π' (47149) user comments in the News Comments forum at Blue's News"> Out of the π - Blue's News Comments

Out of the π

I mentioned that "Broken Arrow" was a misused term among the links of the day yesterday, but RoboRay sent along a note to question the accuracy of that, and in further investigation, I learn I erred when I researched this some time back, and that this is actually the proper term to use for a Nuclear Weapon that is damaged or detonated. Thanks to RoboRay for the correction, and apologies to John Woo for doubting him (though I still think he owes the rest of us an apology for that flick).

R.I.P.: Palmolive pitchwoman 'Madge' dead.

Play Time: Which Irrational Number Are You? Thanks Bronco. My results below.
Stories of the Day: 'Mister Ed' gets a new voice. From Red Ryder to George Jefferson.
Man says former co-worker thrown to lions.
Teen finds his picture on missing children's Web site.
Science!: Experts: Ocean studies will move to other planets.
Russia to build new spacecraft.
Flu Vaccine to Change Next Year (registration required).
Media of the Day: American Idolatry. Thanks Bronco.
Image of the Day: Holy Grail Of El-Spyware! Thanks Ant.
Follow-up: Brain fingerprints under scrutiny.
Thanks Mike Martinez.

What Irrational Number Are You?
You are π

Of all the irrational numbers, you are the most famous. You have many friends and fans. Like many people, non-Euclidean geometry makes you feel uncomfortable. You are involved in so many things that it seems like it would take two of you to make ends meet.

You are particularly close to the rational number 22/7. However, you and e have been called "remarkable."

Your lucky number is approximately 3.14159265

Shiny Lemur
Straif's Blog
View : : :
79 Replies. 4 pages. Viewing page 1.
Newer [  1  2  3  4  ] Older
79.
 
Re: what irrational number are you...
Feb 24, 2004, 20:13
79.
Re: what irrational number are you... Feb 24, 2004, 20:13
Feb 24, 2004, 20:13
 
math is a game... play around with it, but make sure to follow the rules

I grapple with the absurdity of a post that first expounds mathematical rigor, then does some proof by hand-waving. Pretending that you can use the mathematics of limits without being tied down by the concept that you may not actually be able to evaluate the limit itself is fallacy, and you certainly can't assume it evaluates to it just because you can show that it's a limit.

Indeed the whole concept is more than a little flawed, because when we talk about real numbers, we're implicitly discussing the Real field <R,+,*>. You can't use these operations on infinity without first defining them, and then ensuring that you maintain that every non-zero element in R has a multiplicative inverse where both operations are also commutative. (we need left and right distributivity as well to maintain that R is a field in order that some normal mathematics keeps working on it).
In particular, you're going to run headlong into a huge great headache with maintaining your multiplicative inverse for non-zero elements. You're mathematically required to have an element such that infinity*x = 1, but by the previous equation, 1/infinity = 0. unfortunately this *completely* breaks the requirement for a ring that for any element a, a*0 = 0.

While I'm at it, I might as well mention Cantor's countability proof. N (natural numbers), Z (integers) and Q (rational numbers) are countably infinite. R is not countably infinite, so it's not even correct to assert that there are as many Real numbers as there are rational numbers, because there are infinitely more.

But just for fun I'll throw a wrench in the works by giving you a random way of picking natural numbers (which should give you methods of picking integers and rationals). Start with 1. roll a die, if the result > 3, add 1 and repeat, otherwise stop (that's not the definition of random from statistics, I know, but result isn't deterministic and is directly based off the flat probability of the different results of the dice roll). It'll give you a poisson (?) distribution for the probability of picking any one number, but does theoretically give you the opertunity to randomly choose a number in an infinite set (not with even probability I'll grant you). Unfortunately, I doubt anyone could repeat this for the real number line, since it's not countable and therefore probably couldn't be approached algorithmically anyway. If we restrict ourselves to flat probability distributions though, I doubt it would be at all possible to randomly pick from any infinite set, not least because once you have infinitessimal probabilities of any element occuring, the definition of random goes out the window because rather than being defined as being the same, all the probabilities are defined as something that is undefined.
Anyway. the point of this whole braintwisting nastyness is surely the concept that 1) any particular real number is one of a set that is much larger than those of the rationals, 2) if one were able to assign elements of rational or real number sets to anyone randomly, the chances that anyone else would have the same number as you would be infinitesimal, and given the finite nature of humanity would imply that duplication would never happen in either case, therefore to the finite perception of man (or woman?) be indistinguisable except to those that sit around thinking too much?

