- a collection of essays on Neodruidic Studies
- a journal of Post-Reconstructionist Neopaganism

Friday, May 3, 2013



Is Yule the beginning of Winter ?

Is Yule the middle of Winter ?

Is Imbolc the middle of Winter?

Is Imbolc the end of Winter ?

Is Imbolc the beginning of Spring ?

Is the Vernal Equinox the end of Winter ?

Is the Vernal Equinox the beginning of Spring ?

Is Beltaine the middle of Spring ?

Is Beltaine the end of Spring?

Is Beltaine the beginning of Summer? 

Ok then... 

What if I tell you that the answers to all of the above are actually “YES” ? 

Individually considered, many of the above seem to be “true”, yet collectively they seem to contradict each other. This brings into focus an area of dispute among modern pagans which actually frames some old time philosophical principles and one revolutionary new field of logic, one in which modern scholars from every domain from physics to sociology are making discoveries that will change the future of human thought.

In a debate with Al Gore in October of 2000, employing his typically brilliant “repartee”, George W. Bush described Gore’s economic plans as employing “fuzzy math”, thereby for many years muddying the public’s ability to apprehend a legitimate new field in the sciences with the unfortunate name “Fuzzy Logic”. At that point, it seems Bush was trying to imply that by nature, math is confusing and not to be trusted. As you may imagine, that did not go over well with the mathematicians(1.). But if I suggest to you we should consider the application of “Fuzzy Logic” when discussing the Wheel of the Year, what would that be about? Ok, we’ll get to that in a bit, but first things first…


This was always a favorite topic of our founder, Isaac Bonewits. From being exposed to his constant references to these principles I’ve condensed my understanding of them into the two definitions below…

A philosophic principle limiting systems of thought into “either-or” sets of two principles assumed to be mutually-exclusive: True vs. False; Good vs. Evil; Love vs. Hate; Matter vs. Spirit; Mind vs. Body; Man vs. Nature

A system of thought which allows for more than one seemingly contradictory view to be held at once. Challenges the notions of “absolutes” upon which systems like Dualism are founded. - earrach (2.)

Yes, Isaac, ADF, myself, and much of Neopaganism were onboard with this (pluralistic) type of thinking long before any of us ever heard of that odd-sounding term “Fuzzy Logic” emerging from the halls of academia.


One needs to realize from the start that 
the word “fuzzy” in the name is not a quality judgment;
it’s actually referring to this new mode of thought's intentional methodology. Fuzzy Logic is a serious attempt to model the world more accurately and productively than is possible from a dualistic viewpoint. We're not talking unicorns and rainbows here, we're talking life and death, and dollars and cents.

Take a bite out of an apple. And another. And so on… Although we definitely started with the state of (“an apple” = “true”), at what point is it no longer “an apple” and therefore, (“an apple” = “false”)? With the first tiny square 1/32nd of an inch of the apple your teeth remove, is it still “an apple”? Once you have eaten 61% of the apple’s mass, is it still “an apple”? So then, as you continue, when does it cease being “an apple”?

fig.1., Fuzzy Logic behind the wheel of your car

Now, looking at the example fuzzy-logic diagram above and, understanding that the vertical (“truth”) axis increases from zero (“false”) to 1.0 (“true”), then try replacing the terms “slow”, “medium”, and “fast” with other term-sets like:

       “cold”, “medium”, and  “hot”
       “young”, “middle aged”, and  “old”
        ( Make a fresh drawing if you have trouble visualizing these alternate versions… )
With these simple examples, we can easily see what the scholars working on Fuzzy Logic mean when they say

      “Truth is not a binary proposition. 
       In the real world, truth is simply a matter of degree.” (3.)


There's lots of folks inside and outside of Paganism who feel that there's something cold or unnatural about the seasonal quarter divisions on the calendar often assuming that the astronomical quarterdays have no "real" functional connection to the changes in weather and greenery. Their arguments are almost always fixated on regional variances in climate and agrarian activity alone. How often have we heard the following kind of statement?:

“The date that a season begins varies with local climate, so it's kind of silly for there to be a declaration that a solstice or equinox is the first day, no matter where one lives. In Irish and Germanic lore Summer Solstice is "Midsummer", not the beginning of Summer. In Celtic folklore the festivals are often called "fire festivals" or by similar terminology. I assume this is because bonfires were usually an important part of the festivities. On Imbolc, depending on where one lived (climate at that time of year in the north of Scotland will vary significantly from that in the south of Ireland, for instance), people were less likely to have outdoor bonfires, but fire is still an important part of the festival in the form of hearthfires, candles, and the focus on Brighid, who is a Goddess of the fires of the hearth and smithy and the fires of inspiration (among many other things).” 
- Kathryn NicDhĂ na (4.) 

