Infinity

[Vincent Murphy]

Does anyone know roughly know how close mathematicians
have got to figuring out the exact value of infinity?
I know they say it's impossible to work it out exactly
but can they say, for example, that it's definitely
between 0 and a billion billion (I assume it must be)?

[Ciotóg]

It's what you get when the digit 8 topples over.

[farel']

Infinity....Worth waiting for.

[PatMan]

.................... ..And Beyond!

[Vincent Murphy]

Nobody's taking this seriously. Fuck sake.

[Vincent Murphy]

a googleplex is the largest named number

What about a googleplex times infinity?

[AngelaMurphy]

Infinity = Boys oh Boys thread posts + 1

[i_hate_ire]

a googleplex is the largest named number
What wrong with Graham's number? I know its not a good name, but it deserves a mention.

[Johnnie Gilles]

Infinity = Number of minutes in Titanic

[hans aus dtschl]

its a reflection on how much of a nerd i am that i find this thread irritating.

[Vincent Murphy]

its a reflection on how much of a nerd i am that i find this thread irritating.

do you know the answer or not?

[The Black Knight]

Does anyone know roughly know how close mathematicians
have got to figuring out the exact value of infinity?
I know they say it's impossible to work it out exactly
but can they say, for example, that it's definitely
between 0 and a billion billion (I assume it must be)?

A billion billion is way too small.
More than that. There is no limit Im afraid. Not matter what number one comes up with there will always be some cunt that adds one to it just to piss off the other.

Of course if you really want to find out what infinity is then you have to apply boundaries, such as the universe. Then again what are you measuring? Metres squared? Centimetres? How many atoms in the universe? etc, but the universe is continuing to expand. No one knows when it will stop expanding but when it does it will begin to shrink and take us with it. Maybe at this point in time we can calculate infinity. This will only happen if we have no space travel, don't destroy ourselves and the earth and aliens don't come to enslave and eat us. Yep Scotty, alot stands in the way of mathematicians and their value for a lop sided 8.

[AngelaMurphy]

A billion billion is way too small.


A billion billion + 1?

[i_hate_ire]

Its actually, a fair bit smaller than transfinity. Dam you Cantor.

[hans aus dtschl]

nice one the black knight.


the whole point of infinity is that it can never be counted.


asking how big it is is a circular question.

very much a head-fuck for a person with a mathematical mind.


here's another one thats a headfuck for someone with a mathematical mind-

if you were to (theoretically) have a hollow tube through the centre of the earth, directly through the centre, and out to the opposite side, what would happen if you jumped in (neglecting windage)

[AngelaMurphy]

nice one the black knight.


the whole point of infinity is that it can never be counted.


asking how big it is is a circular question.

very much a head-fuck for a person with a mathematical mind.


here's another one thats a headfuck for someone with a mathematical mind-

if you were to (theoretically) have a hollow tube through the centre of the earth, directly through the centre, and out to the opposite side, what would happen if you jumped in (neglecting windage)

Depends where you jumped in, but I reckon you'd end up in Australia.

[Ciotóg]

It's the number of orange molecules you get in a full glass of diluted Kia-Ora.

[The Black Knight]

A billion billion + 1?

Just about covers the surface area of your tits.

[hans aus dtschl]

Depends where you jumped in, but I reckon you'd end up in Australia.


how, angela?

think harder.

[i_hate_ire]

nice one the black knight.


the whole point of infinity is that it can never be counted.


asking how big it is is a circular question.

very much a head-fuck for a person with a mathematical mind.


here's another one thats a headfuck for someone with a mathematical mind-

if you were to (theoretically) have a hollow tube through the centre of the earth, directly through the centre, and out to the opposite side, what would happen if you jumped in (neglecting windage)


You would fall to the center and swing around for a while (in some sort of aproximation to Hooke's law. You would eventually come to rest in the center. The interesting thing here would be the pressures involved, which I believe would increase as you got closer to the center, but would be nil at the center.

