2018

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Today is the last day of 2017. I will probably stay up tonight to “see in” 2018, but I’m not about to follow other traditions, such “first footing“. It’s all superstition anyway.

I think it’s interesting and a little illogical that we celebrate arbitrary dates throughout the year, such as midsummer’s day or May Day, though I understand that the origins of these celebrations. When the Church ruled (in at least the part of the world that I come from) and when times were uncertain and you could be fine one minute and dead of the plague the next, superstition comes naturally.

I can understand the joy that a winter solstice or other celebrations at that time of can bring. We are, at those times, at the lowest point of the year, and things can only go up from there. Strangely the low point of the year in the Northern Hemisphere comes at the top of the calendar. Who arranged that?

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There are no equivalent large celebrations around the time of the summer solstice, at least in the places in the Northern Hemisphere that I have lived. In the middle of the summer, winter is so far away, and I guess that we don’t want to celebrate it. In the Southern Hemisphere the summer solstice occurs round about the time of Christmas and New Year. In either hemisphere we celebrate the summer solstice by getting out in the sun more.

In the spring, in the Northern Hemisphere, there are some celebrations of May Day, around the time of the Vernal Equinox. At that time of year, we are leaving the darkness of winter and the short days for the longer sunny days of summer, and that is probably worth a celebration. May Day actually falls closer to the middle of the climactic spring than the equinox does.

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Of course any spring festival coincides with the increased fertility of the soil, plants and growing and animals are mating, spring plantings are complete, humans also respond to this. Some spring festivals acknowledge this time of the quickening of the blood in various ways, and sometimes the establishment, notably the Church, tries to suppress or at least put the reins on some of the excesses.

Autumn is the time of harvest and any festivals around the Autumnal Equinox acknowledge this fact. However the tone of such celebrations is likely to be restrained as people buckle down for the chills of winter.

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In the Southern Hemisphere, all this is messed up. The calendar is the same, so the southern Spring Equinox happens in September, around the twenty first of the month. Since most of the traditions have been imported from the Northern Hemisphere, mainly from Europe and particularly the UK, there is no obvious spring celebration to copy.

However, the southern Autumnal Equinox happens in March, and there is a northern celebration at the beginning of May. May Day is celebrated as an almost purely political holiday, with roots in the union movement, and is not, generally celebrated in the same way as May Day is in the Northern Hemisphere.

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When people emigrate from the Northern Hemisphere, specifically from Europe, they often experience homesickness. It can take a lifetime to shake off, but most people eventually relocate their roots. In particular, people from the Northern Hemisphere often find it strange that Christmas falls in the summertime.

People from the Northern Hemisphere expect Christmas to be in the winter. Short days, inclement weather and the perennial question “Will it be a white Christmas?” At one time carollers used to travel from door to door, wrapped up in thick coats, scarves and wearing woollen hats. Father Christmas is well wrapped in thick red and white clothes as he takes orders in the frantic malls before Christmas.

In the Southern Hemisphere, Father Christmas still wears his thick red and white clothes, and sits in a grotto decorated with fake snow and snowflakes, but he is most likely to be near hypothermia as the mercury rises.

There is however a southern version of Father Christmas. This version wears red swimming trunks and usually retains the red hat with the white rim and the white bobble, but may sport sunglasses and wear jandals on his feet. He may even carry a surfboard. He may be lying in a sun lounger shaded by a parasol, and with a non-alcoholic (of course) fruit based drink to hand.

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While Rudolph and his team may feature south of the equator, in Australia Santa’s sleigh is pulled by six white kangaroos, known as “boomers” (at least according to the song recorded by Rolf Harris). The implication is that the traditional reindeer can’t handle the summer heat in the Southern Hemisphere.

I’ve drifted somewhat from my initial topic, which was the New Year. New year in the Southern Hemisphere is about beach parties, if you are below a certain age. For those above a certain age, New Year means backyard barbecues.

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Beach parties can be riotous, to the point where police intervention is required, but largely they are good natured and convivial gatherings. New Year comes towards the beginner of the seasonal summer, and the celebration doesn’t really equate to any Northern Hemisphere celebration.

