Seasons (again)

This is a bit of a repeat, since I almost forgot about writing this week. I decided to revisit the seasons thing.

English: Kukulkan at its finest during the Spr...
English: Kukulkan at its finest during the Spring Equinox. Chichen Itza Equinox March 2009. The famous descent of the snake at the temple. (Photo credit: Wikipedia)

We have just begun the season of Southern Hemisphere spring. This officially starts on 1st September and runs through to 1st December. Then summer starts and runs through to 1st March, then autumn runs through until 1st June, and winter extend to 1st September and the cycle repeats.

The reason that the seasons are defined like this goes back to 1780 when an organisation called “Societas Meteorologica Palatina” defined them as above. The organisation chose those dates because the seasons pretty much aligned with those dates in terms of temperature and rainfall and so on. The coldest three months in the Northern Hemisphere tended to be December, January and February, the warmest tended to be June, July and August, and so on.

The mute Hendrick Avercamp painted almost excl...
The mute Hendrick Avercamp painted almost exclusively winter scenes of crowds seen from some distance. (Photo credit: Wikipedia)

Since the seasons are reversed in the Southern Hemisphere, the southern cycle is as described above. We have Christmas on the beach and spend July wrapped up and close to any source of heat!

Astronomers do it differently. They divide the year into four seasons, but the seasons are not aligned climatically, but are defined relative to the Earth’s position in its orbit around the Sun.

English: Illustration shows the relative posit...
English: Illustration shows the relative positions and timing of solstice, equinox and seasons in relation to the Earth’s orbit around the sun. (Photo credit: Wikipedia)

Because the Earth’s axis is tilted relative to its orbit around the sun, the axis is be tilted towards the sun at one time of the year and away from it six months later. When the axis is tilted towards the sun, the sun is at its highest in the sky and more energy is received on Earth per square metre than at any other time of the year. It’s summer and warmer. When it is tilted away, the sun is at its lowest and we receive less energy than at any other time of the year. It’s winter and colder. (But read on).

On Earth, when the sun is high it is in the sky longer than when it is lower. The day is therefore longest and the night is the shortest in the yearly cycle. When the sun is midway between its highest and its lowest, the day and the night are of equal length.

English: Midnight Sun in Tromsø, seen from the...
English: Midnight Sun in Tromsø, seen from the old port. (Photo credit: Wikipedia)

The time when the sun is highest or lowest in the sky is called a “solstice“, either a winter solstice, or a summer solstice. The times when it is half way are called “equinoxes“, either an autumnal equinox or a vernal equinox, and the night and day are equal in length. These are the four main signposts of the seasons, as used by astronomers.

Strictly speaking, to say “Today is the summer solstice” or “Today is the autumnal equinox” are incorrect. Since the day and night lengths are changing all the time, the solstices and equinoxes are points in time, not whole days.

English: Two equinoxes are shown as the inters...
English: Two equinoxes are shown as the intersection of the ecliptic and celestial Ecuador, and the solstice’s times of the year in which the Sun reaches its maximum southern or northern position. Español: Se muestran los dos equinoccios como la intersección del ecuador celeste y la eclíptica, y los solsticios momentos del año en los que el Sol alcanza su máxima posición meridional o boreal. (Photo credit: Wikipedia)

There are four lesser known and less important signposts of the seasons, they are Beltane, Lughnasadh, Samhain and Imbolc. I’ve used the Gaelic names, but they correspond, in order, to the Christian festivals of May Day, Lammas, Halloween, and St Brigid’s Day. These all fall more or less halfway between the four main seasonal signposts.

Astronomically the Winter Solstice, which occurs around 21st December in the Northern Hemisphere. Many sources identify the date of the solstice as the beginning of winter. Similarly the Summer Solstice is identified as the start of summer, and the equinoxes are identified as the start of their respective seasons.

English: Beltane Fire Festival is an annual pa...
English: Beltane Fire Festival is an annual participatory arts event and ritual drama, held on April 30 on Calton Hill in Edinburgh. (Photo credit: Wikipedia)

This is odd, as the climatic seasons are usually considered to start three weeks earlier, with Northern Hemisphere winter climatically starting around the 1st December, and similarly for the other seasons. Starting the astronomical seasons on the 21st (or sometimes 22nd) of the month misses out 3 weeks or nearly a quarter of the season!

It’s also odd for another reason. The Northern Hemisphere winter solstice is when the sun is at its lowest point in its apparent position in the sky, so it is at its turning point in the cycle of the season and indeed the word “solstice” means “the point where the sun stands still”. It seems to me that this should be considered the mid point of the season, not the beginning of it.

English: Wheel of the Year with Fire Festivals...
English: Wheel of the Year with Fire Festivals and Quarter Festivals, Neopagan holidays: Yule, Imbolc, Ostara, Beltane, Litha, Lughnasadh, Mabon, Samhain (Photo credit: Wikipedia)

This is obviously true for the summer solstice too, and the equinoxes, being halfway between the solstices are add the mid points of the sun’s climb or descent to the solstices. They too also should be the mid points of their seasons, not the beginning points.

If the solstices and equinoxes are the middles of their seasons, where are the start end points then? Well, they would then coincide with the Gaelic or pagan festivals of Beltane, Lughnasadh, Samhain, and Imbolc! For example Beltane is about halfway between the Northern Hemisphere spring equinox and summer solstice on 1st May.

Original caption: Jack Frost Battles with The ...
Original caption: Jack Frost Battles with The Green Man at the Imbolc festival in 2008. Stendedge visitor center,Marsden, Huddersfield. (Photo credit: Wikipedia)

Although Beltane is a Gaelic or pagan festival and has mostly fallen out of favour, some cultures do celebrate the festival and some of the customs persist, such as the custom of dancing around a Maypole. Beltane and the other three similar festivals coincide with important agricultural events, such as sowing seeds and gathering in of harvests, so were of interest in earlier times.

However, if the astronomical seasons starts and ends were to be moved to coincide with the Gaelic festivals they would not coincide with the climatic seasons. The reason for this is that there is a seasonal shift because of the time that the seas and land take to warm up in spring and to cool down in winter. This pushes the climatic seasons back a few weeks and the start of climatic spring in the Northern Hemisphere is pushed back to about the 1st March and the same for all the other seasons.

English: Lammas growth on Quercus robur. Eglin...
English: Lammas growth on Quercus robur. Eglinton Country Park, (Photo credit: Wikipedia)

That’s why I think that the current idea of the astronomical seasons starting at the solstices and equinoxes is wrong! They should coincide with the Gaelic festivals instead, and then the astronomical and climatic seasons are related by the seasonal shift, instead of not being related properly at all.