[Presentation Brother]

nice one the black knight.


the whole point of infinity is that it can never be counted.


asking how big it is is a circular question.

very much a head-fuck for a person with a mathematical mind.


here's another one thats a headfuck for someone with a mathematical mind-

if you were to (theoretically) have a hollow tube through the centre of the earth, directly through the centre, and out to the opposite side, what would happen if you jumped in (neglecting windage)

You'd execute simple harmonic motion in the tunnel, going from one end to the other. Leaving cert applied math biy.

[hans aus dtschl]

indeed.


fantastic concept.




kept the lads at our house entertained for hours!


i'll leave you fellas argue, and stick two fingers up at the original thread starter-there's more than one way to wreck a head!

[i_hate_ire]

Not quite as far out there as infinity, is it?

[hans aus dtschl]

You'd execute simple harmonic motion in the tunnel, going from one end to the other. Leaving cert applied math biy.


perpetual motion?

[Presentation Brother]

perpetual motion?

Conservation of energy.

[AngelaMurphy]

indeed.


fantastic concept.




kept the lads at our house entertained for hours!


i'll leave you fellas argue, and stick two fingers up at the original thread starter-there's more than one way to wreck a head!


I don't know. I know a guy who reckons he's done it. Galvin. Although he did do it the other way around (from Australia to Ireland) so maybe it's different depending on where you start.

[i_hate_ire]

perpetual motion?
You shall not break the laws of thermo dynamics in this house. Shit, did anyone see my light inextensible string?

[hans aus dtschl]

Conservation of energy.

valid-neglecting windage, i did say, after all.


but what about air pressure on either side, due to atmospheric effects?

[Presentation Brother]

valid-neglecting windage, i did say, after all.


but what about air pressure on either side, due to atmospheric effects?

Dunno. Ask Cyrill.

[hans aus dtschl]

haha

a house of six engineers, we gave up on it. decided a beer would be the only logical answer.

[The Black Knight]

I suppose there is a point of zero gravity within the earths core. Never thought of this before but I would assume you would eventually reach a point where both ways are up and maybe there is a point of zero gravity.

Of course there could be a union between the two gravities in which case your body is being pulled either way by gravity. I imagine this would create a big strain on internal organs such as the heart and lungs.

Damn you hans. I wonder if anyone knows the real answer to this. I must find out!

[AngelaMurphy]

I suppose there is a point of zero gravity within the earths core. Never thought of this before but I would assume you would eventually reach a point where both ways are up and maybe there is a point of zero gravity.

Of course there could be a union between the two gravities in which case your body is being pulled either way by gravity. I imagine this would create a big strain on internal organs such as the heart and lungs.

Damn you hans. I wonder if anyone knows the real answer to this. I must find out!

only one way to find out Knighty, start digging!

bagsy me first go on the slide though!

[Vincent Murphy]

I don't know any of these words.

[i_hate_ire]

Iain M Banks uses this in The Algebraist. Except there it is someone wearing a pressure suit in the center of a liquid planet. Quite cool actually.

[AngelaMurphy]

I don't know any of these words.

look what you've started Vince

[The Black Knight]

Of course another possibility is that one pull gets stronger as the other gets weaker. When you throw yourself through the hole, you eventually reach terminal velocity then once the other gravitational pull gets weaker you begin to fall the other way and keep going back and forth like in a game of ping poing forever, or infinity as some might say.

[hans aus dtschl]

sorry black knight.


its actually my favourite riddle at the moment.


if anyone does get a (internationally accepted) answer to this (or a variant of this) puzzle, do PM me, in case i miss it on here...

[Presentation Brother]

People, this is leaving cert applied maths. I already gave you the answer: it undergoes simple harmonic motion. The problem is identical to that of the motion of a simple pendulum.

There is no great mystery here.

[thegillabbeygowl]

For ever and ever and ever and ever and ever.

