to infinity and beyond!

[Ch3tan]

Surprised Lamp did not post this yet, a great watch on bbc last night

BBC iPlayer - Horizon: 2009-2010: To Infinity and Beyond

Some pretty mind bending stuff, and lots I'll never understand, but great viewing.

 

[CorNokZ]

BBC iPlayer

 

[Moriath]

was a cool prog saw it this evening on recorded

infinity + infinity = infinity
infinity - infinity = anything

 

[Bugz]

Good show but they ruin it with all the dramatic black&white shit and that bald prick who does stupid faces.

 

[Bugz]

The most interesting use of infinity, in my opinion is with probability.

Infinity in terms of numerics is a vision most of us won't get to ever experience. But infinity in probability is more accessible.

 

[ileks]

Why do they have to make it so cheesy Some of it really made me cringe. I remember thinking the same when i watched the physics one a few months ago.

 

[Bugz]

The most interesting use of infinity, in my opinion is with probability.

Infinity in terms of numerics is a vision most of us won't get to ever experience. But infinity in probability is more accessible.

To add to this - they need to look more closely at the relationship between 0 and infinity etc.

If the probability of something not happening is 0. What is the probability of said thing not happening in an infinite number of trials?

If I have a bag with 2 red balls & 0 green balls. If I have 500,000 trials; the probability of getting a green ball is 0. If I have an infinite number of trials, the probability of getting a green ball is undetermined. Even though we KNOW rationally it is 0; we can not prove it beyond all doubt.

Not sure about you but I find that enthralling.

 

[Azurus]

Bugz stop ruining the magic with your maths talk! Us simple minded people enjoy the cheesiness and drama.

 

[old.Tohtori]

 

[Marc]

To add to this - they need to look more closely at the relationship between 0 and infinity etc.

If the probability of something not happening is 0. What is the probability of said thing not happening in an infinite number of trials?

If I have a bag with 2 red balls & 0 green balls. If I have 500,000 trials; the probability of getting a green ball is 0. If I have an infinite number of trials, the probability of getting a green ball is undetermined. Even though we KNOW rationally it is 0; we can not prove it beyond all doubt.

Not sure about you but I find that enthralling.

I find it zzzzzzzzzzzzzzz

 

[CorNokZ]

I get so fucking hard when you agree with someone! And I burst like a teenage zit when you agree with me!

 

[old.Tohtori]

To add to this - they need to look more closely at the relationship between 0 and infinity etc.

If the probability of something not happening is 0. What is the probability of said thing not happening in an infinite number of trials?

If I have a bag with 2 red balls & 0 green balls. If I have 500,000 trials; the probability of getting a green ball is 0. If I have an infinite number of trials, the probability of getting a green ball is undetermined. Even though we KNOW rationally it is 0; we can not prove it beyond all doubt.

Not sure about you but I find that enthralling.

Was talking about similar yesterday;

There's a chance, very very small, that you'll be teleported ot mars at any given moment. It's a possibility, by how small percent it may be.

As such, can we really say that there's a 0 chance of anything?

Ofcourse this combats against some of my personal convictions and beliefs, but that's what makes it fun as it's possible that something i believe will change, there's an equal chance(of some percentage) that it will not

 

[Lamp]

Yeah saw it, thought it was very interesting. Didn't agree with everyone's views but mind boggling stuff - eg:

Graham's number - Wikipedia, the free encyclopedia

 

[Ingafgrinn Macabre]

To add to this - they need to look more closely at the relationship between 0 and infinity etc.

If the probability of something not happening is 0. What is the probability of said thing not happening in an infinite number of trials?

If I have a bag with 2 red balls & 0 green balls. If I have 500,000 trials; the probability of getting a green ball is 0. If I have an infinite number of trials, the probability of getting a green ball is undetermined. Even though we KNOW rationally it is 0; we can not prove it beyond all doubt.

Not sure about you but I find that enthralling.