Illumination of the earth during various seasons
Illumination of the earth during various seasons (Photo credit: Wikipedia)

Feedback

A Kahn process network of three processes with...
A Kahn process network of three processes without feedback communication. Edges A, B and C are communication channels. One of the processes is named process P. (Photo credit: Wikipedia)

When an output of a process is taken and fed back to the input of a process it causes changes to the output. This changed output is then fed back to the input and so on. This basic idea has myriads of applications, in nature, in science, and in real life.

Feedback can be positive or negative. If it is positive, it adds to the input, which increases the output, which is then fed back to the input, which increases it still more, and we have a runaway increase. This is what causes the howl that occurs when the output from a microphone amplifier is accidentally fed back to the microphone.

US664A University Sound Dynamic Supercardioid ...
US664A University Sound Dynamic Supercardioid Microphone (Photo credit: Wikipedia)

Negative feedback subtracts from the input, which can result in a reduction of the output  of the process. It won’t necessarily result in NO output however, as the amount of feedback is reduced as a result of the output being reduced, and therefore the output may drop to a fixed value. There are relatively complex equations which govern feedback behaviour which I’m not going to go into here.

Of course the input and output must be related for feedback to be possible. Electrical circuits are a classic example, of course where the input and output are both voltages, and in the case of a cruise control system, the speed of the car is converted to a signal (which may be a voltage, I’d guess) and the feedback is via a signal applied to the fuel control system, which again could be a voltage.

Illustration for bowden cable. Highlighted vie...
Illustration for bowden cable. Highlighted view of the throttle cables on a 1998 model Chrysler Town & Country minivan. To the best of my knowledge, one cable comes from the gas pedal and one comes from the cruise control. (Photo credit: Wikipedia)

Feedback is inevitably delayed with respect to the inputs. In any real system the input takes time to be fed back, and sometimes this interferes with the intended operation of the feedback loop. It can cause swings in the size of the output, and the system state oscillates.

This is how electronic oscillators are designed to work, but in control systems such oscillations are unwanted and could be destructive. One way to deal with this is to “damp” the circuit, which effectively slows the feedback so that the system state moves more slowly towards the desired state rather than attempting to jump directly to it. Such damping helps reduces overshoot where the momentum of the raw feedback would cause the output to go past the required value.


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The input and output together with the feedback form a feedback loop. Feedback loops can be found everywhere, in mechanical and electrical systems, in climate systems and biological systems.

One interesting question is whether or not there is a long term feedback loop that will react to global warming to reduce the effects after a while. If so, would the feedback be more detrimental to the human race than global warming itself.


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Such feedback could be something like increased storms and disappearance of seasonal rain that will eventually finish off the human race, perhaps. According to the Gaia hypothesis the Earth is a dynamical system that help to maintain life on Earth. If that is true, it may be broken by global warming, or it may react against global warming in ways which may not yet be apparent.

Systems may have more complex feedback going on than a single simple positive/negative. A process may have several independent positive and negative feedback loops operating at the same time. The various loops may be connected in complex ways and the behaviour may be impossible to accurately predict.

A general representation of a closed loop feed...
A general representation of a closed loop feedback system (Photo credit: Wikipedia)

A biological example is the case of the rabbits and the foxes. The population of the rabbits depends on many things – how many bunnies there are, the extent of their food supply, the maturity of the average bunny – how many are mature enough to be able to produce more bunnies. Similarly such factors apply to Basil Brush and his cohorts.

If the rabbits food is plentiful, then they will breed, well, like rabbits and the population will rise. This provides an increased food supply for the foxes and their population increases. Eventually the rabbits manage to increase to the stage where the food becomes limited and the population stops increasing.

Die Gartenlaube (1889) b 497
Die Gartenlaube (1889) b 497 (Photo credit: Wikipedia)

Alternatively the increase in the fox population may grow faster than the rabbit population. The foxes kill more rabbits than the rabbits can replace and the rabbit population crashes. The foxes then starve to death as the rabbits start to recover. There are various opinions as to the exact mechanism is concerned, but there is no doubt that boom and bust cycles are seen in the predator/prey relationship, and there is no doubt that feedback cycles are involved somehow.

It is often said that negative feedback acts to return the system to equilibrium. While this may be true in the short term, any such equilibrium is temporary, and as the rabbits and foxes example shows, it is more likely that a system will only temporarily return to the equilibrium and often a system will pass through equilibrium many times as it oscillates too and fro.


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In fact, in most cases the “equilibrium position” will rarely be occupied by the system for any length of time. The typical system that oscillates about an “equilibrium position” is a pendulum. A pendulum is travelling its fastest when it passes the lowest point of its arc. The “feedback” in this case is provided by gravity of course.

Feedback also describes the missives and reports sent to an organisation about its services. The organisation may have sought such feedback by distributing questionnaires, by links on a web site, or maybe by word of mouth. Respondents have the opportunity to provide both positive and negative feedback depending on their experience with the organisation.

English: Overview of four different options to...
English: Overview of four different options to be A/B tested for Wikimedia’s Article Feedback Tool V5. This A/B test would let us compare these different options for an improved feedback form, to find out which version is most effective for engaging readers and improving article quality. See project page (Photo credit: Wikipedia)

Such research and feedback is called “market research” and has seen organisations change their stance on some topics. McDonald’s Corporation has banned plastic food containers (in 1990) and plastic drink containers (in 2013) as a result of feedback from environmental lobby groups.

Politicians also get feedback from the voters in the form of opinion polls and surveys. It would be a brave politician (perhaps a soon to be former politician) who ignores the opinion polls. Such a politician would be looking for a fresh job after the next election.

UNDP Helen Clark meeting with New Zealand Prim...
UNDP Helen Clark meeting with New Zealand Prime Minister John Key (Photo credit: Wikipedia)

(I believe that I am now all caught up on the posts that I missed. Yeah!)

 

HIJKLMNO

Impact from a water drop causes an upward &quo...
Impact from a water drop causes an upward “rebound” jet surrounded by circular capillary waves. (Photo credit: Wikipedia)

The title of my post may look odd, but it represents one of the most important chemical compounds on earth. Without it, life would not exist and the search for evidence of the possible existence of life on other planets often comes down to looking for this molecule. It is of course, water.

If you still don’t understand my title, the formula for water is H2O, where the “2” should be subscript representing the fact that there are two Hydrogen atoms in water and one Oxygen atom. This could be misheard as “H to O”, hence my title.

The water molecule with its electric charges
The water molecule with its electric charges (Photo credit: Wikipedia)

Water could be considered to be an oxide of hydrogen, or hydrogen oxide. There is a closely related compound called hydrogen peroxide (which has two oxygen atoms) which is sometimes used as a bleach and disinfectant. Surely everyone over a certain age has heard of “peroxide blondes“.

Water is sometimes referred to, usually jokingly, as dihydogen monoxide. This silly pseudo-scientific name in sometimes used to create fake polemics against water to trick gullible people, causing them to call for a ban on this noxious and toxic chemical!

