Re: To John Harshman -- re Isochrons

Zoe doesn't understand the difference between zero and non-existence.
Discussion is Few Tile
You will be illogicated

Dr Sidethink

"Eric Rowley" <poiuy@xxxxxxxxxxxx> wrote in message
news:WinLMSG.4405f79c.2698.40b1@xxxxxxxxxxxxxx
From: Zoe <muze10@xxxxxxx>:
On 26 Feb 2006 18:51:26 -0800, "John Drayton"
<bitbucket55@xxxxxxxxxxx> wrote:
<snip>

oh, dear, it seems I'm being drawn back into the wearisome
isochron discussion.

Yes, the whole point of the isochron is that the slope is
unchanged, and that is my question. The figures used to
calculate
the slope are figures that come from total D/Di. It seems
reasonable that if the ratios measured represent total D/Di,
that
the slope that results from these figures must also represent
total D/Di. Unless...

Unless the D/Di ratio is homoginized in which case OldD / Di
doesn't affect the slope.

Here is where the clever math comes in. Use ratios. Also, use a
premise of zero age at solidification.

I wish you could phrase that differently, it is self evident that
the rock is zero years old at solidification, it didn't exist
before that.

Now we're good to go.

The slope of the isochron is obtained by calculating the
differences between the ratios of D/Di in one sample to another,
in relation to their P/Di ratios. And it is taken for granted
that because the magma is homogenous, that at time of
solidification, the samples will all have taken up isotopes in
same ratios and as a result, they will plot at a single point on
the isochron.

No, on a horizontal line.
If they all plot on a single point there is no slope to calculate.

The age at solidification is therefore zero,

By definition, just like your age is zero at birth.

and
there will be no slope at that time. But as time passes, newD/Di
will increase, creating a slope that emerges from the
differences in the samples.

Ok.

My question is, okay, so once the isochron is drawn, and you
obtain a Y intercept that indicates the level at which oldD/Di
is supposedly present at time of solidification, then you should
be able to double check your results using the non-isochron
method by simply subtracting now-known oldD from total D, thus
getting new D.

Yes.

And the differences between samples should now
reflect what would be a shallower slope if represented on a
graph.

No.
Why should it be shallower?
As you write above it is the newD that creates the slope,
with just oldD the slope was zero.

So take three samples measured for isotopes as follows:

Sample Total D/Di

1 20D/2Di

2 30D/2Di

3 40D/2Di

Drawing an isochron with those reduced ratios of 10, 15, and 20,
in relation to whatever P happens to be, you get a slope that
intercepts the Y-axis at, let's say, 3. And since the assumption
is that the isotopes are taken up in equal ratios due to
homogenization of the magma, it is decided that all old D/Di
ratios would be the same. So
you get the following hypothetical reasoning:

If sample 1 were to have 6 oldD, it must have taken up isotopes
in the ratio of 6:2 (or 3).

Ok.

If sample 2 were to have 12 oldD, it
must have taken up isotopes in the ratio of 12:4 (or 3).

But Zoe, sample 2 only has 2Di!
Di stays constant, it doesn't go anywhere, it doesn't decay,
and it isn't the product of the decay of anything else.
If sample 2 takes up D and Di in the ratio 3 then it must take up
6 D just like sample 1.

And if sample 3 were to have 18 oldD, then it must have taken
up isotopes in the ratio of 18:6 (or 3).

Same error here and same answer, sample 3 starts with 6 D just
like samples 1 and 2

Therefore, all samples, at
the time of solidification, would plot at a single point,

Not a single point I hope, separate points along a horisontal line
or there will be no isochron, not to start with and not at any
time in the future.

and any slope above zero would be an
indication of accumulation of newD/Di.

Right.

And if I have that straight, then that is the scenario which I
am questioning.

I'm sure there must be many studies of just how homogeneous the
isotope ratios of fresh lava are but they may all be relatively
old since it's now known and there would be no need to keep
measuring it all the time.