Yes, you can prove that beyond all doubt.

First you have to determine that the number of attempts (n) is natural (n ∈ ℕ). Since you cannot pick 2.5 times (you either pick, or you don't), this happens to be the case.

To get started, we need a mathematical means to test the cases. For this we need some boundaries.
Say we have 70 red marbles, 30 blue marbles and 0 black marbles, and after each draw we throw the drawn marble back.

n=1: probability of drawing a black marble:

P1 = 0 / (70+30) = 0 / 100 = 0

Then, with using mathematical induction we can prove that this is the case for all values of n. First we have to define a generic function:

Pn = 0 / (70+30)

We have already defined that the outcome is actually 0 for n=1, thus we now have to relate that to the next value of n:

Pn = P(n+1)

Since there is no actual value n in the function, this is rather trivial:

0 / (70+30) = 0 / (70+30)
0 / 100 = 0 / 100
0 = 0

QED.


Okay, let's spice it up a bit. Say you have a bag with an infinite number of red and blue marbles in the same relative quantity (70% red, 30% blue) and you don't throw the marbles back in the bag after each pull.
You still yearn for that black ball.

Let's set up a general function.
Pn = (number of black marbles in pouch) / (number of total marbles in pouch)
Since you take one marble out each time you draw, the total marbles count changes with each n.

1: Statement:
Pn => 0 / ((0.7∞ + 0.3∞) - (n-1)) = 0

2: Try for P1:
P1 => 0 / (∞ - (1-1)) = 0 / ∞ = 0

Spoiler

We've come to a little problem now. Is 0 / ∞ actually 0?

1: Statement:
0 / n = 0

2: Try for n=1:
0 / 1 = 0

3: If for n=1, then try for n=n+1
0 / (n+1) ?= 0
0 / (n+1) = (0 / 1) * (1 / (n+1))
As shown in step 2, (0 / 1) can be replaced by 0, therefor
0 / (n+1) = 0 * (n / (n+1)) = 0

So yes, 0 / ∞ = 0

3: If for P1, then try for Pn+1
Pn+1 => 0 / (∞ - ((n+1) - 1)) = 0
=> 0 / (∞ - n) = 0
=> (0 / 1) * (1 / (∞ - n)) = 0
=> 0 * (1 / (∞ - n)) = 0
Since anything multiplied by 0 equals 0, this is correct.
Therefor even with an infinitely large pouch with an infinite number of pebbles, you cannot draw a color marble that you simply haven't put in.

QED.

 

[Bugz]

My understanding of proof by induction is to prove something using a natural number set.

Infinity is not a natural number and I don't think bending it to natural-number means, without knowing for sure, what it is, can be 100% accurate.

 

[Ingafgrinn Macabre]

My understanding of proof by induction is to prove something using a natural number set.

Infinity is not a natural number and I don't think bending it to natural-number means, without knowing for sure, what it is, can be 100% accurate.

Infinity can be Natural, Rational or whatever you choose it to be. In this case (picking marbles from a pouch) the number of pickings and marbles cannot be anything other than a number in ℕ0 ({0,1,2,...>), therefor the number infinity as in the uncountably large number denominating the draw number, is also part of ℕ0 resulting in proof by induction to be a valid verification.

 

[cog]

I liked the bit about the chance of 1 monkey typing out the complete works of Shakespeare randomly being roughly the same probability as the same person winning the lottery each and every week for 29,000 years.

 

[Lamp]

I liked the bit about the chance of 1 monkey typing out the complete works of Shakespeare randomly being roughly the same probability as the same person winning the lottery each and every week for 29,000 years.

aye

 

[Job]

If before you were alive is the same as being dead afterwards then I have allready been dead for ever, so how can I be alive?

 

[Job]

I'm still not sure about mathamatics, it all seems too easy to be honest,
it may seem a bit daunting if you don't know the language, but on a big scale of things it's just a list of rules and I'm really think we're missing something.

 

[Lamp]