The Roman calendar was a 12 month lunar calendar, like the Jewish calendar, this drifted with the seasons, so from time to time they included ‘intercalated’ days and months. These were calculated by priests, but the calendar drifted as the priests either added in extra days due to politics, or they forgot to make the corrections. Adding extra days allowed favoured politicians to remain in office longer.

Romulus is supposed to have created the first calendar, with 10 months. This was dramatically out of sync with the seasons -but is why we have September, October, November and December (the seventh, eighth, ninth and tenth months). Other months were named for various Gods (e.g. Mars). The days were called kalends, and the month had special days called nones, March 7th, and Ides, march 15th.

So march 9th was called VII Ides, six days before Ides. March 13th, 2 days before Ides was III ides.

A 304 day calendar wasn’t tremendously useful due to the variation of the seasons, so two extra months were added, Januarius and Februarius.

This gave 355 days in the year, which was better – but still flawed. They tried an extra month, but that made the year too long, then they added an extra month every eight years – which worked better, but still relied on the priests to remember to add in that extra month – and they forgot.

Caesar, returning from Egypt, found the system was in a mess – and ordered reform. To re-align the calendar, extra months were added and 46 BC lasted 445 days. Caesar also moved the start of the year to January instead of March (which is why the 10th month of October is named for the number 8). Caesar also ordered that the extra ten days be aded throughout the year. This gave a calendar with months of 30 or 31 days (alternating) – though February had 29 days. Thereafter we had the Julian calendar of 365 days with a leap year of 366 days every fourth year.

Later, the calendar was tinkered with again, with leap years coming every 3 years instead of 4, but this was corrected by Augustus (in whose honour Sextilis was renamed).

Annoyingly, they tweaked the lengths of the months for political reasons – August was beefed up to honour Augustus by stealing a day from February. Other changes were made which wrecked the neat pattern established in the length of the months. They also renamed other months to honour other Caesars – but these changes did not stick.

The Julian calendar continued in this way for a millenia and a half until Pope Gregory XIII made a reform in 1582, even then, the Julian calendar continued to be used in some countries who by then were not under the influence of the Papacy. The United Kingdom did not change until the 18th century, Sweden had a hybrid of the Julian Calendar and Gregorian reforms – they did not observe the modified Gregorian rule for not having a leap year if the century was not divisible by 400.

In the UK, Parliament were careful to specify how the calendar change of 11 days would affect contracts, birthdays, prison terms and so on. The same number of ‘natural’ days were to pass. Given that the year pre-reform started on the 25th March in the UK, this meant that taxes were not due until the 6th April. In the UK we still use this date as the start of a new tax year.

In the 4th century AD, the Roman empire was stagnating. Constantine acted to halt the decline by consolidating its structures – and as a result kept Rome going for another 100 years in the west. In the east it lasted another 1000 years.

A predecessor of Constantine had divided the Roman Empire into Eastern and Western halves. Constantine chose Byzantium (Constantinople) as his Capital. When Rome fell in the west, the Greek speaking Roman Empire would remain as the Byzantine Empire – which would persist until it fell to the Ottomans in 1453. The Byzantine Empire was a name given to it later, at the time the west referred to it as the Empire of the Greeks, and in the east, the Muslim world simply called it Rûm.

Constantine chose a new religion of the east to secure his political holding, and it wasn’t clear which one. There were many popular sects, and a military victory at the time was attributed to several Gods.

Later, the story was that Constantine is said to have had a dream that he would be assured victory in battle if he marched under the banner of Christ. It was said that due to this, Constantine embraced Christianity, however, the story came after the decision – Christianity was more as an act of politics than anything else.

In Rome, Constantine built the arch of Constantine dedicating his victory to the old Roman Gods, thus keeping the pagans happy. This can be seen today next to the Colosseum.

Christianity eventually won out, and it affected the Roman Calendar. Sunday was named as the holy day, which changed the precedent previously set in both Judaism and Roman paganism that Saturday would be the day of worship. The reason for this was that Christ is crucified on the sixth day of the Jewish week, and rose on the first day of the following week – a Sunday. As the calendar spread, some day names from existing cultures ’stuck’. So in English we have Woden’s Day (Wednesday), Woden being the god of poetry. This replaced Mercurius’ day – named for the Roman God of communication. Friday is Freyja’s or Frigg’s day – a West Germanic translation of dies Veneris, or Venus’s day (Vendredi in French)

Choosing Sunday as the holy day, dies Solis, also pleased the various sun worshippers. This must have annoyed the bishops who made the best of it by proclaiming that Christ was lighting up the world.

