Back to "Dogs of my own" Contents Back to Home                                                                3   I S   T H E    N U M B E R   O F  T H E   M Y S T I C S   I know that from the auld lang syne and up to now, 3 has been and is still the number - or one of the preferred numbers - of the mystics, and of course of every kind of witches ! Nevertheless, that's not the reason why I think of it today.  Come to that, I don't consider at all the number 3 has more qualities that the other numbers ! ! ! ... 3 !  3 !  3 ! Mathematics have been the greatest pleasure that enlightened my schooldays, they were too the best things to fill my free time. The pleasure of numbers still remains inside of me, and I often can't help to use - and to play with - numbers at the earliest opportunity. This explains why my Croatian Sheepdogs conjure up for me the number 3. First, my current litter is the 3rd of mine, at least in Croatian Sheepdog - because with my Mudi one, it's the 4th litter, but isn't the number 4 the integral of 3 ? (more exactly, the integral of 3 is 1/4 of 4) 3 is he number of my imported Croatian Sheepdogs. 3 is the number of the pups of my first litter, more exactly the registered pups. 3 is the number of the pups of my second litter. But 3 isn't the number of the pups of my 3rd litter ! Nevertheless, it's the number of the males of this litter, and up to now it's also the number of the pups that I kept at home, although that may change one day. 3 is also the number of the "angels", that is to say Fango and his 2 sons that reminds very much of him, and who are precisely named "angel" in Croatian. One of them, Andeo, reminds so much of Fango that sometimes I'm not able to know who I'm seeing at first sight, and then I look at the tail, for Fango's one has been cut when he was young. Andelko and Andeo appear overall similar, while their brother, Arslan, with a smallest height can be easily differentiated from them. My first litter was born from the same parents, so comparison is possible, at least with the V-litter male, Vuk. Vuk 's height was precisely between those of Arslan and the two angels (who have about the same). His coat was rather like Arslan's one, his head too. The bitch had the same coat than the two angels, and a pretty head expression that seems to originate in Fango. Unfortunately, genetics can't be reduced to mere rules of mathematics ... !  It would be so much simple ! For example, mathematics would maintain that a pup is made of half the mother and half the father, or in another way, that the mother gives one half of the child, and the father the other one. Every one can observe how things reveal to be more complicated ! ! ! Now, with my B-litter from another male, I can compare offspring in another point of view, searching differences between V- and A-litters and the B-one. First, it seems that the mother doesn't leave many marks in her offspring, and let the father fully express his characteristics. Nevertheless, Snasha's dark brown eyes are able to improve those of both Fango and Gidan, but the improvement seems to be more important in Gidan's offspring than in Fango's one, although the two males have similar eyes-colour (dark brown in the center, light brown around). I noticed too that the rounded skull of Snasha left a little mark to some of her offspring (less than half offspring). Gidan's head seems to leave important marks in his offspring, regarding both his morphology and his expression, and I consider the head as the first difference between the V-A-litters and the B-one. Ears appear to be precocious in Gidan's offspring than in Fango's one. It's still too early to judge of the B-litter adult coat. But genetics shouldn't be classed as mathematics, even statistics, that is to say a part of mathematics. And another litter with the same parents could bring the surprise of different offspring !  2 + 1 litters  can't allow to draw any conclusion about the genotype of my 3 dogs that got offspring. Statistically, 2 + 1 litters don't mean anything.   I didn't meet any hereditary problem in these 3 litters - at least for the time being - but nothing can be concluded for all that. In the opposite, it is said that any new hereditary characteristic can appear in a litter although that has never been found before, because mutation may happen in any litter, and with mutation, new gen can appear in a blood line. That means that, because of mutation, new characteristics may appear in one pup, although this characteristic doesn't exist in both parents genotype ... Half mother  +  half father  =  the child, that belongs to mathematics but not to genetics ! ! ! Perhaps should a 3rd factor be envisaged ? ? ? During my schooldays, I enjoyed particularly any kind of (hard enough) equation. If  1/2 mother  +  1/2 father  =  the child  can't be considered as a true proposition, I would rather write : the child  =  a x 1/2 x mother   +  b x 1/2 x father  +  c x 3rd factor In this proposition, a, b and c coefficients are weightings that depend on every case, that are different in each case and for each pup - for example, in my litters it seems that in any case the coefficient a is always low, while b seems to be higher, but that depends of c, for it could be considered that in any case :  a  +  b  +  c  =  1. What about the "3rd factor" ? That means in fact all that is out of mathematics ! That means all that could appear as incomprehensible, included what may happen because of mutation. That means too all that could be called "the luck" - good or bad luck ...  That means also things that the breeders can't do anything about (or against ...). So I enjoyed especially equations when I was at school. But now I get older, and times have changed. Although I still enjoy as much as I did before to solve mathematical problems and particularly equations, time made me be able to take fun to design my own equation ! If the number 3 led me from my Croatian Sheepdogs to genetics, I must manage to concoct something with 3 unknowns, so with 3 equations.           3        2                 2      3 x   +  y    z   =    y  z     -  13/4      x y   -  z   =   -  3/2   x          3      x y   +  z   =   z  y It's more than easy to reduce to 2, then to 1 unknown, and so that's really easy to solve. BUT ... But in fact, what really mean x, y and z  ? ? ? !   !   ! 06/02/07 Isabelle Coquinot Back to "Dogs of my own " Contents Back to Home