World Clock: Interesting Statistics

[DaJudge]

Clicky. (http://www.poodwaddle.com/worldclock.swf)

[Steve]

I note the Earth Temp (WTF is that???) has 12 significant digits. Sorry, that's impossible.

[Dave McDonald]

I note the Earth Temp (WTF is that???) has 12 significant digits. Sorry, that's impossible.

Statistically speaking, it is not impossible.

[Sound_Man]

:shrug:

[Steve]

Statistically speaking, it is not impossible.

Ummm...yes, it is impossible unless you have a way to actually measure it to that accuracy, which is not possible. Just because a calculator has that many digits doesn't mean they are accurate.

Wanna argue statistics and significant digits, big boy? :boxing:

:flipoff2:

[Oscar]

You guys speak english or only engineer?

[CannonBall]

Pi ~= 3
-Nate

[Waifer2112]

Watching that cancer one roll around is damn frightening!

[Machete]

Pi ~= 3
-Nate

Pi = 3
Exactly.
None of this irrational crap.

:D

[Trango]

Wanna argue statistics and significant digits, big boy? :boxing:

:flipoff2:

<whispering>Nerd. Nheeerrrddd.</whispering>

[OFRD_GRL]

<whispering>Nerd. Nheeerrrddd.</whispering>

i thinkn dweeb may be more fitting in this scenario :D

[Steve]

<whispering>Nerd. Nheeerrrddd.</whispering>

Geek, not nerd. GEEK! :P

And Bob, I'm confident you could join in the conversation... :flipoff2:

[Hardcor4x4]

Ummm...yes, it is impossible unless you have a way to actually measure it to that accuracy, which is not possible. Just because a calculator has that many digits doesn't mean they are accurate.

Wanna argue statistics and significant digits, big boy? :boxing:

:flipoff2:

I think the temp thing is more for showing the rate of increase vs actual exact temp. It just increases so slow they have to draw it out 12 places to show real time for us to see it change in the 1 minute we stare at it. They could draw it out 20 places just to show the smaller end of it moving faster for kicks.

[Dave McDonald]

Ummm...yes, it is impossible unless you have a way to actually measure it to that accuracy, which is not possible. Just because a calculator has that many digits doesn't mean they are accurate.

Wanna argue statistics and significant digits, big boy? :boxing:

:flipoff2:

Nope. No argument here - it's not a temperature reading. If it were you'd be right. Instead it's an average which can be carried as many digits as anyone likes to prove their point (legitimately or not) regarding global warming trends.

:flipoff2:

[Trango]

Sigfigs are always relevant. Just not cool. :)

[potter]

I can't believe there are that many species extinct. That's crazy, what are all of them?

[Willy36]

I can't believe there are that many species extinct. That's crazy, what are all of them?

well there was this really weird looking bug today that i stepped on and damn did he make a nice crunch. :thumbsup: :D

[DaJudge]

I can't believe there are that many species extinct. That's crazy, what are all of them?
How many extinct species?

The number of described living species still increases dramatically in groups like bacteria, mites and insects. In groups like vertebrates or spermatophytes, the number of described living species shows signs of saturation. How about the number of extinct species? The conditions allowing fossilization to occur are rare. Most layers containing fossils are inaccessible. The number of discovered accessible layers gradually increases with research intensity. Here we will try to use preliminary knowledge about the number of living species for estimating the number of extinct ones. Suppose that a species gives rise to a new one with a constant probability rate, say , and that it becomes extinct with another constant probability rate, say http://www.bio.vu.nl/thb/course/tb/exam/exam/img9.png. The latter implies that the existence time of a species follows an exponential distribution, with a mean existence time of . If denotes the number of living species at time http://www.bio.vu.nl/thb/course/tb/exam/exam/img25.png, the cumulative number of species and the simultaneous probability that the number of living species equals and that the cumulative number of species equals , then can be expressed as a function of :

(12.1)



When we transport the term from the left to the right, divide both sides by and let , we arrive at

(12.2)


This simple model defines the probability evolution of both numbers of species, if we specify the initial condition, e.g. . So we start with one single species for sure. The marginal probability evolution of (, obtained by dropping the index in (12.2 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:dpmn)),) is known as the linear birth and death process. We can extract useful information from (12.2 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:dpmn)), without actually solving the complete probability distribution as a function of time. The expected number of living species, , is found from (12.2 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:dpmn)) by multiplying both sides with and summing over all and . It is for this purpose convenient to define for negative values of and as well, but put them equal to zero. This allows us to sum over We then arrive at