Suppose the hypothesized quantities of oldD really did occur in
reality, then, using the generic approach, you should be able to
take the original quantities of oldD from total D and get newD.

Yes.

So sample 1 would be 20 totalD -6 old D = 14 newD

Right.

sample 2 would be 30 totalD -12 oldD = 18 newD

Wrong, 30 totalD -6 oldD = 24 newD

sample 3 would be 40 totalD -18 oldD = 22 newD

Wrong, 40 totalD -6 oldD = 34 newD

With these two sets of figures, (the ratios for the isochron and
the actual hard count for a generic graph), the isochron should
show a slope of 5,

Depends on what the values of P are but ok.

and the generic graph should show a slope of 4.

Wrong, with the corrected values of newD you get

14 newD / 2Di = 7
24 newD / 2Di = 12
34 newD / 2Di = 17

which with the same values of P as before give you a slope of 5!

Yet what happens if you work with ratios and carry the D/Di
ratios over to a generic graph (meaning, 3, 3, and 3)? Both the
isochron and the generic graph will have the same slope. The
slope will not change.

Exactly, and that is how the isochron works.

A clever mathematical trick --those ratios. And it will keep the
slope unchanged. But in the real world, you can't subtract
oldD/Di from total D/Di and have the same number.

No, you don't get the same numbers but the difference between the
numbers stays the same.

And since the slope is dependant on the difference between the
numbers rather than the actual size of the numbers it stays the
same as well.

The slope should decrease.

No it shouldn't.

It doesn't.

Exactly.

That was one question. Of course, if I've misunderstood anything
in the above, I'm sure I'll hear about it.

All I got in reply was that "we have special tricks" of
mathematics >> that can get rid of the effect of oldD/Di. >
Perhaps there was some poor choice of words there. >Most likely
everyone assumed that you knew that reality >doesn't change
because of any mathematical "trick".

exactly. The reality that oldD/Di is mixed with new D/Di, and
there is no way to separate them is why the need for
mathematical
intervention. >
How more clearly can I say this: >
No math changes reality.

exactly my point.

The mathematical "trick" here
simply demonstrated the reality that the variable has no
effect. It never did have any effect. The math didn't change
that. It didn't stop the variable from having any effect. It
wasn't even an attempt to stop the variable from having >any
effect. It simply showed that the variable has no effect.

the variable has no effect mathematically, but in the real world
it has to have an effect.

Not on the slope!

It effects the height of the line and it's Y-intercept but not
how much it leans.

And the reasoning upon which the math
is based is that the variable has no effect because of the
assumption that the magma was homogenous so, therefore, you
could start your slope at zero age.

Well the slope starts itself, scientists just measure it,
and there is also the conclusion that if it wasn't
homogenous the point would be randomly placed and very unlikely
to form a straight line.

That was my other question. What is the mechanism for making
magma homogenous?

That's been answered many times, diffusion and convection.

Eric



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Relevant Pages

  • Re: To John Harshman -- re Isochrons
    ... ability to create a slope on an isochron due to their having become ... isochron purports to explain. ... same number by use of ratios. ... I didn't say they were the exact same crystals. ...
    (talk.origins)
  • Re: To John Harshman -- re Isochrons
    ... isochron discussion. ... reasonable that if the ratios measured represent total D/Di, ... premise of zero age at solidification. ... If they all plot on a single point there is no slope to calculate. ...
    (talk.origins)
  • Re: To John Harshman -- re Isochrons
    ... isochron discussion. ... reasonable that if the ratios measured represent total D/Di, ... If they all plot on a single point there is no slope to calculate. ...
    (talk.origins)
  • Re: To John Harshman -- re Isochrons
    ... The whole point of the isochron is ... that the slope is unchanged. ... figures that come from total D/Di. ... Use ratios. ...
    (talk.origins)
  • Re: To John Harshman -- re Isochrons
    ... shallower slope. ... Remove the Di and it would be just newD and P. ... without regard for its real-world numbers? ... They are perfectly good real-world ratios. ...
    (talk.origins)
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