《暮江訡》

# Εὕρηκα!

Today I eventually found out da reason y my legend function was inavailable. Close scrutiny revealed that ther were overall three files which definited da function itself, different from each other respectively. I attempted to force all of da three versions to come to agreement according to Goddard’s, yet da function still simply refused to run. I started to suspect if da definition by Goddard would b problematic.

When I finished reading its explanation within da file, all came to enlighten me! It reads

NOTE: This procedure is *deprecated* because IDL 8.0 contains a LEGEND() function written in IDL. Both can be used provided that the one found later in one’s !PATH is explicitly compiled in one’s startup file. However we strongly recommend the use of AL_LEGEND, which is identical in use to LEGEND. legend.pro will eventually be removed from future releases of the IDL Astron library.

This procedure makes a legend for a plot. The legend can contain a mixture of symbols, linestyles, Hershey characters (vectorfont), and filled polygons (usersym). A test procedure, legendtest.pro, shows legend’s capabilities. Placement of the legend is controlled with keywords like /right, /top, and /center or by using a position keyword for exact placement (position=[x,y]) or via mouse (/position).

No wonder would I fail to exploit da legend function! It had been deprecated according to da Goddard’s file! After deleting d other files which contradicted IDL 8.0’s definition, I had da legend() function work again! 🙂

Nor has da problem been entirely tackled. I realized that combinations of scripts, perhaps inappropriately, removed da functions of TexToIDL. For instance, if I intend to display Greek words or symbols, only da first Romanized letter would appear. Ther may well be some conflict between these lines.

Well, something beyond, today I played a pick-up match against Đội Tuyển Bóng Đá Việt Nam with da university soccer team. For consideration of my convalescence, da coach arranged me as a substitute. We scored an opener at da first half, yet had to b forced to draw soon after da second half due to lapses between our back n da goali. Facts hav proven that it wouldn’t be anything serious, for we resumed fierce attacks with harvest of two more scores. I substituted da goali at around 75-min. Quite relaxed around my area, I received few threats. Da referee whistled d end of da friendly match, n da match board fixed at a victory of 3-1 against Đội Việt Nam.

Judging from today’s match, I think I could become da No.1 keeper soon. Despite elder than d other goalie, I’m a new comer so I must get evrything familiarized. Cố lên!

# Damn, wher’s my legend?

Today I encountered with a weird error with IDL — I planed to edit my program which calculates da compund HG model by Marcus n juz ran d original one at first, however, I was notified with da words that da LEGEND is an undefined procedure or function n thus da plot halted! How come? All my attempts were proven to vain; I’m absolutely pretty kinda disappointed for da simple reason that I couldn’t fix it… 😦

Besides, none has been recent days without any “accomplishment”. At least I’ve been learning writing routines to work with fits images. I’v created a fits image to make a 2-D Gaussian function:

It’s of great necessity for me to master da skills to process fits images and to make analysis with them within IDL. I deeply sense that public softwares for amateur astronomers hav ady failed to suffice me now. For instance, it’s painstaking for me to process LASCO n STEREO images by specified manners to achieve da target for serious photometry. So elaborate it’ll b, that none of da public softwares I possess, including Fitswork, MaxIm DL, IRIS, n ImageJ, hav da capability to simply carry out da work. Instead, IDL has.

Ok, b4 dreaming great dreams, pratically I hav to find out da ways to solve da problem with da LEGND() function. Lack of tutorials, I’m afraid it’ll b a truly arduous journey to tackle d error… Good luck to myself!

# HG Model Plotting

I generated two plots by writing scripts in both Python and IDL respectively. Da function I intended to plot is Marcus’ compound HG model, namely,

$\phi(\theta)=\frac{\delta_{90}}{1+\delta_{90}}[k(\frac{1+g_f^2}{1+g_f^2-2g_f\cos(180-\theta)})^{\frac{3}{2}}+(1-k)(\frac{1+g_b^2}{1+g_b^2-2g_b\cos(180-\theta)})^{\frac{3}{2}}+\frac{1}{\delta_{90}}]$

where $\theta$ is the phase angle, $\phi(\theta)$ is the scattering function, which can be easily converted into the form in terms of magnitudes by the relationship $\Phi(\theta)=-2.5\log{[\phi(\theta)]}$, $\delta_{90}$ is the dust-to-gas light ratio of the coma at phase angle $\theta$=90°, $g_f$ and $g_b$ are respectively the asymmetry factors for forward scattering and the backscattering with confinements $0\leqslant g_f\leqslant1$ and $-1\leqslant g_f\leqslant0$, and $k$ is called the partitioning coefficient between foward scattering and backscattering with the property $0\leqslant k\leqslant1$.