The northern Christmas and New Year celebrations are constrained by the short days and the long nights and are celebrated indoors in cosy snugness. In contrast the southern celebrations revel in the long days and short but warm nights and celebrate the outdoors.

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I think that we in the southern hemisphere got the best deal. If Christmas and New Year in the northern hemisphere had, for whatever reason, fallen in the summer, then the southern hemisphere Christmas and New Year would have fallen in the winter, and we would have got the short nights and the bad weather.

We would have had to celebrate Christmas and New Year indoors and during the short winter days. There’s no doubt that it would be enjoyable, the interactions with family and friends, but I’m glad that our main holiday falls in the summer.

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But, whatever, the New Year is in ninety five minutes, at least here in Wellington, so, when it swings around to you, I hope that you have a good and enjoyable New Year. I’ll sit here in my t-shirt and shorts, with bare feet enjoying their freedom from shoes, and wish all you there in the Northern Hemisphere, togged up in your woolies and gloves and hats, a Happy New Year.

Tau Hou hari!

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About Mums, and a little about Dads too.

Mother hen with chicks02
Mother hen with chicks02 (Photo credit: Wikipedia)

I wrote about cuteness a couple of posts ago, and this started me thinking about mothers, both human and animals and how the bonds that they form with their offspring.

Many animals do not look after their offspring, just casting their fertilised eggs into the seas like many fish or placing their eggs on a food plant as butterflies and moths mostly do. However, many animals do look after their eggs and young offspring, often for extended periods of time.

Danaus Plexippus, Monarch Butterly, picture ta...
Danaus Plexippus, Monarch Butterly, picture taken in NewYork, October 2008 (Photo credit: Wikipedia)

It is common for the mother of an animal to look after it rather than the father, but it is not uncommon for the father to look after the offspring, and more commonly both parents will look after their progeny.

For example, the egg laid by most species of Kiwi is incubated by the male member of a pair of birds. Also, in the Seahorse, the female deposits her eggs inside the male’s “brood pouch” and the young of the Seahorse develop there.

Once young animals are born, often the female parent will take care of them for some time after they are born, but this is not a definite rule. Sometimes the male parent is around and provides some support and protection, and even if the male parent is around, he may remain fairly distant, with the female doing most of the caring for the young animals.

A common sight is a mother hen closely followed by her chicks, with the aloof cockerel strutting around the farmyard. In a pride of lions, the nucleus of the pride consists of the females and offspring while the associated males remain close.

English: Four Lionesses take down a bull cape ...
English: Four Lionesses take down a bull cape buffalo in the central Serengeti (Photo credit: Wikipedia)

In humans, the so called “nuclear family” is common, at least in Western cultures. A nuclear family usually consists of a couple and their children living in a single house, and is a relatively recent phenomenon, with extended families being common in many cultures, including Western cultures, until fairly recently.

In such a nuclear family, the father goes out to earn money for the family every day, leaving the children in the care of the mother for the day. Such role separation and assignment could be seen as “natural” and “obvious”. This can be problematic when the couple are not male and female, when role assignment is trickier.

Guarani nuclear family of Mato Grosso do Sul, ...
Guarani nuclear family of Mato Grosso do Sul, Brasil (Photo credit: Wikipedia)

It is likely that there is an instinctive drive for a mother to care for her children and for the father to be assigned the role of provider for the family. Certainly this tendency for children to be cared for by the mother and for the father to fill another role can be seen in most societies, even those without the concept of the nuclear family.

In a family consisting of a couple of same sex parents, this role division is not well defined and indeed such couples may decide to share both provider and carer roles within the family group, which could speculatively lead to kids who are unclear about the distinction between the carer and provider roles.


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Kids are resilient though, and being more willing to share the roles when they grow up and form their own, probably heterosexual, relationships and families may even be an advantage. That’s not to say that the father in a heterosexual couple whose parents are also a heterosexual couple are not capable of caring! The roles in Western societies are not so strictly defined that a father cannot be a carer for some of the time, and that a mother cannot be a provider.

