University of Bonn researchers think that they may have taught fish to count. They
tested the fact that many life forms can note the difference in small
quantities between “one more” and “one less,” at least up to five items,
on fish. Not much work had been done on fish in this area so they
decided to test eight freshwater stingrays and eight cichlids:
All of the fish were taught to
recognize blue as corresponding to “more” and yellow to “less.” The fish
or stingrays entered an experimental arena where they saw a test
stimulus: a card showing a set of geometric shapes (square, circle,
triangle) in either yellow or blue. In a separate compartment of the
tank, the fish were then presented with a choice stimulus: two gates
showing different numbers of shapes in the same color. When the fish
were presented with blue shapes, they were supposed to swim toward the
gate with one more shape than the test stimulus image. When presented
yellow shapes, the animals were supposed to choose the gate with one
less. Correct choices were rewarded with a food pellet. Three of the
eight stingrays and six cichlids successfully learned to complete this
task.
Rafael Núñez, a cognitive
scientist at the University of California, San Diego, who was not
involved in the study, regards the study as “well conducted,” adding
that “the problem is the interpretation.” For him, the paper provides
information about what he termed “quantical cognition” — the ability to
differentiate between quantities — in a 2017 paper. According to Núñez,
arithmetic or counting doesn’t have to be invoked to explain the results
in the present paper. “I could explain this result by . . . a fish or
stingray having the perceptual ability to discriminate quantities: in
this case, this will be to learn how to pick, in the case of blue, the
most similar but more, and in the case of yellow, the most similar but
less. There’s no arithmetic here, just more and less and similar.”
The problem, as Núñez says, is with interpretation. Animal cognition researcher Silke Goebelpoints out that
many life forms can distinguish between “more” and “less” in large
numbers. Researchers have also found that, so far, infants, fish, and
bees can recognize changes in number between 1 and 3. But they don’t get
much beyond that.
To say seriously that fish “do math” would, of course, be misleading.
Mathematics is an abstract enterprise. The same operations that work
for single digits work for arbitrarily large numbers. It is possible to
calculate using infinite (hyperreal) numbers. There are imaginary numbers,unexplained/unexplainable numbers, and at least one unknowable number. But we are stepping out into territory here that will not get a fish its food pellet.
Still, it’s a remarkable discovery that many life forms can
manipulate quantities in a practical way. Here are some other recent
highlights.
Read the rest at Mind Matters News, published by Discovery Institute’s Bradley Center for Natural and Artificial Intelligence.
We’ve just ended the first quarter of the year. It’s a long way to New Year’s Eve 2022. But this new open access paper from
senior author Sara Walker (Arizona State) and her collaborators will be
hard to top, in the “Wow, that is so interesting!” category. (The first
author of this paper is Dylan Gagler, so we’ll refer to it as “Gagler et al. 2022” below.)
1. Back in the day, the best evidence for a single Tree of
Life, rooted in the Last Universal Common Ancestor (LUCA), was the
apparent biochemical and molecular universality of Earth life.
Leading neo-Darwinian Theodosius Dobzhansky expressed this point eloquently in his famous 1973 essay, “Nothing in biology makes sense except in the light of evolution”:
The unity of life is no less
remarkable than its diversity…Not only is the DNA-RNA genetic code
universal, but so is the method of translation of the sequences of the
“letters” in DNA-RNA into sequences of amino acids in proteins. The same
20 amino acids compose countless different proteins in all, or at least
in most, organisms. Different amino acids are coded by one to six
nucleotide triplets in DNA and RNA. And the biochemical universals
extend beyond the genetic code and its translation into proteins:
striking uniformities prevail in the cellular metabolism of the most
diverse living beings. Adenosine triphosphate, biotin, riboflavin,
hemes, pyridoxin, vitamins K and B12, and folic acid implement metabolic
processes everywhere. What do these biochemical or biologic
universals mean? They suggest that life arose from inanimate matter only
once and that all organisms, no matter now diverse, in other respects,
conserve the basic features of the primordial life.[Emphasis added.]
