jueves, julio 12, 2012

The Dial of Ahaz

...The vacuum bubbles are the same whatever the external lines, and give an overall multiplicative factor. The denominator is the sum over all vacuum bubbles, and dividing gets rid of the second factor.

The vacuum bubbles then are only useful for determining Z itself, which from the definition of the path integral is equal to:

 Z= \int e^{-S} D\phi = e^{-HT} = e^{-\rho V}

where \rho is the energy density in the vacuum. Each vacuum bubble contains a factor of \delta(k) zeroing the total k at each vertex, and when there are no external lines, this contains a factor of \delta(0), because the momentum conservation is over-enforced. In finite volume, this factor can be identified as the total volume of space time. Dividing by the volume, the remaining integral for the vacuum bubble has an interpretation: it is a contribution to the energy density of the vacuum...

Richard Feinman

3 Versions of Bulles, J.B. Chardin 18th century.

F.T. - Sketch for IMU-1
Pencil and gouache on tracing paper 2006 15x30cm

Why you should never throw away an old auction catalogue.

This was a fabulous auction with a few pieces that knocked my socks off .

Thanks to this catalogue, I became aware of the existence of a Hartmann Dial in Toledo in the Museum of Santa Cruz where it is in storage. My fascination for this object inspired me to look for them and find meaning behind their appearance.

The evolutionary step of drinking water from our hands to drinking it from a cup was fast. Our collective subconscious has been looking at water and its reflections for a long time.

Gottland Bullau

Humankind it seems, has always understood bubbles! You only need to look at north european use of water and polarizing sun crystals or sun stones as an aid to tell time and place. In the east, the Jomon Pots,  are fundamental not only in the Tea Ceremony today, but have created a tangible cross cultural timeline for thousands of years. They fascinate us from the beginning, from the moment they were made. These ancient people understood cosmic principles, and we can go all the way back to 18,000 BC.

There is no reason why we should not understand these fundamental principles too. I believe space, time and light to be humankind's obsession. The three things that we try so hard to understand, the three things we try to always reconcile. (1)  (2)  How do we fit in to the whole picture? what is our metabolism in relation to our environment?

Why is is there so much conflict now, such economic and social hardship, fear and retribution? Why is there so much symmetry between good and evil?

I think its called the Double Bubble Conjecture.

Aristarchus and Eratosthenes

F.T. Luna, Paris - 1997

The scaphe (or skaphe, also scaphium or scaphion) was a sundial said to have been
invented by Aristarchus in the 3rd century BC with aristotle's words still in the air.

Eratosthenes of Cyrene a hundred years later, measured the length of the Earth's meridian arc. It is highly likely that the sun and the behavior of light in a bowl of water, or a bubble, would have had an effect on whoever started thinking of time & space in a bowl!