Well, yuck. As a self-styled “astronomer-priest”, enraptured by solstices and equinoxes and such, quotes like the above always paralyse me in frustration by its multiple whammy of a dozen missed points and, well… it is the reason compelling me to write this very essay. Nonetheless, don’t get me wrong, Kathryn is a careful editor of Wikipedia topics touching on Celtic Reconstructionism (“CR”) and her comments are generally more than worthy of one’s attention.  But then


fig.2., Fuzzy Logic solves the Dualistic Paganthink 
regarding the seasons and the Wheel of the Year !

(Uh huh.)

SO, "When - do - the seasons begin and end?" 

The most appropriate answer here is  "THEY DON'T".

They simply increase or decrease in degree, relative to their proximity to the seasons to which they are adjacent.

IMO, "beginnings" and "endings" are simply human concepts and are not found in Nature...


SEASONAL QUARTERS (astronomical/ calendrical) :   
“The annual spans of time framed by the solstices and their adjacent equinoxes.”  - The word "seasons" here is referring to the four sectors of the Earth's annual orbit of the Sun framed by the astronomical quarterdays.

1.) The northern hemisphere's seasonal quarters carry their opposite names in the southern hemisphere: winter is summer; spring is autumn.  
2.) Actually not just a case of 365.242/4, each of the four "seasonal" sectors of the Earth's orbit contains a different number of days (northern nomenclature used here...):
     • Winter =    88 .99 days 
     • Spring =    92 .76 days 
     • Summer = 93. 65 days 
     • Autumn =  89. 84 days  
Regardless, "quarters" remains a common descriptive term for these four sectors framed by the quarterdays (solstices and equinoxes).

CLIMATIC SEASONS (weather based / agrarian) :   
The weather norms traditionally associated with a time of year in a general locale.”  See the above discussion of the critics of the astronomical/calendrical "quarters".

CaveatUltimately, all annual extended weather sequences are driven (CAUSED-DIRECTLY) by the effects framed by the solstices and equinoxes framing the seasonal quarters of the year. 


A striking analogy can be seen by comparing the temperature of times of one day with the dates of the solstices and equinoxes relative to the typical temperature extremes found throughout the year: 

Midnight ( = least Sun, but not coldest time yet), followed by the

Wee-Hours ( when then it’s the coldest.), 
    which, is not unlike
Yule Solstice ( = least sun, but not coldest time yetin relation to
Jan. / Feb. ( when then it’s the coldest.)

Noon ( = highest Sun, but not the hottest time yet), followed by
Mid-afternoon ( = when then it’s the hottest.)
    which, is not unlike
June Solstice ( = highest Sun, but not the hottest time yet.), followed by
July / Aug. ( = when then it’s the hottest.)

SO, the "seasons" of a day and the seasons of a year are remarkably similar in basically the same ways when we consider the effect of the lag in temperature relative to the quartered framework in time. With the Sun at its very highest, Noon is an obvious quarter-point of the day, yet the day will not reach its hottest for a couple more hours, during "mid-afternoon". Still, this does not really detract from the primacy in the cycle that we see in the moments of midnight and noon, or of the December and June solstices; they still are clearly the source of the effects that follow.

So, when larger systems appear to us as being wonderfully resonant of the earlier forms on which they are built at the miniature scale, we remember that we as reflective observers are forever fixed at the junction between the macroscopic and microscopic domains and we cannot help but recall 
the Hermetic maxim...

"As above, so below"...
( When in doubt, consult your local cauliflower... )


1. http://www.nytimes.com/2000/10/06/opinion/l-bush-vs-gore-debate-aftermath-fuzzy-math-520543.html   

2, Earrach of Pittsburgh (2003), 
"Do You Believe in the Gods and Goddesses ? Part II "
from Belief and Neopagan Spirituality :  

3. Kesko, Bart  Fuzzy Thinking, the New Science of Fuzzy Logic, NY Hyperion, 1993

4. From Kathyrn’s comments on  http://en.wikipedia.org/wiki/Talk:Wheel_of_the_Year