N now da plot generated by Python:

N da plot by IDL:

Careful enough, u might hav noticed that ther’s a difference between da y-axes of da plot by Python n da plot by IDL. Right, but da y-axis in da plot by Python isn’t inverse to achieve our common sense that da brighter a body is, da smaller its magnitude is. When writing da script in Python, I was permanently notified by an error that d inversion format had been incorrect. So lazy I was, that I directly deleted the scripts n juz added another negative to da phase function $\Phi(\theta)$.

D above’s not somthing serious whatsoever. In fact da two plots r totally da same. Weird results with a great difference at y-axes was obtained that d original one by Python plotted a dusty comet’s curve finally came merely to mag. 20, which is absolutely implausible otherwise great comets visible in broad daylight would hav occurred on a frequent basis. I din’t realize where da mistake was until juz now I suddenly understood that da function “log” in Python actually means $\ln$ other than $\log$ after reviewing da tutorials! Evrything turned normal juz with da correction of d error.

Frankly speaking I’m not content with da legend. A special routine called TEXTOIDL has been applied, however, it din’t correctly exhibit Greek letters to me. $d_{90}$ within da plot by IDL should actually hav been $\delta_{90}$. Yet once exploiting da window graph, da Greek letters stood normally. I havn’t yet found out ways to solve da bug, roping still.

Lately I’v been preoccupied with learning IDL myself. Seems that professional astronomers won’t implement da softwares that are widely used amongst amateur astronomers. Da more I learn about IDL, da more important IDL’s to me. Once getting hang of it, I’l b capable of processing images in a scientific means n conduct analysis relatively with ease.

I’v adopted M. Knight’s procedures to analyze LASCO/STEREO images, however, simultaneously none of da softwares I possess has da capability to do photometric work — da dynamic range becomes too short for, for instance, Astrometrica to simply illustrate these images, so that makes measurements impossible.

It’s of great necessity for me to calibrate da LASCO/STEREO images and proceed to analysis; I has some ideas with bodies within these images to write a paper. Before this I must master IDL as soon as possible. In addition, da coach of my uni’s soccer team called me to join da team himself, and if it doesn’t rain, I need to go to da training evry two days. Definitely I become even busier!

I must make good use of time n hurry up. Gambate n Cố lên!

# A New Comet Detected by Rob Matson!

Yesterday when routinely checking the NEOCP, I stumbled on a familiar name — MATSON indicating an extraordinarily bright object compared to other commonly seen objects listed in that page. I know it must be a comet!

Veteran as Rob is in detection of unknown comets in SWAN images, he has already discovered three comets in this way. So in accordance with my experience, I boldly conclude that this time he was again reporting a suspicion in SWAN images.

The first confirmation came from Siding Spring Obs (E12) on Sep 04. By far there had been 13 astrometric and rough photometric observations, all of which were fed into a software for orbital calculation and hence I obtained a possible orbital solution:

Since the arc is very small still, there’s great uncertainty.

I took a look if we visual comet hunters would have been capable of discovering this comet before Rob’s detection in SWAN, and I found out that the answer turned out to be very certain — absolutely we could have!

The chart above illustrates the comet’s path from Aug 26 to Sep 5. The blue slope line in the lower right corner indicates the horizon at 20:00 local time on Sep 05 at Canton. As the comet heads towards the north, the conditions turns better. The souther the latitude a visual comet hunter is situated, the more opportunity he would have been able to detect the comet prior to Rob’s detection. But why nobody managed to catch it? My interpretation is the sheer reduction in the number of visual comet hunters.