ח  הִנְנִי מֵשִׁיב אֶת-צֵל הַמַּעֲלוֹת אֲשֶׁר יָרְדָה בְמַעֲלוֹת אָחָז בַּשֶּׁמֶשׁ, אֲחֹרַנִּית--עֶשֶׂר מַעֲלוֹת; וַתָּשָׁב הַשֶּׁמֶשׁ עֶשֶׂר מַעֲלוֹת, בַּמַּעֲלוֹת אֲשֶׁר יָרָדָה.  {ס}
8 behold, I will cause the shadow of the dial, which is gone down on the sun-dial of Ahaz, to return backward ten degrees.' So the sun returned ten degrees, by which degrees it was gone down. {S}
ט  מִכְתָּב, לְחִזְקִיָּהוּ מֶלֶךְ-יְהוּדָה, בַּחֲלֹתוֹ, וַיְחִי מֵחָלְיוֹ.
9 The writing of Hezekiah king of Judah, when he had been sick, and was recovered of his sickness.
י  אֲנִי אָמַרְתִּי, בִּדְמִי יָמַי אֵלֵכָה--בְּשַׁעֲרֵי שְׁאוֹל; פֻּקַּדְתִּי, יֶתֶר שְׁנוֹתָי.
10 I said: In the noontide of my days I shall go, even to the gates of the nether-world; I am deprived of the residue of my years.
יא  אָמַרְתִּי לֹא-אֶרְאֶה יָהּ, יָהּ בְּאֶרֶץ הַחַיִּים; לֹא-אַבִּיט אָדָם עוֹד, עִם-יוֹשְׁבֵי חָדֶל.
11 I said: I shall not see the LORD, even the LORD in the land of the living; I shall behold man no more with the inhabitants of the world.
יב  דּוֹרִי, נִסַּע וְנִגְלָה מִנִּי--כְּאֹהֶל רֹעִי; קִפַּדְתִּי כָאֹרֵג חַיַּי מִדַּלָּה יְבַצְּעֵנִי, מִיּוֹם עַד-לַיְלָה תַּשְׁלִימֵנִי.
12 My habitation is plucked up and carried away from me as a shepherd's tent; I have rolled up like a weaver my life; He will cut me off from the thrum; from day even to night wilt Thou make an end of me.
יג  שִׁוִּיתִי עַד-בֹּקֶר כָּאֲרִי, כֵּן יְשַׁבֵּר כָּל-עַצְמוֹתָי; מִיּוֹם עַד-לַיְלָה, תַּשְׁלִימֵנִי.
13 The more I make myself like unto a lion until morning, the more it breaketh all my bones; from day even to night wilt Thou make an end of me.
יד  כְּסוּס עָגוּר כֵּן אֲצַפְצֵף, אֶהְגֶּה כַּיּוֹנָה; דַּלּוּ עֵינַי לַמָּרוֹם, אֲדֹנָי עָשְׁקָה-לִּי עָרְבֵנִי.
14 Like a swallow or a crane, so do I chatter, I do moan as a dove; mine eyes fail with looking upward. O LORD, I am oppressed, be Thou my surety.
טו  מָה-אֲדַבֵּר וְאָמַר-לִי, וְהוּא עָשָׂה; אֶדַּדֶּה כָל-שְׁנוֹתַי, עַל-מַר נַפְשִׁי.
15 What shall I say? He hath both spoken unto me, and Himself hath done it; I shall go softly all my years for the bitterness of my soul.
טז  אֲדֹנָי, עֲלֵיהֶם יִחְיוּ; וּלְכָל-בָּהֶן חַיֵּי רוּחִי, וְתַחֲלִימֵנִי וְהַחֲיֵנִי.
16 O Lord, by these things men live, and altogether therein is the life of my spirit; wherefore recover Thou me, and make me to live.

The vessel

Below is a collection of greek vessels with lines and circles symbolizing rebirth and continuity.

These burial vessels reveal the fascination for cosmic events and the cycle of life and death.
Dipylon Krater, National Archhaeological Museum, 800 - 700 BCE, Athens

Diptylon Krater Metropolitan Museum of Art, New York 800-700 BCE, Athens

Late Geometric I Period, 760-735 B.C
Dipylon krater by the Hirschfeld Painter from a male grave, Athens, Kerameikos
Athens, National Archaeological Museum

Skyphoi and urn, Proto-Geometric Period, 1025-900 B.C.

Terracotta. h. 4 7/8 in.early 6th century BCE
Etruscan, Rhode Island School of Design Museum
Mary B. Jackson Fund inv. nº33.028

Krannert Art Museum, IllinoisAttic black-figure kylix, ca. 530 BCE
Follower of Exekias (Greece, active ca. 550–525 BCE)
Earthenware, slip 4 1/2 x 14 1/2 inches (including handles)
Gift of Theresa E. and Harlan E. Moore 1970-8-1

Owl. Attic red-figure skyphos, last quarter of the 5th century BC.
Museum of Fine Arts, Lyon. Photo, Marie-Lan Nguyen

Black-gloss skyphos of the glaux type,
which there are two circularly shaped handles,
one horizontal handle and one vertical.
This glaux skyphos is from Athens, ca. 450–400 BC. 
H. 2 ¾ in. (7.2cm ) 
Louvre, Paris 
Image Courtesy of Marie-Lan Nguyen/Wikimedia Commons