Course. I'm just gibbering now.
This comment was edited on Feb 24, 21:57.
78.
 
Re: what irrational number are you...
Feb 20, 2004, 19:19
78.
Re: what irrational number are you... Feb 20, 2004, 19:19
Feb 20, 2004, 19:19
 
f you like discrete math in any manner you might also like number theory or probability theory...

Okay I probably gave you the wrong impression with all the stuff I've been writing. I actually hate math, especially calculus & discrete math (both of which I'm doing this semester). So no, I don't think I'd enjoy probability or number theory all that much.

ack, got to go for now... I'll probably be back to finsh this up late

Well, yeah eh, you haven't finished refuting my dumb ass yet.

PZ
------------
Reading: Robert Pirsig's "Zen & The Art of Motorcycle Maintenance"
Listening To: Nothing in particular
PZ
------------
77.
 
Re: what irrational number are you...
Feb 20, 2004, 16:49
77.
Re: what irrational number are you... Feb 20, 2004, 16:49
Feb 20, 2004, 16:49
 
hey Pedle (and moog ;)),
1st off, I think it's awesome that you're interested enough in math to keep coming back to this thread. math is a game... play around with it, but make sure to follow the rules. if you like discrete math in any manner you might also like number theory or probability theory...

wouldn't this equation just be undefined, rather than 0? How can you divide something by an amount that isn't a number?

ahhh... but when you take 1/(SomeReallyBigNumber) you get closer and closer to zero the bigger your number gets. because of this, it's not that much of a stretch to assume that 1/infinity is defined as 0. I'm not saying that R increases in any manner (as its size is fixed), but that its size is infinite. therefore 1/(SizeOfTheReals) is similar to 1/infinity which equals 0. I'm not using limits at all really: only the "definition" of 1/infinity, and the fact that the reals are infinite.


ack, got to go for now... I'll probably be back to finsh this up later

Avatar 13889
76.
 
Re: what irrational number are you...
Feb 20, 2004, 09:38
76.
Re: what irrational number are you... Feb 20, 2004, 09:38
Feb 20, 2004, 09:38
 
lol..
i was just getting irrational...
But it would be 2/3 not one third, as integers are still rational.

We cannot eat solar panels, nor solar power.
We cannot eat wind power, nor wind turbines.
92% of the world relies on eating oil, via fertilizer, pesticides, transport, and irrigation.
How long until oil is too valuble for farming?
www.dieoff.org
STAY RIGHT WHERE YOU ARE, GET OUT OF THAT BED AND GET DOWN ON THE FLOOR, GET OUTSIDE RIGHT NOW, RIGHT HERE: GET DOWN ON THE CEMENT, I DONT CARE IF YOU'RE NUDE, GET DOWN ON THE CEMENT, I DON'T CARE IF ITS FREEZING! WHERES THE DRUGS, WE KNOW YOU GOT THE DRU
75.
 
Re: what irrational number are you...
Feb 20, 2004, 00:04
75.
Re: what irrational number are you... Feb 20, 2004, 00:04
Feb 20, 2004, 00:04
 
Yeah, what the hell were you thinking.

~Steve

74.
 
Re: what irrational number are you...
Feb 19, 2004, 23:55
74.
Re: what irrational number are you... Feb 19, 2004, 23:55
Feb 19, 2004, 23:55
 
we have infinity + infinity, or 2infinty, which means the equation really is infinity/2infinity = 1/2.

The only problem is that this isn't valid, infinity isn't a number, so infinity + infinity is NOT 2 * infinity, just like infinity / infinity is NOT 1.

By your reasoning, not only would the reals be 2infinity, but rather since the integers are infinite, and the rationals are the integers plus the rational non-whole number numbers (of which there are infinitely many), then the rationals would be 2infinity, and thus the reals would be 2infinity + infinity = 3infinity, and then probability would be 1/3.