Easter was, and still is, a big deal for Christians. It’s the defining act of Christianity. The trouble is that it is based on the Jewish calendar, a Lunar calendar – and the Roman world was adopting a Solar calendar. The two drift against each other.

It didn’t matter to Constantine when Easter was celebrated, as long as there was agreement – it was part of bringing the Empire together.

Constantine held a council at Nicaea (Νίκαια), which was Greek for ‘Victory’. Constantine was keen for the meeting to be attended by as many Bishops as possible, and he paid for their travel and lodgings along the road. The purpose of the meeting was to settle questions about Christianity. Wikipedia lists the agenda thus:

1. The Arian question regarding the relationship between God the Father and Jesus; i.e. are the Father and Son one in purpose only or also one in being;
2. The date of celebration of the Paschal/Easter observation
3. The Meletian schism;
4. The validity of baptism by heretics;
5. The status of the lapsed in the persecution under Licinius.

Christians had celebrated Easter according to the Jewish lunar calendar. Matthew, Mark and Luke place the event on the Sunday after the passover feast, whereas John indicates a different Sunday (straight away, a literal interpretation of the Bible is not a defensible position).

The early Christians had different interpretations – a major embarrassment for the most holy of occasions, add to this the issue of anti-Semitism which was arising, and it caused problems for early Christians to base their holy day on a Jewish calendar and decisions about the calendar by the Jewish priests.

The decision was made to link easter to the solar year, and base it upon the Vernal equinox. It was decided that Easter would be the first sunday on the first full moon after the equinox – but it shall never be on the Jewish festival of Passover.

This was problematic, as establishing this date was not easy – the date of the vernal equinox was not easy to establish (for practical purposes March 21st was used, but the equinox does drift). In addition the lunar calendar drifts against the solar calendar – the dates of the full moons are not the same each year.

Add into this the fact that the Julian Calendar of 365¼ days was 11 minutes out, and over time, the calculation of the ‘true’ date of Easter was a real problem for Christianity. During the dark ages in Europe, it was this problem that kept scientific enquiry on life-support – whereas it flourished in the east.

By the time of Pope Gregory, the 11 minutes error had built up significantly, the equinox was on the 14th March, and using the 21st could give large errors in the ‘true’ date of Easter. Add to this some political problems, where in Rome the 25th March was used as the equinox, but in the east the 21st was used. There were also differences in how the lunar cycle was computed. This lead to an east-west split in the church which persists to this day.

It was the issue of celebrating easter on the wrong day that lead Pope Gregory XIII to issue his bull making the correction – a decree made after the church had begun to fragment in western europe – which meant that it took almost 200 years for the calendars to move back into synchronisation – though several countries did not adopt the Gregorian calendar until the 20th Century.

Different calendars are still used in the world today. For example, it is 2001 in Ethiopia and 1430 in the Islamic Calendar. There are many others.

This isn’t the end of the story. There are various reforms of the Gregorian calendar proposed. The tinkering with the length of months in Roman times means that the year doesn’t neatly divide into quarters. The first quarter has 90 days, the second has 91, the third has 92, the fourth has 92. This means that financial comparisons between quarters are not valid.

One such reform is the ‘World Calendar‘ This has 30 days in January, 31 in February, 30 in March. The pattern of 30/31/30 repeats over the year with Jan 1st always being a Sunday. This gives 364 days. The 365th day is called a ‘Worlds Day’ and is not a named day of the week – it would be between December 30th and January 1st.

In leap years, there would be a Worlds Day between June and July.

This calendar was close to adoption in the 20th century, but failed due to the USA not following through on the proposals. There are also religious objections as due to the intercalary days, the holy day would not be every seven days.

So, for the foreseeable future, our Calendar with it’s foibles, due to its contorted history of religion and politics looks set to stay – I think it’s doubtful that the World Calendar will be adopted in 2012 (as the World Calendar Association proposes).

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Post tags: Astronomy, Easter, religion, Science

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I want to get some myself now – so much fun for such a simple thing!