Partially black glazed Greek bowl - 400 BC  Denmark

The Morgantina Silver, Greek - 250 BCE,  Aidone, Sicily 

Cermonial drinking horns - 250 BCE                source

Roofed Spherical Sundial in the shape of a skyphos, Louvre

1st or 2nd century AD
Found in Carthage(?)
Bas relief and engraving on marble
H. 30 cm; Diam. (including handles): 73 cm
Gift of the Friends of the Louvre, 1999
N° d'entrée MNE 1178 (n° usuel Ma 5074)
Greek, Etruscan, and Roman Antiquities

This sundial dates from the imperial era and is an exceptional example of a scaphe, or bowl sundial, with a hole to let through a ray of sunlight. The interior is engraved with lines and inscriptions in Greek; the spot lit by the sunbeam would give the month, day, and hour. This sundial is in the shape of a skyphos or drinking vessel, a fashionable shape for luxury Roman tableware at the end of the republic. The exterior is decorated with oak twigs and acorns.

El Reloj Romano de Belo, Museo Arqueológico Nacional, Madrid 100 AD

The Belo Sundial, Madrid

Pila Bautismal Gótica, Iglesia de San Miguel el Alto, Toledo - Foto: RTK
Water is fundamental in spiritual and spatial discourse.

Georg Hartmann was an exceptional sixteenth- century German cosmological
instrument - maker and engraver. He was born in 1489 in Eggolsheim near Forchheim, Bavaria. He died on April 9, 1564 in Nuremberg. He was a German engineer, instrument maker, author, printer, humanist, churchman, and astronomer.

Refracting scaphe sundials

The Harvard Dial of Ahaz
Nuremberg - 1548
Guilt brass, Collection of Historical Scientific Instruments,
Department of the History of Science (lot.7397) Harvard University.

The Oxford Dial of Ahaz Nuremberg - 1539

Sothebys Dial of Ahaz, Nuremberg - 1547
Sotheby's, 27-04-1999

The Madrid Dial of Ahaz
Museo Nacional de Ciencia y Tecnología, Madrid

At the age of 17, he began studying theology and mathematics at the University of Cologne. After finishing his studies, he travelled through Italy and finally settled in Nuremberg in 1518.

He constructed astrolabes, globes, sundials, quadrants, and other instruments. Hartmann was possibly the first to discover the inclination of Earth's magnetic field. As an anecdote, during his arrival in July, there was The Dancing Plague of 1518. A case of dancing mania in Strasbourg in which many people died from constant dancing.

The Toledo Dial of Ahaz

Museo de Santa Cruz
Nº Inventario  general 5045

Santa Cruz Museum, Toledo, Tuesday July 10th 2012

The Dial

The dial was presented in very good condition, complete with its lid.  It keeps well under the foam sheet in which the two pieces are wrapped in separately, and are well preserved in the dry climate of the city. Unfortunately the original box is missing.

Upon examination of the piece without ever touching it with my fingers, I Iooked at the gnomon to see if it was in any way bent or damaged, but it was perfect, except for the soft rub of time. The text has polish incrustation, and there are oxydized fingerprints, as well as a few small drops of red seal wax on the lid.

The condition of the brass is excellent with microscratches over the surface but not in the least interfering with the high quality finish of the alloy’s proportions of metals. The brass is quite pale indicating a low concentration of copper and a higher concentration of harder white metals.

The brass dial was fired into a mold, and subsequently refined on a high speed lathe with a chisel by the evidence of the fine circular lines over the whole surface.

None of the dials discovered so far by Hartmanns hand have an original needle.
There is also no evidence of the compass bowl to have ever posessed a glass covering, and does not show evidence of having been designed for it. I will explain the reason for this below.

The smaller round bowl of the compass at the bottom has two holes where the freshly fired bowl was clamped to the lathe and fixed to it with two bolts through the holes, to prevent it from slipping while applying the chisel. Underneath one can see the rivet for the tiny compass pin, and the hammering and filing to level the base.

The engraved lines and text

The border lines are engraved on the surface with the chisel and the text is embossed the meridian lines 




POLVS   GR 41 · MI · 41


V   VI   VII   VIII    IX    X   XI   XII   I   II   III   IIII   V   VI   VII




The bowl: 153mm diameter x 94mm high
The base: 90mm x 22mm high
The compass: 20mm
Thickness : 2.5mm

How does the dial work?

