the slippery slope

Danger: Slippery Slope
I think it time to share Shields’ Slippery Slope Axiom (although I’m sure someone else has said this before):

The truth lies half way down the slippery slope.

Many set off down the slope and slide to the bottom. Many remain at the top seeking to avoid the slope having seen too many slide to the bottom. Few brave souls set off down the slope and struggle to remain neither near the bottom nor the top, viewed by those at both extremities as being in the wrong.

a model prayer?

This prayer shows that the predilection for self-interest expressed in some streams of modern christianity is nothing new. It is a prayer of one John Ward, M.P., from 1727:

O Lord, Thou knowest that I have nine houses in the city of London, and that I have lately purchased an estate in fee simple in Essex. I beseech Thee to preserve the two counties of Middlesex and Essex from fires and earthquakes. And, as I have also a mortgage in Hertfordshire, I beg Thee also to have an eye on compassion on that county, and for the rest of the counties Thou mayest deal with them as Thou art pleased. O Lord, enable the Banks to answer all their bills, and make all debtors good men. Give prosporous voyage and safe return to the Mermaid sloop because I have not insured it. And because Thou has said: ‘The days of the wicked are but short,’ I trust Thee that Thou will not forget Thy promise, as I have an estate in reversion on the death of the profligate young man, Sir [name withheld].

(Source: Peter Bowler, The True Believers: Oddities and curiosities of religious faith [Methuen, 1986], a very amusing little volume if you ever find a copy.)

noah’s ark

Well, here it is, in all its rendered lego glory, Noah’s ark. Now you may notice a larger cube next to it (sort of a timber borg-cube?). That’s Utnapishtim’s ark which, although shorter, is considerably wider and taller (well, it is cube shaped). The latter also has more than three times the volume, making for a considerably roomier, although perhaps less seaworthy (given the cubic shape) vessel.

Noah's and Utnapishtim's arks

the crimes of santa claus

In time for Christmas, I’m resurrecting something I wrote some years back…

nosantaSanta Claus has long been held up as a jolly figure to be admired and respected, particularly by the kiddies. In reality he is a far darker and more sinister figure who promotes greed and self interest. Below is a list of the evils (both proved and alleged) perpetrated by Mr S. Claus.

Santa Claus promotes Racial Discrimination

Mr Claus demonstrably prefers to deliver gifts to specific racial groups. In South Africa, under apartheid, for example, Mr Claus generally delivered gifts to the children of white families but not black families. In spite of the fact that apartheid has now been abolished, Mr Claus continues to demonstrate this blatantly discriminatory behaviour.

Santa Claus promotes Class Distinctions based on wealth

Mr Claus delivers more gifts, and more expensive gifts, to the children of wealthy families. Poor families receive poor quality (or no) gifts. The role Mr Claus has in preserving such social distinctions serves to perpetuate the subjugation of millions of people around the world, contributes to continuing racial tension, promotes envy and discord amongst peoples, and ultimately leads to the premature deaths of millions in the third world. In fact, Mr Claus is wanted for questioning regarding his role in starting World War II.

Santa Claus is a pawn of Big Business

Mr Claus can frequently be seen advertising for major businesses. He exhibits no ethical basis for making decisions regarding what products or businesses he chooses to endorse, often promoting alcoholic or other products which constitute major social problems and which are entirely inappropriate for the kiddies.

Santa Claus fails to deliver

Whilst Mr Claus encourages kiddies to write in with their Christmas wishes, he apparently ignores a large number of these requests.

Santa Claus promotes greed and self-interest

Since Mr Claus provides Christmas gifts, there is clearly no need for people to give each other gifts, so their focus becomes completely centred upon what they wish to receive.

Santa Clause promotes an arbitrary ethical measure of “goodness”

Mr Claus is said to reward children whose behaviour has reached an arbitrary standard, whilst those whose behaviour has failed to reach this level receive no reward. What we want to know is who gave Mr Claus the right to establish what level of good behaviour is acceptable.

Santa Claus is inconsistent

In spite of claiming to only provide gifts to “good” children, Mr Claus generally will deliver gifts to children of rich white families regardless of their behaviour during the year, whilst children in the third world will not receive gifts regardless of whether they have been good or bad.

Santa Clause claims credit where it is not due to him

Mr Claus frequently claims credit for gifts which he did not provide, but which have been provided by other people.

Santa Claus exhibits a disturbing preoccupation with small kiddies

It has generally become accepted that older males exhibiting a preoccupation with small children is a clear warning sign to parents. That is, unless the old male is wearing a large red suit and sports an extremely generous quantity of white facial hair…

Santa Claus promotes bad eating habits

Mr Claus sets himself up as an example to many kiddies. Yet what sort of example is he? Aside from the serious issues raised above, his obesity and propensity to leave food gifts of a fattening (or intoxicating) nature makes him an inappropriate role model.