The logo of DHMO.org, primary current residenc...
The logo of DHMO.org, primary current residence of the dihydrogen monoxide hoax (Photo credit: Wikipedia)

We see water all around us, in all three normal states of matter, solid, liquid and gas. Well, ice and water can be nearly transparent, and water in the gaseous state is invisible – we can only see the water vapour that forms when water in the gaseous state condenses into small particles of liquid water suspended in the air.

Water molecules have a slight “V” shape which gives it some amazing properties. it has a minimum density at 4 degrees Centigrade. It freezes at 0 degrees Centigrade so ice is slightly less dense than liquid water and the ice floats. This results in icebergs and the inevitable reference to the Titanic, which as everyone knows hit an iceberg on its maiden voyage, and endless discussions on whether or not both Jack and Rose could have survived the disaster.

TITANIC life boats on way to CARPATHIA
TITANIC life boats on way to CARPATHIA (Photo credit: Wikipedia)

Not only does ice keep our drinks cool, but it also forms a skin over ponds and puddles in winter which has the effect of protecting small plants and animals from the worst of winter. This is because the ice acts as an insulating layer and allows some warmth to remain in the waters of the pond.

Most animals can’t survive freezing but some really small ones, like certain frogs and toads and some spiders and insects survive being frozen solid. It is believed that this is because of some constituents of their blood acting as an anti-freeze agent, prevention the destructive formation of ice crystals in the cells and blood of the animal.

English: Frozen pond The water here has frozen...
English: Frozen pond The water here has frozen hard. It is believed to be excess field water not a natural pond. (Photo credit: Wikipedia)

Gaseous water is found all around us. It is dissolved, as it were, in air. It’s the water in the air which gives it its humidity. Gaseous water is swept up by the air and boosted to high altitudes by air currents and condenses to clouds, which are masses of water vapour. Ultimately the water falls to earth as rain and runs off into the seas. This whole cycle is driven by heat energy from the sun which causes the evaporation.

On average a human being’s body contains approximately 60% water. It can be higher as in a new-born baby or lower as in obese persons. If a normal person refrains from drinking liquids he or she may become dehydrated, which can result in mental issues and physical ones (which usually go away if the person is rehydrated.

(From source) This cholera patient is drinking...
(From source) This cholera patient is drinking oral rehydration solution (ORS) in order to counteract his cholera-induced dehydration. The cholera patient should be encouraged to drink the Oral Rehydration Solution (ORS). Even patients who are vomiting can often be treated orally if they take small frequent sips. Their vomiting will subside when their acidosis is corrected. (Photo credit: Wikipedia)

A person loses water by sweating and by urinating. If he or she is in an arid environment, such as a desert, he or she will lose water faster than usual, and if it is not replaced, the dehydration could kill. In hot humid climates, sweating is less effective in controlling the person’s temperature and he or she may die of overheating.

Our planet is (mostly) blue from space mainly because the presence of the water that makes up the seas. However in small quantities and in very shallow depths the colour of water is often due more to the mineral content of the water than anything else. This leads to rivers being called “Blue Nile” (because of the black sediment carried by the river – the word for black is also used for blue in the local dialect) or “White Nile” (because of the light clay sediment carried by the river) for example.

The Earth seen from Apollo 17.
The Earth seen from Apollo 17. (Photo credit: Wikipedia)

Apart from making up most of our bodies, and being essential for the body’s proper functioning, water has a myriad of uses to humans. It forms a part of many industrial processes for example, and it often provides the power for them, by way of hydroelectric generation. It helps make our crops grow, and we use it and flavour it to provide our beverages.

We also use water for recreation. We swim in the seas and rivers, we sail on them and we dive under them. We hike many kilometres in some cases to view places where water flows over a drop, and we even explore the caves created by the action of water on some rocks.

A windsurfer with modern gear tilts the rig an...
A windsurfer with modern gear tilts the rig and carves the board to perform a planing jibe (downwind turn) close to shore in Maui, Hawaii, one of the popular destinations for windsurfing. (Photo credit: Wikipedia)

The deep waters of the seas provide much of our food. Our fishermen haul great numbers of them from the seas with some difficulty and at some expense. There are people who believe that we are doing great damage to the planet by doing this, and that we are causing much marine life to become extinct, which seems to be a big risk to us in the future.

We look for water on other planets, to determine whether or not they will or have supported life. The reasoning behind this is that our way of life, and the way of life of all creatures on Earth depends on water. We cannot conceive of a life form that does not depend on water in some ways. That doesn’t mean, of course, that such life forms do not exist, but just that we can’t currently conceive of a way that such a life form could exist. As Mr Spock might say “It’s life, Jim, but not as we know it”.

Heaven and Hell

English: Punishment Monument An historic colle...
English: Punishment Monument An historic collection of punishment equipment. (Photo credit: Wikipedia)

As children we learn that there are consequences to everything. If we misbehave, we are punished in some ways. In earlier days we may have been smacked, but, thank goodness, those days are past. While corporal punishment has done little harm to most people who have suffered it as children, it is very very rarely justified and other options are available.

A child learns quickly that misbehaving leads to withdrawal of treats and privileges, which serves them well when they become adults and the punishments become imprisonment, restriction (like the loss of a drivers license) or the financial punishment of a fine.

English: The Prison
English: The Prison (Photo credit: Wikipedia)

The other side of the coin is rewards. For children the rewards for being good are treats and privileges. For adults the rewards of a virtuous life are esteem and again privilege. A virtuous life might also bring financial rewards – you are more likely to go back to a good lawyer, or a good mechanic if he or she does a good job and you may be prepared to spend a little more to do so.

When humans first contemplated death, the obvious question is what happened to the person, his self, his personality, after death. The answer that he just stopped is disagreeable and possibly upsetting. So it was natural to conjecture a non-physical something, a “soul” which encapsulated the persons personality which in some sense continued after the person died.

English: Depiction of a soul being carried to ...
English: Depiction of a soul being carried to heaven by two angels. (Photo credit: Wikipedia)

Some individuals claim to have had contact with souls after death, and claim to pass messages on to the living. Such “mediums” often get money or gifts in thanks or as a reward from the living relatives of the deceased person. Many so-called mediums have been discredited and proved to be merely charlatans, to the extent that to call someone a medium is tantamount to insinuating that they are a fraud.

It’s debatable whether a self-professed medium is a con artist or whether such a person is deluding themselves, but the concept of a soul is to my mind merely wishful thinking, or another name for the personality of the person, which is embedded in and part of a person’s mind. Since the mind is probably an emergent property of the brain I can’t see the soul or personality surviving the death of the brain.