PZ
------------
Reading: Robert Pirsig's "Zen & The Art of Motorcycle Maintenance"
Listening To: Nothing in particular
This comment was edited on Feb 20, 00:06.
PZ
------------
73.
 
Re: what irrational number are you...
Feb 19, 2004, 20:36
73.
Re: what irrational number are you... Feb 19, 2004, 20:36
Feb 19, 2004, 20:36
 
so if it is infinity/infinity, real numbers are rational + irrational, irrational = i and rational = r, and irrational and rational are both infinite, we have infinity + infinity, or 2infinty, which means the equation really is infinity/2infinity = 1/2. The probability is one half.

We cannot eat solar panels, nor solar power.
We cannot eat wind power, nor wind turbines.
92% of the world relies on eating oil, via fertilizer, pesticides, transport, and irrigation.
How long until oil is too valuble for farming?
www.dieoff.org
STAY RIGHT WHERE YOU ARE, GET OUT OF THAT BED AND GET DOWN ON THE FLOOR, GET OUTSIDE RIGHT NOW, RIGHT HERE: GET DOWN ON THE CEMENT, I DONT CARE IF YOU'RE NUDE, GET DOWN ON THE CEMENT, I DON'T CARE IF ITS FREEZING! WHERES THE DRUGS, WE KNOW YOU GOT THE DRU
72.
 
Re: what irrational number are you...
Feb 19, 2004, 20:03
72.
Re: what irrational number are you... Feb 19, 2004, 20:03
Feb 19, 2004, 20:03
 
given any small number you can prove that this probability would still be smaller...

Okay I'll start by qualifying this with the obvious: you know way more about this stuff than I do, so I'm probably wrong.

Having said that, the probability of selecting a rational number at random would be the cardinality of the set of rational numbers (lets call it Q) divided by the cardinality of the set of real numbers (call it R). Then this would be:

Q/R

But, since R is uncountable, wouldn't this equation just be undefined, rather than 0? How can you divide something by an amount that isn't a number?

It seems to me that when you say that this equation becomes 1/infinity (or for all intents & puproses 0), you're making a claim that R grows without bound and thus results in 1 over infinity. That is, something like a limit such as:

lim R->infinity 1/R = 0 (the limit as R goes to infinity in 1/R is 0)

But the problem with this is that R isn't a variable, it represents a constant value (the size of the reals, which while infinite & uncountable, is still unchanging).

For that matter, even though Q is countable, it is also still infinite, so really you don't have 1/infinity, but rather infinity/infinity. When presented with a limit of the indeterminate form infinity/infinity, you generally apply L'Hospitals rule, take the derivitives of the numerator & denominator and see if that allows a limit to come out of it. But in this case we don't have a differentiable function in either the numerator or denominator, so L'Hospital doesn't seem to apply. Even if it did, since Q & R represent fixed values, their derivitives would be 0, so you'd get 0/0, which isn't 0, but undefined.

Okay, I'm done, refute me.


PZ
------------
Reading: Robert Pirsig's "Zen & The Art of Motorcycle Maintenance"
Listening To: Nothing in particular
This comment was edited on Feb 20, 00:00.
PZ
------------
71.
 
me love the synths
Feb 19, 2004, 19:16
71.
me love the synths Feb 19, 2004, 19:16
Feb 19, 2004, 19:16
 
got an Ion, MKS-70, Evolver, and SidStation

but my very first was a moog/radioshack MG-1... and the osc sync sound on that sucker has YET to be surpassed!! I'd love to get some more but its so damn expensive


_____________________________________________
Give me slack. Or kill me.
______________________________________________
"When the bomb drops it'll be a bank holiday
Everybody happy in their tents and caravans
Everybody happy in their ignorance and apathy
No one realizes until the television breaks down..."

- SUBHUMANS
70.
 
Re: what irrational number are you...
Feb 19, 2004, 18:52
70.
Re: what irrational number are you... Feb 19, 2004, 18:52
Feb 19, 2004, 18:52
 

quit being irrational moog

Avatar 13889
69.
 