For Dobzhansky, as for all neo-Darwinians (by definition), the
apparent molecular universality of life on Earth confirmed Darwin’s
prediction that all organisms “have descended from some one primordial
form, into which life was first breathed” (1859, 494) — an entity now
known as the Last Universal Common Ancestor, or LUCA. So strong is the
pull of this apparent universality, rooted in LUCA, that any other
historical geometry seems unimaginable.
The “Laws of Life”
Theoretician Sara Walker and her team of collaborators, however, are looking for an account of what they call (in Gagler et al. 2022)
the “laws of life” that would apply “to all possible biochemistries” —
including organisms found elsewhere in the universe, if any exist. To
that end, they wanted to know if the molecular universality explained
under neo-Darwinian theory as material descent from LUCA (a) really
exists, and (b) if not, what patterns do exist, and how might those be explained without presupposing a single common ancestor.
And a single common ancestor, LUCA? That’s what they didn’t find.
2. Count up the different enzyme functions — and then map that number within the total functional space.
Many thousands of different enzyme functional classes,
necessary for the living state, have been described and catalogued in
the Enzyme Commission Classification, according to their designated EC
numbers. These designators have four digits, corresponding to
progressively more specific functional classes. For instance, consider
the enzyme tyrosine-tRNA ligase. Its EC number,
6.1.1.1, indicates a nested set of classes: EC 6 comprises the ligases
(bond-forming enzymes); EC 6.1, those ligases forming carbon-oxygen
bonds; 6.1.1, ligases forming aminoacyl-tRNA and related compounds;
finally, 6.1.1.1, the specific ligases forming tyrosine tRNA. (See
Figure 1.)
The Main Takeaway from This Pattern?
Being a ligase — namely, an enzyme that forms bonds using ATP — entails belonging to a functional group, but not a group with material identity among its members.
A rough parallel to a natural language such as English may be helpful.
Suppose you wanted to express the idea of “darkness” or “darkened”
(i.e., the relative absence of light). English supplies a wide range of
synonyms for “darkened,” such as:
murky
shaded
shadowed
dimmed
obscured
The same would be the case — the existence of a set of synonyms,
i.e., words with the same general meaning, but not the same sequence
identity — for any other idea. The concept of something being “blocked,”
for instance, takes the synonyms:
jammed
occluded
prevented
obstructed
hindered
While these words convey (approximately) the same meaning, and hence fall into the same semantic functional classes, they are not the same character strings.
Their locations in an English dictionary, ordered by alphabet sequence,
may be hundreds of pages apart. Moreover, as studied by the discipline
of comparative philology, the historical roots of a word such as
“hindered” will diverge radically from its functional synonyms, such as
“blocked.” These two words, although semantically largely synonymous,
enter English from originally divergent or unrelated antecedents — a
character string gap still reflected by their very different spellings.
A strikingly similar pattern obtains with the critical (essential) components of all organisms. Gagler et al. 2022
looked at the abundances of enzyme functions across the three major
domains of life (Bacteria, Archaea, Eukarya), as well as in metagenomes
(environmentally sampled DNA). What they found was remarkable — a
finding (see below) which may be easier for non-biological readers to
understand via another analogy.
3. A segue into computer architectures — then back to enzymes.
The basic architecture of laptop computers includes components present in any such machine, defined by their functional roles:
Central processing unit (CPU) — the primary logic operator
Memory — storage of coded information
Power supply — electrons (energy) needed for anything at all to be computed
And so on. (Although exploring this point in detail would take us far
afield, it is worth noting that in 1936, when Alan Turing defined a
universal computational machine, he did so with no idea about the
arrival, decades down the road, of silicon-based integrated circuits,
miniaturized transistors, motherboards, solid-state memory devices, or
any of the rest of the material parts of computers now so familiar to us. Rather, his parts were functionally, not materiallydefined, asabstractions
occupying the various roles those parts would play in the computational
process — whatever their material instantiation would later turn out to
be.) Now suppose we examined 100,000 laptops, randomly sampled from
around the United States, to see what type of CPU — meaning which materialpart (e.g., built by which manufacturer) — each machine used as its primary logic operator.
