What is heavier?

originally posted by: tridentblue
a reply to: AllIsOne

It makes for less trouble in the mind if you replace the word with "unlimited". The limit generally comes from somewhere else.

edit: If are a math guy who wants a way to look at this that fits your intuition that that the hammers should weigh more as I do, think of a 20 sided dice, with 10 red sides labelled 0-9 and 10 green sides labelled 0-9. To use it, you role it and write down the digit, and role again if it was green, or stop if you got a red digit.

How many outcomes can this dice produce using it that way? An infinite amount. The odds of a 100 digit number (get green sides 100 times in a row) are low, but possible. Even lower for 1000 or a billion digits, but still possible. Even though there are an infinite number of outcomes, there is still an *expected value*, which is the amount you would expect to get on average each round if you played this game and got the amount (in dollars) written down on the paper each time. Infinite sets in this way can have finite expected values. Multiplying that number times the "weight"/"payout" gives you a way to think of infinite sets in finite terms. Thinking this way is about seeing probability as fundamental.

Thanks for responding. You mean well, but now that I've read your post I'm even more confused … lol. I guess my brain is very limited ;-)

a reply to: AllIsOne

Now that i think about it , if this question were possible to answer , would not everything be filled by hammers and feathers the instant you started your experiment question thingy . So do not try this at home kids .

a reply to: AllIsOne

Nice counter, i blame a brain fart

originally posted by: AllIsOne
I seem to have a hard time with the abstract term "infinity". So here is my question. What is heavier: an infinite amount of feathers, or an infinite amount of hammers?

Mods: please move if in the wrong forum. I wasn't sure where to post.

I've just contacted a buddy who holds a PhD in math. I'll keep you posted …

How could you possibly weigh two things that are never ending? Would you need two scales that could weigh something like that? You would unfortunately get no results. Interesting question though. I could actually hear the wheels grinding in my head.

The answer is simple.

The question is invalid.

Infinity is not a number. It is a concept. You can not weigh a concept. You cannot use infinity in any equation.

Zero has two functions. It is a place holder in our numbering system and it is the concept of nothingness. You cannot use it in equations either.

Infinity and zero are ideas, you can't really use them. So many people, some with years of study, just don't get it.

P

If you fill up a 5 gallon bucket with feathers and another one with hammers , the hammers are more dense and will weigh more. Same would be the case if you could fill an infinite space with feathers or hammers.

originally posted by: AllIsOne
I seem to have a hard time with the abstract term "infinity". So here is my question. What is heavier: an infinite amount of feathers, or an infinite amount of hammers?

Right now, the the snow I have to shovel seems heavier than both.

a reply to: AllIsOne

Eh, we're all connected to the supreme spirit. It doesn't judge. If you're the sort of guy who loves numbers, you'll see what I'm talking about after time and inquiry. If you're the sort of guy who relates to the supreme through something else, like good acts, or writing or music or art, you'll come to unique enlightenment in your own way. One just has to find one's path. Finding one's own path is a million times more important than trying to understand what someone on a different path is trying to tell you.

Peace!
Me

originally posted by: pheonix358
The answer is simple.

The question is invalid.

Why?

Infinity is not a number. It is a concept. You can not weigh a concept.

Yes, that's why I'm trying to weigh hammers and feathers … ;-)

You cannot use infinity in any equation.

What is a singularity? Some solutions of the equations of the general theory of relativity allow for finite mass distributions of zero size, and thus infinite density.

Zero has two functions. It is a place holder in our numbering system and it is the concept of nothingness. You cannot use it in equations either.

Infinity and zero are ideas, you can't really use them. So many people, some with years of study, just don't get it.
P

Two other examples occur in inverse-square force laws of the gravitational force equation of Newtonian gravity and Coulomb's law of electrostatics. At r=0 these equations evaluate to infinities.

Source: en.wikipedia.org...

a reply to: AllIsOne

They are wrong.

You cannot use infinity in an equation. It is not a numerical value.

6 divided by zero is saying 'How many nothings are in 6' It is a stupid question.

I would even suggest you think about infinity over infinity. Most people will tell you the answer is 1.