[i_hate_ire]

sorry black knight.


its actually my favourite riddle at the moment.


if anyone does get a (internationally accepted) answer to this (or a variant of this) puzzle, do PM me, in case i miss it on here...
Not an answer, but some help in working it out

#
Weight at Earth's Core
Would your body weigh more or less if standing on the Earth's core? What about above sea level?

As you go further inside the Earth, the force you feel due to gravity lessens, assuming the Earth is has a uniform density all the way throughout. Less force means you weigh less.

The reason is that the mass attracting you is inside a sphere, and is given by M = (4/3) * pi * (radius)3 * density

The force you feel is given by F = G * M * (your mass) / (radius)2

This means the net force is F = G * (4/3) * pi * radius * density * (your mass)

(pi=3.14159 and G = Newton's gravitational constant)

So as you go further inside the Earth, the radius is decreasing, so the force you feel is decreasing. The mass above you oddly enough doesn't contribute at all to any net force on your body.

In reality, of course, the Earth is not of uniform density, and there is a slight increase in force as you go down from the surface, before it begins to decrease again. Still, you weigh less standing on the Earth's core.

As far as what happens above sea level - you must realize that what happens outside the Earth is different from what happens inside the Earth. Inside, as you go deeper and deeper, the mass attracting you is less and less (as stated). Above sea level (the surface of the Earth, specifically) as you go further and further away, the mass remains constant (obviously), but the distance gets larger and larger, which makes the force (given by F = G * M(Earth) * M(you) / r2) smaller.

Notice that the formula that applies inside the Earth is different from the one that applies outside.

Dr. Louis Barbier
(October 2003)

#
Gravity at Earth's Core
Gravity pulls us downward on all sides on the Earth. Does this mean that at the center of the Earth, there is no gravity?

First, the most important thing to know is that gravity exists absolutely everywhere in the universe. Every bit of matter exerts a force on every other bit of matter. This means that you are attracted, and attract, everything in the universe! The force exerted depends on the distance of the object and the mass. The Earth exerts the most force on you because it is close (right here!) and very massive.

Forces add like vectors, so their direction is very important. If you could be at the exact center, the forces that each bit of Earth matter exerted on you would cancel out (up cancelling down, east cancelling west, etc.). This only occurs for a single point, though, and you would still feel a gravitational force on the rest of your body.

Remember, gravity is universal and exists everywhere. This is the fundamental law of physics.

Angela Richard
(March 2003)

from http://helios.gsfc.nasa.gov/qa_earth.html

[hans aus dtschl]

no, there's actually a fair bit more to it than that, because gravity isnt equal at all points on the earths surface.




edit-above post

the moon coming closer to the earth at some point will also affect it....etc etc etc.


lets leave out "neglecting windage"


and what answer do we have?

[hans aus dtschl]

like, i think we can all agree that you're gonna end in the centre, in some capacity (windage aside, you're gonna have friction problems with the sides of the tunnel, after some amount of time-you're not "dropping" in, you're "jumping" in, so you're moving horizontally, to some degree.


so what happens at the centre.that is the question.

[i_hate_ire]

like, i think we can all agree that you're gonna end in the centre, in some capacity (windage aside, you're gonna have friction problems with the sides of the tunnel, after some amount of time-you're not "dropping" in, you're "jumping" in, so you're moving horizontally, to some degree.


so what happens at the centre.that is the question.
See above.

[St_Cyrill_of_Tyrrenhaes]

What Presentation Brother said earlier about simple harmonic motion is correct. A first approximation is to assume that the earth is perfectly spherical and that there is no air resistance - simple harmonic motion is what you observe in this case. Adding in air resistance simply results in a damped simple harmonic oscillator. Taking atmospheric pressure into account gives exactly the same thing: damped simple harmonic motion.

