Archive for Quaternions

Euclid Update – Revised Timeline

Posted in Euclid, mathematics, The Universe and Stuff with tags , , , , , , , , on June 16, 2026 by telescoper

In a post last week I hinted that I hoped soon to be able to provide an update on progress with the European Space Agency’s Euclid Mission. People within the Euclid Consortium have known for some time, but it has now been officially announced by ESA, that the timeline for the first full Data Release (DR1; originally scheduled for October 2026) has now been revised.

The plan now is for DR1 to happen in stages, with a first tranche to occur in November 2026 (precise date yet to be announced). The complete data release will take place in mid-2027 (probably in June). The sky area covered by DR1 will be about covering a large sky area of about 1900 deg².

To give a little more background, the data products from the Euclid survey are divided into three levels of data processing function:

  • LE1 – the “raw” data frames, prior to calibration, generated at the Science Operations Centre from the time-ordered data and telemetry received from the spacecraft
  • LE2 – the calibrated and corrected data for the two instruments (VIS and NISP) – images, spectra, catalogues of point sources, etc
  • LE3 – the high-level data products (galaxy catalogues, cosmic shear maps, etc) designed for cosmological analysis

The first release will comprise LE1 and LE2 only. This will be called DR-Foundation. The LE3 data will be added next year to make the full DR1. Since LE3 is required for the cosmological analysis that is the prime motivation for the Euclid mission, it follows that there will be no official cosmology results from Euclid DR1 until mid-2027 at the earliest. Other results based on “Foundation” data may of course emerge before then.

I hope this clarifies the situation.

P.S. Irish physicists and astronomers will be particularly interested to know that the LE1 data includes information about the spacecraft and instrument pointing orientations, which is stored in the form of quaternions…

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Happy Birthday, Quaternions!

Posted in History, mathematics with tags , , , , on October 16, 2019 by telescoper

Sir William Rowan Hamilton (1805-1865)

Today, October 16th, is Hamilton day! It was on this day 176 years ago, in 1843, that  William Rowan Hamilton first wrote down the fundamental result of quaternions. Apparently he was walking from his residence at Dunsink Observatory into Dublin when he had a sudden flash of inspiration  and wrote the result down on the spot, now marked by a plaque:

 

Picture Credit: Brian Dolan

This episode  is commemorated by an annual Hamilton Walk. Sadly,  Broombridge (Droichead Broome) is near the bridge (Broom Bridge) where Hamilton had his Eureka moment and it is on the main commuter line from Maynooth into Dublin. This is ironic because Quaternion algebra does not commute. (Geddit?)

Although it is quite easy to reach Broombridge from Maynooth, I sadly can’t attend the walk this year because I’m teaching this afternoon.

P.S. Maynooth is also home to the Hamilton Institute which promotes and facilitates research links between mathematics and other fields.

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Planes, Trains and Quaternions

Posted in Biographical, History, mathematics, Maynooth with tags , , , , , , , , on January 4, 2018 by telescoper

Well, here I am in Maynooth for the first time in 2018. I flew over from Cardiff yesterday. The flight was rather bumpy owing to the strong winds following Storm Eleanor, and it was rather chilly waiting for the bus to Maynooth from Dublin Airport; nevertheless I got to my flat safely and on time and found everything in order after the Christmas break.

This morning I had to make a trip by train to Dublin city  to keep an appointment at the Intreo Centre in Parnell Street, which is about 15 minutes walk from Dublin Connolly train station. I bought an Adult Day Return which costs the princely sum of €8.80. Trains, stations and track in Ireland are maintained and operated by Irish Rail (Iarnród Éireann), which is publicly owned. Just saying.

The distance between Maynooth and Dublin about 25 km, which takes about 40 minutes on the local stopping train or about 25 minutes on the longer distance trains which run nonstop from Maynooth to Dublin. As it happens I took one of the fast trains this morning, which arrived on schedule, as did the return journey on a commuter train. My first experience of the Irish railway system was therefore rather positive.

I had thought of having a bit of a wander around the city on my way to Parnell Street but it was raining and very cold so I headed straight there. I arrived about 20 minutes ahead of my scheduled appointment, but was seen straight away.

The reason for the interview was to acquire a Personal Public Services Number (PPSN), which is the equivalent of the National Insurance Number we have in the United Kingdom. This number is needed to be registered properly on the tax and benefit system in Ireland and is the key to access a host of public services, the electoral roll, and so on. You have to present yourself in person to get a PPSN, presumably to reduce the opportunity for fraud, and I was told the interview would take 15 minutes. In fact, it only took about 5 minutes and at the end a photograph was taken to go on the ID card that is issued with the number on it.

So there I was, all finished before I was even due to start. The staff were very friendly and it all seems rather easy. Fingers crossed that the letter informing me of my number will arrive soon. It should take a week or so, so I’m told. After that I should be able to access as many personal services as I want whenever I want them. (Are you sure you have the right idea? Ed.)

For  the return trip  to Maynooth I got one of the slower commuter trains, stopping at intermediate stations and running right next to the Royal Canal, which runs from Dublin for 90 miles through  Counties Dublin, Kildare, Meath and Westmeath before entering County Longford, where it joins the River Shannon. One of the intermediate stations along the route next to the canal is Broombridge, the name of which stirred a distant memory.

A quick application of Google reminded me that the town of Broombridge is the site of the bridge (Broom Bridge) beside which William Rowan Hamilton first wrote down the fundamental result of quaternions (on 16th October 1843). Apparently he was walking from Dunsink Observatory into town when he had a sudden flash of inspiration  and wrote the result down on the spot, now marked by a plaque:

Picture Credit: Brian Dolan

 

This episode  is commemorated on 16th October each year by an annual Hamilton Walk. I look forward to reporting from the 2018 walk in due course!

P.S. Maynooth is home to the Hamilton Institute which promotes and facilitates research links between mathematics and other fields.

 

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