Santa Claus operates under a series of pseudonyms

Mr Claus also goes under a number of other names: Father Christmas, Saint Nick, Fatty Boom Bah (all right, I just threw the last one in to see if you were still paying attention). Operating under a range of pseudonyms is a frequent ploy of criminals. Whilst the precise meaning of some of these terms is obscure, it is perhaps no accident that “Santa” is a palindrome of “Satan” (note that the Bible says that “even Satan disguises himself as an angel of light” [2Cor 11:14]–or, in this case, as a fat bearded bloke wearing a red suit!).

Santa Claus is not an equal opportunity employer

Mr Claus has been accused of actively discriminating against tall people, choosing to employ exclusively vertically challenged people whom he inappropriately designates “elves.”

Santa Claus has been linked with child exploitation

An analysis of gifts left by Mr Claus reveals that a large number appear to have originated in locations which exploit child labour and other unethical working practices.

Santa Claus operates a business of dubious legality

Mr Claus reputedly operates from a base at or near the North Pole, a little known tax haven. Mr Claus thus makes no reports regarding his income or worth, and is not accountable to anyone. Such practices inevitably attract (or are set up) by organised crime. Fortunately, however, the onset of global warming may result in the melting of Mr Claus’s euphemistically named “workshop.”

Santa Claus invades your privacy

Widely disseminated information on Mr Claus indicates that “he knows when you are sleeping, he knows when you’re awake.” Sounds creepy, particularly when you know a little more about this man. We suggest you consider taking out a restraining order.

Santa Claus may be responsible for global warming

Let’s face it, he’s supposedly based at the North Pole, and polar ice has been receding rapidly of late. I don’t think it’s a coincidence.

Santa Claus obscures the true meaning of Christmas

Mr Claus has successfully turned almost all attention to himself at Christmas, obscuring the fact that it is originally a celebration of the birth of Jesus Christ. God is not happy that Mr Claus has hijacked Christmas in this way. You really don’t want to be offside with God.

I suggest that if you see Mr Claus, you report him to your local authorities.

go west, young man!

I like precision. If my watch is more than 2 seconds off the real time, I feel the need to rectify it (if only Aus had an atomic radio signal like most of the civilised world). Not only do I like to know precisely what time it is, I like to know precisely where I am and where I’m supposed to be going. So when people head east or west, north or south, I don’t want them heading off a few degrees either side of these headings!

So it is pretty clear that I wouldn’t fit in the ancient world with this kind of attitude. They didn’t have watches at all, and the old wrist sundial was notoriously imprecise. Furthermore, it seems probable that people had no idea where they were going (well, not by my standards of precision). And it is that consideration which has provided the opportunity to introduce a little mathematical fun to my blogging today.

But before we get to the maths (or “math” for those of you in the US), let’s recap what we know about directions. In a previous post on the location of Eden I referred to the possible significance of the easterly migration through Gen 3–11 and the subsequent instruction by God to Abram, “Go west, young(ish) man!” Now it’s well known that, in ancient Israel, the primary direction (the direction you’d put at the top of the map) was east, where the sun rose.

Actually, we here in Aus know that the ancient Egyptians had it right, aligning the top of their map with the source of the Nile. This link will show you why this correctly reveals the true arrangement of a world map.

Anyway, a while back this got me wondering about just how imprecise using the sunrise as the basis for orientation could be, so I set out estimating just how far the sun ranges from sunrise in mid winter to sunrise in mid summer around Jerusalem. For those of you who’d rather not wade through the maths, skip to the end. For the rest of you, here goes (and if you spot any glaring mathematical errors, please let me know).

Before we begin, some housekeeping. I’m using standard spherical polar coordinates here, as described at MathWorld.

For simplicity, we shall make a couple of assumptions about our system, which are:

  • The earth is a perfect sphere. In fact, the earth is better described as an oblate spheroid, but this somewhat complicates the calculations and would only minimally alter the results (refer to the discussion at the end of this section), and
  • The sun is infinitely distant from the earth. (This actually assumes that the ratio of the earth’s radius over the distance to the sun is close to zero, a reasonable consideration. Furthermore, any error introduced into these calculations by this would be made redundant by the fact that the sun’s radius exceeds the earth’s and so the earth-sun vector below would still point at the sun, even if not precisely at its centre.)

Given these constraints, we may proceed to calculate the extreme points of sunrise. To do so we require the following data:

  • Angle between axis of earth and normal vector to orbital plane: 23.45°.
  • Latitude of Jerusalem: 31° 46′ North of the equator.

Jerusalem is thus defined as the point P on the globe, and since we are assuming that the sun is infinitely distant, we may (for simplicity) simply define this as a unit vector:

P = (1, θ, 90°–31° 46′)

Where θ ranges from 0° to 360° as the earth rotates during the day. For our purposes we shall determine what value of θ is appropriate for sunrise in mid-summer and mid-winter.