Herunder my experiment with the three Kylix made by the master Antonio Portela. The experiment was made to reveal the simplicity of the device, and the patience of the priests and doctors who had to mark the passage of that sharp point of light, over a period of many years. Kylix were used in the symposia, inside or outside, and were a topic of conversation and a simple way to measure time.

Kylix, Antonio Portela, Toledo - 2007

Unsuccessful event, the gnomon is under water. It is the same when there is NO water.

Successful event. Correct water level for lensing. The gnomon pierces the water membrane.I left some dust to distinguish the water. The event is only visible if the tip of the gnomon touches the edge of the surface. The geranium petal in the water shows the same event at the point where it touches the membrane of the water. The distotion of that membrane bends the light and concentrates it to that point by an effect called lensing. Gravity bends light particles, and this is a good example of it.

The experiment on dark pottery is very successful

The point of light gives you your position in relation to the cosmos. To level it, it has to be filled to the tip of the gnomon with water. The compass came much later and helped speed up precision when placing the gnomon due north.

It consists of a hemispherical bowl which has a  gnomon attached inside it, with the top of the gnomon level with the edge of the bowl or in some cases where the waterline has been indicated. The gnomon has to pierce or push the membrane of the surface of the water with its tip for the event to visible


Unless you have a compass at hand,  or a little magnetized compass needle which you place in the compass bowl, which I did not,  I had to place the dial by eye with my Iphone compass. Before smart-phones were invented and allowed me to place the bowl due magnetic north, a renaissance person would have to place the bowl at night, pointing the little star embossed on the lip of the edge, in line with the gnomon towards the North Star. You could also magnetize a little flat and rhomboid piece of metal.


To level the dial we use water. The base of the dial has two little holes that are simply plugged with bees wax from below, in our case we used blue-tack so as not to damage the bowl, and filled it to the brim with water, in our case distilled water. The experiment was done at 13:55  Spain summer time. It is 1 hour less in Nüremberg (ignoring the modern time zones). You also have to calculate that Hartmann was using the Paris Meridian time, subtract again 1 hour, which gives us the perfect time, adjusted for today: 10:55am.

The word IMITATVR (“copy” in latin) is embossed above the constellation of Piscis (the age of Cristianity). It shows the three main stars of the small Triangulum constellation (symb. The Holy Trinity); Hamal to the right of IMITATVR, Rasal Mothallah (Caput Trianguli) to the left. The third star just above the O of ARTIFICIO is the star Deltotum.

At sunrise on a hill in Nüremberg, around summer solstice, the dial will come alive at around 5:00 am. Because the summer solstice celebrations on June 21st were already a long established pre-Christian festival, known as Litha in some cultures, centuries later the church followed their normal custom and made June 24th a religious feast day, that of St. John the Baptist. One of the 'quarter days' which welcome each of the four seasons, it is halfway to the commemoration of the Christ's birth on December 24, and as such celebrated as the day of St. John's birth six months before that of Jesus.

However, although the clergy's intention was to keep the pagan and Christian festivities separate, Sommer-Sonnenwende and Johannisnacht, Summer Solstice and Midsummer Night, became almost inter-changeable.

However, centuries after the town council of Nuremberg on June 20, 1653 issued a decree to 'do away with all such unbecoming superstition, paganism and peril of fire on this coming day of St. John', after sunset on June 23rd throughout Germany there are fires on mountains, hillsides, and open spaces, as well as beside lakes and rivers.

Georg Hartmann Astrolabes

British Museum Astrolabe, 1537

The Black Astrolabe, 1527  Oxford

Dials by Others 

Scaphe Dial and Surveyor's Compass
Alexander Ravillius, Italian, 1537
Museum of the History of Science, Oxford

The Philadelphia Dial of Ahaz 1578
American Philosophical Society Museum Collection

Christopher Schissler’s Dial of Ahaz, completed in 1578.