A range of outcomes is possible (see Figures 2A and 2B). For
instance, if we plot CPUs from different manufacturers on the y axis,
against the total number of laptop parts inspected on the x axis, it
might be the case that the distribution of differently manufactured
(i.e., materially distinct) CPUs would scale linearly with laptops
inspected (Figure 2A). In other words, as our sample of inspected laptop
parts grows, the number of different CPUs discovered would trend
upwards correspondingly.
Or — and this fits, of course, with the actual situation we find (see
Figure 2B) — most of the laptops would contain CPUs manufactured either
by Intel or AMD. In this case, we would plot a line whose slope would
change much more slowly, staying largely flat, in fact, after the CPUs
from Intel and AMD were tallied.
The Core Rationale of Their Approach
Now consider Figure 3 (below), from the Gagler et al. 2022
paper. This shows the core rationale of their approach: tally the
EC-classified enzyme “parts” within each of the major domains, and from
metagenomes, and then plot that tally against the total EC numbers.
Figure 3 is used from Gagler et al. 2022 under Creative Commons License 4.0 (CC BY-NC-ND).
Figure 3 also shows their main finding. As the enzyme reaction space
grows (on the horizontal axis — total EC numbers), so do the number of
unique functions (on the vertical axis — EC numbers in each EC class).
The lesson that Gagler et al. 2022 draw from this discovery? The pattern is NOT due to material descent from a single common ancestor, LUCA. Indeed,
under the heading, “Universality in Scaling of Enzyme Function Is Not
Explained by Universally Shared Components,” they explain that material
descent from LUCA would entail shared “microscale features,” meaning
“specific molecules and reactions used by all life,” or “shared
component chemistry across systems.” If we use the CPU / laptop analogy,
this microscale commonality would be equivalent to finding CPUs from
the same manufacturer, with the same internal logic circuits, in every
laptop we examine.
But what Gagler et al. 2022 found was a macroscale pattern,
“which does not directly correlate with a high degree of microscale
universality,” and “cannot be explained directly by the universality of
the underlying component functions.” In an accompanying news story,
project co-author Chris Kempes, of the Santa Fe Institute, described
their main finding in terms of functional synonyms: macroscale functions
are required, but not the identical lower-level components:
“Here we find that you get these
scaling relationships without needing to conserve exact membership. You
need a certain number of transferases, but not particular transferases,”
says SFI Professor Chris Kempes, a co-author on the paper. “There are a
lot [of] ‘synonyms,’ and those synonyms scale in systematic ways.”
As Gagler et al. frame the point in the paper itself (emphasis added):
A critical question is whether the
universality classes identified herein are a product of the shared
ancestry of life. A limitation of the traditional view of biochemical
universality is that universality can only be explained in terms of
evolutionary contingency and shared history, which challenges our
ability to generalize beyond the singular ancestry of life as we know
it. …Instead, we showed here that universality classes are not directly correlated with component universality,
which is indicative that it emerges as a macroscopic regularity in the
large-scale statistics of catalytic functional diversity. Furthermore, EC universality cannot simply be explained due to phylogenetic relatedness since the range of total enzyme functions spans two orders of magnitude, evidencing a wide coverage of genomic diversity.
Sounds Like Intelligent Design
It is interesting to note that this paper was edited (for the PNAS)
by Eugene Koonin of the National Center for Biotechnology Information.
For many years, Koonin has argued in his own work that the putative
“universality due to ancestry” premise of neo-Darwinian theory no longer
holds, due in large measure to what he and others have termed
“non-orthologous gene displacement” (NOGD). NOGD is a pervasive pattern
of the use of functional synonyms — enzyme functions being carried out
by different molecular actors — in different species. In 2016, Koonin wrote:
As the genome database grows, it
is becoming clear that NOGD reaches across most of the functional
systems and pathways such that there are very few functions that are
truly “monomorphic”, i.e. represented by genes from the same orthologous
lineage in all organisms that are endowed with these functions.
Accordingly, the universal core of life has shrunk almost to the point
of vanishing…there is no universal genetic core of life, owing to the
(near) ubiquity of NOGD.
Universal functional requirements, but without the identity of material components — sounds like design.