This is my Picture of the Day for the 5th March, 2009

Link - (Come and Comment - I like comments!) | Original : Pic A Day – March 5th 2009 | © Murky, 2009. | Add to del.icio.us
Post tags: 2009, Cube, Magnet, March, Neodymium, Pic a Day

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INTERNATIONAL EARTH ROTATION AND REFERENCE SYSTEMS SERVICE (IERS)

SERVICE INTERNATIONAL DE LA ROTATION TERRESTRE ET DES SYSTEMES DE REFERENCE

SERVICE DE LA ROTATION TERRESTRE
OBSERVATOIRE DE PARIS
61, Av. de l’Observatoire 75014 PARIS (France)
Tel. : 33 (0) 1 40 51 22 26
FAX : 33 (0) 1 40 51 22 91
e-mail : services.iers@obspm.fr

http://hpiers.obspm.fr/eop-pc

Paris, 4 July 2008

Bulletin C 36

To authorities responsible
for the measurement and
distribution of time

UTC TIME STEP
on the 1st of January 2009

A positive leap second will be introduced at the end of December 2008.
The sequence of dates of the UTC second markers will be:

2008 December 31, 23h 59m 59s
2008 December 31, 23h 59m 60s
2009 January 1, 0h 0m 0s

The difference between UTC and the International Atomic Time TAI is:

from 2006 January 1, 0h UTC, to 2009 January 1 0h UTC : UTC-TAI = – 33s
from 2009 January 1, 0h UTC, until further notice : UTC-TAI = – 34s

Leap seconds can be introduced in UTC at the end of the months of December
or June, depending on the evolution of UT1-TAI. Bulletin C is mailed every
six months, either to announce a time step in UTC or to confirm that there
will be no time step at the next possible date.

Daniel GAMBIS
Head
Earth Orientation Center of IERS
Observatoire de Paris, France

(Source)

The last time this happened was at the end of 2005, and before that was 1998. The most up to date information is always given in Bulletin C. The history of modifications is listed here and here. The DUT bulletins give information about the difference between UCT and UT1 (i.e. time based on rotation of Earth alone).

The reason for this is that the earth’s spin is irregular, affected by gravitational pulls of nearby objects. In addition, the tidal effect of the moon gradually lengthens the day. This means that without correction the earth would gradually go out of sync with the Earth’s rotation (a more extreme version of this lead to the introduction of the leap year with the Gregorian Calendar).

The decision was made to keep the standard time within 0.9 seconds of the Earth’s time, and this is monitored in Paris by the IERS, of l’observatoire de Paris. Having a standard time is very important, as an accurate timestamp is important in many modern applications, one such example being GPS. What that time standard should be is a matter of lesser importance.

The trouble with the current standard is the arbitrary shifts, which happen at irregular intervals (such as on the 31st December). This can make it hard to cope with in certain applications. Therefore in 2003 a meeting was held to discuss the future of timekeeping. The proposal is that the broadcast standard time signal would no longer have ‘leap seconds’. As a result of this, the broadcast time would gradually slip out of sync with the Earth. This would not be noticeable for social reasons for a long time, generations, but eventually midnight on the standard time would slip to being in daylight. The correction would be dealt with by introducing a ‘timezone’-like correction. I.e. clocks should be synchronized to standard time minus 3 seconds, then standard time minus four seconds. All machines would use standard time (as they use UCT now) for talking to themselves and to each other, but would add the appropriate correction (plus the needed time shift due to longitude) before talking to humans.

As an example, this website is running on a machine which thinks it is 7 hours earlier than it actually is. The machine is running on UCT (which as I write is 10:30am), but the machine reports the time is 03:30 when I use the unix date command. The WordPress software I’m using now has been told what my timezone is, and it makes a different correction to UCT, and reports the time correctly (for me). Allowing ’standard time’ to drift would mean that the machine would make a correction of a few more seconds before reporting the time to the human. This would make it easier for machines to do date based calculations (as they wouldn’t have to worry about the time shifts) and would allow the relevant corrections to be made once they were needed. The proposed date for this change is by 2022.

Of course, only folks whose timezone is currently the same as UCT will ’see’ this leap-second as the year ticks over (i.e. London, Lisbon and places in the same timezone). Other locales will have their leap seconds at the corresponding local time (the whole world changes at once). I.e. 01:00 in Madrid and Paris, 05:30 in Delhi and 19:00 in New York. (I know that London and Lisbon aren’t the same timezone, London uses GMT in winter, and Lisbon uses WET, but what is the difference between them?)

