Classification

"Father! Father! / Tell me what ails thee...
“Father! Father! / Tell me what ails thee? / With dismay thou art filling thy child!” (Photo credit: Wikipedia)

Oh, wow, drat and other words of dismay. I haven’t thought of a topic for this week and it is time to write my post. Time to get started.

OK, people seem to like classifying things. This can be so that they can find one item in a large collection of things, or it may be simply a means of bolstering prejudices that they might have. Or any of a myriad number of other reasons.

Garbage Can
Garbage Can (Photo credit: Wikipedia)

When faced with a profusion of things, the human impulse is to classify them. One of the most famous classification systems is that of Carl Linnaeus, whose classification system is used for the not so trivial task of classifying all living things. His system, with modifications is still the basis for biological classification of all organisms.

Digitally improved version of Alexander Roslin...
Digitally improved version of Alexander Roslin’s painting of Carl von Linné. This particular version has had dust and missing specs of paint deleted. (Photo credit: Wikipedia)

When Linnaeus started his classification, it is likely that partial schemes would likely have been in place to classify small groups of organisms, but Linnaeus extended this to all organisms, in an organised way. When someone states that mankind’s scientific name is “Homo Sapiens”, he or she is using the Linnaeus system, at least partially.

“Homo” represents mankind’s Genus, and “Sapiens” is mankind’s  Species, but the species is merely a leaf on the classification tree, which is rooted in the Animalia Kingdom, and descends through Phylum, Class, Order, Family, and Tribe, (which I’m not going to list here) and finally to the Genus and Species.

Darwin's tree of life
Darwin’s tree of life (Photo credit: Wikipedia)

Linnaeus’ system is still in use today, but the emphasis has changed somewhat. When he was doing his work, the classification was based on appearance, and while that is often a good guide to an organism’s place in nature, emphasis has now shifted to the genetic make up of organisms to determine their correct classification.

Agapornis phylogeny
Agapornis phylogeny (Photo credit: Wikipedia)

This has sometimes resulted in whole chunks of the classification tree being moved from one branch to another as knowledge of the genetics of the organisms has come to light. It is obvious that if two organisms have similar genetic make ups, then they must be closely related. Also, it implies that they almost certainly have a common ancestor, and such an ancestor is also fitted into the tree of life and given a species name.

Horned Dinosaur Phylogeny
Horned Dinosaur Phylogeny (Photo credit: Scott Wurzel)

This adds a time dimension to the genetic tree, turning it from a static representation of living organisms into a dynamic picture of all life over all time. The tree of life is evolving.

Another great classification system is the Dewey Decimal Classification system, a proprietary library classification system used to classify books. Every book in a library is assigned a number, which in most cases would not be unique. The number consists of two parts separated by a period (‘.’). Most library users would be aware of the system, and will have used it to locate books.

Spine Books Label show Call Number for Dewey D...
Spine Books Label show Call Number for Dewey Decimal Classification. (Photo credit: Wikipedia)

While the system can classify books in great detail, merely by extending the number after the period to many decimal points, most libraries classify their books in much less detail, using only two or three digits as a suffix. This results in groups of books receiving the same number, with the books in a group sharing a common topic, while differing in detail.

get to know the dewey decimal system
get to know the dewey decimal system (Photo credit: susannaryan)

For instance a particular number may be assigned by the library whose topic might be the geography of the country of Bolivia. (The actual number is 918.4). The library might have only one or two books on the subject of the country of Bolivia, so that number is sufficient to locate any of them.

In the country of Bolivia itself, however, there will almost certainly be many more books on the topic and the Dewey Decimal Classification almost certainly contains more detailed classification numbers which would have to be used in Bolivia libraries to classify the geography books. (I’ve not checked this “factoid” but it is probably true).

Shelf of Books on South America
Shelf of Books on South America (Photo credit: pkdon50)

So the Dewey Decimal Classification system can be hair-splittingly  accurate or broadly general in its application and this flexibility is ideal for libraries. Sometime libraries use a sort of hybrid system, probably driven by the need for a sub-classification where some books have been already more generally classified, where some books are classified as “something.12” and other books are classified as “something.123”. In most cases this inconsistency doesn’t matter.

Topographic map of Bolivia. Created with GMT f...
Topographic map of Bolivia. Created with GMT from public domain GLOBE data. (Photo credit: Wikipedia)

I’ve just realised on writing that, that it may not be inconsistency at all. Instead the “something.123” books may be more specific than the “something.12” books, which would therefore be more general.

An obvious difficulty with the Dewey Decimal Classification system is that there is no cross-reference possible. In the Bolivia example, a book may cover the topic of the geographic causes of distribution of various related Bolivian species of some organism or other. Is this to be classified as biology and be assigned to a class in the 500s (Pure Science), or should it be classified as geography and assigned to a class in the 900s?

English:
English: (Photo credit: Wikipedia)

Nowadays one can do a computer search and come up with a bunch of numbers that fit the topic that is being researched. In the days before computers there were card-based “Topic Catalogs” which would also provide the searcher with a bunch of numbers. The trouble is, many searches would result in multiple numbers, either as a result of a card search or a computer search.  One would then have to go to several locations to decide if the required topic was covered by this Dewey Decimal Classification number or one of the others. I make it sound bad, but really, it wasn’t, and the issue is more a user confusion about what was covered by each topic in the system rather than an issue with the system itself.

Banner for Wikipedia:WikiProject Lists of topics
Banner for Wikipedia:WikiProject Lists of topics (Photo credit: Wikipedia)

A computer search (on Google for example) will provide a list of possible references to a search term, but as anyone has used a computer search is aware, a search term can refer to many topics. A search for the word Socrates gave me a list including a Wikipedia article on the philosopher himself, a list of quotes taken from his work, a biography of the philosopher and a site where his philosophies could be discussed. And that is just the first four items out of an estimated 6 million or so.

Google
Google (Photo credit: warrantedarrest)

Classification of things seems to be a trait of humans. I think that we classify things to simplify things for ourselves, to make it easy to identify threats and possibilities. As such, it is probably an inherited trait possessed by at least the more developed organisms on the planet. However classification can add complexity if one is searching for something, so it is something of a trade off.

google_logo
google_logo (Photo credit: keso)

Time waits for no man

time travel
time travel (Photo credit: flyzipper)

Time is an odd thing. We say it passes, but it sometimes feels more like we are travelling through. As the old joke goes, we all travel through time – at a rate of one second per second.

While that might bring a smile, it does raise a question about time travel, because if one travels through time, one presumably travels through it at some rate or other, say ten years per minute. The problem with that it is that we are measuring a rate, which is a change of some variable with respect to another, but in this case we are measuring the rate of change of time with respect to time as well.

English: Acceleration as derivative of velocit...
English: Acceleration as derivative of velocity along trajectory (Photo credit: Wikipedia)

The time intervals over which the traveller is passing are measured in the usual way by a clock, but how does the traveller measure his time by? He could carry a clock with him, which he could then use to estimate his progress along the standard time scale. In other words the time traveller would somehow have to carry his own time scale with him which is different to the usual time scale.

