

The key being 'negligible' of course. I'd hazard a guess it affects it by one part in hundreds of millions.
To all intent and measurable purposes, random.

Yep. As I've said in this thread - random for all practical purposes

 

[Greasy Chap Butty]

Ok. I asked because I thought there was more to it than that.

There are quite a few really interesting probability and statistical "paradoxes", I thought I might be about to learn a new one.

Back to getting my head round Newcomb ;-)

You need to know about the 'buttered cat' paradox.
As we know, when a buttered slice of toast is dropped, Sods Law states it will always land butter side down.
When a cat is dropped, Law of Nature, states it will always land feet down.
So, if you smear a cats back with butter, and drop it, it will just spin mid-air indefinitely, as neither law can be broken.
Fact.

 

[Th!stledo]

You need to know about the 'buttered cat' paradox.
As we know, when a buttered slice of toast is dropped, Sods Law states it will always land butter side down.
When a cat is dropped, Law of Nature, states it will always land feet down.
So, if you smear a cats back with butter, and drop it, it will just spin mid-air indefinitely, as neither law can be broken.
Fact.

You will not have enough butter left to butter your toast.
Fact.

 

[Greasy Chap Butty]

You will not have enough butter left to butter your toast.
Fact.

False.
I hold the toast out towards the cat, and let the spinning cat smear it on. Eventually, all the butter from the cats back will be used up, breaking the paradox, and the cat will then fall safely to the floor on its feet.
Fact.

 

[Th!stledo]

False.
I hold the toast out towards the cat, and let the spinning cat smear it on. Eventually, all the butter from the cats back will be used up, breaking the paradox, and the cat will then fall safely to the floor on its feet.
Fact.

I can see you've given this a lot of thought and may even have a couple of degrees on the subject.
Just don't invite me around for buttered toast.

 

[SouthEssexBlade]

I think I might have once had buttered cat at a Chinese in Wakefield.

 

[I should coco]

False.
I hold the toast out towards the cat, and let the spinning cat smear it on. Eventually, all the butter from the cats back will be used up, breaking the paradox, and the cat will then fall safely to the floor on its feet.
Fact.

Fact!

9 out of 10 people prefer their toast without cat hairs on it.

 

[Sabella's Socks]

When a cat is dropped, Law of Nature, states it will always land feet down.

Funny you should mention this but...

Given it has nothing to work against, how does an upside-down cat in free fall manage to turn 180 degrees in mid-air and land on its feet.

 

[Th!stledo]

Funny you should mention this but...

Given it has nothing to work against, how does an upside-down cat in free fall manage to turn 180 degrees in mid-air and land on its feet.

Some geeky scientists would say it has the ability to move its body and shift its weight around to cause the effect, but I think it just has the ability to squirt a butter-like substance on its belly.

 

[Greasy Chap Butty]

Funny you should mention this but...

Given it has nothing to work against, how does an upside-down cat in free fall manage to turn 180 degrees in mid-air and land on its feet.

Basically, if a cat is dropped they almost always tend to land on their feet because they use the conservation of angular momentum to change their orientation. When a cat falls, as you would expect, its centre of mass follows a parabolic path. The cat falls with a definite angular momentum about an axis through the cat's centre of mass. When the cat is in the air, no net external torque acts on it about its centre of mass, so the angular momentum about the cats centre of mass cannot change. By pulling in its legs, the cat can considerably reduce it rotational inertia about the same axis and thus considerably increase its angular speed. Stretching out its legs increases its rotational inertia and thus slows the cat's angular speed. The conservation of angular momentum allows the cat to rotate its body and slow its rate of rotation enough so that it lands on its feet safely.

 

[Greasy Chap Butty]

Fact!

9 out of 10 people prefer their toast without cat hairs on it.

But, since this is a thread partly on statistics, as well as buttered cats, this shows that 1 in 10 of us prefer cat hair in our toast

 

[Greasy Chap Butty]

Some geeky scientists would say it has the ability to move its body and shift its weight around to cause the effect, but I think it just has the ability to squirt a butter-like substance on its belly.

I can do that, but that's another story

 

[Greasy Chap Butty]

Funny you should mention this but...

Given it has nothing to work against, how does an upside-down cat in free fall manage to turn 180 degrees in mid-air and land on its feet.

Actually, after you said this I had no idea either, since it hasn't got anything to push against, and my basic understanding of physics gets stuck. Luckily, this bloke and NASA (who both have way too much time and money on their hands) show how it's done

 

[Sabella's Socks]

Actually, after you said this I had no idea either, since it hasn't got anything to push against, and my basic understanding of physics gets stuck. Luckily, this bloke and NASA (who both have way too much time and money on their hands) show how it's done

This was the video I was thinking of

 

[Sabella's Socks]

When a cat falls, as you would expect, its centre of mass follows a parabolic path.

I think you'd have to throw* the cat to achieve this effect.

*Or ballistically launch

 

[PokerBlade]

Good idea. How are you measuring exact time, exactly? First peep of the whistle? Last peep? Perfection & exactness are the issues here. The difficulty is in order to get around the "fact" that drawing balls out of a bag is not perfectly random, you layer on more & more slightly inexact & slightly imperfect processes.

Problem solved.

 

[Ball_Sup (Phil)]

Problem solved.

Sigh.....

 

[Sabella's Socks]

Problem solved.

RFC 1149.5 specifies 4 as the standard IEEE-vetted random number.

;-)

 

[Sabella's Socks]

Sigh.....

IKR. There's no way that dice could have been random. See earlier in thread for details.

 

[PokerBlade]

Sigh.....

Well, I thought it was funny and sort of relevant.

Otherwise what you've said reduces to some kind of determinism and, while there's some arguments against that, I don't really want to get into that.

 

[Greasy Chap Butty]

IKR. There's no way that dice could have been random. See earlier in thread for details.

Are dice weighted to take account of the dots? If not, surely '1' being the heaviset side would be most likely to land face down, making '6' the most likely number to come up.

 

[Greasy Chap Butty]

RFC 1149.5 specifies 4 as the standard IEEE-vetted random number.

;-)

And 4.0000000000000 is the standard IEEE random float, also generated by a dice.

 

[Sabella's Socks]

Are dice weighted to take account of the dots? If not, surely '1' being the heaviset side would be most likely to land face down, making '6' the most likely number to come up.

Ask Ball_Sup (Phil). I'm sure he'd be delighted to go into the details (again)

 

[Greasy Chap Butty]

Ask Ball_Sup (Phil). I'm sure he'd be delighted to go into the details (again)

It was a semi serious question, I don't know how much more likely, but in a mega-bucks gambling industry, surely it would have an influence on millions of throws??

 

[BigBed]

Probably the same as the odds for a "new supporter", to get tickets to the Liverpool or Citeh games.

 

[PokerBlade]

It was a semi serious question, I don't know how much more likely, but in a mega-bucks gambling industry, surely it would have an influence on millions of throws??

Things only need to be good enough and when it comes to dice it's not that hard to achieve. Casino dice typically fill in the holes and use a different colour so that the weight distribution of the dice is as close to even as possible. I think mostly they use transparent or translucent dice as well so you can see they aren't weighted (although I've never actually been at a casino with an open craps table, it's more of an American game).

There are ways of biasing a dice roll by the thrower and what casinos that offer craps do is say that a legal roll has to be shaken in your hand and then bounced off a bumper on the table. That makes it so that it's close to impossible to force a roll.

And, as ever, the casino's ultimate defence is that if they suspect someone is cheating they'll stop you from playing.