Regardless of such quibbles, mothers tend to be more caring and nurturing than fathers in Western societies. Both boys and girls tend to go first to Mum when a knee is scraped or an elbow bashed, and they go to Dad for the resolution of disputes, such as when a sibling has stolen a favourite toy and won’t return it.

This is probably because the mother has more invested in the children than the father. She has carried the child for nine months, culminating in a painful delivery, while the father has watched on and the only pain that he has suffered was when his spouse squeezed his hand too hard during a contraction and left nail marks in it. Of course, I am drastically under valuing the support that the mother has received from her spouse.


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Mother have a close bond with their children, and we can see it in modern society, where a couple is not always “till death do us part”. When a couple splits the children more often seem to go with the mother, although there are blended families where some of the kids are the father’s and some are the mother’s.

Mothers can be particularly close to their daughters, but they are even close to their sons. No other person has changed your nappy (diaper), clothed you, nursed you through minor ailments, and fed you from the moment of birth until you leave home. Step daughters and sons can sometimes have difficulty getting as close to step mothers, and this can cause issues.


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Poor old Dad. He gets the affection, the love, but usually not to the same depth as the children love their mother. Actually, I think that the bonds that form between a man and his kids are just as deep as mother love, but they are manifested in different ways. Dad is the one that the kids look to for protection much of the time, Dads tend to be the ones who encourage the kids to stand on their own feet.

The difference is that Dads are in general more able to form relationships at a distance. He may mainly see his kids in the evenings and at weekend. Modern life has pretty much forced a hands off approach to parenting for Dads. When a split up comes it is frequently easier for a father to move away from his children, painful though it may be than for a mother to move away from them.


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Breaking up a family is always difficult, but with nuclear families it is more difficult. In an extended family there are always granddads. grandmas, cousins and aunties and uncles to take up the slack. The modern child doesn’t have quite so much support. It’s a wonder that, in general, they still turn out OK.

English: This is the photograph of an extended...
English: This is the photograph of an extended family belonging to the Pais-Prabhu, a Mangalorean Catholic clan hailing from Falnir in Mangalore. (Photo credit: Wikipedia)

Thinking Inside of the Box

Illustration of the expansion of the Universe ...
Illustration of the expansion of the Universe after the Big bang. In Bulgarian. (Photo credit: Wikipedia)

Science aims to explain things, and by extension to explain everything. Is this even possible? Suppose the Universe consisted of a box, 20 million metres in each direction. Scientists inside this box could investigate this universe, but could they explain everything about this universal Box?

Suppose that the Box had impenetrable walls, so scientists could not probe outside of it. So they could say that the width, height, depth of the universe was 20 million metres and they could describe what was in it. They could also say that one side of the cube attracted everything in the Box and that side could be labelled “down” and the opposite side “up”.

English: Snapshot from a simulation of large s...
English: Snapshot from a simulation of large scale structure formation in a ΛCDM universe. The size of the box is (50 h -1 Mpc) 3 . Run using GADGET (GPL software) (Photo credit: Wikipedia)

There also might be statistical laws, so that the temperature, on average, might be 20 degrees Celsius, but could differ from that norm from place to place and from time to time. Box scientists might determine that everything appeared to be made up of tiny indivisible particles. Box atoms.

Some Box philosophers might ponder what was beyond the limits of the Box. They’d ponder the fact that starting from one side of the Box, one could travel 20 million metres in a perpendicular direction, but one could not travel 20 million and one metres. Why not?


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I’m sure that they would have plenty of theories. For instance, one philosopher might contend that the Box was embedded in an infinite impenetrable bedrock, while another might say that it was obvious – the Box was embedded in nothing. No space, no time, no thing!

Meanwhile scientists probing the Box atoms might split them and discover a whole new world of sub-atomic particles. Others might conceive of space in the Box as being a seething mass of pairs of virtual particles, being created and moving apart for a brief instant and then merging into nothing, no thing, again.