Illustration of a light cone, based on Image:L...
Illustration of a light cone, based on Image:Light cone.png (Photo credit: Wikipedia)

Of course, Einstein’s Special Relativity shows that, in a way, we do carry our own time frames around with us, and if we are in motion relative to some other frame then time passes differently the two frames.  Of course, to simply travel in time, we would not want to travel in space, so we can’t use Special Relativity to allow us to use a different time frame, so far as I can see.

Also, we can only travel forward in time by using this loophole. No matter how fast we move relative to someone else, we both move forward in time, so we can’t use Special Relativity to go back in time and kill dear old Grandad.

The Grandfather Paradox
The Grandfather Paradox (Photo credit: Kaptain Kobold)

Einstein’s General Relativity considers that space-time (the conjunction of space and time) possesses curvature, and some theories use this to allow backwards time travel. However these solutions produce “closed time-like curves” which is not so much time travel as a time loop, perhaps like the loop in “Groundhog Day” where Bill Murray’s character repeatedly awakes to the same day.

groundhog day!
groundhog day! (Photo credit: NapaneeGal)

It appears that we need to look further for some way to travel in time. If we can’t use current physics, we will need to consider something more “science fiction” than modern physics. Of course science fiction time travellers don’t seem to explain their travels in more than a cursory way, because, after all, the mechanism is only secondary to the story line.

Time Machine Clockwork
Time Machine Clockwork (Photo credit: Pierre J.)

Two different possible mechanisms spring to mind.

Firstly, one way is to assume a sort of parallel world. A time traveller can enter this parallel world from any point in time and re-enter the standard universe at a different point, earlier or later in time. The traveller travels in time by analogously travelling in space in a world which has its own space-time with one of its space dimensions parallel to the conventional world’s time dimension.

parallel worlds
parallel worlds (Photo credit: aloshbennett)

Secondly, the author can conjecture a viciously curved space-time so that the characters can, at certain locations, move from one part of space-time to another part of time which is either earlier or later in the time dimension. Typically the character will “step sideways” or something to jump between times, either with the help of a machine or maybe not.

HELP ME HELP MYSELF!
HELP ME HELP MYSELF! (Photo credit: eyewashdesign: A. Golden)

One such tale of the second sort is “By His Bootstraps” by Robert A Heinlein, is which the main character passes through a portal to a distant future, only to entangle himself with later (and, relatively, earlier) versions of himself. He encounters a mysterious character who identifies himself as “Diktor”.   I’ll leave it there, as I don’t want to spoil the story for those who haven’t read it yet.

By His Bootstraps
By His Bootstraps (Photo credit: Wikipedia)

An example of the first sort is “The Corridors of Time” by Poul Anderson, where the main character is recruited into a war raging up and down the “corridors of time”.

Most stories, however, don’t specify in more than a cursory way the physics that is supposedly employed by the time traveller.

Train travel
Train travel (Photo credit: Wikipedia)

The effects of time travel are what is explored by these stories. If the traveller goes back in time he or she must interact with the world at the earlier time from when he started. There are time stories in which the traveller changes things so the state of the future time from which he can is changed.

Future World 2012 (Explored)
Future World 2012 (Explored) (Photo credit: Scottwdw)

This is the premise behind the Terminator series of films, where the Cyborg assassin (played by Arnold Schwarzenegger) is sent back in time to kill the mother of John  Connor, the leader of the rebellion against the killer machines. Obviously, in the future from which the Terminator comes, John Connor is born so the Terminator is trying to change the future from which he comes.

The Terminator
The Terminator (Photo credit: Dunechaser)

The obvious paradox here is that the Terminator risks changing the future into one in which he was never created. In which case he would not be able to come back in time to kill Sarah Connor.

The other sort of time travel story treats time as if it were immutable. Any events that happen are eventually shown to have logically been the consequence of the time travel in the first place. For instance, the mysterious stranger on the street turns out to be the time traveller, keeping an eye on the earlier version of himself. All is explained so that the stream of events is logical both from the time sequential point of view and also from the point of view of the traveller. The aforementioned “By His Bootstraps” is a story of this sort.

The Mysterious Stranger
The Mysterious Stranger (Photo credit: Wikipedia)

Is it possible that events in the past could have changed? We would not know it! As far as we would be concerned the past event would have have always happened, since there would be a temporal progression from the past event to our current time. Of course the language is tricky here, as it does not handle such matters as changes to the past.

Einstein's Theory Fights Off Challengers (NASA...
Einstein’s Theory Fights Off Challengers (NASA, Chandra, 04/14/10) (Photo credit: NASA’s Marshall Space Flight Center)

To use the physicists’ favourite analogy of a rubber sheet, if time is considered to be along one dimension of the sheet, and space along the other, then an event which changes the past is like someone pulling a point on the sheet to one side, which affects all the points from both the future and the past of the point which has been moved. But the sheet itself remains intact.

Rubber sheet undergone drying in smoke. Three ...
Rubber sheet undergone drying in smoke. Three versions are there in the picture. 1. Fresh sheet. 2. Little dried in sun light. 3. Dried in smoke. (Photo credit: Wikipedia)

However, I think that this scenario is unlikely. There doesn’t seem (at the present time) any physical mechanism by which time travel could be achieved, and even though it appears that time travel is logically possible (under the sort of scenario as in “By His Bootstraps”) in a deterministic universe, the simplest conclusion is that time travel is most likely unachievable in this universe.

A "jumpgate" of the X Universe, part...
A “jumpgate” of the X Universe, part of a space-travel network. (Photo credit: Wikipedia)

 

 

 

 

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)

 

 

 

Is “schooling” an education?

School
School (Photo credit: Krzysztof Pacholak)

Well, schooling should be an education. It should prepare the pupil for life. Dictionary.com has this as a prime definition of education:

The act or process of imparting or acquiring general knowledge, developing the powers of reasoning and judgement, and generally of preparing oneself or others intellectually for life.

Schooling doesn’t always do this – Greek history is probably of little use to a car mechanic and scientists are only interested in Greek history in so far as it has cool cast list of names and an alphabet from which they can plunder names for obscure fundamental particles or asteroids.

View from one end of Eros across the gouge on ...
View from one end of Eros across the gouge on its side towards the opposite end.(greyscale) (Photo credit: Wikipedia)

Arguably, though, Greek history is a fascinating window into an early culture, and studying events in Greek history can provide insights into contemporary society and while it may not be of obvious direct benefit to the mechanic and the scientist, such studies can inform sociologists, political studies specialists and many others, and it is worth remembering that mathematics, science, logic, philosophy, politics and many other fields of human endeavour have their roots in ancient Greece.

Temple Statue of Poseidon
Temple Statue of Poseidon (Photo credit: greekgeek)

But back to schooling. Everyone has been bored at school, for a number of reasons. The subject could be more than the student can handle, or it could be too simple, or it may not be a subject in which the student has no interest.

One of the issues with schooling is that we are taught, well, “subjects”. Well, we are taught “maths” or “biology” or “French”, or “Woodworking” or whatever. We are taught “English”, which is about how sentences are formed and we are drilled in verbs, nouns, adjectives and more esoteric beasts of the English language. Then there is “English Literature”, which largely consists of forcing pupils to read and “study” relatively old English language texts ranging from Shakespeare to Dickens. Rarely anything more modern.