Actually I haven’t got surprised whatsoever after seeing the candidate in the NEOCP, as I currently never cover regions in dusk, but areas at predawn, due to severe light pollution from the south to the northwest at Sưi Sỉnh Hạ. I know opportunity will always be there, despite scarcity. It’s a matter of whether people are willing to go into practice or not. Will I succeed in discovering my own comet in nightsky? I don’t know. But I already have set off and have been striving for my dream. In fact I don’t have to long for harvest eagerly at all but will only focus on admiring the beauty of the sky through an eyepiece regardless of reputation and vanity.

Finally, congratulations to Rob on the brilliant discovery!

# Antikythera Mechanism (Part II)

Ctesibius was fortunately to be born in Alexandria, a place where all the knowledge of the ancient classical world was held in one vast library, a place where the great thinkers of antiquity studied, and where shelves held the thousand of scrolls recording their work. The library was such a great institution, that people came here from all over the world to learn and to invent. It was here that Ctesibius’ revolutionary invention was recorded, and where the young Archimedes may first have read his work. Ctesibius is a figure who is often forgotten in history, yet his work paid off the way for technical revolution—the measurement of time.

Yet Ctesibius came from humble beginnings. He was a son of a simple barber. As a young man, he worked at his father’s shop at Alexandria, inventing gauges such as adjustable mirrors. And here he was surrounded by the constant dripping of water, which would inspire his great invention. Ctesibius knew for thousands of years the Egyptian used ordinary water timers to mark the hours of day. The famous Karnak water clock is one example. Despite the intrigued hieroglyphics, strange symbols and images of gods and animals, it’s a simple device, as the reproduction shows. It was filled to the top of water and as it ran out through a spot at the bottom, the time could be read as the level dropped. Markings inside show the passing hours, but these varied as the number of hours from sun rise to sun set varies from month to month. The clock allowed the ancient Egyptians to measure the passing of time during the day or night, but this is still only a timer, not a constant clock.

In sophisticated ancient Greek society, the ability to tell the time accurately had become extremely important. Their society needed order and schedules which meant they had to be able to tell the time accurately. Sundials could be used at certain times and could be seen on important surviving universal buildings such as the Tower of the Winds in Athens. But when the Sun went behind the cloud, or night fell, how would they know what time it was then? The first Greek solution to this age-old dilemma was their own water timer, called Clepsydra, or “water thief”.

“The Clepsydra was an elegant device for measuring periods of time. In most examples it gave an equal amount of time to lawyers in a court room, or speakers at a particular assembly. It worked very simply. You filled the large vessel with water, and when you were ready to start timing, you simply took the bump out of the bottom, and the water ran slowly out of the vessel.” said Christopher Kelly.

Lawyers and minor legal cases may have been allowed the time it takes one clepsydra to empty to give their argument. However for a serious case like a murder a whole row may have been needed to allow more time for evidence. But when the water was gone, your time was up. It was the origin of the phrase “running out of time” but that was quite literally what happened. For breaks or over night a bump could be put in effectively pausing the session.

“The clepsydra has one significant limitation,” said Christopher Kelly, “it’s a timer, not a clock. The problem is when the vessel is full, the water gushes out of the bottom. But as the water level drops, so the pressure reduces, finally to a dribble.”

The ancient Greeks made their clepsydra more and more ornate but they still had the same problem—the fact the water ran more quickly at the beginning than the end. They created graduated scales to compensate for this but they couldn’t make it run at a constant speed. Ctesibius, however, solved the solution. He realized that if the vessel was always full, then the water pressure would always be the same. If he could master that, he knew he could create an accurate device which would change the world. This thing was the challenge he decided to settle himself.

“Ctesibius thought that the way to simplify the Egyptian clepsydra was not to utilize outflow of water,” said Dr. Alan Mills, University of Leicester, “but to try and obtain uniform inflow of water.”

Dr. Alan Mills, a researcher of University of Leicester, has used classical references to Ctesibius’ work to build a replica of one of his earliest water clocks.

“It’s very sophisticated. It’s one of these inventions that is easy once some geniuses had thought of it.” Alan Mills added.