The Florence Scaphe Dial
16th century; Italian
Brass; 175 mm in diameter
Museo Galileo, Florence

Hemispherical bowl mounted on a turned foot with a single, short conical column. The interior of the bowl is engraved with a series of undivided hour lines for Italian hours reading from 9 to 23 and traversed by the meridian and the equinoctial line. The pointed gnomon is rigidly set at the foot of the meridian and on the outside of the bowl on the side opposite the gnomon is the base for a compass with fleur-de-lis bracket. Of this only the pivot and what seems to be a declination line for 18? east now survive. The turned and stepped cover has a central, independently applied relief oakleaf cluster design composed of three separate elements on both sides. 

This instrument appears to correspond with that mentioned in the following entries in the Medici inventories: 'Scodella d'ottone con un coperchio dentrovi un oriuolo da Sole in sua busta di cuoio nera' (Guard. Med. N. 87 Inv. Delle robe del Granduca Cosimo I, 1574: car. 337); 'Oriuolo a Sole dentro una scodella d'ottone' (Guard. Med. N 190 Inv. Delle robe del Granduca Ferdinand I, 1595 car 363); 'Orologio da Sole d'ottone fatto a mezza palla con coperchi e piede simile e sua bussola da una parte numerata 24' (Guard. Lorenese n. 94, 1578-61). Anthony J. Turner

 Instituto e Museo di Storia della Scienza, Firenze 
Inventory no. 241

One of the oldest forms of sundial, (not a water dial) scaphe dials have a concave shape that mirrors the curvature of the Earth. This example can be adjusted for use at any latitude north of the equator.
It was part of the collection of instruments owned by Cardinal Francesco Barberini. The chief inquisitor of Galileo
Royal Museums, Greenwich

The Octavius Morgan Dial of Ahaz

Scaphe-dial in form of chalice; c.1580-1600; gilt-brass; hexagonal; latitude 49 degrees; bottom of interior: compass set for declination N8E; internal hour-scales; scales marked with zodiac signs; short pin instead of original polar gnomon; dial of direction; base maybe later replacement.

Inscription Type: 
Inscription Content: LATIT: 49 GR

Width: 95 millimetres (max)
Height: 137 millimetres Acquisition date
: 1888

 Acquisition name: 
Bequeathed by Octavius Morgan
British Museum, London

Bartholomaeus Madauer Chalice, guilt copper,  Aldersbach - 1554  British Museum 

This gilt brass chalice serves as an altitude dial for telling the time of day. The outside of the chalice is plain, only the joint between the cup and the foot is decorated with a raised acanthus-leaf.
The inner surface is engraved with eight curved lines for equal hours, the hour scale numbered I to VIII from the bottom to the top and IIII to XII in reverse order. A date scale, represented by symbols for the zodiacal signs (in pairs, clockwise from the hour scale: Cancer/Gemini; Leo/Taurus; Virgo/Aries; Libra/Pisces; Scorpio/Aquarius; Sagittarius/Capricorn) compensates for the fact that the solar altitude changes during the year. Every pair of signs is divided to 10°. The edge of the cup has a single degree scale. A vertical scale of solar altitudes runs from 0° to 65°, numbered by 5° and divided to 1°. The vertical spike acting as a gnomon situated at the centre of the cup is a replacement.
The name of the maker and the date are engraved in a cartouche on the inner surface.
Around the bottom of the inside of the cup is an inscription indicating the latitude for which the dial serves.

Inscription Type: inscription
Inscription Position: inner surface, in cartouche
Inscription Language: Latin
Inscription Translation: Bartholomeus, abbot of Aldersbach, made [this] in the year 1554
Inscription Comment: signature of maker, place and date of production

Inscription Type: inscription
Inscription Position: inner surface, bottom
Inscription Language: Latin
Inscription Content: HOROLOGIVM IN CRATERE AD ELENA{TIO} [recte: elevatio] PO{lis} 48
Inscription Comment: indicating latitude served by dial

