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InvisibleOrgoneConclusion
Blue Fish Group
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Registered: 04/01/07
Posts: 45,432
Loc: Under the C
Re: The Size Of Infinity [Re: Diploid]
    #14404123 - 05/05/11 08:18 AM (12 years, 9 months ago)

BTW, I can't believe you deleted my detailed post wherein I tied gravity into the nuclear weak-force while peaking on acid. :shakefist:


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InvisibleCups
technically "here"
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Registered: 12/24/09
Posts: 1,925
Re: The Size Of Infinity [Re: Diploid]
    #14404163 - 05/05/11 08:30 AM (12 years, 9 months ago)

Quote:

Diploid said:
I tried, but none of them knew how to program a computer. :confused:




Is that geek speak for blowjob?

:lol:


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InvisibleDieCommie

Registered: 12/11/03
Posts: 29,258
Re: The Size Of Infinity [Re: Diploid]
    #14405804 - 05/05/11 03:23 PM (12 years, 9 months ago)

Quote:

Diploid said:
Otherwise, the previous explanations revolving around orders of magnitude sufficiently explain the other situations you just listed.

If that were true, it would be seen in random numbers, but it's not. Yet it's seen in measured generally random numbers like river lengths or the lengths of files on a hard drive.






It is seen in random numbers, as long as you restrict them to the proper interval.  If you take random numbers between 0 and 1999 you will see it.  If you take them between 0 and 9999 you will not.  The same goes for measured quantities.  If you measure them such that they fall on an interval like 0 to 1999 you will see it, if you measure them such that they fall on an interval between 0 and 9999 you will not.

Note that generally, we use units such that measured numbers hover around an order of magnitude.  We generally take random numbers to span an entire order of magnitude. 


(Also, I wonder if you know what the logical fallacy is when a data set is presented as evidence, then that same data set is used to negate the claim prompting the claimant to then dismiss the data set as too small and not indicitive... ???  :grin:)

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InvisibleDiploidM
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Folding@home Statistics
Registered: 01/09/03
Posts: 19,274
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Re: The Size Of Infinity [Re: DieCommie]
    #14406259 - 05/05/11 04:52 PM (12 years, 9 months ago)

if you measure them such that they fall on an interval between 0 and 9999 you will not

I don't think that's the case. The entire premise of the Benford Law is that that is not the case. But we'll see what my analysis turns up.

I wonder if you know what the logical fallacy is when a data set is presented as evidence, then that same data set is used to negate the claim prompting the claimant to then dismiss the data set as too small and not indicitive

It's called a Yo-Mamaism. :razz:

Edit: I give up for now. I need several large data sets to prove my point, like the billing records for the top 10 Dow companies or something like that. I can't find anything online. The best I can find is a Wiki article about river lengths (which does conform to the Benford distribution) but it's not near enough to give a convincing analysis.

But for the record, income tax fraud has been discovered by analyzing tax returns for the Benford distribution. Fraudsters make ups random numbers in their fraudulent returns, and we already know that random numbers don't have the Benford distribution. But intuition suggests that real-world tax return values would be randomly distributed, so I think there's something to Benford.

Anyway, I wrote the analysis program for nothing, but if I ever find the right kind of data to analyze, I'll resurrect this thread and tell you NEENER NEENER! :evil:


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Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

Edited by Diploid (09/19/12 09:23 PM)

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InvisibleOrgoneConclusion
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Re: The Size Of Infinity [Re: Diploid]
    #14406806 - 05/05/11 06:51 PM (12 years, 9 months ago)

Quote:

It's called a Yo-YoMamaism.






?


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InvisibleCups
technically "here"
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Registered: 12/24/09
Posts: 1,925
Re: The Size Of Infinity [Re: Diploid]
    #14417467 - 05/08/11 12:04 AM (12 years, 9 months ago)

Quote:

Diploid said:
I don't think that's the case. The entire premise of the Benford Law is that that is not the case. But we'll see what my analysis turns up.





:popcorn:

While we're waiting can I ask an unrelated math question?

Quote from the last scene of the final episode of Battle Star Galactica.

"Law of averages. Mathematics. Let a complex system repeat itself long enough, eventually something surprising might occur. "

Is that true?


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Offlinescoredon
I dont know
Male

Registered: 04/28/09
Posts: 487
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Re: The Size Of Infinity [Re: FocusHawaii]
    #14417615 - 05/08/11 12:51 AM (12 years, 9 months ago)

Quote:

FocusHawaii said:
Well, the mathematical proof that this holds might be much, much more complex but it may be intuitively understandable with the above.

The really amazing part to me is that something can be infinitely large yet somehow smaller than something also infinite in size.



Gabriels Horn/Torricellis Trumpet is a solid with infinitley large surface area and a definite volume. You make it by wrapping the inverse function around the x-axis. Cool stuff.
http://www.wolframalpha.com/input/?i=gabriels+horn
http://en.wikipedia.org/wiki/Gabriel%27s_Horn



As for the Cantor proof,It took me a minute to understand. It makes sense in an obvious way.

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OfflineAhimsa
µdose
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Registered: 01/11/07
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Re: The Size Of Infinity [Re: Diploid]
    #14418617 - 05/08/11 08:55 AM (12 years, 9 months ago)

I think the reason that there can be more elements in one infinite set than in another is because any multiple of infinity equals infinity.

For example, make for every Natural number in the one set a Natural number bis, tris, etc... Like so:

N, N', N'', N''',... (example: 4, 4', 4'', 4''',...)