But if you first look at 1 over infinity then the answer can be 0

Putting that into the first part then has infinity multiplied by nothing and that is nonsensical.

Most people can't get it at this level. They can only fall back on what they were taught by rote.

P

If infinity is a function of density then they have to be equal

originally posted by: pheonix358
a reply to: AllIsOne

They are wrong.

You cannot use infinity in an equation. It is not a numerical value.

6 divided by zero is saying 'How many nothings are in 6' It is a stupid question.

I would even suggest you think about infinity over infinity. Most people will tell you the answer is 1.

But if you first look at 1 over infinity then the answer can be 0

Putting that into the first part then has infinity multiplied by nothing and that is nonsensical.

Most people can't get it at this level. They can only fall back on what they were taught by rote.

P

Sorry, but I take Einstein's word (equations) over yours. ---> Mass distribution of zero size and infinite density.

a reply to: AllIsOne

That is your choice. He is wrong

I don't give a flying kick who he is. Wrong is wrong.

P

a reply to: AllIsOne Let me take a stab at this. Which is heavier a lb of hammers or a lb of feathers? It is a trick question of sorts. A lb of anything is still a lb. So comparing two object does not matter. They both weight a lb.

Infinite in your example = same

a reply to: pheonix358

Actually you can use infinity in an equation to mark infinity. It's not a number but it's still there.

Like zero, it has it's place.

Also, just because something is an idea doesn't mean that it can't be explored and thought about.

Right now, to our knowledge it's impossible to accelerate an object faster than the speed of light(or even get anywhere near it) But that didn't stop Einstein from imagining it which helped him come up with his special relativity.

Imagination is important even when dealing with ideas that aren't realistic in any sense.

Obviously an infinite number of feathers is not based on a realistic situation, therefore it will always be an idea.

However if you add one to infinity it will always be infinity, therefore the feathers and the hammers would weigh the same in an infinite space even if they might weigh more or less than one another when in a place that is finite because the added weight would mean nothing.

Ohh my head hurts now.

Time for more coffee.

originally posted by: pheonix358
a reply to: AllIsOne

That is your choice. He is wrong

I don't give a flying kick who he is. Wrong is wrong.

P

That's what the flat earth folks said …

originally posted by: Ceeker63
a reply to: AllIsOne Let me take a stab at this. Which is heavier a lb of hammers or a lb of feathers? It is a trick question of sorts. A lb of anything is still a lb. So comparing two object does not matter. They both weight a lb.

Infinite in your example = same

In my example "infinity" is not the fixed / predetermined value as 1 lb of anything is. I could also ask you to multiply 1 lb, or 1/2 lb by infinity. The gut feeling is that 1 lb will always be heavier (by infinite addition), but I think that infinity makes them equal.

I'm still waiting on my friend's answer. He's got a PhD in math. I could be totally wrong!

Thanks for your post.

originally posted by: OrphanApology
a reply to: pheonix358

Actually you can use infinity in an equation to mark infinity. It's not a number but it's still there.

Like zero, it has it's place.

Also, just because something is an idea doesn't mean that it can't be explored and thought about.

Right now, to our knowledge it's impossible to accelerate an object faster than the speed of light(or even get anywhere near it) But that didn't stop Einstein from imagining it which helped him come up with his special relativity.

Imagination is important even when dealing with ideas that aren't realistic in any sense.

Obviously an infinite number of feathers is not based on a realistic situation, therefore it will always be an idea.

However if you add one to infinity it will always be infinity, therefore the feathers and the hammers would weigh the same in an infinite space even if they might weigh more or less than one another when in a place that is finite because the added weight would mean nothing.

Ohh my head hurts now.

Time for more coffee.

That's exactly what I'm thinking. But there is a cognitive dissonance because my gut tells me that hammers will always (does always mean "infinite"???) be heavier than feathers when you multiply by the same amount which "infinity" is.

Yep, coffee :-)

a reply to: AllIsOne

Well no because infinity is not a number and doesn't behave like a number.

That's why if you add 1 to infinity you end up with infinity, if you take one away it is still infinity.

It doesn't behave like a normal number.

Therefore adding extra weight would mean nothing as both the hammer and the feather would= infinity

Hope that makes sense.