Diameter: 105 millimetres
Height: 142 millimetres

Curator's comments
This unusual altitude dial in the form of a chalice, with an hour scale and a solar altitude scale inscribed on the inner surface, could be used for telling the time during the day. The chalice is rotated until the shadow of the pin gnomon projecting inwards lies in the correct month which can be identified by the zodiacal sign. The shadow of the tip of the gnomon then indicates true solar time in equal hours.
The chalice can also be turned until the shadow of the tip of the gnomon falls on the solar altitude scale thus indicating the solar altitude.
The instrument is laid out for latitude 48°, thus corresponding roughly to the latitude of Passau. It is the earliest extant chalice dial of ten so far recorded. Chalice dials appear briefly in southern Germany in the late 16th and early 17th centuries.
Bartholomaeus Madauer (abbot of Aldersbach 1552-77, died 1579) also signed a similar silver-gilt sundial (undated) which is now lost, but was kept in the Kunstkammer in Munich in 1599. 
[S. Ackermann, EPACT 1998, http://www.mhs.ox.ac.uk/epact/catalogue.php?ENumber=97084]

Scaphe dial with adjustable hour grid
Amelli, late 16th century, Italian
Museum of the History of Science, Oxford

Scaphe Dial
Stefano Buonsignori, Florence - 1584
Cosmographer to Francesco I de Medici
Museo Galileo, Florence

Sumerian Star Chart

Sky Map of Ancient Nineveh 3300 BC

A reproduction of a Sumerian star map or “planisphere” recovered from the 650BC underground library of Ashurbanipal in Nineveh, Iraq in the late 19th century. Long thought to be an Assyrian tablet, computer analysis has matched it with the sky above Mesopotamia in 3300BC and proves it to be of much more ancient Sumerian origin. The tablet is an “Astrolabe”, the earliest known astronomical instrument. It usually consisted of a segmented, disc shaped star chart with marked units of angle measure inscribed upon the rim. Unfortunately considerable parts of the planisphere are missing ( approx 40%), damage which dates to the sacking of Nineveh. The reverse of the tablet is not inscribed. Still under study by modern scholars, the planisphere provides extraordinary proof of the existence of Sumerian astronomy.

Hans Holbein, The Ambassadors

In 1527 Kratzner and Holbein collaborated on the ceiling design of a temporary royal theatre at Greenwich showing the arrangement of the heavens; and in 1528 Holbein illuminated an instruction book written by Kratzer on the use of an astronomical instrument given to Henry VIII as a New Year’s gift.

Henry VIII Astrolabe, British Museum
Shortly before Holbein’s own death in 1543, he also produced a beautiful design for a “clocksalt” – a combination of a mechanical clock, an hourglass, a sundial, and a compass – that was given to HenryVII by the courtier Anthony Denny. Holbein was thus an artist actively engaged with the representation of time.

Also described Isaiah 38: There is a needle compass at the bottom of the bowl to facilitate proper alignment.

Ivars Peterson reports on Christopher Schissler’s Bowl of Ahaz in his article “Turning back time: an antique sundial simulates a biblical miracle” (Science News, February 10, 1990). 

Owen Gingerich is there quoted as indicating that Schissler’s dial “was not in any sense an attempt to explain the miracle of Isaiah...It was a just a way of simulating it.” The same is likely true of Hartmann. Peter Dear, “Miracles, Experiments, and the Ordinary Causes of Nature” in Isis 81, no. 4 (1990): 663–683.Steven Shapin, “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke disputes,” Isis 72, no. 2 (1981): 187 – 215.For an extensive discussion of miracles and their relationship to science, see Malcolm Diamond, “Miracles” in Religious Studies, Vol. 9 No. 3 (1973): 307 – 324.

Hartmann was not the only instrument maker to construct a bowl of Ahaz.These instruments were very important to other Map & Map-makers. 
The Periplus of the Eritrean Sea, 1st - 3rd centuries 
Tabula Peutingeriana (4th century) 
Isidore of Sevilla's T and O map (c. 636)
Juan de la Cosa map (1500)
Piri Reis map (1513)


Jan Táborský of Klokotská Hora (1500–1572)

He was a versatile bookman of his time. As early as in his youth, he attended lectures on mathematics and astronomy at the Prague university. He ran a scribal and calligraphic workshop in Prague, which copied old manuscripts, mainly hymnbooks. There are over twenty of them that are known to have been created in his workshop.

He maintained, repaired and improved the Prague astronomical clock for thirty years. His manuscript “Report on the Prague Astronomical Clock” (1570) was the first detailed description of the clock

Juanelo Turriano 1500 - 1585  Pompeo Leoni  -  Museo de Santa Cruz 16th century

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