English: Literature
English: Literature (Photo credit: Wikipedia)

There is a syllabus, specifying what we are to be taught. This is used to constrain the teachers and students, so that they can be set examinations to see, basically, how much the teachers have been able to force into usually unwilling minds.

writing/editing my environmental sustainabilit...
writing/editing my environmental sustainability cornerstone seminar syllabus at nabolom bakery in berkeley (Photo credit: davidsilver)

This all seems mechanical and soulless, but a good teacher will try to insert into the gaps and voids of the subject and the syllabus a little education. He or she will try to convey the beauty of the English language as used by Shakespeare and the other authors, he or she will try to make Romeo and Juliet into real people for the students, he or she will explain the societal background of the Dickens tales.

English: Title page of the second quarto editi...
English: Title page of the second quarto edition (Q2) of William Shakespeare’s play Romeo and Juliet printed by Thomas Creede in 1599. (Photo credit: Wikipedia)

The good teacher will teach something more – how to look beyond the surface story to the people and the societal background, not just in the set books or any books, but in all the situations that life may throw at the student over the years.

"Good Teacher"
“Good Teacher” (Photo credit: MightyBoyBrian)

A study of literature can not only give the student the knowledge of what is in the books, and maybe an appreciation of the era in which the books are set but may also provide the student with the ability to look critically at the era in which they are living. For some, maybe more than a few of the students, this will provide them with the tools to examine sources like the media and consider such things as bias and veracity.

A book pile illustrating the theme of the fest...
A book pile illustrating the theme of the festival of 2005 “Education, why?”. (Photo credit: Wikipedia)

A teacher of maths will try to not only enable the students to pass their maths exams but also to prepare them, a little, for life. The simple techniques of addition and subtraction may be all that they need, but sometimes they may need a bit more. Some of the students may go on to be mathematicians, to study the subject in its own right. But many more may acquire the tools to understand some of the numbers that surround us all in our daily lives.

Day 304: Problem Solving Strategies for Math
Day 304: Problem Solving Strategies for Math (Photo credit: Old Shoe Woman)

For instance, when a poll result is given on television, often they also quote a ‘margin of error’. A small but significant number of people will have some idea of what that actually means from some long ago statistics class. The vast majority doesn’t have a clue as to what it means, but the brightest might gather that it relates to how accurately the poll represents the wider population.

Margin of error-visual
Margin of error-visual (Photo credit: Wikipedia)

Another example of a mathematical tool that could be useful is contained in an episode of the British sitcom, “Please Sir!”. This is a comedy about an inspirational teacher and a class of pupils who are rejects from other classes. The teacher follows an informal teaching agenda as it is evident that his class is not going to pass any exams.

English: Statue of Sir Hugh Owen , A Pioneer o...
English: Statue of Sir Hugh Owen , A Pioneer of Welsh Education Sir Hugh Owen was a pioneer of secondary and tertiary education in Wales. (Photo credit: Wikipedia)

He tries to instil some mathematics into his students, using as an example a bet on a horse race. He calculates the odds only for one of his students, the son of a bookie, to correct him. The teacher is astounded that the student can calculate the odds so accurately in his head, saying to the student that he didn’t know that the student was good with maths. The student replies that this wasn’t maths, it was “odds”.

At the bookies
At the bookies (Photo credit: Phil Burns)

Science, likewise, has ramifications beyond the bland and often boring stuff a student learns at school. While he or she may come close to disaster in a lab, he or she may take away the concept of analysis and the scientific method that may help him or her in later life. At least when one of the TV detectives grabs a scrap of clothing or a sample of blood or something and sends it for analysis, he or she may have an inkling of what is happening. Though these shows are an education of a sort in themselves.

Day 53 - West Midlands Police Forensic Scene I...
Day 53 – West Midlands Police Forensic Scene Investigators Lab (Photo credit: West Midlands Police)

So why is the educational system focussed on schooling rather than educating? Well, for one thing it is easier to measure schooling rather than education. Facts trotted out for an exam yield a measurable yardstick to judge both student and teacher. It’s altogether more difficult to measure education.

Seal of the United States Department of Education
Seal of the United States Department of Education (Photo credit: Wikipedia)

That’s because an education is not about facts learned. It’s about facts learned and a deeper understanding of how the facts interrelate within the system, be it Greek history, English literature, maths or science. Nevertheless, the best teachers provide an education as well as schooling. They should be applauded for it.

English: Primary School in "open air"...
English: Primary School in “open air”, in Bucharest, around 1842. Wood engraving, 11x22cm (Photo credit: Wikipedia)

 

Random musings

sigh-ness#1
sigh-ness#1 (Photo credit: parth joshi)

 

My musings are pretty random anyway, so here’s some musings on randomness.

Most people have an inkling of what the word ‘random’ means, but if you try and tie it down, it proves to be a concept that is difficult to define. OK, let me start with a dictionary definition from Dictionary.com:

Lacking any definite plan or prearranged order; haphazard

That’s just one of many similar definitions of ‘random’ to be found at Dictionary.com. But hang on a minute – isn’t having no definite plan a plan of sorts. We can imagine Mad King Wotzit from Philopotamia talking with his generals. “Look, we don’t know where the enemy is, and we don’t know many of them there are, and we don’t know if they have muskets, so the plan is to go ahead with no plan and react to circumstances as they arise. Are we all agreed?”

Coup d'oeil #25
Coup d’oeil #25 (Photo credit: ryansarnowski)

I don’t think that definition is strong enough. We often proceed without a plan, but not randomly, and the obstacles in our way may appear haphazard but there will be a reason why every single one exists.

Randomness for a mathematician, a statistician or a philosopher is something deeper. Take, for instance, the tossing of a coin. It may come down head up or tail up and there are no other options (if we declare the case where it lands on its edge as a no throw). So a sequence of throws could go H, T, T, T, H, T…..

 

Commandant of the Marine Corps James T. Conway...
Commandant of the Marine Corps James T. Conway participates in the coin toss at the New Orleans Saints Military Appreciation Game against the Atlanta Falcons at the Louisiana Superdome. (Photo credit: Wikipedia)

The critical thing is that any toss doesn’t depend on any of the previous tosses, so it has a 50% chance of being heads and 50% chance of being tails. If we have tossed the coin one million times we would ‘expect’ to get 500,000 heads  and 500,000 tails, but, if fact we may get 499,997 heads meaning we tossed a tail 500,003 times. The average number of heads we would get if we did this a number of times would be very close to 500,000, but it might, by chance, be several hundred away.

English: Five flips of a fair coin. Español: C...
English: Five flips of a fair coin. Español: Cinco lanzamientos de una moneda. (Photo credit: Wikipedia)

Suppose we had thrown the fair coin a million times and we came up with 499.000 heads and 501,000 tails, and we continue for another million tosses. Should we expect more heads this time, so that the average comes out right? I believe that it is obvious that if the coin and tosses are fair, then we cannot tell before hand if the gap between heads and tails would close or get wider. The second million, like the first million will result in about 500,000 each heads and tails.

One-tenth penny coins from British West Africa...

One-tenth penny coins from British West Africa, dated 1936 and 1939. (Photo credit: Wikipedia)

Nevertheless gamblers waste their money on the belief that the odds will even up over time. This is therefore known as the Gambler’s Fallacy.