(12.3)


For , we can solve :

(12.4)


In a similar way, we can multiply both sides of (12.2 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:dpmn)) by , sum over all and , arriving at

(12.5)


For , we can solve :

(12.6)


As an aside, we can evaluate the variance of as follows. First we multiply both sides of (12.2 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:dpmn)) by and sum over all and , arriving at

(12.7)



We then subtract the derivative of , which is :

(12.8)


For and noting, in general that has as solution, we find

(12.9)


This means that the variation coefficient of is given by

(12.10)


So, as for branching processes, the variation coefficient approaches a constant value. This is not mere coincidence, because the linear birth and death process can be conceived as a branching process by letting the generation time shrink to an infinitesimally small time increment , while the offspring distribution for 0,1 or 2 young has been tied to this increment via the probabilities , and . In a similar way, we obtain

(12.11)


which gives for :

(12.12)


and

(12.13)


which gives for :

(12.14)


from which follows that ) for large http://www.bio.vu.nl/thb/course/tb/exam/exam/img25.png, and that the correlation coefficient between and approaches 1 for large http://www.bio.vu.nl/thb/course/tb/exam/exam/img25.png. The expected number of extinct species is given by . Using (12.6 (http://www.bio.vu.nl/thb/course/tb/exam/exam/node33.html#eq:emt)), we find that . Since http://www.bio.vu.nl/thb/course/tb/exam/exam/img9.png equals (mean species existence time) and equals (ln expected no of living species)/(evolution time), we have that






For vertebrates, which fossilize relatively well, due to their hard bones, the evolution time took some 600 Ma to arrive at some 42000 living species. The mean existence time of vertebrate species is estimated to be some 2-3 Ma, based on fossil records, which means that for each living species, we expect some 600/(2.5 ln 42000) 23 extinct ones. The values for and http://www.bio.vu.nl/thb/course/tb/exam/exam/img9.png might differ between phyla. If we roughly estimate 30 million living eukaryotic species to exist, which took some 2000 Ma to evolve, and if we adopt the vertebrate mean species existence time, we expect some 46 extinct species for each living one. This model is irrealistically simple. This is obvious from the fact that, for this model, the extinction probability of a richly diversified group is extremely small. Yet such groups, like trilobites, ammonites and dinosaurs, became extinct, nonetheless. At present, the possible occurrence of periodic mass extinctions is in hot debate. Such complicating phenomena would only increase the number of extinct species to be expected. The above calculations could therefore be considered as a lower bound on the number of extinct species. During the last 300 year, 150 vertebrate species have been recorded to became extinct, mainly due to direct or indirect action of man. The expected extinction rate equals , which amounts to some 5.6 species in the last 300 year. The proper answer to the question posed in the title is therefore: too many! Further reading on vertebrate evolution: [#!Carr88!#]; On 'natural' and man-induced extinctions: [#!Stan87!#,#!Lewi86!#]. Example 6 for extinction and variation coefficients in branching processes.

[Steve]

Here's the Cliff Notes version of what DaJudge posted: the number of extinct species is a complete WAG.

;)

[Clod Hopper]

Sigfigs are always relevant. Just not cool. :)
Not cool to you. Once you have been deposed by a lawyer on the significant figures provided in a report you signed and stamped as a professional, suddenly they take on a whole new meaning. :slap:

[Steve]

Once you have been deposed by a lawyer on the significant figures provided in a report you signed and stamped as a professional, suddenly they take on a whole new meaning. :slap:

Aren't lawsuit depositions fun? :D

[creepycrawler]

Here's the Cliff Notes version of what DaJudge posted: the number of extinct species aren't nearly what they should be.

;)




:thumbsup:

[Mack]

Sigfigs are always relevant. Just not cool. :)

...ohhhhhh, that explains the buggyfab SO well :flipoff2:

[SCOUTMAN67]

More than twice as many births as there are deaths?

We need a good ol' fashioned plague! :D

[Grandpa Jeep]

Nearly as many abortions as deaths? I don't think I believe that.

[Clod Hopper]

Aren't lawsuit depositions fun? :D

nope. :mad: Being grilled for hours about stupid insignificant topics that have no relation to the lawsuit in the intent of trying to discredit me as a professional.... BULLCROPPY I SAY!! And I was just a material witness on that one!:eek: Glad I wasn't the defendant!