Wow, the new Long Story Short video is out now, and I think
it’s the best one yet — it’s amazingly clear and quite funny. You’ll
want to share it with friends. Some past entries in the series have
considered the problems associated with chemical evolution, or
abiogenesis, how life could have emerged from non-life on the early
Earth without guidance or design. The new video examines cell membranes,
which some might imagine as little more than a soap bubble or an
elastic balloon. This is VERY far from the case.
To keep the cell alive, there’s an astonishing number of complex and
contradictory things a cell membrane needs to do. If unassisted by
intelligent design, how did the very first cell manage these tricks?
It’s a puzzle, since “The membrane had to be extremely complex from the
very BEGINNING, or life could never begin.” Some materialists have an
answer: protocells, a simpler version of the simplest cells we know of
today. But, asks Long Story, could a necessarily fragile,
simpler cell survive without assistance from its environment, something
like a hospital ICU? It seems not. If so, that makes any unguided
scenario of abiogenesis a non-starter. We’ll have more to say in coming
days about the science behind this.
The latest video in the Long Story Short series was released
this week on YouTube. The video explains how cell membranes in all of
life display complexity that cannot be explained by purely natural
processes. See my comments from yesterday, “New Animated Video: Cell Membranes by Natural Processes Alone?,” adding some supporting details to the argument. Here’s more.
As we uncover layer after layer of the astounding complexity of even
the simplest forms of life, the origin-of-life research community
increasingly relies upon their trump card: imaginary protocells that
supposedly existed long ago and were dramatically simpler than existing
life. As the story goes, modern life may indeed be very complex, but
protocells used to be much simpler, and there was plenty of time for the
complexity to develop.
Protocells conveniently fill the uncomfortably large gap between the
simple molecules that can be produced by prebiotic processes and the
staggering complexity of all extant life. But there are three major
problems with the concept of protocells. These problems are all backed
by strong empirical support, in sharp contrast with the concept of
protocells.
A Coddling Environment
First, scientists have been working for decades to simplify existing
life, trying to arrive at a minimal viable life form by jettisoning
anything that is not essential from the simplest extant cells. The
success of Craig Venter’s group is well known. Building on their efforts
to produce synthetic life (“Synthia” or “Mycoplasma labritorium”) in 2010,1,2 in 2016 they introduced the current record holder for the simplest autonomously reproducing cell (JVCI Syn3.0).3 With
a genome of only 473 genes and 520,000 base pairs of DNA, JVCI Syn3.0
can reproduce autonomously, but it certainly isn’t robust. Keeping it
alive requires a coddling environment — essentially a life-support
system. To arrive at a slightly more stable and robust organism that
reproduced faster, the team later added back 19 genes to arrive at JVCI
Syn3A.4 When combined, this work provides an approximate
boundary for the simplest possible self-replicating life. We are clearly
approaching the limit of viable cell simplicity. It seems safe to
conclude that at least 400 genes (and approximately 500,000 base pairs
of DNA) are the minimum requirements to produce a self-replicating
cell.
Exporting to the Environment
Second, we know that the process of simplifying an existing cell by
removing some of its functionality doesn’t actually simplify the overall
problem — it only exports the required complexity to the environment. A
complex, robust cell can survive in changing conditions with varying
food sources. A simplified cell becomes dependent on the environment to
provide a constant, precise stream of the required nutrients. In other
words, the simplified cell has reduced ability to maintain homeostasis,
so the cell can only remain alive if the environment takes on the
responsibility for homeostasis. Referring to JVCI Syn3A, Thornberg et al. conclude,
“Unlike most organisms, which have synthesis pathways for most of
[their] building blocks, Syn3A has been reduced to the point where it
relies on having to transport them in.”5 This implies that
the environment must provide a continuous supply of more specific and
complex nutrients. The only energy source that JVCI Syn3A can process is
glucose,4 so the environment must provide a continuous
supply of its only tolerable food. Intelligent humans can provide such a
coddling life-support environment, but a prebiotic Earth could not.
Protocells would therefore place untenable requirements on their
environment, and the requirements would have to be consistently met for
millions of years.