The only complication is that the tunnel has to be drilled directly through the centre of the earth. A common misconception is that drilling a tunnel off-centre will still give you simple harmonic motion. It won't: it'll result in heavily damped motion because you'll be pulled toward the side of the tunnel that's closer to the centre of the planet, thus increasing friction.

As said earlier, this really isn't as difficult as people are trying to make it out.

[hans aus dtschl]

weightlessness?


because gravity should exist everywhere, right? next to a large object...


so....gravity is what, 9.8m/s or so, its basically not strong enough to rip you apart, i'd imagine. ..could you climb out?

[hans aus dtschl]

What Presentation Brother said earlier about simple harmonic motion is correct. A first approximation is to assume that the earth is perfectly spherical and that there is no air resistance - simple harmonic motion is what you observe in this case. Adding in air resistance simply results in a damped simple harmonic oscillator. Taking atmospheric pressure into account gives exactly the same thing: damped simple harmonic motion.

The only complication is that the tunnel has to be drilled directly through the centre of the earth. A common misconception is that drilling a tunnel off-centre will still give you simple harmonic motion. It won't: it'll result in heavily damped motion because you'll be pulled toward the side of the tunnel that's closer to the centre of the planet, thus increasing friction.

As said earlier, this really isn't as difficult as people are trying to make it out.


but you're jumping in.

you're moving in a direction.

if you neglect windage, you HAVE to take direction into account.
so you'll touch the sides.

and the central approximation is also right.


neglecting any sort of damping whatsoever, continuous oscillatory motion is right.

[St_Cyrill_of_Tyrrenhaes]

but you're jumping in.

you're moving in a direction.

if you neglect windage, you HAVE to take direction into account.
so you'll touch the sides.

and the central approximation is also right.


neglecting any sort of damping whatsoever, continuous oscillatory motion is right.


Firstly, it's called friction, not windage. Secondly, it matters not whether you jump in or step in; the only difference is that if you "jump" in, you'll obtain a higher maximum velocity at the centre of the tunnel.

On the other hand, if by "jump" you're talking about possibly bouncing off of the sides of the tunnel, then no exact analytic solution to the problem exists. The behaviour would still qualitatively be the same, i.e., damped oscillation, but you'd have to solve it numerically in this case.

I think you're adding needless complication to things.

[shamoverhere]

The Hollow Earth people would grab you on the way through, bring you for a spin and make you some tea.

[MonTheHoops]

http://chooseability.org/uploaded_images/stephen_hawking-768653.jpg

You fucking morons. The universe is constantly expanding. Christ!

[The Black Knight]

http://chooseability.org/uploaded_images/stephen_hawking-768653.jpg

You fucking morons. The universe is constantly expanding. Christ!


already been said ;)

[t_mccarthy]

so let's get back to the nitty gritty.... how big is infinity?

[The Black Knight]

so let's get back to the nitty gritty.... how big is infinity?
I've come up with quite alot of possible solutions to hans hole in the earth riddle.

Haven't had time to apply math to it. This thread will resurface someday with possible solutions.

[hughjass]

so let's get back to the nitty gritty.... how big is infinity?

Pointless question. Infinity is defined precisely as an unbounded limit - you cant put a number cap on it. Infinity is a well defined mathematical concept, and the notion of "finding" out how big infinity is is just nonsense...

Its kinda like asking someone how small zero is. Its just zero, thats it. Same kinda idea with infinity, its pointless asking how large it is.

[hughjass]

I've come up with quite alot of possible solutions to hans hole in the earth riddle.

Haven't had time to apply math to it. This thread will resurface someday with possible solutions.

There isnt several solutions, just whats been mentioned before by St Cyrill and a few others. You will oscillate about the centre in simple harmonic motion. If you include friction and pressure changes, you will oscillate in damped harmonic motion, eventually coming to a rest at the centre. Small factors like the unevenness of the Earths surface, and what speed you jump into the hole will have a negligible influence and the result will be qualitatively the same.

Theres no mystery here folks, its a simple question with a simple answer.