Now there will be an infinite number of Natural numbers too that don't map into the set of Real numbers.

The result is that both set now contain an equal infinite amount of unmappable numbers.

The reason i believe lies in the fact that any multiple of infinity equals infinity.

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InvisiblePoid
Shroomery's #1 Spellir
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Registered: 02/04/08
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Re: The Size Of Infinity [Re: Ahimsa]
    #14420166 - 05/08/11 03:37 PM (12 years, 9 months ago)

Infinity is not a real number and operations on the real numbers do not apply to infinity. There are other ways to define number systems that include "infinity", such as cardinals (see: Aleph number), in which you can do arithmetic on "infinities" but they do not, in general, have the same properties as arithmetic operations on the real numbers.


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Well I try my best to be just like I am, but everybody wants you to be just like them. --  Bob Dylan
fireworks_god said:
It's one thing to simply enjoy a style of life that one enjoys, but it's another thing altogether to refer to another person's choice as "wrong" or to rationalize their behavior as being pathological or resulting from some sort of inadequacy or failing so as to create a sense of superiority or separation as yet another projection of a personal fear or control issue.

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OfflineAhimsa
µdose
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Re: The Size Of Infinity [Re: Poid]
    #14420209 - 05/08/11 03:48 PM (12 years, 9 months ago)

Thank you!

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Offlinedzza
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Registered: 12/31/10
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Re: The Size Of Infinity [Re: Diploid]
    #14421146 - 05/08/11 06:54 PM (12 years, 9 months ago)

Quote:

Diploid said:

Now, notice three things.

1. This list is infinitely long since there are infinitely many Naturals.

2. If you consider the digits in diagonal (), then the string of them itself is an Irrational Real number. You can write it like this 0.3231512... and so on to infinity because the list is infinitely long.

3. And if you add  1 to each of those digits in the diagonal (), you get the following 0.4342623. All I've done is take the Irrational from #2 above and added  1 to each numeral to get a new Irrational.

Now think about the consequences here. There are two possibilities.

A. Our new Irrational (from #3 above) can NEVER appear in our list.

or

B. If we insert our new Irrational (from #3 above) into our list, then we can construct ANOTHER irrational by the diagonal () technique that is not in the list. And if we insert THAT ONE, then we can find yet ANOTHER one by the diagonal () technique that is not in the list. And so on ad infinitum.

No matter how many of these diagonal () Irrationals we find and add to the list, there will ALWAYS be another one we can find by the same method that is not in the list.

That is to say, at the end of the list, we can still find one more that is not in the list.






The method in step 3 can be problematic.  By adding 1 to each number you do not necessarily create a new irrational because we have that 0.99999... = 1.000 in the real numbers.  A workaround would be to assign every nth digit of every nth number a value, say 3, if that digit did not already equal 3, and 4 otherwise.  Then you can be assured that you avoid the paradox and create a truly distinct new number.

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OfflineLittileSkierDude
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Re: The Size Of Infinity [Re: Diploid]
    #14427056 - 05/09/11 09:31 PM (12 years, 9 months ago)

Quote:



Code:


Natural >>> Some random Real

0 >>> 0.(3)913228
1 >>> 0.2(2)19242
2 >>> 0.35(3)4238
3 >>> 0.437(1)186
4 >>> 0.5813(5)63
5 >>> 0.05267(1)9
6 >>> 0.567728(2)








ok im confused. not that i think you are wrong but i need a little help understanding. if each place value can only consist of numbers 0-9, then even if there were an infinite number of places wouldnt a number eventually repeat when using your +1 method to the numbers in parentheses? assuming an infinite number of places in one irrational is the same number of places in any other irrational of course, wouldnt it statistically HAVE to repeat eventually? i could be wrong...i still dont quite grasp what you are saying...

the best way i can grasp infinity in a real life scenario seems to be a situation in which i am holding a mirror while facing a mirror, creating an infinite number of reflections of myself...although i suppose the reflection would eventually be so small that it would be smaller than the light particles and therefore wouldnt exist....

btw this is my first post on the shroomery and i love this site

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InvisibleCups
technically "here"
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Registered: 12/24/09
Posts: 1,925
Re: The Size Of Infinity [Re: Cups]
    #14467835 - 05/17/11 01:01 PM (12 years, 9 months ago)

KA-Bump

Quote:

Cups said:
Quote:

Diploid said:
I don't think that's the case. The entire premise of the Benford Law is that that is not the case. But we'll see what my analysis turns up.





:popcorn:

While we're waiting can I ask an unrelated math question?

Quote from the last scene of the final episode of Battle Star Galactica.

"Law of averages. Mathematics. Let a complex system repeat itself long enough, eventually something surprising might occur. "

Is that true?




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What's up everybody?!

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InvisibleDieCommie

Registered: 12/11/03
Posts: 29,258
Re: The Size Of Infinity [Re: Cups]
    #14467895 - 05/17/11 01:15 PM (12 years, 9 months ago)

Thats not really a question that can be answered.  What does 'surprising' mean?  It has no mathematical definition.  Note that a complex system is defined as one that, though completely deterministic, displays large variations in output as a function of small variations of input.  Of course what is 'large' and 'small' is relative, so there is very much a fuzzy boundary between a chaotic and non-chaotic system.

That Battlestar Galacita quote is sci-fi techno babble, which is fun - but not meaningful.

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InvisibleCups
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Registered: 12/24/09
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Re: The Size Of Infinity [Re: DieCommie]
    #14467912 - 05/17/11 01:19 PM (12 years, 9 months ago)

Werd....Thanks Diecommie


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