English: Main regions of the vertebrate brain,...
English: Main regions of the vertebrate brain, shown for a shark and a human brain (the human brain is sliced along the midline). The two brains are not on the same scale. (Photo credit: Wikipedia)

Nevertheless, if you allow the concept of a soul, which inhabits a body during life, what does happen to it during and after death? Does it “softly and suddenly vanish away” like a sailor who has met a Boojum? Or does it continue, either in this world or some other? There are those who have claimed to have encountered incorporeal beings or ghosts, but like the stories of mediums, these claims are dubious.

The most common claim is that souls have passed on to other worlds, to some other realm, and this is where heaven and hell come into the picture. If a person has been a good person, then his soul goes to a better place, and if he has not, then his soul goes to a place of endless punishment of a mental and physical type.


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Many people over the year have been vouchsafed visions of both heaven and hell. Such visions are often weird and look to me more like the utterances of someone who is not completely sane, but the thing that strikes me is that they are all intensely physical – the sinner is thrown into a fiery pit for all time, and good person gets to consort with heavenly virgins or to worship the deity while being in his presence and partaking in his glory.

We know the physical because we live in it. We are it, in some senses. It seems to me that those with visions, even those whose visions are a result of their inner mental issues, can only talk of heaven and hell is physical terms. It is impossible for us to consider a world that is not physical. The very concepts of heaven and hell are concepts of places and places are physical.


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If, for the sake of discussion, we assume the visions are of something real, then if these visions represent something they are interpretations of something so different from out physical being that they must be severely distorted and much will have been lost in the translation. I myself don’t think that they represent anything more than the scrambled thoughts of a probably mentally sick person.

However that hasn’t stopped people building on the earlier visions of others. What happens to someone who dies? In the Christian tradition, if they are good they are allowed entry to heaven, and into the presence of the Deity and to worship Him. There is a certain blandness to this vision, and presumably the presence of the Deity makes up for this.

Pandemonium - One out of a set of mezzotints w...
Pandemonium – One out of a set of mezzotints with the same title (Photo credit: Wikipedia)

Those who are sinners (that is, pretty much everyone!) is sent to hell. Eternal fire and so on. Now things get complicated. Pretty much everyone has sinned at some time, so everyone is going to burn in eternal fire. Theologians (alone with their private damning thoughts) came up with a number of issues. What about those innocent who died before having a chance to sin but had not been accepted into the Church? The theologians came up with the concept of Limbo, where these children, mainly those that died in the womb, can reside.

There are other complications, but probably the most famous complex description of hell comes from the Dante’s “Divine Comedy“. The hell contained in the work has nine circles and is a complex system within those. Dante’s Purgatory and Paradise are similarly complicated.

Frontispiece to Purgatory by Dante
Frontispiece to Purgatory by Dante (Photo credit: Wikipedia)

All these visions of the afterlife are enthralling and entertaining it is true, but (seeing as no one has verifiably been there and returned), surely there contradictions embedded in the concepts of heaven and hell as found in religious and other literature.

It seems to me that the idea of heaven and hell as places which have a physical nature cannot be true. Dante’s heaven and hell for example, has physical attributes like distance and extent. Things are nearby or over there. Time also passes which allow the narrative development of course.


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However, distance and time are attributes of the physical world, and while scientists have postulated other worlds, the worlds that they postulate are very similar to the world that we experience. Heaven and hell, and any other layers of the afterlife, are conceptually in a different realm, and I can’t see why such a different realm would have anything recognisable as physics.

The Garden of Earthly Delights (c. 1480-1505) ...
The Garden of Earthly Delights (c. 1480-1505) by Hieronymus Bosch. Oil on wood triptych, 220 cm x 389 cm, now in the Museo del Prado. High-resolution version from The Prado in Google Earth. (Photo credit: Wikipedia)

Trust

English: Feathers and wedges are being used to...
English: Feathers and wedges are being used to split a large slab of sandstone. A three pound sledge hammer is being used to drive the wedges into holes drilled in the stone. The crack is just visible as a ragged line connecting the holes. (Photo credit: Wikipedia)

“Trust me, I know what I’m doing”. Sledge Hammer’s famous line encapsulates many things about trust in its seven words. The ironic twist is that the first iconic series ends with Hammer saying the words as he tries to dismantle an atomic bomb. He is not successful!

Trust is a belief that the person or thing that is trusted can be relied upon to do what is promised. There is trust between you and the bank. You trust them to look after the money that you hand over to them to invest and maybe pay you some interest. You also trust them to give you the money back when you request it. There may be conditions on the investment, such as minimum deposit periods or maximum withdrawals, interest rates and so on, but fundamentally you can get you money back.

California Bank & Trust Building in LA
California Bank & Trust Building in LA (Photo credit: Wikipedia)

Similarly the bank may loan you money, under conditions, which you can use to purchase a house, or a boat, or for any other reasons. They trust you to pay back the loan sooner or later, together with interest, and have the right to pursue you through the law if you don’t repay it.

The money in your pocket requires you to trust in it. After all the value of ordinary coins and notes in terms of the metal and paper is negligible, although gold sovereigns are nowadays worth much more than their nominal one pound sterling. Every coin or note represents something much more nebulous than the distinct coins and notes. Early notes had a “promise to pay” written on them, with the signature of a financial authority to encourage people to trust in them as money.

English: .
English: . (Photo credit: Wikipedia)

Hammer’s exhortation implies that his companions don’t trust him, which is ironic because, in a back-handed, gun-related way, he usually did. As is evidenced by the way that he encouraged a suicidal jumper to abandon his intents by shooting chunks out of the ledge that the jumper was standing on. His companions’ distrust was related to the non-standard way that he approached problems and their prior knowledge of his previous actions in such circumstances.

As in Hammer’s case, when two or more people interact, they need to trust each other in many ways. Threats are promises of harm, and there may be promises of benefits. Two people may form an alliance against a joint threat, and in such a case they need to trust each other. Each one trusts the other to back them up.

English: Toronto: TD Canada Trust Tower
English: Toronto: TD Canada Trust Tower (Photo credit: Wikipedia)

Often conditions are written down in the form of a contract. All the things that are expected by both parties, that are promised by both parties, or as many of them as can be, are written down, and both parties make their mark or sign the document. The contract can be authorised by a third-party or each party may merely carry away a copy of the document.

A contract strengthens the trust between two parties. If a contract in place, goes the reasoning, then all parties know exactly what is required of them, and what the consequences are if one party or another doesn’t do what is required. If there is complete trust between two parties, then no contract would be required, of course, but there never is complete trust.


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However we trust other people all the time without contracts or other documentation. In fact we are sometimes too trusting. Sometimes nefarious characters arrive on our doorsteps and we let them in if they, for example, claim to be from the Gas Board. It is recommended that we always ask for proof of identity if someone who we don’t know knocks on the door. Of course we have to trust the proof of identification if any is proffered, and it could conceivably be faked.