 

English: Simulation illustrating the Law of La...
English: Simulation illustrating the Law of Large Numbers. Each frame, you flip a coin that is red on one side and blue on the other, and put a dot in the corresponding column. A pie chart notes the proportion of red and blue so far. Notice that the proportion varies a lot at first, but gradually approaches 50%. Animation made in Mathematica–I’m happy to give you the source code if you want to improve the animation or for any other reason. (Photo credit: Wikipedia)

But how do you know if a real coin, as opposed to a theoretical coin is fair. Well, you test it of course. You toss the coin, say 1,000,000 times and see if you achieve 500,000 heads and 500,000 tails. If you get 500,000 heads or near that number, you can say that the coin is ‘probably fair’. What you can’t say, of course, is that the coin is ‘definitely fair’ as the coin could be a dud, but still produce, by chance, the result that a fair coin would.

Shove ha'penny for charity
Shove ha’penny for charity (Photo credit: HowardLake) A coin, at a fair – fair coin?

In addition a real coin is subject to physical laws. Given the starting conditions of the flip, and given the laws of physics, a tossed coin behaves deterministically, resulting in only one possible outcome for the toss. So the toss is not random as people usually use the term. Calculating  what the result might be will likely forever be impossible though.

 

Uni Cricket: Captain PJ and the Coin Toss
Uni Cricket: Captain PJ and the Coin Toss (Photo credit: pj_in_oz)

Do things happen randomly? I don’t believe that real events can be random. If an event is truly random it cannot depend on events that have gone before, because otherwise it would be, in principle, be predictable from the earlier events. The real events that come closest to being unpredictable are decay events and other events at the quantum level, but even there the outcome is fixed, and only the time that the event happens is variable.

 

English: Simulation of many identical atoms un...
English: Simulation of many identical atoms undergoing radioactive decay, starting with either four atoms (left) or 400 atoms (right). The number at the top indicates how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is less random. Image made with Mathematica, I am happy to send the source code if you would like to make this image more beautiful, or for any other reason. (Photo credit: Wikipedia)

Computer science requires randomness for various purposes, most notably for generation of keys for ciphers for encryption. However the numbers that are generated are not truly random, but involve some heavy computation with very large integers. Encrypted information requires decryption, which also requires some very heavy computational lifting. Often extra ‘entropy’ is added from mouse movements and key presses.

 

Thermodynamic system with a small entropy
Thermodynamic system with a small entropy (Photo credit: Wikipedia)

Computer and other physical random numbers can use physical sources such as cosmic rays or the decay of an unstable atom to seed the calculation of a random number. Both the cosmic ray count and the decay of an unstable atom appear to be random locally, but cosmologically both events are the result of the state of the universe and its history to that point in time which is deterministic and deterministic processes are the opposite of random.

 

Thermodynamic system with a high entropy
Thermodynamic system with a high entropy (Photo credit: Wikipedia)

I feel strongly that the universe is deterministic, and at a classical level this is almost indisputable, but at the quantum level things are not so clear and at our current level of understanding, I believe that it is correct to say that happenings at the quantum level appear to be only statistically predictable. I understand that this is not because of some aspect of quantum mechanics that is currently unknown. There are no ‘hidden variables‘. Some other way around this dilemma may be found, probably involving another way of looking at the problem.

 

TESORO DE CORAL, NOSTOC
TESORO DE CORAL, NOSTOC (Photo credit: PROYECTO AGUA** /** WATER PROJECT)

Since the numbers generated by a computational process are not truly random, it is theoretically possible to crack the cipher and decode the message without the key. The numbers involved are so large that this would be extremely difficult and time-consuming using conventional techniques. Quantum computing techniques can theoretically be used to crack current classical encryption schemes.

Mathematical randomness is a totally different thing. Any finite number can be generated by many methods and if the method is known, then the number can’t be called random. This is the basis of a mathematical game where a sequence of numbers is given and the next number is required to solve the puzzle. I don’t like these games because it is possible that two different algorithms may produce the required answer, and an algorithm could be imagined that gives an answer different to the ‘solution’. In other words there is not one unique solution.

 

A roulette wheel.
A roulette wheel. (Photo credit: Wikipedia)

This makes it extremely hard, if not impossible to decide if a ‘black-box’ algorithm (one where the working are unknown) is producing a random sequence of numbers. Beyond that point, I’m not going to go, as I do not have the knowledge, nor currently the space in this post, to make a stab at a decent discussion. Maybe I’ll come back to the topic.

Toledo 65 algorithm - 8 / 12
Toledo 65 algorithm – 8 / 12 (Photo credit: jm_escalante)

 

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Where sex came from

Sex
Sex (Photo credit: danielito311)

When I decide on a topic, I usually hold onto it in my mind, and maybe flesh out a few ideas mentally. I’ve mentioned this before. This topic suddenly came to mind for no good reason, and I haven’t thought of any significant lines of discussion. I wish I could snapshot the “Related Articles” that have popped up, but it looks like they will lead me to places I do not intend to go. An example is “Casual sex isn’t just for college kids”. Mmm. As if college kids a) invented it b) have a monopoly in it.

The Cool Kids
The Cool Kids (Photo credit: TheMarque)

But I digress. Sex. Most living organisms have it. Amoeba, the popularly held archetype of the simple single celled organism, was believed to reproduce simply by fission. I’m unable to understand much of the scientific literature about amoeba reproduction, and there doesn’t seem to be much material about it anyway, but fission, I believe, results in each child organism having half the genetic material of the parent cell.

AMOEBA PROTEUS
AMOEBA PROTEUS (Photo credit: PROYECTO AGUA** /** WATER PROJECT)

Maybe nuclear genetic material is doubled before the split. Maybe each ‘individual’ is half an individual and needs to find another ‘individual’ in the same state to merge with? Merging has been observed in amoeba.

What is certain is the enormous size of the genome of an amoeba species. Some of them have genomes which are more than 200 times the size of the human genome. Amoeba are presented to us in school as possibly the simplest organism that there is. Based simply on the size of genome, this isn’t true.

human genome
human genome (Photo credit: vaXzine)

I can conjecture, based on little to no knowledge at all of the genetics of amoeba, that fission and fusion would enable amoeba species to mix and match their genetic material with much greater freedom than simple sexual reproduction.

So, amoeba splitting and merging could create an enormous genome, even in a simple organism. The size of a genome could be just a result of a less restrictive reproductive process than applies to more “advanced” multi-celled organisms (not to mention more “advanced” single-celled organisms.

Martin Krzywinski, Circles of Life - a compari...
Martin Krzywinski, Circles of Life – a comparison of human and dog genomes (Photo credit: chrisjohnbeckett)

If I’m correct or anywhere near close to correct about the amoeba genome and its reproduction, amoeba may represent an early stage of sexual reproduction. Amoeba were inventing reproduction, in a way. One can imagine that early organisms would absorb other weaker organisms, and in doing so, acquire their genetic material or proto-genetic material.

a haploid cell
a haploid cell (Photo credit: Wikipedia)

Of course in most cases they would simply digest it,  but in those days, the early days of life, when the chemical processes and genetic processes of life were shaking down into the rules that we know today, things would have been more fluid and the genetic material could have been incorporated into the organism’s own genetic material. Indeed, in the beginning the genetic material would probably not be distinguishable from other material in the organism. There wouldn’t have been a nucleus, as such.