Striving for Simplicity
Third, we know that existing microbes are constantly trying to
simplify themselves, to the extent that their environment will allow. In
Richard Lenski’s famous E. coli experiment, the bacteria
simplified themselves by jettisoning their ribose operons after a few
thousand generations, because they didn’t need to metabolize ribose and
they could replicate 2 percent faster without it, providing a selective
advantage.6 Furthermore, Kuo and Ochman studied the
well-established preference of prokaryotes to minimize their own DNA,
concluding: “deletions outweigh insertions by at least a factor of 10 in
most prokaryotes.”7 This means that existing life has been
trying from the very start to be as simple as possible. Therefore, it is
likely that extant life has already reached something close to the
simplest possible form, unless experimenters like Lenski provide a
coddling environment for a long duration that allows further
simplification. But such an environment requires the intervention of
intelligent humans to provide just the right ingredients, at the right
concentrations, and at the right time. No prebiotic environment could do
this. Therefore, scientists need not try to simplify existing life — we
already have good approximations of the simplest form. Indeed, Mycoplasma genitalium has a genome of 580,000 base pairs and 468 genes8 whereas Craig Venter’s minimal “synthetic cell” JVCI Syn3.0 has a comparable genome of 520,000 base pairs and 473 genes.3
The data provide a clear picture: the surprising complexity of even
the simplest forms of existing life — 500,00 base pairs of DNA — cannot
be avoided and cannot be reduced unless intelligent agents provide a
complex life-support environment. Because protocells would have had to
survive and reproduce on a harsh and otherwise lifeless planet,
protocells are not a viable concept. Protocells place origin-of-life
researchers in a rather awkward position: relying upon an imaginary
entity to sustain their belief that only matter and energy exist.
References
Gibson DG et al. Creation of a bacterial cell controlled by a chemically synthesized genome. Science 2010; 329:52–56.
Thornburg ZR et al. Fundamental behaviors emerge from simulations of a living minimal cell. Cell 2022; 185: 345-360.
Cooper VS et al. Mechanisms causing rapid and parallel loss of ribose catabolism in evolving populations of Escherichia coli B. J Bacteriology 2001, 2834-2841.
Kuo, CH and Ochman H. Deletional bias across the three domains of life. Genome. Biol. Evol. 1:145–152.
Fraser CM et al. The minimal gene complement of Mycoplasma genitalium. Science. 1995; 270; 397-403.
The etymology of Byzantium is unknown. It has been suggested that the name is of Thracian origin.[4] It may be derived from the Thracian personal name Byzas which means "he-goat".[5][6] Ancient Greek legend refers to the Greek king Byzas, the leader of the Megarian colonists and founder of the city.[7] The name Lygos for the city, which likely corresponds to an earlier Thracian settlement,[4] is mentioned by Pliny the Elder in his Natural History.[8]
Byzántios, plural Byzántioi (Ancient Greek: Βυζάντιος, Βυζάντιοι, Latin: Byzantius; adjective the same) referred to Byzantion's inhabitants, also used as an ethnonym for the people of the city and as a family name.[5] In the Middle Ages, Byzántion was also a synecdoche for the eastern Roman Empire. (An ellipsis of Medieval Greek: Βυζάντιον κράτος, romanized: Byzántion krátos).[5]Byzantinós (Medieval Greek: Βυζαντινός, Latin: Byzantinus) denoted an inhabitant of the empire.[5] The Anglicization of Latin Byzantinus yielded "Byzantine", with 15th and 16th century forms including Byzantin, Bizantin(e), Bezantin(e), and Bysantin as well as Byzantian and Bizantian.[9]
The name Byzantius and Byzantinus were applied from the 9th century to gold Byzantine coinage, reflected in the French besant (d'or), Italian bisante, and English besant, byzant, or bezant.[5] The English usage, derived from Old French besan (pl. besanz), and relating to the coin, dates from the 12th century.[10]
Later, the name Byzantium became common in the West to refer to the Eastern Roman Empire, whose capital was Constantinople. As a term for the east Roman state as a whole, Byzantium was introduced by the historian Hieronymus Wolf
only in 1555, a century after the last remnants of the empire, whose
inhabitants continued to refer to their polity as the Roman Empire (Medieval Greek: Βασιλεία τῶν Ῥωμαίων, romanized: Basileía tōn Rhōmaíōn, lit. 'empire of the Romans'), had ceased to exist.[11]
The origins of Byzantium are shrouded in legend. Tradition says that Byzas of Megara (a city-state near Athens) founded the city when he sailed northeast across the Aegean Sea. The date is usually given as 667 BC on the authority of Herodotus, who states the city was founded 17 years after Chalcedon. Eusebius,
who wrote almost 800 years later, dates the founding of Chalcedon to
685/4 BC, but he also dates the founding of Byzantium to 656 BC (or a
few years earlier depending on the edition). Herodotus' dating was later
favored by Constantine the Great, who celebrated Byzantium's 1000th anniversary between the years 333 and 334.[12]
Byzanitium was mainly a trading city due to its location at the Black Sea's only entrance. Byzantium later conquered Chalcedon, across the Bosphorus on the Asiatic side.