The position of the sun will remain constant. For mid-summer in Jerusalem, we shall position the sun at:

s = (1, 0°, 90°–23.45°)

For mid-winter the position of the sun will be:
s = (1, 0°, 90°+23.45°)

The local coordinate system at Jerusalem may thus be defined by the spanning vectors:

spanning vectors

(Here k is the vector (0, 0, 1) in the main coordinate system.) This system defines the local directions up = iJ, east = jJ, and north = kJ. Consequently, the local vector to the sun may be defined as:

(siJ, sjJ, skJ)

At last we are in a position to define sunrise (or sunset) as occuring when the direction to the sun has no vertical component in the local coordinate system—that is when

siJ = 0

Converting these values from spherical to rectangular coordinates gives the following:

iJ = ( sin(58°14′) cos θ, sin(58°14′) sin θ, cos(58°14′) )
s = ( sin(66.55°), 0, cos(66.55°) )

Substituting into the previous equation and solving for θ gives:

Calculating the result gives: θ = ±105° 34′ 52″

Given this value, we may now determine the position on the horizon where the sun will rise mid-summer in Jerusalem by converting the vector s to local coordinates. We now know that at sunrise, the position of Jerusalem is defined as:

P = (1, –105° 34′ 52″, 58° 14′)

This allows us to determine the entire set of local coordinates (according to the set of equations set out above) and gives the rectangular values:

iJ = ( –0.2284, –0.8190, 0.5265 )
jJ = ( 0.9633, –0.2686, 0 )
kJ = ( 0.1414, 0.5071, 0.8502 )

Converting s to the local coordinate system gives the following result:

sJ = ( 0, 0.8837, 0.4681 )

Consequently, the angle from true East to the position of sunrise in mid-summer here works out as:

That is, in mid-summer, the sun rises 27° 54′ 32″ north of true east. Now to save going through this all again, I’ll just note that the winter calculation reveals sunrise occurs at a similar angle south of true east, so the entire angular range through which sunrise travels throughout the year is 56°.

Now recall that we did make a couple of assumptions so as to keep the calculations above simple, so this is a rough value. But it does clearly show that using sunrise is not a precise means to define a direction.

Does this actually tell us anything useful? No, not really. Just a curiosity.

Perhaps my next post will contain something which proves to be more than an opportunity to play with some maths. We shall have to wait and see!

the dirt on dirt

I’ve just seen yet another ad for a product which will kill 99.9% of all household germs.

I’m worried about the 0.1% that are tough enough to survive and then have free reign since our anti-bacterial wonder-sprays have left the field completely free from competition. Surely they’re the germs we really should be worrying about, and the elimination of the rest is just making it worse in the long run!

educational nursery rhymes

Just a quick post this week. It has long struck me that there are educational opportunities we miss with young children, one of them being in the realm of nursery rhymes and other songs we teach the kiddies. In our house I’ve tried (with limited success) to introduce some variations to the normal wording in order to enhance the pedagogical potential of a couple of very common songs, and I thought I’d share these with the world (i.e. you). I’d also be keen to hear of any suggestions you have for more.

So here goes, beginning with the educational version of Twinkle, Twinkle, Little Star:

Twinkle, twinkle, big fat star,
How I wonder what you are.
Up above the world so high,
Like a thermonuclear fusion reaction in the sky.
Twinkle, twinkle, big fat star,
Now I know what you are.

My other (rather lame) attempt at enhancing a song takes a shot at Old Macdonald’s Farm:

Old Macdonald had a farm,
A-E-I-O-U,
And on that farm he had a …

OK, you get the idea. Why waste the opportunity afforded by the meaningless recitation of “E-I-E-I-O” when you could be teaching the vowels?

Doubtless this approach could be expanded to include a vast array of popular songs. Perhaps my aim ought to be to teach next year’s Genesis course using only enhanced rhymes like these?

Or, on second thoughts, perhaps sanity should prevail.

בראשית or ΕΝ ΑΡΧΗ or “in the beginning” part II

OK, I’ve been having some trouble getting unicode to display with WordPress, I tried upgrading, but nothing seemed to work. Finally I managed to get it working by editing wp-includes/wp-db.php and commenting out the lines setting the $collation_query to “SET NAMES utf8”. For some reason, this now seems to have things working and I can (at last) finish off my first real post on the blog (coming soon)!

Just for good measure, here’s a little unicode Hebrew: בראשית ברא אלהים את השמים ואת הארץ.

In the beginning…

For years I’ve resisted starting a blog, happily confining myself to posting comments on other blogs, writing posts to forums, and the like.

Why the change? I’ve been driven to start this blog through frustration after trying to post a comment to a blog with moderated comments but having the comment refused. That will probably produce one of the first substantial posts on the blog in the coming days, when I’ve sorted out how to get WordPress configured and running to my satisfaction.