I hope you enjoy your ‘extra’ second!

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Post tags: Astronomy, Calendar, Leap Second, Science, Second, Time

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First we must consider the nature of light (this can be generalised to any particle once we get all quantum mechanical, but let’s stick with light for now).

Classically, light can be thought of as a wave. It’s a transverse wave meaning that the ‘oscillations’ of the thing doing the waving are at right angles to the direction that the wave is travelling in. Another example of transverse waves are waves on the surface of water.

Picture showing waves horizontally and vertically polarised

These oscillations defined a ‘plane’ in which the waves are oscillating, and this plane can be oriented at any angle. Waves on the surface of water are vertically polarised. Though the plane of polarisation can be any angle, it is convenient to pick two planes which are at 90 degrees to each other. We can express any polarisation by talking about how much of each is present. Hence, we can talk of ‘vertical’ and ‘horizontal’ polarization. Here is an applet which demonstrates this.

You can see polaroid filters in action if you have a pair of polaroid glasses (often sold as ‘anti-glare’). Find a light shining on a surface such as a desk. You don’t want to be ’square on’ to the surface, the light should be bouncing at an angle, 45 degrees is a good start. For the most obvious effect, don’t use a mirror.

Look at the surface through your polaroid glasses, then rotate them 90 degrees, and keep looking. You should see the glare change in brightness. You will find that polaroid glasses are best at reducing glare from horizontal reflections when held normally. (See: Brewsters’ Angle)

If you use your glasses for driving, you may find that you have trouble with the LCD screens on petrol pumps, this is because the LCD screen relies on polarising light!

If you take a polarised filter, this will ensure that all the light which passes through has the same polarisation. Classically, if a particular wave comes in with an amplitude of A, and a plane of polarisation at angle θ to the plane of polarisation, the amount of light which emerges has amplitude Acosθ.

Picture showing the effect of multiple polarising filters

Suppose that we have two polaroid filters. Unpolarised light hits the first and emerges polarised. It emerges with amplitude, A (on average). This light hits the second filter. The two filters have an angle θ between their planes of polarisation – the amount of light which emerges is Acosθ. So, if the filters are aligned, the second filter has no effect. If it is turned 90 degrees, no light emerges (note, if it is turned 180 degrees, it has no effect – the sign of the amplitude doesn’t matter, it’s not ‘negative light’!)

(Note that for real filters, there is a little scattering, so 90 degrees doesn’t give total black, and zero degrees does give some reduction in intensity)

Imagine we have two filters, aligned at 90 degrees. No light emerges. This is because the cosine of 90 degrees is zero.

Now, insert a filter at 45 degrees between the two. What happens? More ’stuff’ can only make the amount of light getting through smaller, right? The cunning reader will have assumed that I wouldn’t ask the question if the answer were obvious. Some light emerges. In this circumstance, two filters allows through less light than three.

This counterintuitive result is easily explained. Imagine the second filter is at an angle of θ compared to the first.  The third is at 90 degrees. In other words, the angle from the second is (90-θ). From the first filter, we have light with amplitude Acosθ. This is then reduced by the third filter by cos(90-θ). The overall light intensity is now Acosθ.cos(90-θ) or Asinθcosθ, this reduces to A(sin2θ)/2. In other words, we get most light out when sin2θ=1, or when 2θ=90°, or when θ=45° 

The newly inserted second filter is changing the polarisation of the light.

Take your time on polarisation, it’s important that you understand the above if you’re to comprehend subsequent articles. We’ll put this aside for a while, though – the next step is to talk about photons.

Link - (Come and Comment - I like comments!) | Original : Quantum Cryptography (a background) | © Murky, 2008. | Add to del.icio.us
Post tags: Cryptography, Light, Modern Cryptography, Physics, Polarisation

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The LHC will collide Hadrons (obviously) at high speeds. Hadrons are particles which contain quarks. Everyday examples are Protons and Neutrons. The LHC can only accelerate charged particles and so it’ll collide protons. The high energy collisions will produce new and interesting particles – and the hope if to find the predicted Higgs Boson. Though if it’s not found, that’ll also be interesting….