English: Tracks of ionizing radiation in a clo...
English: Tracks of ionizing radiation in a cloud chamber (thick, short: alpha particles; long, thin: beta particles). Français : Traces d’ionisation matérialisées sous forme de micro-trainées de condensation par des particules radioactives dans une chambre à brouillard ; Les trainées épaisses et courtes signalent des particules alpha ; les longues et files matérialisent le passage de particules beta). (Photo credit: Wikipedia)

But, says one bright spark, what about a particle pair created on the boundary of the Box? One particle would enter the Box, and the other would travel somewhere else! This would lead to other speculation – if the second particle travelled in another Box, then that other Box would presumably be a mirror image of our Box!

Such speculation would wait on experimentation by the Box scientists and I’m aware that I cannot push the Box analogy too far with out it breaking. But, just as in the case of the Box scientists, philosophers and scientists in this Universe have similar issue.

An illustration of a ramified analogy, one com...
An illustration of a ramified analogy, one component of Gordon Pask’s Conversation Theory. Self-made (Photo credit: Wikipedia)

In our Universe there are no bounds (under current theories, I believe) but that doesn’t mean that we can’t speculate about what is beyond our Universe, whatever “beyond” may mean in this context.

The Box scientists could potentially explain every thing in the Box, maybe even the fact that it had existed, pretty much unchanged (on average) for all time, and that is periodically, over astronomically long time scale is doomed to repeat itself, time and time again.

Mesquita, repeat ad infinitum
Mesquita, repeat ad infinitum (Photo credit: Wikipedia)

When they go further than that, it is pure speculation, as all the data that they have relates to the Box. They have no data from outside of the Box. All the waves and particles that are observed originate in the Box. All the forces and fields are part of the Box. While scientists may speculate about “other Boxes”, that is all that they can do.

That’s the problem. The Box scientists, and the scientists from our Universe, can only observe events in the Universe in which they are embedded. Observations relate only to events in the local Universe.

English: Multiverse, a light sculpture by Leo ...
English: Multiverse, a light sculpture by Leo Villareal featuring 41,000 computer-programmed LED nodes, located between the National Gallery of Art’s East and West Buildings, on the National Mall in Washington, D.C. (Photo credit: Wikipedia)

Some conjectures suggest that our Universe is one of many universes all linked together in some way. Some conjectures suggest that the laws of our Universe apply in many other similar universes separate from ours. Some people conjecture that universes may exist where there are no laws or the laws that there are have no similarity in any way to the laws of our Universe.

In the Box universe these conjecture would amount to ideas that there may be other Box universes out there with similar laws to the Box universe, maybe linked in some way to the hypothetical Box universe. There may even be universes which have laws which are not at all similar to those of the Box universe. For instance a universe which springs from a single point in a vast explosion and expands at a vast rate either forever or to a certain point only to collapse once again. How bizarre!

The Big Bang era of the universe, presented as...
The Big Bang era of the universe, presented as a manifold in two dimensions (1-space and time); the shape is right (approximately), but it’s not to scale. (Photo credit: Wikipedia)

The Box scientists would not have any way to decide whether or not their were any other Boxes as their observations would only observe events in their own Box. The only way that events in one Box could possibly affect the events in another Box would be if there was a link between them in some way.

This doesn’t necessarily mean that the event would be observable as the effect of one universe on the other universe. It would just appear as an event in each universe as it transpires as a result of the laws of the universe in question.


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The theory may posit a link between two universes but the events in one universe can only result from events within that universe. If this were not so, the event in the universe would appear to happen without any causation in the universe. In other words it would be an anomaly or a miracle.

In other words, suppose a scientist in one universe knows of a law where he can cause an effect in another universe. If he can cause this effect in his universe then in the other universe something will also appear to cause this effect. Maybe this cause will be a scientist in the other universe trying to create an effect in the first universe!


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This possible symmetry of cause and effect across more than one universe would mean that it would be difficult if not impossible to detect the presence of another universe by its effects on our universe.

The person in the Box universe would likely be in the same position. This means that he would never know if there were anything outside of his 20 million metre cube. He could postulate an infinite series of Boxes stacked like bricks in an endless array. Or he could postulate Boxes grouped into “houses”. Or he could postulate that his was the only Box and that speculations about universes started from “Big Bang” explosions are mere fiction.