The city was taken by the Persian Empire at the time of the Scythian campaign (513 BC) of King Darius I (r. 522–486 BC), and was added to the administrative province of Skudra.[13] Though Achaemenid control of the city was never as stable as compared to other cities in Thrace, it was considered, alongside Sestos, to be one of the foremost Achaemenid ports on the European coast of the Bosphorus and the Hellespont.[13]
Byzantium was besieged by Greek forces during the Peloponnesian War. As part of Sparta's
strategy for cutting off grain supplies to Athens during their siege of
Athens, Sparta took control of the city in 411 BC, to bring the
Athenians into submission. The Athenian military later retook the city in 408 BC, when the Spartans had withdrawn following their settlement.[14]
After siding with Pescennius Niger against the victorious Septimius Severus, the city was besieged by Roman forces and suffered extensive damage in AD 196.[15] Byzantium was rebuilt by Septimius Severus, now emperor, and quickly regained its previous prosperity. It was bound to Perinthus during the period of Septimius Severus.[citation needed] The strategic and highly defensible (due to being surrounded by water on almost all sides) location of Byzantium attracted Roman EmperorConstantine I who, in AD 330, refounded it as an imperial residence inspired by Rome itself, known as Nova Roma. Later the city was called Constantinople (Greek Κωνσταντινούπολις, Konstantinoupolis, "city of Constantine").
This combination of imperialism and location would affect
Constantinople's role as the nexus between the continents of Europe and
Asia. It was a commercial, cultural, and diplomatic centre and for
centuries formed the capital of the Byzantine Empire,
which decorated the city with numerous monuments, some still standing
today. With its strategic position, Constantinople controlled the major
trade routes between Asia and Europe, as well as the passage from the Mediterranean Sea to the Black Sea. On May 29, 1453, the city fell to the Ottoman Turks, and again became the capital of a powerful state, the Ottoman Empire.
The Turks called the city "Istanbul" (although it was not officially
renamed until 1930); the name derives from "eis-ten-polin" (Greek:
"to-the-city"). To this day it remains the largest and most populous
city in Turkey, although Ankara is now the national capital.
Emblem
By the late Hellenistic or early Roman period (1st century BC), the star and crescent motif was associated to some degree with Byzantium; even though it became more widely used as the royal emblem of Mithradates VI Eupator (who for a time incorporated the city into his empire).[16]
Some Byzantine coins of the 1st century BC and later show the head of Artemis with bow and quiver, and feature a crescent with what appears to be an eight-rayed star on the reverse.
According to accounts which vary in some of the details, in 340 BC the Byzantines and their allies the Athenians were under siege by the troops of Philip of Macedon.
On a particularly dark and wet night Philip attempted a surprise attack
but was thwarted by the appearance of a bright light in the sky. This
light is occasionally described by subsequent interpreters as a meteor,
sometimes as the moon, and some accounts also mention the barking of
dogs. However, the original accounts mention only a bright light in the
sky, without specifying the moon.[a][b] To commemorate the event the Byzantines erected a statue of Hecatelampadephoros (light-bearer or bringer). This story survived in the works of Hesychius of Miletus, who in all probability lived in the time of Justinian I. His works survive only in fragments preserved in Photius and the tenth century lexicographer Suidas. The tale is also related by Stephanus of Byzantium, and Eustathius.