[Bwana_Dik]

I think ye're overlooking the effect of the earth's rotation.
Simple harmonic motion yes if the earth were "stationary", but rotation would cause you to clatter into the side of the tunnel as you decended/fell. I think! No?

[The Black Knight]

There isnt several solutions, just whats been mentioned before by St Cyrill and a few others. You will oscillate about the centre in simple harmonic motion. If you include friction and pressure changes, you will oscillate in damped harmonic motion, eventually coming to a rest at the centre. Small factors like the unevenness of the Earths surface, and what speed you jump into the hole will have a negligible influence and the result will be qualitatively the same.

Theres no mystery here folks, its a simple question with a simple answer.

Well yeah, that's one of the things I was thinking but then again there's alot of factors not being taken into account here too in this solution. Such as do the two opposite gravitational pulls form a union. I'm not convinced your answer is accurate.

Bwana Dik, the earths rotation wouldn't come into it I think. This is because you are already rotating this much anyway so this factor cancels out. It's like dropping off the top of the empire state building. You'll end up directly below where you began. If the earths rotation mattered then one should end up somewhat to the left or right of where they jumped from.

[St_Cyrill_of_Tyrrenhaes]

Well yeah, that's one of the things I was thinking but then again there's alot of factors not being taken into account here too in this solution. Such as do the two opposite gravitational pulls form a union. I'm not convinced your answer is accurate.

What two opposite gravitational pulls? There's only one force due to gravity and that always points toward the centre of the earth.

[The Black Knight]

What two opposite gravitational pulls? There's only one force due to gravity and that always points toward the centre of the earth.

Ok well I'm going to have to read up on it all. I'm not to hot on gravitational pulls.

[i_didnt_do_nawtin]

Ok well I'm going to have to read up on it all. I'm not to hot on gravitational pulls.

lol

[Wolfy Van Der Greylocks]

have you included the impact of the doppler effect?

[The Black Knight]

lol

Ah yes, I realised what I wrote but decided to leave it there.

[xvis]

wouldn't you just disintegrate with the heat before you reached the Earths centre? ..if we're to analyse the reality of the situation.

[The Black Knight]

wouldn't you just disintegrate with the heat before you reached the Earths centre? ..if we're to analyse the reality of the situation.
This too crossed my mind. I've been thinking about this since this thread was put up. Quite the headwrecker.

[Wolfy Van Der Greylocks]

wouldn't you just disintegrate with the heat before you reached the Earths centre? ..if we're to analyse the reality of the situation.

the reality of the situation is that if you were to drill a hole straight through the earth - it would cause an implosion and a "black hole" would be created.

[xvis]

the reality of the situation is that if you were to drill a hole straight through the earth - it would cause an implosion and a "black hole" would be created.

well fuck that then. ..best stick with Qantas.

[t_mccarthy]

well fuck that then. ..best stick with Qantas.



me too

[jmurphy]

infinity = waiting to get into the girls bathroom inside in the savoy

[spatterbag]

infinity = having a shit and running out of toilet paper

[Wolfy Van Der Greylocks]

Depends where you jumped in, but I reckon you'd end up in Australia.

my money's on new zealand

[fintan fogerty]

If you counted to infinity, there would be as many even numbers as odd and even numbers put together.

[Wolfy Van Der Greylocks]

stop fucking with my brain finner.

[fintan fogerty]

Listen to this one Wolfer.

If a monkey was typing on a typewriter for all infinity, he'd eventually go mental, rant about the BoBs and have a dirty protest in his bedsit.

[Vincent Murphy]

i love you to infinity finner

[fintan fogerty]

Thanks Vince.

[Vincent Murphy]

your welky

[hands]

Listen to this one Wolfer.

If a monkey was typing on a typewriter for all infinity, he'd eventually go mental, rant about the BoBs and have a dirty protest in his bedsit.

And try pork Locky :vamp: