Looking at the anchoring
Becker has created a mean value curve (a chronology) which, he claims, ends at year 859.To anchor this curve into the then current late time chronology, starting at year 832, he needed and found a stem, the Eiche Aalen, that should bridge the time gap.
In a curve diagram, shown in the previous section, he demonstrated how the Eiche Aalen matches the historical standardcurve and how his new chronology matches the Eiche Aalen.
We will now look into the details of this matching.
Steps to go through for the analysis
1. The whole Master chronology of Becker covering the time BC370-AD1950.
2. The 120 years long late end segment of the Frümittelalteriche Eichen Maintal chronology taken from Becker's diagram covering the time AD740-859 according to Becker.
3. The Eiche Aalen sample covering AD744-980 taken from the diagram.
4. The early segment of the Huber standardcurve covering AD832-986 taken from the diagram.
To get the full length Huber standardcurve we will use the AD982-AD1950 segment of Becker's master chronology and add the standardcurve segment AD832-986 from the diagram (4. above).
We will then first analyse and show that Eiche Aalen really matches the full length Historical standardcurve as created above.
To study the anchoring process we need the full length of the Frümittelalteriche Eichen Maintal chronology starting at BC370 and ending at AD859. To create that we will use the segment BC370-AD740 of Becker's Master chronology (see discussion below) and add the late end segment AD740-859 of the Frümittelalteriche Eichen Maintal chronology from the diagram (2. above).
We will then add the Eiche Aalen to the Historical standardcurve to make a new reference and then see how the full length Frümittelalteriche Eichen Maintal chronology is
anchored into the full length Historical standardcurve (with Eiche Aalen included). That anchoring itself seems to be severely in error!
A further analysis of the Frümittelalteriche Eichen Maintal chronology reveals that the late end segment of 154 years matches AD859 (the intended place)
with a T-value of only 3.1 but with a T-value of 6.6 at AD1076!
That clearly indicates that at least the late end of Becker's Frümittelalteriche Eichen Maintal chronology is incorrect.
Adding the ring width pattern from AD922-1076 into the chronology at AD705-859 also made the final Becker chronology have two look-alike segments laying 217 years apart.
Testing that the Eiche Aalen sample really matches the Historical standard curve
To create that segment from the full chronology:
Open the Master Chronology by double-clicking on the member BECMCR.
In the "Look at a single block.." frame on the Curve display tab, set Start at = 0 (corresponds to 1950) and End at = 967 (corresponds to year 982).
Click the Create sample from block button to create the block/segment.
Save the new segment as e.g. MCR982.wid and add it to your collection at offset 0 (year 1950) as shown above.
See that only the members BECAAL, BECSTD and MCR982 are checked as above.
Save them with the command Collections/Write Collection as Decadal file WITH comments as LateBeckerChronology.rwl
That file is available for your reference and research as LateBeckerChronology.rwl
Click the Create mean value sample button with the two members checked as shown above to get the Historical Standardcurve in its full length as a reference.
A double-click on the unchecked BECAAL (the Eiche Aalen) member will then open that sample in a new window with the standard curve as the reference.
A correlation analys shows:
Transformation: Baillie/Pilcher (5,-2,T,eLog) --Rel Over Corr TTest GLK (year) -year lap coeff 970 147 0.36 4.7 0.67 (980) (as dated) 777 235 0.28 4.4 0.60 (1173) 981 136 0.26 3.2 0.52 (969) 918 199 0.20 2.9 0.56 (1032) 34 235 0.19 2.9 0.55 (1916) 631 235 0.18 2.8 0.54 (1319) 620 235 0.18 2.8 0.51 (1330) 951 166 0.21 2.8 0.55 (999) 577 235 0.17 2.7 0.57 (1373) 535 235 0.17 2.7 0.55 (1415) 997 120 0.23 2.6 0.56 (953)Using instead the Hollstein transformation gives CorrCoeff=0.38 and TTest=5.0.
Checking with our HollsteinBestLateToYear410 collection as the reference gives
--Rel Over Corr TTest GLK (year) -year lap coeff 994 235 0.34 5.6 0.66 (980) (as dated) 1400 163 0.26 3.4 0.59 (574) 351 235 0.21 3.3 0.56 (1623)With the Hollstein transformation the values are CorrCoeff=0.36, TTest=6.0
So Beckers dating of Eiche Aalen is reasonable!
Testing how the Maintal chronology matches the sum of Eiche Aalen and the Historical standard curve
When you then click the Create mean value sample button, you get a reference of about the same quality as that Becker had when he had added the Eiche Aalen sample to the Historical standard curve.
For this we have not the extention of the actual Maintal chronology but only a mean value of several chronologies as published as Becker's Master Chronology.
As the Maintal chronology taken from the diagram has a correlation coefficient of 0.73 towards the Master Chronology, it seems reasonable
to use a segment from the Master in place of the missing extension of the Maintal chronology.
Open the Master Chronology in a new sample window and create a block/segment covering the years BC 369 - AD 745 (index 1205-2317), save it in a .wid file as e.g. MTO745.wid and then add that to the new collection as shown above. Save the collection as e.g. MaintalExtended.rwl.
When you click the Create Mean value sample button you get
an approximate extended Maintal chronology with all the data that Becker wanted to anchor into
the Eiche Aalen sample and the Huber Historical Standard curve!
Baillie/Pilcher (5,-2,T,eLog)
--Rel Over Corr TTest GLK (year)
-year lap coeff
1029 176 0.28 3.9 0.56 (921)
874 331 0.20 3.7 0.57 (1076)
1067 138 0.27 3.2 0.56 (883)
1091 114 0.28 3.1 0.65 (859) (as dated)
705 500 0.14 3.1 0.52 (1245)
766 439 0.14 2.9 0.51 (1184)
377 828 0.10 2.9 0.54 (1573)
1163 42 0.41 2.9 0.67 (787)
1098 107 0.27 2.8 0.55 (852)
:
Testing the MaintalExtended collection towards ONLY the Eiche Aalen sample:
193 42 0.41 2.9 0.64 (787)
97 138 0.37 4.7 0.58 (883)
-1064 163 0.33 4.5 0.59 (2044)
121 114 0.33 3.7 0.63 (859) (as dated)
184 51 0.31 2.3 0.60 (796)
-204 235 0.26 4.1 0.59 (1184)
59 176 0.25 3.4 0.55 (921)
:
A block correlation towards the sum of the LateBeckerChronology collection reveals:
:
Block length: 150 Table sorted by Corr coeff.
Block -----Aimed------ -------Best ------------Three best matches with {hitAt,Corr coeff.,SetsSampleTo}
start --------at year around that ---1stBestMatch------- ---2ndBestMatch------- ---3rdBestMatch-------
0 1091 0.28 859 1091 0.28 874 0.47 874 (1076) 1163 0.41 1163 (787) 1154 0.31 1154 (796)
10 1101 0.26 849 1101 0.26 884 0.50 874 (1076) 1108 0.33 1098 (852) 443 0.31 433 (1517)
20 1111 0.23 839 1111 0.23 894 0.48 874 (1076) 1159 0.36 1139 (811) 842 0.29 822 (1128)
30 1121 0.30 829 1121 0.30 904 0.45 874 (1076) 852 0.30 822 (1128) 1121 0.30 1091 (859)
40 1131 0.25 819 1131 0.25 1151 0.39 1111 (839) 914 0.34 874 (1076) 1069 0.31 1029 (921)
50 1141 0.26 809 1141 0.26 1161 0.40 1111 (839) 1148 0.31 1098 (852) 1079 0.30 1029 (921)
60 1151 0.22 799 1151 0.22 1158 0.34 1098 (852) 1157 0.33 1097 (853) 1089 0.32 1029 (921)
70 1161 0.24 789 1161 0.24 1099 0.38 1029 (921) 927 0.31 857 (1093) 733 0.29 663 (1287)
I.e. a 150 years long block at the late end of the Maintal chronology ending at year 859, matches much (!!) better at year 1076.
If we create a 154 years long block from the late end of the sum of our extended Maintal collection, that block matches towards the LateBeckerChronology like this:
Transformation: Baillie/Pilcher (5,-2,T,eLog) compared to the reference LateBeckerChronology_2.d15 Dated to 1950 Minimum overlap used when finding best match: 40 Table sorted by TTest --Rel Over Corr TTest GLK (year) -year lap coeff 874 154 0.47 6.6 0.66 (1076) 1029 154 0.30 3.9 0.58 (921) 846 154 0.28 3.5 0.53 (1104) 483 154 0.27 3.4 0.60 (1467) 433 154 0.26 3.3 0.52 (1517) 1067 138 0.27 3.2 0.56 (883) 1091 114 0.28 3.1 0.65 (859) (as dated) 338 154 0.24 3.1 0.62 (1612) 174 154 0.23 3.0 0.60 (1776) 451 154 0.23 2.9 0.52 (1499) 524 154 0.23 2.9 0.61 (1426) 822 154 0.23 2.9 0.58 (1128) 1163 42 0.41 2.9 0.67 (787) 1098 107 0.27 2.8 0.55 (852) 20 154 0.22 2.8 0.59 (1930)My conclusion: There is something wrong with the late end of Becker's Frühmittelalterliche Eichen Maintal chronology and its dating to year 859!
Note:What may have happended is this:
The late end of Beckers Maintal chronology is not correct because it is based on a tree from year 1076 and not from 859.
Then Becker added the Eiche Aalen to that erroneous Maintal chronology according to this:
Transformation: Baillie/Pilcher (5,-2,T,eLog) --Rel Over Corr TTest BaPi Skel Skel GLK (year) -year lap coeff corr Chi2 corr -97 138 0.37 4.7 0.38 7.2 0.33 0.58 (956) 1064 163 0.33 4.5 0.33 17.1 0.32 0.59 (-205) 204 235 0.26 4.1 0.26 9.4 0.22 0.59 (655) -121 114 0.33 3.7 0.32 5.5 0.34 0.64 (980) (as dated) 1041 186 0.25 3.5 0.25 6.6 0.20 0.64 (-182) -59 176 0.25 3.4 0.25 10.8 0.28 0.55 (918)Becker selected the 980 match because of the 0.64 GLK-value!