Devotion to Hecate
was especially favored by the Byzantines for her aid in having
protected them from the incursions of Philip of Macedon. Her symbols
were the crescent and star, and the walls of her city were her
provenance.[19]
It is unclear precisely how the symbol Hecate/Artemis, one of many goddesses[c]
would have been transferred to the city itself, but it seems likely to
have been an effect of being credited with the intervention against
Philip and the subsequent honors. This was a common process in ancient
Greece, as in Athens where the city was named after Athena in honor of such an intervention in time of war.
Cities in the Roman Empire
often continued to issue their own coinage. "Of the many themes that
were used on local coinage, celestial and astral symbols often appeared,
mostly stars or crescent moons."[21]
The wide variety of these issues, and the varying explanations for the
significance of the star and crescent on Roman coinage precludes their
discussion here. It is, however, apparent that by the time of the
Romans, coins featuring a star or crescent in some combination were not
at all rare.
People
Homerus, tragedian, lived in the early 3rd century BC
"In
324 Byzantium had a number of operative cults to traditional gods and
goddesses tied to its very foundation eight hundred years before. Rhea,
called "the mother of the gods" by Zosimus, had a well-ensconced cult in
Byzantium from its very foundation. [...] Devotion to Hecate
was especially favored by the Byzantines [...] Constantine would also
have found Artemis-Selene and Aphrodite along with the banished Apollo
Zeuxippus on the Acropolis in the old Greek section of the city. Other
gods mentioned in the sources are Athena, Hera, Zeus, Hermes, and
Demeter and Kore. Even evidence of Isis and Serapis appears from the
Roman era on coins during the reign of Caracalla and from inscriptions."
[20]
References
Molnar, Michael R. (1999). The Star of Bethlehem. Rutgers University Press. p. 48.
Sources
Balcer, Jack Martin (1990). "BYZANTIUM". In Yarshater, Ehsan (ed.). Encyclopædia Iranica, Volume IV/6: Burial II–Calendars II. London and New York: Routledge & Kegan Paul. pp. 599–600. ISBN978-0-71009-129-1.
Harris, Jonathan, Constantinople: Capital of Byzantium (Hambledon/Continuum, London, 2007). ISBN978-1-84725-179-4
Jeffreys, Elizabeth and Michael, and Moffatt, Ann, Byzantine Papers: Proceedings of the First Australian Byzantine Studies Conference, Canberra, 17–19 May 1978 (Australian National University, Canberra, 1979).
The Oxford Dictionary of Byzantium (Oxford University Press, 1991) ISBN0-19-504652-8
Yeats, William Butler, "Sailing to Byzantium",
"In
340 BC, however, the Byzantines, with the aid of the Athenians,
withstood a siege successfully, an occurrence the more remarkable as
they were attacked by the greatest general of the age, Philip of
Macedon. In the course of this beleaguerment, it is related, on a
certain wet and moonless night the enemy attempted a surprise, but were
foiled by reason of a bright light which, appearing suddenly in the
heavens, startled all the dogs in the town and thus roused the garrison
to a sense of their danger. To commemorate this timely phenomenon, which
was attributed to Hecate, they erected a public statue to that goddess [...]"[17]
"If any goddess had a connection with the walls in Constantinople, it was Hecate. Hecate
had a cult in Byzantium from the time of its founding. Like Byzas in
one legend, she had her origins in Thrace. Since Hecate was the guardian
of "liminal places," in Byzantium small temples in her honor were
placed close to the gates of the city. Hecate's
importance to Byzantium was above all as deity of protection. When
Philip of Macedon was about to attack the city, according to the legend
she alerted the townspeople with her ever-present torches, and with her
pack of dogs, which served as her constant companions. Her mythic
qualities thenceforth forever entered the fabric of Byzantine history. A
statue known as the 'Lampadephoros' was erected on the hill above the
Bosphorous to commemorate Hecate's defensive aid."[18]
Speake, Jennifer (2003). Literature of Travel and Exploration: A to F. p. 160. ISBN9781579584252.