The challenge was to keep the reservoir of the clepsydra full at all times. As this is how Ctesibius did it, firstly he added another water tank about the main reservoir. This pulled water into the top faster than it could flow out, meaning the reservoir was always full. And any excess water could just run off into an overflow container. The water would always come out from the reservoir at the same speed. Now Ctesibius just had to measure it. To do this, he decided to put another water tank under the constant outflow. In this container, he placed a float with a pointer on top and the scale next to it. When the level of the water rose, the pointer rose at a constant speed. It was a stroke of a genius! Ctesibius had created the world’s first mechanical clock, thanks to the dripping water in a barber shop.

He had harnessed the power of water and in the process he had become a master of time. But measuring hours and minutes was only the start. What else could this unique water clock do?

The answer to that was kept here in the great library of Alexandria. Anyone in the ancient world wanted to understand time could come here and read Ctesibius’ books, which described the wonderful machines he was now building and the whole new subject he invented – hydraulics. Before long his clocks were not just dripping taps, but ornate machines decorated with gilded figures of gods and animals. And their workings were yet more elaborate too. He devised the complex scale for the hours too, showing here in white for the day and blue for the night. One nymph holding a shell from which drips the constant supply of water, whilst another travels up the scale holding the pointer that indicates the hour of the day or night. But that was only the start. He even used water to sound the whistle and make a model owl move. He had invented the world’s first cuckoo clock. Increasingly complicated series of gears of wheels also allowed the scale to rotate very slowly to indicate the days within each month of the year. This clock now is also a calendar, and automatic, day and night, month and year, cuckoo clock.

Archimedes was clearly fascinated by Ctesibius’ creations. He started his clocks, and used own genius for inventions to continue the work. In an Arabic translation of Archimedes’ work, dating back over a thousand years, we can see a tantalizing glimpse of his editions to Ctesibius’ water clocks. This modern reconstruction shows Archimedes’ elaborations to Ctesibius’ clock. He had a bird who drops small stones onto a bell, making the clock chime on the hour. The woman is a Gorgon, with snakes for hair. When the bell triumphs, you look up to see her eyes change color indicating the time. This is the first automatic chiming clock in history. One could only imagine the spectacle when Archimedes unveiled his daring design. In Greek mythology, anyone who looked into the eyes of the Gorgon would be turned to stone. But with Ctesibius’ help, Archimedes could the man who dared to look into the face of the Gorgon.

Alexandria today is a busy modern port. A new building now stands in place of the famous library. Tragically, the original library was burnt to the ground and with it was lost nearly all the knowledge of the ancient world. Only a very few ancient texts remained which mentioned Ctesibius’ work. We may never know what else he invented as none single page of his own work had survived.

So much information has been lost, that Ctesibius has been largely forgotten. However, there is one legacy of his work, one clue, which is still standing. This unassuming tower topped away to a corner of Athens is one of the best preserved buildings from antiquity. Its survival almost untouched is a miracle and one due to fact for centuries it was believed to be the tomb of the philosophers Socrates and Plato. But it isn’t a tomb. Carved on the eight faces a clue to its weird use, on each side a sculpture of eight winds can still be seen, along with a sundial. It was actually built by an astronomer around two hundred years after the death of Ctesibius, but it’s a monument to his genius. The building, now known as the Tower of the Winds, was the public clock of ancient Athens. Inside this tower, there once stood a huge and complex water clock, based on Ctesibius’ design.

This clock was fed by a constant stream of water which ran from a spring on the acropolis, from which the whole population of Athens could tell the time. But this was more than just a clock or a calendar. Some believed this strange building had the device and even charted the movement of the Sun and Moon in relation to the constellations or zodiacs. We know the Greeks were measuring hours, days and months during the time of Ctesibius. Could it be that they also had also started to look up above and measure the heavens? One man believed the answer may lie in the wheels of the Antikythera mechanism.

In 1951, an English physicist, Derek de Solla Price, decided to find out for himself and examined the mechanism in detail for the first time. De Solla Price traveled to Athens to look at the mechanism. The pieces had lain largely untouched since its discovery fifty years earlier. The device had disintegrated further exposing pieces of the gears which was able to study. He began determined to crack the secret of the Antikythera mechanism.

De Solla Price spent much of his time at the National Museum of Athens probing the secrets of the ancient enigma. Something told him that these fragments were the real treasure from the Antikythera wreck.