English: In telophase, the nucleus of one cell...
English: In telophase, the nucleus of one cell is divided equally into two nuclei.It is the last stage of mitosis and directly proceeds interphase. (Photo credit: Wikipedia)

One can imagine that in the beginning, organisms just didn’t reproduce, by fission or any other method. They would have fairly quickly died out. Then organisms could have happened which just grew and grew until they split. Parts would have died off, parts would have lived.

The parts that survived would have been changed, modified by the environment, until the bits that would have earlier died, survived as new individuals. Maybe they couldn’t themselves reproduce, but eventually, the split off bits would have survived and been able to reproduce.

Diagram of bacterial binary fission.
Diagram of bacterial binary fission. (Photo credit: Wikipedia)

In retrospect, it appears that the best way to be able to reproduce is to separate the reproductive materials and functions mainly into a single location, the nucleus.

Organisms can they reproduce simply by duplication of the genetic information in the nucleus, producing a clone of themselves, which they can hive off as a new individual. Some organisms bud off a clone of themselves as a reproductive process.

Production of new individuals along a leaf mar...
Production of new individuals along a leaf margin of the air plant, Kalanchoe pinnata. The small plant in front is about 1 cm tall (Photo credit: Wikipedia)

This doesn’t allow for change in environment though. A self-cloning organism can’t react to environment changes. However if organisms can exchange genetic material while creating a child, it may be that the child’s genetic make up may allow it to survive where its parents would struggle.

The process used by amoebas, that is to say the process of division and merging of individual organisations could be the first step in that direction. Of course, uncontrolled merging could result in possibly viable individuals with large genomes, which is what we see in some amoeba.

Immature and mature fruits of Cocculus orbicul...
Immature and mature fruits of Cocculus orbiculatus….Trái của dây Sâm, dây xanh, Mộc Phòng kỷ … (Photo credit: Vietnam Plants & The USA. plants)

There are two routes here. Either an organism would clone its nucleus including its genetic material, then split, producing two identical organisms. or it could halve its genetic material and merge with a similarly haploid organism, resulting in a diploid individual.

The advantages of the haploid/diploid cycle are obvious – genetic material is mixed so at least some individuals may survive an environmental change, because the expression of the genome in the individual (the phenotype) allows them to differ from their parents and survive the change.

English: Illustration of the chromosomal organ...
English: Illustration of the chromosomal organisation of haploid and diploid organisms. (Photo credit: Wikipedia)

What is less obvious is why organisms split into male and female sexualities. It’s possible that the difference is caused by the necessity of one set of haploid individuals to supply an environment in which the child organism can develop. The other set of haploid individuals merely supplies the other half of the necessary genetic material.

So the female supplies the support environment plus the genetic material, or egg (ovum) and the male supplies only the genetic material, the sperm. One can imagine that originally organisms would directly exchange genetic material by fusion and fission, like amoeba, but at some time it became more efficient to disseminate genetic material outside the organism.

English: Electron microscope image of sperm.
English: Electron microscope image of sperm. (Photo credit: Wikipedia)

Cells within multicellular organisms or possibly unicellular organisms developed the ability to create new haploid cells with a copy of half the genetic information leaving behind unicellular haploid organisms or haploid cells within a diploid organism.  In female organisms the haploid cell would be an egg and would have the support environment to create a new diploid individual, and in male organism the haploid cell would just have half the genetic material and be a sperm.

Description unavailable
Description unavailable (Photo credit: EYECCD)

There are some hermaphroditic animals, for example some snails and slugs, which produce both eggs and sperms and many plants have both male and female characteristics, but many, many animals have separate male and female individuals. (I’m not keen on saying the majority of animals display sexual differentiation, because I don’t know if it is true.)

English: hermaphrodite symbol
English: hermaphrodite symbol (Photo credit: Wikipedia)

So, when life began it would have been simple unprotected self-replicating molecules. Growth would have been by accretion. At some stage the molecules would have evolved to the point where they developed some structure around themselves, maybe by rejecting some unwelcome molecules. Organelles, small biological factories would have developed as the organisms became more complex, all enclosed in a membrane that allowed the necessary chemicals in and unwanted ones out. This membrane would eventually enclose the nucleus of the cell. More complexity, more biological factories, and the cell would have formed an outer membrane, that enclosed all the necessary mechanisms that modern cells contain and require. (OK, I’m no expert so some of these conjectures may be wrong).

High magnification transmission electron micro...
High magnification transmission electron microscope image of a human leukocyte, showing golgi, which is a structure involved in protein transport in the cytoplasm of the cell. JEOL 100CX TEM (Photo credit: Wikipedia)

Cells would initially have not had any reproductive mechanism. They would grow and then split when they got too big. When cells developed specialised mechanisms for reproduction they needed some way of passing on the genetic material. Some cells would have developed a method of creating haploid individuals and these would have then merged with other haploid individuals to create normal diploid individuals.

English: Male and Female Superb Fairy-Wren.Tak...
English: Male and Female Superb Fairy-Wren.Taken in Ensay, Victoria. (Photo credit: Wikipedia)

Or maybe so-called haploid individuals arose first and diploid individuals arose from the merger of two haploid individuals.  When multi-cellular organism arose, they evolved special organs related to reproduction. Such organs created haploid versions of the organism and a method of delivery to the outside world of these eggs and sperm.

Once individuals have evolved to specifically create eggs or sperm, they are sexual individuals. If an individual evolved to create a support system for their haploid genetic material, for example eggs, it would find it difficult to find similar individuals to merge with since eggs are not particularly mobile. Sperm on the other hand are specialised to be mobile, so are ideal for merging with the eggs.

English: Male and female Sockeye salmon (Oncor...
English: Male and female Sockeye salmon (Oncorhynchus nerka) specimens. (Photo credit: Wikipedia)

Once the individuals have sexual differentiating characteristics this would flow through to the phenotype (physical expression of the genetic material – the multi-cellular organism). And that is my guess, as a complete amateur in the field of genetics is where sex came from. So the above may make sense at some level, or not. Even it does make a sort of sense, I may well be wrong about the detail! But it has been fun speculating.

here comes life
here comes life (Photo credit: AlicePopkorn)

 

 

 

 

 

 

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Death of print

English: A stack of copy paper.
English: A stack of copy paper. (Photo credit: Wikipedia)

It’s amazing how the world has changed in a lifetime. My lifetime. Phones, TV, the Internet, electronic funds transfers, payment by waving a plastic card.

My parents were paid by their employers in cash and they paid for everything in cash. Most people didn’t have cars and relied on public transport and paid in cash for their tickets. Today cash is endangered.

Money Cards
Money Cards (Photo credit: jacqui.brown33)

A little later, people started to acquire bank accounts, usually in conjunction with a mortgage. Their pay was paid into their bank accounts and the mortgage payments were extracted from the bank account directly. The thing was, the bank account came a lot of paperwork. There were statements and cheque books. To whip out a cheque book and offer to pay for something was a real show of status. Today cheques are almost unused, being almost completely replaced by credit cards, debit cards and charge cards. Some younger people have never seen a cheque and most shops will not accept one. Many banks will supply statements over the Internet these days.