Detail of the bricks in the Great Wall at Muti...
Detail of the bricks in the Great Wall at Mutianyu. (Photo credit: Wikipedia)

Holidays

English: Holiday in village
English: Holiday in village (Photo credit: Wikipedia)

I should imagine that going on holiday, for many people would be a relatively new thing. While those with money might decide to shift operations from home to another location, which might or might not be near a beach, those who work from them would mostly have no respite from day to day toil, since their employers would still require looking after as usual.

As ordinary people became wealthy, and the old social structures faded away for the most part, it would have become more usual for ordinary people to go away, just as their employers used to.

Rangiputa, Karikari Peninsula, Northland, New ...
Rangiputa, Karikari Peninsula, Northland, New Zealand. Rangiputa is a beach and bach (holiday home) community on the west side of the peninsula (Photo credit: Wikipedia)

The word “holiday” itself is a  contraction of “holy day”, and on holy days there were celebrations and less formal work. The word has come to mean a day on which one does not have to work. Most countries these days would have statutory holidays on which which people would not have to work. There may be other restrictions, such as legislation that shops should remain closed.

It’s understandable that some countries require shop closures, as this means that shop staff get the holiday too, but many countries these days allow shops to stay open if they wish and some of the best retail days are on statutory holidays. Usually shops that stay open are required to compensate staff who are required to work.

English: Brixham - Harbourside Shops These sho...
English: Brixham – Harbourside Shops These shops mainly cater to the holiday trade who visit the harbour. (Photo credit: Wikipedia)

Holidays are disruptions to normal schedules. When one goes away, one is in a different environment and one has to make do. Even something as simple as making a cup of tea may be complicated by the need to find a spoon, a cup, and a teabag, not to mention the need to figure out the operation of a different jug!

These things are not an enormous issue, and in fact draw attention to the fact that one is on holiday. All schedules are voided and one can do whatever one wants. Often this may amount to doing nothing.


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A “holiday industry” has evolved, which provides accommodation, and resources for those temporarily away from home. It also provides entertainments or “attractions” if the holiday maker doesn’t just want to lay on the beach. The holiday maker may do all sorts of things that he or she doesn’t usually do, from the exciting (bungy jumping or similar) to the restful (a gentle walk around gardens or maybe a castle visit or may a zoo).

These facilities are all staffed by helpful people who arrange things so that the holiday maker can enjoy his or her self without worries. These people are of course employed by the facilities, but many of them enjoy their work very much anyway. It’s a sort of bonus for helping people.

English: Ultra Dynamics Dowty Turbocraft water...
English: Ultra Dynamics Dowty Turbocraft waterjet boat (Photo credit: Wikipedia)

Holiday makers must also be fed, and this has become a huge industry too. In any seaside towns so-called fast food outlets can be found in abundance, along with more up market restaurants and cafés, for more leisurely eating. For many people one of the advantages of being on holiday is that one doesn’t have to cook, and one can choose to eat things that one doesn’t normally eat.

Holidays can be expensive. Since we are close to the Pacific Islands, like Tonga, Samoa and Fiji, many people fly out to the islands on their summer holidays. This means flight and accommodation has to be booked and paid for.

English: Great Frigate Birds (Fregata minor) o...
English: Great Frigate Birds (Fregata minor) on Johnston Atoll, Pacific Island Wildlife Refuges (Photo credit: Wikipedia)

When the holiday makers arrive at their destinations, they have to pay for food and entertainment. Other expenses may be for sun screen cream, snacks, tours, tips, and the odd item of clothing which may have been accidentally left at home.

Holiday entertainment may comprise guided tours, or visiting monuments or zoos. Amusement parks are often an attraction as are aquariums. All this can cost a lot, but unless you are content to veg out on the beach, you’ll have to pay for it. Even vegging out on the beach comes at a cost, from sun protection through to drink to offset the dehydration caused by the sun.

English: Roller coaster, M&Ds Theme Park, Stra...
English: Roller coaster, M&Ds Theme Park, Strathclyde Country Park The larger and older of the two roller coasters, at the very southern end of the park. (Photo credit: Wikipedia)

So, why do we throw over the usual daily regime, and drag our family on an often uncomfortable road, sea, or plane trip, to a location where we know little of the environment, which will cost us money, to spend the days traipsing from “attraction” to “attraction” spending more money and feeding on often costly food of unknown quality or provenance?