Georgacas, Demetrius John (1947). "The Names of Constantinople". Transactions and Proceedings of the American Philological Association. The Johns Hopkins University Press. 78: 347–67. doi:10.2307/283503. JSTOR283503.
Room, Adrian (2006). Placenames
of the World: Origins and Meanings of the Names for 6,600 Countries,
Cities, Territories, Natural Features, and Historic Sites (2nd ed.). Jefferson, NC: McFarland & Company. ISBN978-0-7864-2248-7.
Traver, Andrew G. (2002) [2001]. From Polis to Empire, the Ancient World, C. 800 B.C.-A.D. 500: A Biographical Dictionary. Greenwood Publishing Group. p. 257. ISBN9780313309427.
Holmes, William Gordon (2003). The Age of Justinian and Theodora. p. 5–6.
Limberis, Vasiliki (1994). Divine Heiress. Routledge. p. 126–127.
In Carl Sagan’s Contact, the extraterrestrials embedded a
message in the irrational number pi (the circumference of a circle
divided by its radius). But some other numbers are critical to the
structure of our universe too — and why they are critical does not make
obvious sense.
Perhaps the most fundamental and mysterious one is the fine structure constantof the universe:
A seemingly harmless, random
number with no units or dimensions has cropped up in so many places in
physics and seems to control one of the most fundamental interactions in
the universe.
Its name is the fine-structure constant, and it’s a
measure of the strength of the interaction between charged particles
and the electromagnetic force. The current estimate of the
fine-structure constant is 0.007 297 352 5693, with an uncertainty of 11
on the last two digits. The number is easier to remember by its
inverse, approximately 1/137.
If it had any other value, life as we know it would be impossible. And yet we have no idea where it comes from.
The brilliant physicist Richard
Feynman (1918-1988) famously thought so, saying there is a number that
all theoretical physicists of worth should “worry about”. He called it
“one of the greatest damn mysteries of physics: a magic number that
comes to us with no understanding by man”…
What’s special about
alpha is that it’s regarded as the best example of a pure number, one
that doesn’t need units. It actually combines three of nature’s
fundamental constants – the speed of light, the electric charge carried
by one electron, and the Planck’s constant, as explains physicist and
astrobiologist Paul Davies to Cosmos magazine. Appearing at the
intersection of such key areas of physics as relativity,
electromagnetism and quantum mechanics is what gives 1/137 its allure.
Nobelist Wolfgang Pauli (1945) is said to have remarked,
“When I die, my first question to the devil will be: What is the
meaning of the fine structure constant?” At any rate, he thought about
it a great deal during his life.
University of Nottingham physics professor Laurence Eaves thinks
the number 1/137 would be good for starting communication with
intelligent aliens as they would be likely to know about it and to
realize they were dealing with other intelligent entities.
Here’s another thought-provoking number. Consider the irrational number known as phi (ϕ) or the Golden Ratio. Jordan Ellenberg author of Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else (2021):
Among the mysteries of the
irrationals, one number holds a special place: the so-called golden
ratio. The golden ratio’s value is about 1.618 (but not exactly 1.618,
since then it would be the ratio 1,618/1,000, and therefore not
irrational) and it’s also referred to by the Greek letter φ, which is
pronounced “fee” if you’re a mathematician and “fie” if you are in a
fraternity. If you want an exact description, the golden ratio can be
expressed as (1/2)(1+√5.)
The golden ratio is sometimes
called the “divine proportion,” because of its frequency in the natural
world. The number of petals on a flower, for instance, will often be a
Fibonacci number. The seeds of sunflowers and pine cones twist in
opposing spirals of Fibonacci numbers. Even the sides of an unpeeled
banana will usually be a Fibonacci number — and the number of ridges on a
peeled banana will usually be a larger Fibonacci number.
RESOURCE LIBRARY, “THE GOLDEN RATIO” AT NATIONAL GEOGRAPHIC SOCIETY
Then there is pi (π), which (outside of Carl Sagan’s novel and film) burbles on forever without forming a pattern, yet it is fundamental in nature too.
Read the rest at Mind Matters News, published by Discovery Institute’s Bradley Center for Natural and Artificial Intelligence.