English: 1912 US cartoon by Rollin Kirby, show...
English: 1912 US cartoon by Rollin Kirby, showing George Walbridge Perkins (with a check book symbolizing control of money) and Amos Pinchot (weilding a letter of support from Theodore Roosevelt campaing manager Senator Joseph M. Dixon) battling for control of the U.S. Progressive Party. Figure in the distance presumbably represents Roosevelt coming with his “big stick” to settle things. (Photo credit: Wikipedia)

Most people got their news through newspapers. Paper newspapers, from the rarefied air of the Times to the slightly more foetid air of the tabloids. The network of distribution of news via started from the printing presses and initially was distributed by vans, trains, and more vans. Bundles of papers were dropped off at strategic points, and newsagents picked them up, sorted them and gave them to young boys and girls to distribute, dropping them into letter boxes, countrywide.

Galveston, Texas, 1943. Newspaper delivery boy...
Galveston, Texas, 1943. Newspaper delivery boys with bicycles. (Photo credit: Wikipedia)

A similar distribution network was used for the evening papers. These however were distributed mostly to the streets around business places and railway stations and similar places where people would pick them up on their way home from work. The main headlines would be prominently displayed as teasers to persuade people to buy them.

Checking the headlines
Checking the headlines (Photo credit: gato-gato-gato)

Newsagents existed to distribute the paper that the news was printed on. As a sideline, they would sell other things, like magazines, tobacco, and confectionery. As newsprint volumes have fallen, the old time newsagents had to specialise in something else, like the confectionery that they used to sell as a sideline, or in some cases groceries, particularly the staples such as canned foods and milk. Some might sell books or glossy magazines, but even these versions of print material are under threat.

dakar newsagent
dakar newsagent (Photo credit: noodlepie)

My letter box is still full of paper. Much of it is the ubiquitous junk mail, of course, the flyers and offers which advertisers hope will entice us into buying. It appears that the expense of creating and sending junk mail is still worthwhile, or so the advertisers believe. Some of the paper is comprised of what can loosely be called “community newspapers”. These papers, largely funded by advertising, and run on the cheap, are distributed free, and contain local news only, mainly sports and local politics.

“Letter boxes” in the UK are slots in the front door of a house, not actual boxes on poles as in many other countries.)

English: Letter Box Detail of an old front doo...
English: Letter Box Detail of an old front door which now graces a small shed. (Photo credit: Wikipedia)

What my letter box rarely contains is an actual letter, written by someone, stamped and posted by someone, sorted and delivered to my letter box by a real postman. There are a few firms that still insist on paper invoices and local tradesmen tend to still prefer papers invoices but apart from that and a few real letters from older relatives, I receive little real mail these days. No wonder that postal services world-wide are having issues.

Typical advertising mail
Typical advertising mail (Photo credit: Wikipedia)

It is easy to see the reason for the decline of the print industries world-wide. In a word, the Internet. When it is simple and cheap to sit at a computer and type an email, or finger tap a  message into a tablet or phone, and have a response in minutes, why would anyone manually write a letter, find an envelope, find or purchase a stamp, and find a post box to drop the letter in? Although the vast majority of letters get through safely, there are exceptions, while email is almost certainly going to be delivered and you will get a message if your email doesn’t go through.

Email email email
Email email email (Photo credit: RambergMediaImages)

Similarly in banking. Once every transaction had a paper trail. All transfers and payments were neatly written in books, all ledgers were balanced by hand and banks shifted huge numbers of notes, cheques, coins and other forms of paper money. These days I rarely carry cash, and I haven’t seen or used a cheque in years.

I do all my banking on the Internet, using my computer or phone. I pay for things, even small things like a cup of coffee (actually I drink tea), with a debit card, with a credit card as backup for emergencies. Gas stations, grocery stores, tradesmen, and every other kind of store takes the plastic.

Swipes, Bytes, and Debit Cards
Swipes, Bytes, and Debit Cards (Photo credit: SimpleIllustrations)

More and more our transactions with government departments, like car licensing or tax matters, are conducted online. Even if you have to go in to a government agency for some matter or other, they will scan your documents rather than copy them. If you fill in a paper form, they will transfer the data to their computer systems while you wait.

Picture Scanner
Picture Scanner (Photo credit: Wikipedia)

In all fields, except possibly the field of junk mail, paper is being used less and less. Even magazines are headed online, with smartphone apps for New Scientist magazine allowing you to read it anywhere that you may be. An added advantage of on-line magazines is that the electronic copy is, in general, cheaper than the paper version.

HTC Aria android 2.2 smart phone review www.li...
HTC Aria android 2.2 smart phone review http://www.liewcf.com/review-htc-aria-android-2-2-6878/ (Photo credit: Wikipedia)

I have forgotten, until now, that I was going to mention books. Books are nice objects to hold, and they make a nice addition to one’s decor. I enjoy reading a book and have several shelves full. Maybe 200 books? But on my electronic devices I have maybe 10 times that number. OK, most are old classics, which are out of copyright, but a number I have bought specifically to read on-line. An on-line reader keeps your place, let’s you bookmark passages and allows you to quickly search for something that you read somewhere in your on-line collection.

books
books (Photo credit: brody4)

Books are not yet redundant, but they are slowly heading on-line. While it may not be soon, and while not every book will disappear on-line, printed books may become rare and expensive.

Print is dying everywhere and the amazing thing is that it has happened in a short period of time. The spread of computers first caused volumes of paper generated to increase, but the Internet and the way that it has allowed sharing of documents, plus the smaller and faster computers and hugely capacious hard drives, culminating is the ubiquitous smart phones has saved millions of trees from destruction.

Tree in Fog
Tree in Fog (Photo credit: Photomatt28)

 

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Two-ness

Lane #2 Swimming
Lane #2 Swimming (Photo credit: clappstar)

Last week’s post was going to be about the number two, but I got diverted into talking about existence/non-existence instead. Existence/non-existence is only one of the many attributes that comes in only two possible varieties or types. Up and down, left and right, in and out, positive and negative.

These attributes might be associated with another attribute representing a magnitude, such as distance, weight or other attribute. So we may say 20 metres to the left, thus locating the object or event in relation to the datum or origin. Both attributes are required in such circumstances, since the directional attribute (left/right) does not completely locate whatever it is, event or object. Neither does distance, by itself, locate the event or object.

Directions
Directions (Photo credit: Gerry Dincher)

Relative to datum, in a three dimensional world, any three axes define direction and the datum itself divides the direction into two opposite parts. If you include the fourth dimension of time, the datum, now, still divides the direction into two parts, before and after. This of course can be extended to as many dimensions as you may choose to conjecture.

English: A compact convex set has finite perim...
English: A compact convex set has finite perimeter in dimension 2 Français : Figure illustrative du fait qu’un compact convex est de périmètre fini en dimension 2. (Photo credit: Wikipedia)

One interesting two-ism is the two-ism of a mirror. When you look in the mirror you see an image of yourself. When you move your left hand, the image appears to move its right hand, and the image’s hair parting appears to be on the opposite side to yours. This is a mind trick, since if you see a person raise the hand on their right as you look at them, your mind says that it is their left hand that has been raised. If they have a parting on the left as you look at them, your mind tells you that their parting is on their right.

English: : A mirror, reflecting a vase. Españo...
English: : A mirror, reflecting a vase. Español: : Un espejo, reflejando un vasija. (Photo credit: Wikipedia)

This illusion is so strong that people misunderstand the reason why words appear reversed in the mirror, and why it is hard to trim your moustache, or pluck hairs in the mirror.