Using new development of X-ray technology he could now see what the discoverers fifty years before could not. Looking through the corrosion, he was amazed. A machine, so complex, it could almost be modern. He had to know what it was for. His meticulous studies of the cogs, gears and inscriptions gave him clues to the possible purpose of the mechanism.

Remnant of a wooden box which held the device also had the Greek writing on, which gave further tantalizing hints. Using this information, de Solla Price developed a theory and put together a model of how he believed the Antikythera mechanism could have worked. He realized the mechanism was an extremely sophisticated device for calculating the relative movement of the Sun and Moon. It also seemed to show the days of the month as lunar phases. De Solla Price has established its mechanical complexity and knew that the knowledge acquired to create such a machine was immense. He believed in the front of the mechanism the bronze dial showed the date and the positions of Sun and Moon. A dial at the back would indicate the month, possible within the twelve months in a year. A further dial at the back seemed to show either a cycle of 47 months or four years. De Solla Price called the mechanism a “calendar computer”. For anyone in the ancient world, such a device would be invaluable. To understand the movement of the Sun and Moon within the heavens was to look into the minds of the gods. Many believed then, and some due today, that the positions of the Sun and Moon and stars of the time of someone’s birth may influence their later life. What complex horoscope software does today the Antikythera mechanism may have done over two millennia earlier. To the priests and astrologers of the day, this extraordinary machine could have been a window on the gods.

But where could such a device come from? De Solla Price had an extraordinary theory. What if machines like the Antikythera mechanism would be part of the municipal clock powered by the very water clock that Ctesibius invented? What if it were in a common place in the Hellenistic world? Was this is a secret to the Tower of the Winds, not just a sundial or even a clock, but an automatic model of the Sun and Moon within the universe? De Solla Price so suggested that building these machines was what interested the great Archimedes. Perhaps the Antikythera mechanism was a later copy of one of Archimedes’ machines? De Solla Price published his findings in 1974 in an article entitled “Gears from the Greeks”. The article generated a storm of international interest.

In particular, one man was to read that article and to spend the next thirty years pondering on de Solla Price’s theory. When Michael Wright from the Science Museum, first grabbed the paper, he was immediately fascinated by the notion that the ancient Greeks had complex engineering. Wright decided to go to Athens to examine and re-X-ray the mechanism for himself.

“We’ve got these few, with several pieces put together, and it helps me to build up a more complete picture of just how the gear wheels were arranged inside the box before they fell apart.” said Michael Wright.

Although intrigued by de Solla Price’s theory of the Antikythera mechanism, Wright believed there was more to the device than de Solla Price had realized.

“I went back and wrote “Gears from the Greeks” scaled, and started to find problems with Price’s account. That’s what I resolved I really had to look at the thing for myself.” added Wright.

But for Michael Wright to understand this strange device, he knew he needed to do more than just looked at it. He needed to build one for himself. After de Solla Price’s publication, many academics simply refused to admit that the mechanism could be so old. The complex gearing seemed too modern. How could ancient people solve calculating they precisely cut the fine teeth on each wheel, they asked? Surely this either was a fake, or a later machine just happened to be lost on the site of the ancient wreck. So Wright set to work, determined to prove them wrong.

Using only tools similar to those available in the ancient world, and with the Greeks’ knowledge of geometry, he set out to copy the elaborate gears in his workshop. Measuring and cutting gears with only apparent compresses, a metal file, and good eyes for detailed was not to be easy, but it was possible. After many hours of practice, Wright proved beyond doubt that with patience and skill, it could be done.

“You can’t deny the evidence of the Antikythera mechanism exists,” said Wright, “When you look at it closely, it’s a very accomplished work, both in design and execution. Why shouldn’t the ancient Greek have done it?”

We know from translation from his work that Archimedes was familiar with these types of cogs. And now it was the study of these gears that was to help to solve yet another mystery involving one of his mechanical marvels – the mystery of odometer. We all use odometers every time we get in a car. It’s the device which the distance we’ve traveled. But remarkably, this device was in use long long before cars, and it was crucial to the development of the Roman Empire.

Next I’ll further introduce the odometer devised by Archimedes. Stay tuned!