This brings up and issue about trust – we can never be absolutely sure that we can trust someone. We could know someone very very well and still not be absolutely sure that we can completely trust them. The extent to which we cannot completely trust them may be very very small of course.

English: Wikibarn of Vardan Mamikonyan for con...
English: Wikibarn of Vardan Mamikonyan for contribution to clauses of Armenian hictory Русский: Викиорден Вардана Мамиконяна за вклад в статьи по истории Армении (Photo credit: Wikipedia)

We cannot even completely trust someone when we have a contract with them. Unexpected occurrences may occur which are not covered by the contract, but relate the the matter that the contract covers. If one of the parties to the contract dies then what happens to the provisions of the contract? Well, there are laws, of course, that relate to contractual matters and it may be that lawyers are needed to sort such matters out.

There’s another sort of trust, other than trust between people. We trust the laws of science. If we throw something up into the air we expect it to come down again. We expect and trust that the sun will come up tomorrow, and it appears that we are justified in our trust. Through many millennia we have trusted that the whole is a sensible logical place where everything has a cause and cause and effect go hand in hand.


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There is a dissenting voice and that voice is the voice of religion. Religions espouse the concert of miracles, that is occasions when the laws of nature are violated, as for instance, water is changed to wine, or a flood covers and destroys the whole earth.

We may trust that the world is a logical place, but we cannot prove that it is. If we keep throwing stones into the air, it is conceivable that one might not come down again. While we can verify that throwing stones into the continues to work, we may for some reason experience a case where the stone does not fall to the ground again.


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If the stone doesn’t come down, our instinct is to look for a reason why it did not, rather than suspect that the law of gravity has been repealed. We trust the law of gravity. The stone may have lodged on a roof of course, or been caught by a passing bird. After we have considered all the possibilities then we might suspect that the law of gravity as we know it has failed.

So we pass it over to the physicists to look into the matter, and they would ponder and experiment, and eventually, we hope come up with a modification to the law of gravity to cover our “special case”. And we can trust the law of gravity again. For now.

Animation showing the motion of a small body (...
Animation showing the motion of a small body (green) in an elliptic orbit around a much more massive body (blue). (Photo credit: Wikipedia)

So, the question arises, when we have found out all that there is to know about the Universe and so be able to predict anything with 100% accuracy. Well, suppose our knowledge of the laws of the Universe is 80% accurate. There’s an old adage that says that the first 80% of anything takes 80% of the time, and the remaining 20% also takes 80% of the time. In other words it is feasible that we could know all the laws of the universe and be able to apply them, but there probably isn’t enough time.

In the meantime, I’m going to trust that the sun is going to come up tomorrow, as, after all 80% is still pretty good!

English: Bình Minh biển Cửa Lò
English: Bình Minh biển Cửa Lò (Photo credit: Wikipedia)

The Solstice Again

The Sun rising over Stonehenge on the morning ...
The Sun rising over Stonehenge on the morning of the summer solstice (21st June 2005). A crowd of between 14,000 and 19,000 people greeted the sun as it rose at 04:58 BST. (Photo credit: Wikipedia)

Today is the summer solstice in the Southern Hemisphere, the time when the sun is furthest south in the sky and hence at its highest. From here on in, the days get shorter as we slide back towards winter.

In the Northern Hemisphere,  it is of course the winter solstice, and those living there can expect the days to lengthen, as they move towards summer. Today is the Northern Hemisphere’s shortest day.

English: Daisy Rock's "solstice gap"...
English: Daisy Rock’s “solstice gap”” This shows the gap in the rock along which the sunset is viewed on the longest day. (Photo credit: Wikipedia)

Seasonal lag means that we can look forward to the warmest months of the year after the solstice, and those unfortunate enough to live in the Northern Hemisphere can look forward to a couple of their coldest months before things start to warm up.

I read somewhere that winter months are the months when people tend to put on weight and this was attributed to the fact that in winter, in the coldest weather people tend to exercise less and eat more. The reduced exercise is attributed to the tendency to stay home in the warm, by the fireside to avoid the often hostile weather.

Brooklyn Museum - Fireside Companion - Platt P...
Brooklyn Museum – Fireside Companion – Platt Powell Ryder – overall (Photo credit: Wikipedia)

And the eating more is because, well, what else is there to do but eat, when you are trapped by the weather. Our ancestors used to use up all the reserves that they had laid up for just this occasion, the hams and preserves, dried fruit and root vegetables and so on.

When the summer solstice happens, the weather is warmer and better, so people can get out an exercise, and, for our ancestors at least, agriculture kept them on the move, and the aim was to replenish the stores for the winter months, hence an emphasis on growing rather than eating. Besides, most crops would not be ready for harvesting.


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The winter solstice is one candidate for the start of the year. It marks a definite point in the cycle of the year. It’s after the solstice (a few months after the solstice) that things start growing again. The summer solstice is probably not a good choice as things are humming along then, ploughing and planting, growing and nurturing so it doesn’t really fit as the start of the year.

The spring or vernal equinox falls in March, around the 21st in the Northern Hemisphere. This is also a candidate for the start of the year, but to my mind, it is too late. Winter is tailing off at that time, things are starting to grow and because of the seasonal lag, it’s the start of spring. The year, are I see it, is already under way.


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Interestingly our fiscal year ends on 31st March. This is the date used by individuals to account for tax obligations. In many countries using the Gregorian calendar, the fiscal year ends on 31st December and almost aligns with the (winter) solstice based year. Other countries which use other calendars have fiscal years which relate to the local calendar.

As I have said the summer solstice in the Southern Hemisphere falls on 21st December (in most years). It is an astronomical point in time, not a whole day and can happen on 20th December. In the decade from 2010 to 2020 it falls on the 20th on three occasions.


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The summer solstice, Christmas Day, and the official 1st January New Year Day all fall within just over a week of each other. There is good reason to suspect historical links between these days, and there is much debate on the actual historical relationship between these events.

It is often said that early Christians adopted the winter solstice in the Northern Hemisphere, to squeeze out or replace a pagan celebration at that time. This may or may not be the case (or it may be partially true), but what is evident is that many cultures outside of the Tropics of Cancer and Capricorn celebrate a festival at around the time of the solstice.

World map with the intertropical zone highligh...
World map with the intertropical zone highlighted in red. (Photo credit: Wikipedia)

Between the two Tropics the sun is overhead twice in a year while the sun reaches a southerly point at the time of the southern solstice (winter in the north and summer in the south) and a northerly point at the time of the northern solstice, the hottest time occurs when the sun is overhead. This divides the year into unequal parts in these latitudes.

The climate of these regions is dependant on local conditions, such as whether or not the region is close to an ocean or is in the middle of a continent, and many tropical areas have wet and dry seasons, typically of unequal extents. One example know to many people outside the tropics is the monsoon season when a regions rainfall may predominantly happen.