Many people are puzzled because a mirror appears to reverse things left-to-right but not up-to-down. It doesn’t – your left hand is still on the left, and your right hand is still on the right, your head is still at the top and your feet are at the bottom.

Flowers in Mirror Image
Flowers in Mirror Image (Photo credit: ClaraDon)

The trick is that your nose is closer to the mirror than the back of your head and the same is true of the image. The image’s nose is closer to the mirror than the back of the image’s head. If you draw a map of yourself, the mirror and the image, you will see that the mirror reverses the axis between the original and the image. The front/back axis. Once you see that, it is obvious, and it is hard to see how you could have thought otherwise. It doesn’t help your coordination when you part your hair though!

"The Strange Case of Dr. Jekyll and Mr. H...
“The Strange Case of Dr. Jekyll and Mr. Hyde” (Photo credit: Profound Whatever)

When we consider the number two, it is an interesting integer, the second of the natural numbers. Interestingly we use the second ordinal number to describe the second natural number, and we use the second ordinal number in that definition too. I’m sure that the circular nature of this description is apparent.

English: Odd numbers : Even numbers Sedgefield...
English: Odd numbers : Even numbers Sedgefield Close of course. Somehow at the time this sign just seemed odd. Even now it still does. (Photo credit: Wikipedia)

I’m a fan of the axiomatic approach to number theory. An axiomatic system consists of a set of axioms that are used as the basis of reasoning. A theorem in such a system is a set of steps leading from a premise to a conclusion. A premise should be the conclusion of a previous theorem.

Skipping a lot of details, one axiomatic approach is to define a function S, the successor function. S(x) then refers to the successor of x, where x is a natural number. So S(7) is 8, S(1,000,000) is 1,000,001. S(1) is 2, and we have a non-circular definition of the number 2. Erm, almost. The number and its successor form a pair and a pair has how many members? Two. There’s still a whiff of circularity there, to my mind.

Two of Arts - 2000 Visual Mashups
Two of Arts – 2000 Visual Mashups (Photo credit: qthomasbower)

Two is an even number and the first of them. An even number is a number which can be split into two in such a way that the two parts are the same number. To put it another way, if you take an even number of stones and put them alternately into two piles, you will be left with two piles each with the same number of stones. If you take an odd number of stones, and perform this test, you will find that the two piles have a different number of stones.

Stone Texture
Stone Texture (Photo credit: Poe Tatum)

If you consider the set of even number and the set of all natural numbers you might conclude that there will be less even numbers than natural numbers. Paradoxically, there are as many even numbers as there are natural numbers.

It is possible to demonstrate this by a process of mapping the even numbers to the natural numbers. 1 then maps to 2, 2 maps to 4, 3 maps to 6 and so on. This mapping process is also called ‘counting’. For each and every natural number there is a corresponding even number and for each and every even number there is a natural number. The two sets of numbers map one to one. If two sets map one to one, it is said that their cardinality is the same, or in common language, they are the same size.

Pack of playing cards.
Pack of playing cards. (Photo credit: Wikipedia)

We are more used to finite sets of things (like the set consisting of a pack of cards) than infinite sets of things (like the set of even numbers or the set of natural numbers). If you take half the members of a finite set away, you have a smaller set of things. For example if you take all the black cards out of a set consisting of a pack of cards, the resulting set is smaller, but for infinite sets of things like the natural numbers this is just not true. If you take the odd numbers from the set of natural numbers, the resulting set of even numbers is the same size as the original set, not smaller.

English: Combe Martin, The "Pack 'o Cards...
English: Combe Martin, The “Pack ‘o Cards” Inn. Built to relate to a pack of cards, i.e. 4 floors to represent suits in a pack and 13 fireplaces to correspond to the number of cards in a suit and reputedly 52 windows as per the number of cards in a pack. (Photo credit: Wikipedia)

Much of the above is far from rigorous, and I’m aware of that. However, the main thrust of the arguments is still, I believe, valid. Numbers are fascinating things, with each one having unique properties, and a whole lifetime could be spent considering just one number.

English: Unusual chimney These brick chimneypo...
English: Unusual chimney These brick chimneypots can be seen on the original school building, dated 1857, which lies behind its successor, see 438699. (Photo credit: Wikipedia)

 

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Existence of things – Ontological questions

unfolding
unfolding (Photo credit: ecstaticist)

“Just the two of us”. This song by Bill_Withers encapsulates the idea of a pair of people (male and female from the context) and the separation of the pair from everyone around them. The lyrics assert that “we can make it if we try”, although what “it” refers to is not made apparent. It’s a pleasant, smooth song and serves well enough to introduce my post for this week. I like it.

Eggistentialism 1.5 or Three of a Perfect Pair
Eggistentialism 1.5 or Three of a Perfect Pair (Photo credit: bitzcelt)

The idea of a couple or pair is a concept that acts to separate or compartmentalise one object and another related object from all possible instances of the class of object. Eleven and twelve. Fred Astaire and Ginger Rogers. POTUS and FLOTUS. Mercury and Venus.

It can also relate members of one class of object with another class of object. Seven and fourteen (the seventh natural number and the seventh even natural number).  28th and January. “x” and “y”.

Complete coloring sample of Clebsch Graph with...
Complete coloring sample of Clebsch Graph with 8 colors (Photo credit: Wikipedia)

It can also be a generator of other objects. The number one and the operation of addition leads to two, three, four and so on for ever. (OK, I missed a huge chunk of detail there and it is nowhere near as simple as that).

Another twoism is the concept of opposites. Black and white, top and bottom, man and woman. OK, that last concept is a bit blurry these days, but everyone (with the exception of a few genetically different individuals) is genetically male or female. XY or XX.

DNA, human male chromosomes
DNA, human male chromosomes (Photo credit: Wikipedia)

The big twoism is the concept of existence/non-existence. Is there a river of lava flowing through my garden? No, there isn’t. Such a river does not exist. But if I lived in Iceland or in Hawaii, or in another location near a volcano, such a river might exist. My cat Madonna doesn’t exist, but my dog Ben does.

This seems such a definite concept, but looked at a bit closer, and it begins to get fuzzy. There is in fact a river of lava flowing through my garden! Eh? Well let me start up Minecraft and the world where I’ve been building a garden, with a lava river flowing through it.

Minecraft/DwarfFortress Entrance with Lava Trap
Minecraft/DwarfFortress Entrance with Lava Trap (Photo credit: colmmcsky)

Of course you might argue that the Minecraft world doesn’t really exist. But it does! It exists in Minecraft, and Minecraft exists in this world, so the Minecraft lava river exists in this world. If A exists in B, and B exists in C then A exists in C.

Actually the Minecraft world only exists in my thoughts. I haven’t built a garden in Minecraft and I haven’t got a river of lava flowing through it, but by the logic above, the river of lava exists in my mind in a Minecraft world, my mind exists in the real world, so the river of lava exists. If A exists in B, and B exists in C then A exists in C.

English: illustration for the transitive relat...
English: illustration for the transitive relation Magyar: illusztráció a tranzitivitáshoz (Photo credit: Wikipedia)

Of course, some people might have issues with that logic. Does the lava river really exist? Well, I maintain that it does, but it is necessary to specify that it exists in my mind. Anything that I can think of exists in my mind and since my mind is part of the real world, “anything that I can think of” exists in the real world.

