Freethought & Rationalism Archive

Valentine Pontifex · 05-09-2002, 09:49 PM

Douglas,

Your errors in this are several.

You seem to be thinking that Di can change over time when you write "where "(D[i]:[Orig]) is just the original amount of D[i] in the rock". If it is a closed system which is the stated assumption of case 1 then Di is a constant. Thus any notion of Diorig is unneeded.

Quote:

At this point, there are two unknowns in the equation: "t" and "D[Orig]".

If you want to know what DOrig just look at the y-intercept is that quantity (divided by Di). In any event, it is clear that you don't quite understand what is going on here.

Basically on measures the isotopic ratios of a bunch of spots on the rock. Then gets out the graph paper. (Okay nitpickers, I know this really done by a computer in a numeric fashion.) Label the y-axis D/Di and label the x-axis P/Di. (For the graph we are plotting the numbers from the here and now.) Plot the data.

To do this you do not need to know either t or Dorig.

(BTW, one thing that I might have made clear in that post is that Dnow/Di = (D/Di)now for reasons that should be obvious.)

Now look at equation again:

(D/Di)now =(e^kt-1)(P/Di)now + (D/Di)orig

This equation demands that the points that were plotted on the graph paper will all be on a lingle line that is called an "isochron." Why? Simple. Anything in the form of y=mx+b where m and b are constants is a line. Remember what we labeled the x-axis and the y-axis? Those are x and y. (D/Di)orig is clearly a constant. e^kt-1 is also a constant since the measurements were done at a particuar point in time (i.e. now when the lab work was done).

Thus to solve for t, one only needs to know the slope. It should be fairly simple to show that t=ln(m+1)/k.

Quote:

Note that, as worded, this only means that it is assumed that for any particular rock sampled (let's say from a particular "lava flow") from a particular geographical location, the ratio of the elements D and D in the rock at the time it formed would be the same throughout, and thus that for any rock sampled from that lava flow (from any rock formed from that flow at the same time), the ratio D/D[i] would be equal to some constant, "k" (that is, for a particular geographical location, rocks from that location would have (D/D[i])[Orig] = k).
The error lies here, from what I can tell. Ardipithecus appears to also assume (in addition to the assumption he gave as he worded it) that the ratio, D/D[i], would be homogeneous throughout [i]ALL the Earth, througout ALL time, and from speaking to a college chemistry professor about this, it seems that this would be a very unlikely scenario. Without this assumption, the particular value of "k" would be unknown (and each sample, "S[j]", would have its own value for "k" [i.e., "k[j]"]).

For example, in the formation of some rock in, say, the area of Egypt thousands of years ago, perhaps there would have been a higher proportion of D to D than, say, in the formation of some rock in Hawaii a few hundred years ago. On this point, I would grant that IF it was known, or there was strong reason to believe, that the ratio of a radioactive daughter element to the non-radioactive isotope of the same element as the daughter would always be the same, throughout all the Earth and throughout all time, then one could probably usually determine D[Orig]. However, it still would be possible to determine D[Orig] from this ONLY IF there actually [i]were some traces of D in the rock sample (if not, then Equation (1) would reflect the fact that one could not determine D[Orig], in that one would be dividing by zero).

Now we hit a really big misunderstanding of what is going on. Case 1 does not care one bit what is going on outside of the rock since it is a close system. Di is a value measured in the lab. Indeed it will likely be different for every point in the rock. The method does NOT assume any constant isotopic ration for the entire planet.

What the method does assume is that the rock was once molten lava. D/Di will be the same because of basic chemistry and physics. The reasons is that these two isotopes, for all practical purposes, act in an identical manner. The only way to vary that ratio is for them to act differently.

Quote:

To summarize: Based on ardipithecus' wording of his "finally stated" assumption, there is no justification for setting (D/D[i])[Orig] to a constant

If the assumption that I just described above, that D/Di is the same throught the rock at formation, then clearly (D/D[i])[Orig] is a constant.