Part of the answer is that the daily regime becomes boring and descends into drudgery. Removing ourselves from the daily regime allows us to escape that drudgery for a while. As far as the cost goes, well, one is prepared to spend a certain amount of money to escape the drudgery for a while.

Money for All
Money for All (Photo credit: Wikipedia)

Removing ourselves from the usual means that we can try the unusual. We may try Mexican food, or Vietnamese food. Or even Scottish cuisine if we choose. The world is our oyster.

We can try sports and pastimes that we have never tried before. Bungee jumping. Skiing, water or snow. We can visit a “Theme Park”, ride a roller coaster, or other ride. We can scare ourselves and excite ourselves.

Skiing
Skiing (Photo credit: Wikipedia)

We can experience different cultures, different scenery, but at the end of the day we know that we will be returning to our mundane lives. We have at the back of our minds the cosy ordinariness of our usual lives, as a sort of safety harness.

We know our comfortable house will be there for us to return to, and while we may enjoy the beds in our hotel, motel, holiday home or tent, we look forward to the return to our own beds. We look forward to drinking the brands of coffee and tea that we prefer and fill the fridge with the foods that we prefer to cook.

English: Hotel room in the Waldorf Hilton, Ald...
English: Hotel room in the Waldorf Hilton, Aldwych, London. (Photo credit: Wikipedia)

Few people would want to live in hotels and sleep in strange beds as a way of life, but there are some people who do so. While we enjoy being on holiday, as a break from our usual lives, we would probably not want to live that way for an extended period. Those who do are unusual people.


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Space – the Final Front Ear

Portrait of William Shatner
Portrait of William Shatner (Photo credit: Wikipedia)

Sorry about the fabricated mondegreen, which obviously references the Star Trek series of films and TV shows. Captain Kirk saw space, or more correctly distance, as a barrier, but it really is one of the factors that determines the structure or shape of our Universe.

It is interesting to me, that, although the Universe is finite, if it derived from a Big Bang, there is a human urge to explore outwards, as if it were infinite. That is probably one of the factors that led scientists such as Fred Hoyle and others to support a Steady State Theory of the Universe.


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Personally, I believe that there is no such thing as a steady state in anything. When we see something which appears to be in a steady state or equilibrium state we should look for the feedback factors that are keeping it that way. For example a pendulum hangs straight down when at rest because any deviation from that position results in gravitation forces pulling it back to the rest position.

If friction is low the pendulum will actually pass through the equilibrium position and swing to the other side, whereupon gravity will slow it and draw it back towards the equilibrium position again. Eventually friction will slow the pendulum down and the pendulum will again hang vertically.

De :en:Image:Pendulum.jpg
De :en:Image:Pendulum.jpg (Photo credit: Wikipedia)

So we have two forces, gravity and friction, resulting in the pendulum returning to the equilibrium position. No pendulum lasts for ever, as the pivot will wear out or an elephant may step on the thing, so the equilibrium will only exist for a finite time, but it will last long enough for us to use in clocks or in scientific experiments.

Space is itself expanding as I understand the theories and some of it is out of our sight, over an event horizon, which is a locus where everything is moving away from us at the speed of light. That doesn’t much our location special – it is true of any point in the Universe. LGM on a planet around a star that is over the event horizon from us have their own event horizon, and while they may be able to see a star inside our event horizon and we in theirs, we cannot see each other.

Alien (creature in Alien franchise)
Alien (creature in Alien franchise) (Photo credit: Wikipedia)

Space separates us form the LGM, but it also separates from things local to us. Ben, our dog, is over there, about 3 metres away. My cup is mere centimetres away. It is fair to say, I think, that this is the essence of space – it is hard to conceive a universe which doesn’t incorporate a spacial concept. Or rather, a separation concept to allow things to be different from one another.

Space is not the only “separation concept” that I can think of. Things can also be separated in time, so two different bodies can exist in the same spacial position, but just not at the same time. Time is so connected to space that Einstein and others were able to link time and space into a complex space/time concept.