Re: synth geeks unite
Feb 19, 2004, 17:47
69.
Re: synth geeks unite Feb 19, 2004, 17:47
Feb 19, 2004, 17:47
 
Memories for now... I had a vintage Minimoog until the great robbery of 2000. The only synth I have bought since is a Korg Vocorder mini, and it kicks ass. Still, I miss the moog... that thing had the A-1 sound. Do you own any synthesisers?


We cannot eat solar panels, nor solar power.
We cannot eat wind power, nor wind turbines.
92% of the world relies on eating oil, via fertilizer, pesticides, transport, and irrigation.
How long until oil is too valuble for farming?
www.dieoff.org
STAY RIGHT WHERE YOU ARE, GET OUT OF THAT BED AND GET DOWN ON THE FLOOR, GET OUTSIDE RIGHT NOW, RIGHT HERE: GET DOWN ON THE CEMENT, I DONT CARE IF YOU'RE NUDE, GET DOWN ON THE CEMENT, I DON'T CARE IF ITS FREEZING! WHERES THE DRUGS, WE KNOW YOU GOT THE DRU
68.
 
synth geeks unite
Feb 19, 2004, 17:23
68.
synth geeks unite Feb 19, 2004, 17:23
Feb 19, 2004, 17:23
 
Hey operator - you never answered my question before... what kind of moogs do you have? Voyager? Mini? Rogue? Memory? do tell!

_____________________________________________
Give me slack. Or kill me.
______________________________________________
"When the bomb drops it'll be a bank holiday
Everybody happy in their tents and caravans
Everybody happy in their ignorance and apathy
No one realizes until the television breaks down..."

- SUBHUMANS
67.
 
Re: what irrational number are you...
Feb 19, 2004, 17:04
67.
Re: what irrational number are you... Feb 19, 2004, 17:04
Feb 19, 2004, 17:04
 
First, you cannot select anything "at random" from any infinite set. It is impossible. Random selection requires a set of limited size. If this size is moog, then:
probability = 1/moog, no matter what you are trying to select. If moog is infinite, the probability is 0, no
matter what, no matter what set.

Your equation:
#Rationals /(N * #Rationals) = 1 / N
shows the probability of choosing a rational number from an infinite set, but, you don't mention the exact same thing applies to irrational numbers. The probability of selecting rational numbers is 0, but so is the probability of selecting any thing out of any infinite set. On an infinite number line, there are no more of either rational or irrational numbers.
It's infinite.

We cannot eat solar panels, nor solar power.
We cannot eat wind power, nor wind turbines.
92% of the world relies on eating oil, via fertilizer, pesticides, transport, and irrigation.
How long until oil is too valuble for farming?
www.dieoff.org
STAY RIGHT WHERE YOU ARE, GET OUT OF THAT BED AND GET DOWN ON THE FLOOR, GET OUTSIDE RIGHT NOW, RIGHT HERE: GET DOWN ON THE CEMENT, I DONT CARE IF YOU'RE NUDE, GET DOWN ON THE CEMENT, I DON'T CARE IF ITS FREEZING! WHERES THE DRUGS, WE KNOW YOU GOT THE DRU
66.
 
Re: what irrational number are you...
Feb 19, 2004, 13:00
66.
Re: what irrational number are you... Feb 19, 2004, 13:00
Feb 19, 2004, 13:00
 
Because then it wouldn't intersec the x-axis (f(x) = 1 is a horizontal line).

sorry, I should have used f(x)=0 but the point holds: you are picking out a number in a non-random fashion.

wouldn't the probibility not be zero, but rather a very very small number?

given any small number you can prove that this probability would still be smaller...

how many copies of the rational numbers are in the reals? Whatever this number is, lets call the number N (i.e. there are N copies of the rationals in the reals). then the probabliity of choosing a rational number (randomly) out of the real number line would be:

#Rationals /(N * #Rationals) = 1 / N

but there aren't N copies of the rationals in the reals...

if we take N copies of the rationals, we still have a countable set while the reals are uncountable. because the reals are uncountable, N must be infinite. then our probability becomes 1/infinity (or for all intents and purposes 0).

side notes:

these copies of the rationals, however many there are needed to make up the reals, would represent the irrationals.

how many copies, N, of the rationals would we need in order to make the reals? we already know that N must be infinite. but not only is this number infinite, but it is uncountably infinite. this is true because the joining together of any countable number of countable sets would still result in a countable set.

for every rational number there are an uncountable number of irrationals...