Now if this extremely safe assumption bothers you, then consider that the test is in the data. If that assumption is false the isochron is destroyed and a line will not form (save for an excedingly improbably coincidence).

Now you may ask why this isotope ratio varies after the rock has solidified. This is quite simple. While two isotopes of the same element act in a virtually identical fashion, two different elements do not. P is not the same element as D. P and D are chemically different, have different melting points, different densities, different pretty much everything. Thus the P/D ratios will be different through the rock. (And if they did not then the plot will have but a single point and the isochron is moot.) Thus different spots in the rock will get different amounts D formed from radioactivity and hense D/Di will vary. Indeed when the rock forms the isochron is a horizontal line (m=0). Afterwords the slope will increase over time.

Again I will emphasize that if any of the assumptions of case 1 are false the proof of the line is invalid and the chance of forming a line is extremely small. Thus the formation of isochron line is a test of the assumptions being made.

[ May 09, 2002: Message edited by: LordValentine ]

Valentine Pontifex · 05-09-2002, 10:06 PM

One thing about the "error" Douglas thought he found. Douglas, did you really think you that in ten minutes you had found an simple high school chemistry error in a line of reasoning that examined by thousand of people including chemists and physicists in a method employed by people who measure those isotopic ratios for a living could not find in 41 years?

Also I recomend that anyone taking part in this debate actually read <a href="http://www.talkorigins.org/faqs/isochron-dating.html" target="_blank">Isochron Dating</a> FAQ. Chapter 3 of Dalrymple's The Age of the Earth is also recomended.

Ragnarok · 05-10-2002, 02:35 PM

Quote:

Originally posted by Douglas J. Bender:
faded_Glory,

...while I still believe there is error in ardipithecus' reasoning, I must say that it is not quite as "obvious" as I had thought. And conclusively determining the nature of the error has taken me a great deal more time than just the 10 minutes I mentioned (I called a few chemistry professors today [I hate chemistry], and wrote down some notes, just to be sure I wasn't mistaken - probably maybe an hour of time, total). So, in that respect, I was wrong (but I'll blame it on ardipithecus' [or, if the heart of his post was copy/pasted, the original author's] poor description of the equation and reasoning).
[ May 09, 2002: Message edited by: Douglas J. Bender ]

ROTFLMAO!

Translation: "I was wrong - but in some mystical sense which only I, the mighty Douglas, can possibly understand, I WAS RIGHT"

Guess what Doug. You weren't right. You made the same mistake I did. You were 100% wrong (so was I but of course it was The Prophet who led me astray).

I read Lord Valentine's and faded_Glory's informative posts above as well as the talk-origins material. Guess what, ardipithecus' post was a correct representation of the Isochron method and the method itself is sound. And the score at the end of nine innings.

Science: 45,000,000,000,000,000
Douglas: 0

<img src="graemlins/boohoo.gif" border="0" alt="[Boo Hoo]" />

AdamWho · 05-10-2002, 02:48 PM

So this philosophy teacher says to his students:

Two negative make a positive but to positives never make a negative.

A skeptical student replies:

Yeah, yeah....

Ragnarok · 05-10-2002, 03:07 PM

Quote:

Originally posted by AdamWho:
So this philosophy teacher says to his students:

Two negative make a positive but to positives never make a negative.

A skeptical student replies:

Yeah, yeah....

S2Focus · 05-10-2002, 07:26 PM

Quote:

Originally posted by Douglas J. Bender:
faded_Glory,

I have to thank you for your reserved and to-the-point last two posts - while I still believe there is error in ardipithecus' reasoning, I must say that it is not quite as "obvious" as I had thought. And conclusively determining the nature of the error has taken me a great deal more time than just the 10 minutes I mentioned (I called a few chemistry professors today [I hate chemistry], and wrote down some notes, just to be sure I wasn't mistaken - probably maybe an hour of time, total). So, in that respect, I was wrong (but I'll blame it on ardipithecus' [or, if the heart of his post was copy/pasted, the original author's] poor description of the equation and reasoning).