Time dilation spacetime diagram06
Time dilation spacetime diagram06 (Photo credit: Wikipedia)

The similarity between the space dimension and the time dimension is striking. You can even measure distance in time units as astronomers do when they talk about light years. We also do it when we say that a distant town is three hours away.

We less frequently talk of time in distance units, for example, when we say things like “six laps later”, to describe the time between two events in a car race. At some level we acknowledge that time and the space dimension have a lot in common.

English: MMTC workout. 10 of 1 mile laps witho...
English: MMTC workout. 10 of 1 mile laps without rest. (Photo credit: Wikipedia)

Space in the sort of concept that everyone knows and experiences but no one thinks deeply about. There’s no doubt that space separates events from one another. You can’t have two solid objects occupying the same space at the same time, without catastrophe ensuing. Scientists have been trying to achieve this for years, with the aim of harvesting the energy generated from the ensuring nuclear fusion.

Space appears on the macro (normal) level to be continuous. We appear to move smoothly from one location to another when we walk, incidentally forcing the air out of way as we do so. There is no sudden jumps that we notice, we don’t hop from point to point like a chess piece on a board.

Animation of the Knight's tour
Animation of the Knight’s tour (Photo credit: Wikipedia)

The philosopher Zeno came up with a number of paradoxes related to movement, that is getting from point A to point B. For instance, the athlete Achilles could not overtake a tortoise in a foot race, because Achilles would need first to reach the tortoise’s starting point, by which time the tortoise would have moved on. Achilles would then have reach the point that the tortoise had reached now, by which time the tortoise would have moved on. And so on, ad infinitum.

Of course Achilles does overtake the tortoise, and I believe the main issue in this case is related to the summation of an infinite number of decreasing distances, which intuitively one might this would sum to an infinite distance. In fact the sum of the distances is a finite number. If Achilles runs 10 times as fast as the tortoise and they start 10 feet apart then Achilles overtakes the tortoise after he has travelled 11 and 1/9 feet exactly.

Triumphant Achilles in Achilleion levelled
Triumphant Achilles in Achilleion levelled (Photo credit: Wikipedia)

Zeno’s paradoxes still inspire debate, but his conclusion was that movement, the smooth transition of something from one place to another is an illusion. One of the assumptions used is that distance is a continuously varying property, but it may be that it is not, and there are hints of that at the quantum level. The Planck length is the smallest distance about which statements can usefully be made and it is impossible to determine the difference between two locations less than one Planck length apart. Perhaps we do hop from place to place like chess pieces, or at least our atoms and their constituent particles do.

Max Planck 1910
Max Planck 1910 (Photo credit: Wikipedia)

Space and time enable events to happen uniquely, and without collisions. Events may happen in the same place as long as they happen at different times. It may be that events of different probabilities happen at the same place and time, so long as the sum of the probabilities of all events is one. It may therefore be that probability is a dimension with the same sort of status as the space and time dimensions. This would require that our view of probability, of one event out of many being the one that actually happens is an illusion and that events of all probabilities happen in a sense.

English: The probability pattern for a single ...
English: The probability pattern for a single electron atom. (Photo credit: Wikipedia)

All things are connected

English: computer network IP address
English: computer network IP address (Photo credit: Wikipedia)

There are networks everywhere. Not just the Internet or the LAN at work, but everywhere. A network could loosely be defined as being comprised of a number of nodes and a number of connections between them. A node is a point or thing which is connected through a connection to another node. A connection is what joins nodes together. This rather circular definition will do for now.

A family can be described by a network. Let’s consider a typical average nuclear family with parents and 2.4 kids. Errm, on second thoughts, lets make that 3 kids. If each person in the family is a node, we can’t really have 0.4 of a kid.

A Date with Your Family
A Date with Your Family (Photo credit: Wikipedia)

So there are multiple connections between any one family member and another. The father has a connection with his wife, his daughter and his sons. The daughter has connections with her father, her mother and her brothers. One way that this could be shown in a diagram is to draw a pentagon, each vertex of which is a member of the family and lines between the family member showing the relationships.