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On the Arctic and Antarctic circle, at the solstices the sun just grazes the horizon at the summer solstice and the day lasts 24 hours. At the winter solstices the sun just barely reaches the horizon and the night lasts 24 hours. Closer to the poles the number of sunless days or days with the sum always above the horizon increase. At the poles the sun is below the horizon for three months and above it for three months. (I hope this is correct. I did research this a little, but I am not 100% sure).

Interestingly, I learnt recently that the sunset will continue to become later for the next few weeks. The reason for this according to the linked article is because we have tied our clocks to 24 hours exactly and the day is not exactly 24 hours long. Not only is it not exactly 24 hours, but its length varies during the year. In Wellington the sunset goes out to around 3 minutes to 9 and doesn’t dip below that time until 7th January 2015.

English: Sunrise at Winter Solstice (December ...
English: Sunrise at Winter Solstice (December 21, 2006 at 8 a.m.) as viewed through the doorway half way up Maiden Tower (Photo credit: Wikipedia)

(December data here, January data here).

While looking up these numbers I noticed that the day length in Auckland is nearly half an hour shorter up there. Also sunset is about a quarter of an hour later in Wellington meaning that when the summer weather finally arrives we will have an extra 14 minutes to enjoy the balmy evenings. That’s yet another reason to prefer Wellington over Auckland! We have more time to celebrate the solstice.

English: Wellington Harbour (New Zealand) view
English: Wellington Harbour (New Zealand) view (Photo credit: Wikipedia)

[Darn! I completed this on Monday but forgot to publish it. Better late than never, I guess!]

Dis-Continuum

English: The Clump looking from the Redhouse
English: The Clump looking from the Redhouse (Photo credit: Wikipedia)

Where ever one looks, things mostly seem to be in lumps or clumps of matter. We live on a lump of matter, one of a number of lumps of matter orbiting an even bigger lump of matter. We look into the sky when the bigger lump of matter is conveniently on the other side of our lump of matter and we see evidence of other lumps of matter similar to the lump of matter that our lump of matter orbits.

We see stars, in short, which poetically speaking float in a void empty of matter. We can see that these stars are not evenly distributed and that they gather together in clumps which we call galaxies. Actually stars seem to clump together in smaller clumps such as the Local Cluster of a dozen or so stars, and most galaxies have arms or other features that show structure at all levels.

Ancient Galaxy Cluster Still Producing Stars
Ancient Galaxy Cluster Still Producing Stars (Photo credit: Wikipedia)

The galaxies, which we can see between the much closer stars of our own galaxy, also appear to be clustered together in clumps, and the clumps seem to be clumped together. Of course, the ultimate clump is the Universe itself, but at all levels the Universe appears to have structure, to be organised, to be formed of lumps and clumps, variously shaped into loops, whorls, sheets, arms, rings, bubbles, and so on.

OK, but in the other direction, towards the smaller rather than the larger, our planet has various systems, weather, orogenic, natural, social and evolutionary. All sorts of systems at all levels, from global scope to the scope of the smallest element.


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In other personal worlds, below the level our interactions with our families, we have all the systems that make up our own bodies. The system that circulates our blood, the system that processes our food, the system that maintains our multiple systems in a state homeostasis.

That is, not a steady state, but a state where all the individual systems self-adjust so that the larger system does not descend into a state of chaos, leading to a disruption of the larger whole. Death.

The main pathways of metabolism in humans, sho...
The main pathways of metabolism in humans, showing all metabolites that account for >1% of an excreted dose. ;Legend PNU-142300, accounts for ~10% of excreted dose at PNU-142586, accounts for ~45% of excreted dose at steady state PNU-173558, accounts for ~3.3% of excreted dose at steady state (Photo credit: Wikipedia)

By and large most systems in our environment are made up of molecules, which are in turn made up of atoms. Atoms are a convenient stopping point on the scale from very large to very small. They are pretty “well defined”, in that they are a very strong concept.

Atoms are rarely found solo. They are sociable critters. They form relationships with other atoms, but some atoms are more sociable than others, forming multiple bonds with other atoms. Some are more promiscuous than others, changing partners frequently.


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These relationships are called molecules, and range from simple to complex, containing from two or three atoms, to millions of atoms. The really large molecules can be broken down to smaller sub-molecules which are linked repeatedly to make up the complex molecules.

To rise higher up the scale for a moment, these molecules, large and small are organised into cells, which are essentially factories for making identical or nearly identical copies of themselves. The differences are necessary to make cells into muscles or organs and other functional features, and cells that make bones and sinews and other structural parts of a body.

A section of DNA; the sequence of the plate-li...
A section of DNA; the sequence of the plate-like units (nucleotides) in the center carries information. (Photo credit: Wikipedia)

As I said, atoms are a convenient stopping point. Every atom of an element is identical at least in its base state. It may lose or gain electrons in a “relationship” or molecule, but basically it is the same as any other element of the same sort.

Each atom consists of a nucleus and surrounding electrons, a model which some people liken to a solar system. There are similarities, but there are also differences (which I won’t go into in this post). The nucleus consists a mix of protons and neutrons. While the number neutrons may vary, they don’t significantly affect the chemical properties of the atom, which makes all atoms of an element effectively the same.

An early, outdated representation of an atom, ...
An early, outdated representation of an atom, with nucleus and electrons described as well-localized particles on well-localized orbits. (Photo credit: Wikipedia)

Each component of an atom is made up of smaller particles called “elementary” particles, although they may not be fundamentally elementary. At this level we reach the blurry level of quantum physics where a particle has an imprecise definition and an imprecise location in macroscopic terms.

Having travelled from the largest to the smallest, I’m now going to talk mathematics. I’ll link back to physics at the end.

Nucleus
Nucleus (Photo credit: Wikipedia)

We are all familiar with counting. One, two, three and so on. These concepts are the atoms of the mathematical world. They can be built up into complex structures, much like atoms can be built into molecules, organelles, cells, tissues and organs. (The analogy is far from perfect. I can think of several ways that it breaks down).

Below the “atomic” level of the integers is the “elementary” level of the rational numbers, what most people would recognise as fractions. Interestingly between any two rational numbers, you can find other rational numbers. These are very roughly equivalent to the elementary particles. Very roughly.

Half of the Hadron Calorimeter
Half of the Hadron Calorimeter (Photo credit: Wikipedia)

One might think that these would exhaust the list of types of numbers, but below (in a sense) the rational numbers is the level of the real numbers. While many of the real numbers are also rational numbers, the majority of the real numbers ate not rational numbers.

The level of the real numbers is also known as the level of the continuum. A continuum implies a line has no gaps, as in a line drawn with a pencil. If the line is made up of dots, no matter how small, it doesn’t represent a continuum.