In any case, I'll just make my next post my explanation of what I understand to be the error in ardipithecus' reasoning, and we'll see what happens. I think that should essentially answer any questions you posed to me in your two posts.

In Christ,

Douglas

[ May 09, 2002: Message edited by: Douglas J. Bender ]

Douglas,

If you want to preserve your dignity (and deny the evilutionists here a great deal of laughter and merriment at your expense), you'll just come straight out and admit that you were wrong, without any qualifiers or weasel-words.

[ May 10, 2002: Message edited by: S2Focus ]

MadMordigan · 05-11-2002, 06:25 AM

TollHouse · 05-11-2002, 10:49 AM

...and that's the end of that chapter.

faded_Glory · 05-11-2002, 02:46 PM

Not much to add to Lord Valentine's excellent explanation. It is hard to clarify in words what is going on, much easier to graph it.

The key, just to repeat ourselves, is that isotopes of the same element (in this case Strontium 87, the daughter product of decaying Rubidium 87; and Strontium 86) are chemically identical (after all, isotope means in the same place, that is, in the same place on the Periodic Table of Elements. And since an element's place in the table determines how it behaves chemically, Sr87 and Sr86 behave identically).

When magma solidifies, minerals are formed from the melt in a series of reactions driven by the magma composition, the temperature and the pressure. The proportion of Sr87/Sr86 in the minerals forming from the same melt will be uniform throughout the resulting rock because the elements are chemically identical and will not be preferentially concentrated in particular parts of the magma. This does not at all mean that the Sr87/Sr86 ratio in some other molten magma body elsewhere is the same!

In the presence of original daughter material (Sr87) at the time of crystallisation, the proportion of Rb/Sr will be different for different mineral grains, because Rb and Sr are different chemical elements and will be involved in different reactions during crystallisation. Since Sr87/Sr86 is constant, the proportion of Rb87/Sr86 will be different as well in different mineral grains. Hence, analyses done on different mineral grains from the same original magma, at time zero, will plot on a straight line parallel to the axis Rb87/Sr86, with an intercept on the Sr87/Sr86 axis equal to the original ratio.

Once crystallised, the various elements are locked up in the mineral grains, and if we take samples from virgin rock we can assume that no atoms have entered or exited the system since solidification. The amount of Sr86 stays the same as it was at crystallisation. However, radioactive decay produces Sr87 at the expense of Rb87. The points will therefore over time move away from their original position on the flat line, in the direction of increasing Sr87 (and thus increasing Sr87/Sr86) and decreasing Rb87 (and thus decreasing Rb87/Sr86), proportional to the original amount of Rb87 in that particular mineral grain. It is easy to show that the points will remain aligned on a straight line, as time progresses, and that the angle of rotation of this line is proportional with the time lapsed since the atoms were locked in place.

So, rather than a trivial algebraic trick, let alone an error, the addition of a third, stable isotope in the analysis is an elegant and perfectly valid way to circumvent the potential error source of an unknown initial quantity of Sr87.

Douglas, does this now convince you of the validity of Rb/Sr dating? If not, why not?

fG

[ May 11, 2002: Message edited by: faded_Glory ]

Valentine Pontifex · 05-12-2002, 09:08 AM

I will add that I also have a post on <a href="http://www.christianforums.com/forums/showthread.php?s=&threadid=12682" target="_blank">Pb-Pb isochrons</a> and <a href="http://www.christianforums.com/forums/showthread.php?s=&threadid=13315" target="_blank">concordia-discordia dating</a>.