There has been idle chat that it could create miniature black holes that’ll destroy the Earth. This will not happen. It probably won’t create black holes. But if it does create black holes they’ll be moving so fast that they’ll leave the Earth. Even if they don’t they’ll evaporate due to Hawking radiation as they’re so small… and in the unlikely event that it does create a black hole that hangs around to destroy the planet – there’ll be nobody to contradict me.

Seriously: cosmic rays have collided with the Earth with huge energies since time immemorial – a particle accelerator experiment in the upper atmosphere. We’re still here.

As Wil Wheaton said on Twitter: "Stupid people at table next to me are convinced LHC will destroy the world tomorrow. Resisting urge to tell them how stupid they are. "

(P.S. I post as someone with a damned good Physics degree. Irrelevantly, I’ve visited LEP, the Large Electon Positron Collider and LHC’s predecessor. Sadly, I took time out of my first USA trip to go to Fermilab. I’ve been to RAL in the UK many times.)

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Post tags: CERN, LHC, Physics, Science, Synchrotron

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It really annoys me every time a presenter on the news ‘jokes’ that they can’t do maths or science. Melvyn Bragg on the usually excellent “in our time” is another. If you can’t do it, then research your topic – or at least stay quiet!

I grew up with Johnny Ball. I really miss him on TV – he was enthusiastic and willing to find out about things which he didn’t know about. Today’s “science” shows are more about blowing things up in the microwave, or the caravan (yes, Braniac, that means you).

An honourable exception is discovery’s mythbusters (UK site) – they don’t always get the scientific terms right (misusing terms like force, pressure etc, the narrator in the UK is especially guilty of this) – but they have the sense of the scientific method, and of exploration.

On UK TV, there is no modern equivalent. We need a modern day Johnny Ball! (Maybe next year it won’t be ‘You could be Nancy‘, but ‘You could be Johnny’ – I can only dream)

I really like the idea. Each week, wannabe Johnny’s would present a piece about some aspect of science. It’d need to be fun, accessible, as well as being good science. The panel would consist of, a non-scientist, a scientist (not Adam Hart-Davies!) and the ‘Lloyd-Webber figure’ – Johnny Ball himself.

Each week, Graham Norton would tell the contenders ‘You could be Johnny’.

The theme tune would end with Jack Nicholson bursting through a door saying “Here’s Johnny!”

The public would vote (usually on style over substance) and there’d be a ‘present-off’ between the two who had the lowest public vote, they’d explain some particularly gnarly bit of science or maths. Johnny would save one of them.

I could be a getting a little flippant here, but I’m deadly serious about the issue at hand. Personally, I think some sort of contest might be a lot of fun, as well as helping to increase interest in science and maths. It could work, couldn’t it?

Link - (Come and Comment - I like comments!) | Original : You could be Johnny | © Murky, 2008. | Add to del.icio.us
Post tags: Johnny Ball, Maths, Mythbusters, Science, UK

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It felt quite improbable, surely this thing must topple to one side – yet it doesn’t. It must be this reasonable expectation which makes it hard to learn to ride a bike in the first place – the brain is convinced it can’t work.

Despite going along, thinking about the precariousness of my situation, I didn’t begin to wobble. It is always a danger that if you start to think about something which you normally do instinctively, you begin not to be able to do it!

(...)
Read the rest of The Bicycle (346 words)

Link - (Come and Comment - I like comments!) | Original : The Bicycle | © Murky, 2008. | Add to del.icio.us
Post tags: Cycling, engineering, Sport

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RIP.

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This in itself should have given the hint that Papal infallibility isn’t what it was.

The current Pope has just gone back on that, saying the trial was ‘reasonable and just’.

It’s a Papal showdown!

Both Popes can’t be right (you can’t apologise if you’ve done nothing wrong, and you can’t have done something wrong if your action was reasonable and just)… yet, both are infallible.

Does not compute…. warning… error…. *BAA-boooom!*

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Post tags: Catholic, Church, Galileo, Papal infallibility, Pope, religion, Space

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My first reaction is ‘how’. My understanding is that roller-coasters are constructed such that once lifted up the climbing hill, the coaster proceeds under gravity. Given that, how could a power cut cause it to stop in the position described?

The big worry for me if there were a power cut whilst I was in a coaster would be the braking system, not gravity ceasing to operate normally!

So, how could this happen?

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