Qunatum dots delivered by ccp
Qunatum dots delivered by ccp (Photo credit: Wikipedia)

A line made up of atoms is not a continuum, nor is a line of elementary particles. While scientists have found ever more fundamental particles, the line has apparently ended with quarks. Quantum physics seems to indicate that nature, at the lowest level, is discrete, or, to loop back to the start of this post, lumpy. There doesn’t seem to be a level of the continuum in nature.

That leaves us with two options. Either there is no level of the continuum in nature and nature is fundamentally lumpy, or the apparent indication of quantum physics that nature is lumpy is wrong.

Pineapple Lumps (240g size)
Pineapple Lumps (240g size) (Photo credit: Wikipedia)

It’s hard to believe that a lumpy universe would permit the concept of the continuum. If the nature of things is discrete, it’s hard to see how one could consider a smooth continuous thing. It’s like considering chess, which fundamentally defines a discontinuous world, where a playing piece is in a particular square and a square contains a playing piece or not.

It’s a weak argument, but the fact that we can conceive the concept of a continuum hints that the universe may be fundamentally continuous, in spite of quantum physics’ indications that it is not continuous.


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The Start of New Year

an old post card
an old post card (Photo credit: Wikipedia)

According to sources on the Internet, the winter solstice in the Southern Hemisphere occurs at 10:51 am UT on 21 June (this year, 2014). That translates to 10:51 pm in New Zealand. Just as in the Northern Hemisphere the start of the year corresponds roughly to the winter solstice  there, I like to think that the winter solstice in the Southern Hemisphere corresponds to the start of the year in the Southern Hemisphere. I don’t think that I would get much support to the start of the year officially changed, though!

The Earth at the start of the 4 (astronomical)...
The Earth at the start of the 4 (astronomical) seasons as seen from the south and ignoring the atmosphere (no clouds, no twilight). (Photo credit: Wikipedia)

The year can be divided into halves by the solstices, the winter solstice marking the sun’s most negative elevation with respect to the South Astronomical Pole since the previous June. From that moment in time the sun starts to move higher into the sky until, at or around 21 December, when the summer solstice occurs.

Midway between the solstices falls a time when the day and night are roughly equal in length. Around this time the sun crosses the celestial equator, and this time is called an equinox. There are two in the year, one when the sun is apparently moving south in the sky (the vernal equinox in the Southern Hemisphere) and one when it is moving north in the sky (the autumnal equinox in the Southern Hemisphere).

The Sun & the ecliptic rotation around the Ear...
The Sun & the ecliptic rotation around the Earth : The green Sun is the one of the vernal equinox (march), it is followed by a summer solstice Sun. Then automn equinox and winter solstice. The ground plane (latitude 50°N) is green, the rotating ecliptic plane is blue. Also represented are the celestial equator, the two tropics and the rotation axis. (Photo credit: Wikipedia)

Each of these quarter points of the year is or was celebrated with a festival of some sort, some of which, particularly the winter solstice were supposedly characterised by “unrestrained revelry“. The summer solstice was comparatively restrained, the vernal equinox was a celebration of new growth, and the autumnal equinox was a harvest festival, a gathering in and celebration of bounty produced by the year’s hard work.

What I wasn’t aware of is that there were other events called “Cross Quarter moments”. These are moments halfway between the equinoxes and solstices, and they are known as Embolc, Beltaine, Lughnasad, and Samhain. The Cross Quarter moments. the solstices and the equinoxes are set out in order for 2014 in the chart referenced here.

English: Wheel of the Year with Fire Festivals...
English: Wheel of the Year with Fire Festivals and Quarter Festivals, Neopagan holidays: Yule, Imbolc, Ostara, Beltane, Litha, Lughnasadh, Mabon, Samhain (Photo credit: Wikipedia)

Two of the Cross Quarter moments I have heard of, Beltane and Samhain. Beltane falls between the vernal equinox and the summer solstice and is roughly at the beginning of May, so corresponds roughly with May Day. It is astronomically the beginning of summer, but seasonal lag means that the season starts a little later than this.

English: Beer brewed during the night of Samha...
English: Beer brewed during the night of Samhain. Français : Bière brassée pendant la nuit de Samain. (Photo credit: Wikipedia)

Children (usually girls) still dance around the maypole or maytree, but few of them, and probably few of the adults have any idea of the origins of this ritual. Although it probably is related to Beltane or the start of summer, the significance and symbolism of the maypole is still debated. Some of the possible suggestions seem dubious and far-fetched, and I don’t think that is wrong to suggest that they reflect the prejudices of the people that make them. In particular it appears that Puritan Christians may have over-emphasised some aspects of the dance and celebration to argue for its banning.

English: Dance around the maypole during the M...
English: Dance around the maypole during the Midsummer celebration, in Åmmeberg, Sweden. (Photo credit: Wikipedia)

Morris dancing is also associated with a spring festival, usually Whitsun. It may possibly have been associated with Beltrane, but I don’t know the history of morris dancing, Whitsun and Beltrane or spring festivals in general well enough to assert this. There is a long tradition of ancient non-Christian rituals being adopted and given a Christian slant, so this may be possible.

Cotswold-style morris dancing in the grounds o...
Cotswold-style morris dancing in the grounds of Wells Cathedral, Wells, England — Exeter Morris Men (Photo credit: Wikipedia)

Samhain also has a long history and probably pre-dates Christianity. It is associated with the beginning of winter and marks the point where all crops are gathered and animals prepared for winter. Once again the Christian church has adopted the festival and the roots of “harvest festivals” are to be found in Samhain’s pre-Christian traditions.

English: A Donjari float used in Saijo's fall ...
English: A Donjari float used in Saijo’s fall harvest festival. I took this photo in October 2004. (Photo credit: Wikipedia)

The Christian church adopted the festival as All Saints (Hallows) Eve or Halloween. I note from the Wikipedia article that I linked to that some people consider that Halloween has no relationship with Samhain, but considering the similarities of the two traditions which happen at the same time of the year, I think that this seems unlikely.

Jack-o-lantern
Jack-o-lantern (Photo credit: Wikipedia)

Bonfires form a great part of the Samhain festival, maybe as an attempt to ward off the coming darkness of winter. I don’t think that it is a coincidence that there are still “celebrations” on 5 November, otherwise known as Guy Fawkes Day. An effigy of Guy Fawkes is burnt on a bonfire, in spite of the fact that Guy Fawkes was actually hanged.

All of the example above refer to the “Gaelic versions” of the various dates and festivals. It’s a bit simplistic to refer to a single “Gaelic version” as the dates and festivals have, naturally, changed over the years. Other cultures of course have their own versions of the various festivals. In the Tropics (between the Tropic of Cancer and the Tropic of Capricorn the sun is overhead at least once in the year, an obvious time for a festival!