05-11-2002, 02:46 PM	#49
faded_Glory Veteran Member Join Date: Jul 2000 Location: Cairo, Egypt Posts: 1,128	Not much to add to Lord Valentine's excellent explanation. It is hard to clarify in words what is going on, much easier to graph it. The key, just to repeat ourselves, is that isotopes of the same element (in this case Strontium 87, the daughter product of decaying Rubidium 87; and Strontium 86) are chemically identical (after all, isotope means in the same place, that is, in the same place on the Periodic Table of Elements. And since an element's place in the table determines how it behaves chemically, Sr87 and Sr86 behave identically). When magma solidifies, minerals are formed from the melt in a series of reactions driven by the magma composition, the temperature and the pressure. The proportion of Sr87/Sr86 in the minerals forming from the same melt will be uniform throughout the resulting rock because the elements are chemically identical and will not be preferentially concentrated in particular parts of the magma. This does not at all mean that the Sr87/Sr86 ratio in some other molten magma body elsewhere is the same! In the presence of original daughter material (Sr87) at the time of crystallisation, the proportion of Rb/Sr will be different for different mineral grains, because Rb and Sr are different chemical elements and will be involved in different reactions during crystallisation. Since Sr87/Sr86 is constant, the proportion of Rb87/Sr86 will be different as well in different mineral grains. Hence, analyses done on different mineral grains from the same original magma, at time zero, will plot on a straight line parallel to the axis Rb87/Sr86, with an intercept on the Sr87/Sr86 axis equal to the original ratio. Once crystallised, the various elements are locked up in the mineral grains, and if we take samples from virgin rock we can assume that no atoms have entered or exited the system since solidification. The amount of Sr86 stays the same as it was at crystallisation. However, radioactive decay produces Sr87 at the expense of Rb87. The points will therefore over time move away from their original position on the flat line, in the direction of increasing Sr87 (and thus increasing Sr87/Sr86) and decreasing Rb87 (and thus decreasing Rb87/Sr86), proportional to the original amount of Rb87 in that particular mineral grain. It is easy to show that the points will remain aligned on a straight line, as time progresses, and that the angle of rotation of this line is proportional with the time lapsed since the atoms were locked in place. So, rather than a trivial algebraic trick, let alone an error, the addition of a third, stable isotope in the analysis is an elegant and perfectly valid way to circumvent the potential error source of an unknown initial quantity of Sr87. Douglas, does this now convince you of the validity of Rb/Sr dating? If not, why not? fG [ May 11, 2002: Message edited by: faded_Glory ]</p>

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05-09-2002, 10:06 PM	#42
Valentine Pontifex Veteran Member Join Date: Jul 2001 Location: Orion Arm of the Milky Way Galaxy Posts: 3,092	One thing about the "error" Douglas thought he found. Douglas, did you really think you that in ten minutes you had found an simple high school chemistry error in a line of reasoning that examined by thousand of people including chemists and physicists in a method employed by people who measure those isotopic ratios for a living could not find in 41 years? Also I recomend that anyone taking part in this debate actually read <a href="http://www.talkorigins.org/faqs/isochron-dating.html" target="_blank">Isochron Dating</a> FAQ. Chapter 3 of Dalrymple's The Age of the Earth is also recomended.

05-10-2002, 02:48 PM	#44
AdamWho Contributor Join Date: May 2001 Location: San Jose, CA Posts: 13,389	So this philosophy teacher says to his students: Two negative make a positive but to positives never make a negative. A skeptical student replies: Yeah, yeah....

05-11-2002, 06:25 AM	#47
MadMordigan Beloved Deceased Join Date: Jul 2000 Location: Vancouver BC Canada Posts: 2,704	<img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />

05-11-2002, 10:49 AM	#48
TollHouse Veteran Member Join Date: Feb 2001 Location: Austin, TX Posts: 8,745	...and that's the end of that chapter.

05-12-2002, 09:08 AM	#50
Valentine Pontifex Veteran Member Join Date: Jul 2001 Location: Orion Arm of the Milky Way Galaxy Posts: 3,092	I will add that I also have a post on <a href="http://www.christianforums.com/forums/showthread.php?s=&threadid=12682" target="_blank">Pb-Pb isochrons</a> and <a href="http://www.christianforums.com/forums/showthread.php?s=&threadid=13315" target="_blank">concordia-discordia dating</a>.

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