Avatar 13889
65.
 
Re: No subject
Feb 19, 2004, 12:30
65.
Re: No subject Feb 19, 2004, 12:30
Feb 19, 2004, 12:30
 
uh huh... because all frustration is always sexual. Projecting much? Many of you will eventually have jobs where your intellect will be the deciding factor as to whether or not you have said job. I manage my department in such a job; we develop software. Those in my department who demonstrate poor english skills, and who don't have the gusto to spell correctly, find themselves looking for new jobs in a big hurry. Nothing is more frustrating than arguing with some fuck who cannot spell, refuses to spell consistently, and tries to tell me their coding skills are sound. If you use words, you may as well be able to spell them.

We cannot eat solar panels, nor solar power.
We cannot eat wind power, nor wind turbines.
92% of the world relies on eating oil, via fertilizer, pesticides, transport, and irrigation.
How long until oil is too valuble for farming?
www.dieoff.org
STAY RIGHT WHERE YOU ARE, GET OUT OF THAT BED AND GET DOWN ON THE FLOOR, GET OUTSIDE RIGHT NOW, RIGHT HERE: GET DOWN ON THE CEMENT, I DONT CARE IF YOU'RE NUDE, GET DOWN ON THE CEMENT, I DON'T CARE IF ITS FREEZING! WHERES THE DRUGS, WE KNOW YOU GOT THE DRU
64.
 
Re: what irrational number are you...
Feb 19, 2004, 12:23
64.
Re: what irrational number are you... Feb 19, 2004, 12:23
Feb 19, 2004, 12:23
 
using your example of f(x)=x-1, why not just use f(x)=1

Because then it wouldn't intersec the x-axis (f(x) = 1 is a horizontal line).

Now, taking the ratio of a countable number over an uncountable number we get zero and our probability becomes zero: an uncountable set is so much larger than a countable set, that this ratio is zero.

Hmm, okay I see your reasoning, but then wouldn't the probibility not be zero, but rather a very very small number?

PZ
------------
Reading: Robert Pirsig's "Zen & The Art of Motorcycle Maintenance"
Listening To: Nothing in particular
PZ
------------
63.
 
Re: No subject
Feb 19, 2004, 10:20
nin
 
63.
Re: No subject Feb 19, 2004, 10:20
Feb 19, 2004, 10:20
 nin
 
<Rainman>
definately, definately needs a bj...yeah...yeah...definately needs a bj
</Rainman>

http://www.depechemode.com/
62.
 
Re: No subject
Feb 19, 2004, 10:16
62.
Re: No subject Feb 19, 2004, 10:16
Feb 19, 2004, 10:16
 
THERE IS NO FUCKING A IN DEFINITELY, ASSHOLES. LEARN TO SPELL.

Never before have I seen a man in such dire need of a blowjob.
This comment was edited on Feb 19, 10:17.
Its not the cough that carries you off but the coffin they carry you off in.
61.
 
Re: No subject
Feb 19, 2004, 10:14
nin
 
61.
Re: No subject Feb 19, 2004, 10:14
Feb 19, 2004, 10:14
 nin
 
Ask him if he smokes...

http://tinyurl.com/2hrlp


edit: I could definately use a drink right now...


http://www.depechemode.com/
This comment was edited on Feb 19, 10:16.
60.
 
Re: No subject
Feb 19, 2004, 10:12
60.
Re: No subject Feb 19, 2004, 10:12
Feb 19, 2004, 10:12
 
THERE IS NO FUCKING A IN DEFINITELY, ASSHOLES. LEARN TO SPELL.

http://www.apa.org/pubinfo/anger.html

-TPFKAS2S
http://www.braglio.com
-TPFKAS2S
Avatar 10139
79 Replies. 4 pages. Viewing page 1.
Newer [  1  2  3  4  ] Older