English: Vector version of a design from the B...
English: Vector version of a design from the Book of Kells, fol. 29r. Traced outlines in black and white representing three intertwined dogs. (Photo credit: Wikipedia)

Since we have just passed the winter solstice, we can look forward to longer days and shorter nights from now until the summer solstice, which for us in the Southern Hemisphere comes around 21 December. So far this year winter has been fairly mild and a little wet. As we move towards the vernal equinox we still have the bulk of winter to come, as the astronomical year does not match the climatic year because of the seasonal lag.

English: Winter landscape off Ham Wall Somerse...
English: Winter landscape off Ham Wall Somerset. The most peaceful place on earth created from worked-out peat diggings. Excellent wetland habitat with characteristic reed beds. (Photo credit: Wikipedia)

Nevertheless it is a time to look forward and one can understand why the winter solstice is a such a time. It is a time of feasting, of using up some of the stores put away at the time of the autumnal equinox, the salted beef and cured hams. It is a time to relax, for mending and repairing, and for staying out of the weather as much as possible, as the weather of winter means that essential tasks only will be undertaken and the rush of springtime is still ahead. While the end of winter may bring shortages , it is still near the beginning and the stores are still full.

Russian Celebration Zakuski
Russian Celebration Zakuski (Photo credit: Wikipedia)

 

 

 

Little Green Men

SETI
SETI

SETI is short for “Search for Extraterrestrial Intelligence”, or in other words, a search for the “Little Green Men”. The main thrust of SETI is to examine the light from other stars for signs of intelligent life, often on well known wavelengths such as wavelengths near the “water hole“,  a section of the electromagnetic spectrum associated with hydrogen and hydroxyl ions emissions lines. Hydrogen and hydroxyl together make water and water is supposedly necessary for life, so the thinking is that technically advanced life would possibly use this frequency to initiate contact with other civilisations.

Denomination of atomic shells and of character...
Denomination of atomic shells and of characteristic emission lines (Photo credit: Wikipedia)

The trouble is that this is just a guess and there are many possible frequencies that might seem plausible to technically advanced civilisations. If the little green men are not made of water, as we essentially are, they might pick a different frequency band to search. XKCD, my favourite web site has a cartoon which makes this point:

XKCD - the search
The Search

Suppose a remote civilisation did decide to broadcast in that waveband. If they are just announcing their presence, they would need to broadcast their signal in all directions, or they would need to pick out some likely looking star systems and send a directed signal in just a few directions.

If they broadcast in all directions, the power that they would require would be huge. The problem is that in any average stellar neighbourhood, there aren’t many stars. In the sun’s neighbourhood there is an average of 0.004 stars in a cubic light year. So the probability of finding a star one light year from a star in a neighbourhood like the sun’s is four in 1,000. If you look two light years out from the star, you will enclose a volume of eight times the volume of the search area up to one light year, meaning that the probability of finding a star in that volume is 0.032. You would need to look further than five light years out for there to be a fifty-fifty chance of finding a star in that volume, which would be 125 time the size of the original volume of one cubic light year. At 15 lightyears, there would likely be at least 10 stars within the search area.

Globular Cluster NGC 6397
Globular Cluster NGC 6397 (Photo credit: Hubble Heritage)

That’s all very well, but most if not all of these stars will be of the wrong type to support planets of the type that will have free water on them. In fact it is extremely unlikely that a suitable star with suitable planets can be found within, say 200 light years of our hypothetical advanced civilisation. (That’s an out and out guess, but see later).

The remnant of a supernova located 6000 light ...
The remnant of a supernova located 6000 light years from Earth in the constellation Taurus. (Photo credit: Smithsonian Institution)

The trouble is that the signal gets weaker and weaker the further it travels. If you use the signal strength at one light year as the yardstick, the strength is reduced to one quarter at two light years, one ninth at three light years and one sixteenth at four light years and so on because the signal is spread over an area proportional to the square of the distance from the source.  So if the signal strength at 200 light years will be 1/40,000th of the strength of the signal at one light year. If the signal has to travel further it will be correspondingly weaker.

My second attempt at illustrating the Inverse ...
My second attempt at illustrating the Inverse Square Law. S represents an ideal source of electromagnetic radiation and A represents an arbitrary segment of the surface of a sphere of radius r. (Photo credit: Wikipedia)

So likely systems are rare and the signal strength will be weak at the distance of a suitable system. This means that the signal needs to be very strong to be detectable.  Very strong means lots of energy. To broadcast to the Universe at large the civilisation would have to expend a considerable amount of its available energy to only potentially contact another civilisation. Imagine trying to get a project like into the planetary budget!

Clark's accompanying book to Civilisation
Clark’s accompanying book to Civilisation (Photo credit: Wikipedia)

So the hypothetical civilisation is probably desperate to make contact. That may be because either they are in trouble themselves, or they want to warn all local civilisations about something. They are unlikely to do it on a whim, as they must know that the chances of success are pretty close to zero. There’s a faint possibility of a sort of “vampire civilisation” that must prey on other civilisations and so chooses to broadcast in the hope of finding a new victim. I consider that highly unlikely, since as I said the chances of success are nearly zero, and such a civilisation would need to find a new host in a relatively short period of time, astronomically speaking.

Mark of the Vampire
Mark of the Vampire (Photo credit: Wikipedia)

If a broadcast signal is very unlikely to find a receiver, how about a directional signal, maybe driven by a laser. The spread of a laser signal is much less than a broadcast signal, but the signal does spread. An advanced civilisation would still have to divert significant resources into sending the signal but it might be possible.

The civilisation would have an issue, though. If they wanted to get a signal to us and they used a ground based laser, their ground station would be in line with us once each local day, and our receiver would be in line with them once in every day too. Since it is unlikely that the day lengths would match, so the window for transmission would be short, even down to a minute or less.

Window of opportunity
Window of opportunity (Photo credit: GioPhotos)

The hypothetical aliens would most likely opt for an orbital laser. That could be pointed in our direction all the time, for every hour of every alien day, unless some local object got in the way. However we have a problem now. We would need to detect that a signal is coming from a point in space, in spite of all the extraneous noise that might mask it, and then we would need to concentrate our resources looking in that direction for a length of time. The hard part would probably be convincing ourselves that a signal is from LGM (little green men).

Littler Green Men
Littler Green Men (Photo credit: JD Hancock)

There’s an equation that purports to estimate the possible frequency of extraterrestrial civilisations, called the “Drake Equation”. It’s the sort of “equation” that gives mathematicians the heebie-jeebies, since it is derived from nothing and nothing is derivable from it. XKCD cruelly lampoons the equation, and while I don’t much like the sentiment expressed, I can understand why the Drake equation raises his ire – it is ad hoc, probabalistic, and presents as constants things which are fundamentally unknown. In other words, your guess is as good as mine, and both will fit comfortably in the Drake equation. I may return to the equation in a later post.

XKCD - the Drake Equation
The Drake equation as extended by XKCD

 

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