With the Eiche Aalen added to his already erroneous Maintal chronology he got a chronology which ended with data that actually SHOULD be anchored at 980.
Transformation: Baillie/Pilcher (5,-2,T,eLog) --Rel Over Corr TTest BaPi Skel Skel GLK (year) -year lap coeff corr Chi2 corr 970 147 0.31 4.0 0.30 3.8 0.33 0.65 (980) (as dated) -253 1095 0.11 3.7 0.11 2.3 0.10 0.53 (2203) -897 451 0.15 3.1 0.15 6.8 0.13 0.54 (2847) 777 340 0.17 3.1 0.16 0.2 0.10 0.52 (1173) -923 425 0.15 3.1 0.15 0.2 0.13 0.59 (2873)So the result depends a lot on in which order we do these things.
High correlation coefficient values and high T-values are not characteristic for the way this GLK technology was carried out.
As it looks, Becker had very limited computer resources! It is the technology he used that led him to make errors.
Using the Hollstein data as a reference
Transformation: Baillie/Pilcher (5,-2,T,eLog) --Rel Over Corr TTest GLK (year) -year lap coeff 898 154 0.41 5.5 0.60 (1076) 870 154 0.32 4.2 0.58 (1104) 475 154 0.29 3.8 0.57 (1499) 1086 154 0.28 3.5 0.58 (888) 1053 154 0.26 3.3 0.56 (921) 18 154 0.26 3.3 0.55 (1956) 946 154 0.26 3.3 0.56 (1028) 1050 154 0.26 3.3 0.54 (924) 1106 154 0.24 3.0 0.56 (868) 1115 154 0.24 3.0 0.56 (859) (as dated) 1011 154 0.23 2.9 0.52 (963) 213 154 0.23 2.9 0.59 (1761) 548 154 0.23 2.9 0.61 (1426)Though, if we look at only the latest 80 years the correlation of that segment/block towards year 859 of HollsteinBest is only at corr-Coeff= 0.03! The rest is at 0.53.
If we cut off these late 80 years from Beckers curve, the rest - back to year 410 - will match almost perfectly towards our HollsteinBestLateToYear410.rwl collection at the time where Becker wanted it to match!
The corresponding curve for our HollsteinBestLateToYear410 collection does not show a corresponding problem at these years.
I.e. there is no sign that Mother Nature has created some sort of same ring patterns for these two periods.
Instead, it looks as Becker has copied the ring width pattern of years 932-1037 into the "year-region" of 715-820
when he anchored his chronology into the Historical standard curve of Huber.
I.e. it looks as Becker had the ring width pattern from the period 932-1037 in the late tail of his chronology ending at AD859.
So either the anchoring of Beckers chronology BC369-AD859 seems wrong
or the late pattern of his Early Middle Ages chronology seems wrong.
With the data of the tables above, I cannot justify Becker's choice of anchoring point!
To me (!) it looks as Becker wanted to anchor his chronology at year 859 because evidence in European history (the calender chronology) said it should be like that.
This all raises the question about other crossdatings done with other chronologies.
With the acceptance of such low correlation values as above, errors have to be common!
The Roman time samples - A comment
BECRSU - Sulz: Sulz does not match properly towards the other samples.
BECRMU - Murrhardt: The late 27 rings have a negative correlation (-0.30) towards the rest of the samples (excluding Sulz).
Except for Sulz, these samples crossdate towards each other with a correlation coefficient between 0.5 and 0.6 giving T-values in the range 7.6-10.
Except for BECRSU and BECRMU (even without the late 27 rings) they all match reasonably well towards the Hollstein Roman collection.
The Sulz problem:
Running a correlation test of BECRSU (Sulz) towards the rest of the samples gives: Transformation: Baillie/Pilcher (5,-2,T,eLog) --Rel Over Corr TTest GLK (year) -year lap coeff 11 99 0.30 3.1 0.63 (170) 46 99 0.28 2.9 0.57 (135) 104 98 0.28 2.8 0.56 (77) (as dated) 5 99 0.22 2.2 0.53 (176) 39 99 0.22 2.2 0.58 (142) -58 41 0.32 2.1 0.55 (239) 25 99 0.20 2.0 0.52 (156) 29 99 0.19 1.9 0.57 (152) -16 83 0.20 1.8 0.52 (197) 124 78 0.19 1.7 0.47 (57) 17 99 0.16 1.6 0.51 (164) 76 99 0.16 1.6 0.54 (105) 30 99 0.16 1.6 0.53 (151) 158 44 0.24 1.6 0.53 (23)I do not understand why the Sulz sample was at all included with the curve diagram - it looks like a mistake.
Continue with the next section, Summary and Conclusions!
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