That’s a total of 15 interrelationships in a small family. Actually depending on the way you look at it, there may be more, as the father is the father of his daughter but the daughter is not the father of the father (obviously). This can be looked at at two relationships, one from father to daughter (A is B’s father) and another from the daughter to the father (B is A’s daughter), or one relationship between father and daughter.


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If you consider that there are two relationships between any two family members, then each relationship can be considered to have a direction and a value. “A is B’s brother” and “B is A’s brother”, for example. Alternatively the relationship could be simple viewed as “brothers”, in which case the relationship has a value, but is non-directional.

I’ve described the familiar relationships in detail to hopefully bring out the facts that relationships between nodes and connections can be complex or describe complex situations. It’s entirely a matter of what you want the network to show.

English: Semantic Network with 7 nodes and 6 links
English: Semantic Network with 7 nodes and 6 links (Photo credit: Wikipedia)

The Internet is what people tend to think of when someone says “network” and it is indeed a complex network with myriads of interconnections across the globe, but in another way it is quite simple. Basically you have a computer, say your desktop or laptop, connected to the Internet. When you request a webpage, your request is sent to another node on the network, which then sends it to another node, and that forwards it on to yet another node and eventually the request arrives at the destination.

The clever part is that you might think that every “node” on the Internet needs to know where all the other nodes are, but in fact all it needs to know is where to send the request next.

English: nodes
English: nodes (Photo credit: Wikipedia)

It seems almost magical. Your computer doesn’t know where wordpress.com is, though it does look up its unique address (known as an IP address). It still doesn’t know where wordpress.com is, so it sends the request and the IP address to your ISP. Your ISP looks at the IP address and sees that it isn’t one local to the ISP, so it passes it on.

As noted above the message is passed on and on until it reaches its destination and then more magic happens as the remote machine responds to the request and sends the response all the way back. It may even travel back by a different route.


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The magic is that some of the nodes know around 200,000 addresses on the Internet and where the next step should go. These addresses are in the most part partial in that the address will be like the street address, without the building number.

So although the Internet is a complex network with many many connections between nodes, the basic principle by which it works is simple, based on an address lookup system (DNS) and a simple unique address for each device on the Internet.


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(OK there’s more to it than that, but the complexities are mainly at the “edges” of the Internet and mainly spring from the need for security and for organisations to have a “gateway” or single address on the Internet).

When we plan a journey over the road network, we generally have some idea of where we are going or we get out a map. We then scan it for the start and end of our journey and work out what direction we need to travel and the intermediate towns.

1945 map of the Pentagon road network, includi...
1945 map of the Pentagon road network, including present-day State Route 27 and part of the Shirley Highway. (Photo credit: Wikipedia)

But if we travelled like a message travels on the Internet we would first travel to the nearest town and ask someone where we need to go to get to our destination. He or she would point us to the next town to which he or she believes we should go. We would then travel to the next destination and ask again.

It would seem that such a process could result in us going round and round in circles, but eventually we will reach a place where the traffic director knows a large part of the roading network and is able to redirect us to another city which is known to be closer to our destination. Once we are on the right road, the process will eventually result in us reaching our destination.

Road to the A48 near Llancarfan - geograph.org...
Road to the A48 near Llancarfan – geograph.org.uk – 1297530 (Photo credit: Wikipedia)

Another network is the network formed by people we know and the people that they know, and the people that they know and so on. There is a theory that to from you, to someone you know to someone they know and so on, it takes six or less steps to reach any person on the planet. This is referred to as “six degrees of separation“.

Similar numbers can be calculated for smaller sets of people. The Kevin Bacon Number relates movie stars through films that they have starred in with other people. Number higher than 4 are rare. The Erdős Number relates people by the number of scientific papers that they have co-authored.

head of Paul Erdös, Budapest fall 1992
head of Paul Erdös, Budapest fall 1992 (Photo credit: Wikipedia)

These somewhat whimsical numbers do demonstrate how closely linked the human race is. So far as I know no study has been done of the importance of bridging individuals is. I’m talking about those who perhaps emigrate to a country, thereby directly linking together two populations that may be less loosely connected, increasing the connectivity and reducing the number of degrees of separation.

Six degrees of separation.
Six degrees of separation. (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!]