There is a difficulty here. Consider the sentence “The present King of France is bald“.  The issue is whether or not this sentence is true. It would appear not, since there is no present King of France, but the negation “It is not true that the present King of France is bald” is also (apparently) not true. The difficulty is that there is no present King of France, since France is a republic.

Portrait of Louis XIV
Portrait of Louis XIV (Photo credit: Wikipedia)

However “the present King of France” exists in my mind, and the mind of anyone who reads the sentence. The King of France in my mind may be bald or he may not, so the sentence may be true or false, and the difficulty does not arise. Provided we consider the sentence as applying to a mental image of the King of France.

The King of France, bald-headed or not, exists in my mind if I consider him, and my mind exists in the real world so in that sense he exists. What though, of the existence of things that exist in the real world, but differently in one’s mind?

Paradoxes, I
Paradoxes, I (Photo credit: Newtown grafitti)

The British TV Series “Call the Midwife” is set in the 1950s. It is obviously not the 50s. At the time Queen Elizabeth was about to ascend the throne, or had already done so. Does Jenny Lee live at Nonnatus House? Since neither exist in the real world, my argument above applies. However,  consider the question “Has Queen Elizabeth II ascended the throne yet?” We have no difficulty in ascertaining that the question is most likely about a fictitious or historical event, since it is well known that she has been Queen for a long time.

Coronation of Queen Elizabeth II X
Coronation of Queen Elizabeth II X (Photo credit: Wikipedia)

I suggest that the same is true of the bald/not bald King of France. We know that there is no present King of France so can conclude that the King of France in question must be a historical or fictional figure. If I have no preconceptions about the fictitious King of France, I might envisage him in ‘period’ costume with a huge powdered wig (is that in period? I’m not sure), so I would probably guess that he was shaven-headed if not bald. But you might disagree. Your “present King of France” could sport a full head of hair.

One Young Man in a Powdered Wig
One Young Man in a Powdered Wig (Photo credit: Emily Barney)

But what of things that don’t exist in the (loosely speaking) real world, and no one has ever thought about? Do they exist in any sense? I believe that the Universe is deterministic, so any future event or thing, is implied by the current state of the Universe, so if anyone will think of something, or if some event happens in the future, then it exists in the present, and not even simply as a potential. If the Universe is deterministic, it must happen.

I was going to talk about Schrödinger’s cat in the context of existence but he was squeezed out by the present King of France. Maybe I’ll get to the cat in another post.

English: Diagram of Schrodinger's cat theory. ...
English: Diagram of Schrodinger’s cat theory. Roughly based on Image:Schroedingerscat3.jpg (Photo credit: Wikipedia)

 

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Little Green Men revisited.

Offset Gregorian antenna used in the Allen Tel...
Offset Gregorian antenna used in the Allen Telescope Array, a radio telescope at the University of California at Berkeley, USA. (Photo credit: Wikipedia)

I’m going to continue the LGM theme. I don’t plan on doing multiple posts on a single subject very often, but there were some things that I want to add to my previous post.

It seems to me that the difficulties of point to point interstellar communication are such that it makes it unlikely that we will be able to find LGM by searching for intentional broadcasting or unicasting of signals, for the reasons that I raised in the previous post. There are other reasons that I haven’t touched too.

 

Radio Transmission Towers Atop Mt. Wilson
Radio Transmission Towers Atop Mt. Wilson (Photo credit: FastLizard4)

One big question is one that occurs to me, probably because I am a computer professional. Why would a civilisation want to be found? If you broadcast something on the Internet, you attract all sorts of undesirables trying to access your systems, your data, your private stuff.

 

US Mail
US Mail

 

Some of the undesirables might be governments of course, depending on your point of view and political affiliations. On a more personal level, people have told friends on social networking sites of a private party and hundreds of people have read this and gatecrashed. As a consequence the party gets overrun and the house gets trashed, the police get called.

 

A party at Colorado State University -- yeah, ...
A party at Colorado State University — yeah, that’s a riot. (11pm on April 27) …item 2.. a combination of Woodstock, ‘Animal House’ and Girls Gone Wild. (08/30/2011) … (Photo credit: marsmet553)

If you broadcast to the Universe the same sort of thing might happen. The LGM might not be friendly and with benign intent. Why would you risk attracting undesirables? Of course, the civilisation sending the signals may not be benign. Such a signal could be a honeypot, designed to attract unwary civilisations.

 

Lavender Attracting Bees
Lavender Attracting Bees (Photo credit: rutthenut)

So, it seems that it might be unwise to respond to alien signals. Murray Leinster’s novelette “First Contact” explores the issues, albeit in a first contact away from the origins of the contactees.

 

Two technologically equal species are making first contact in deep space. Both desire the technology and trade the other can provide, but neither can risk the fate of the home planet based on unfounded trust.

Another danger would be encountering a more advanced civilisations. In all cases where this has happened on earth, this has always resulted in disaster and absorption of the less advanced civilisation. This usually starts with disease, both sexual and non-sexual, which may be common in the more advanced civilisation but which the less advanced civilisation has no defence against. However, ultimately it is foreign ideas that cause the destruction of the less advanced civilisation and there’s no vaccine against that.

 

With masks over their faces, members of the Am...
With masks over their faces, members of the American Red Cross remove a victim of the Spanish Flu from a house at Etzel and Page Avenues, St. Louis, Missouri. (Photo credit: Wikipedia)

So, maybe we should avoid alien civilisations, at least until we can be sure that contact will not harm us. But how will we know that they are there, so that we can avoid them? Can we detect them before we blunder into something we can’t handle?

 

One possible way would be to observe the rate of emission of radio waves from a stellar system. If the electromagnetic spectrum emission in the wavelengths that are used for TV and radio is unusually high, it may indicate that a civilisation exists in the stellar system.

 

United States radio spectrum frequency allocat...
United States radio spectrum frequency allocations chart as of 2003 (Photo credit: Wikipedia)

So if an otherwise unremarkable star should suddenly (in astronomical terms) start emit radio waves it might indicate that an advanced civilisation might have discovered radio on a planet orbiting the star. Or, rather, that it did discover it, a long time ago. If we did discover such a star (and I’ve no idea if it is remotely possible to detect such an anomalous production of radio waves), it may be thousands of light years away, which means that the waves have been on their way for thousands of years.

 

A supernova remnant about 20,000 light years f...
A supernova remnant about 20,000 light years from Earth (Photo credit: Smithsonian Institution)

If we then send an expedition to a star at, say 20,000 light years, it would take us 20,000 years at least to get there, and probably many, many more. That 40,000 years that would have passed since the wave were generated and no civilisation that we know off has lasted for more than a few hundred. They might have all died out or reverted to savagery or evolved into something that we can’t understand. We might have done similar in the 20,000 years that it would take to get there.

 

Cycle of paintings History of civilisation in ...
Cycle of paintings History of civilisation in Poland. (Photo credit: Wikipedia)

It’s unclear why we would want to contact them anyway. A conversation that takes millennia would be a strange one. About all we could say would be “Hi from Earth. Here are some snaps from our family album”. Of course, when we decode their signals, as XKCD notes, we would most likely find that they are unintentionally broadcasting the alien equivalent of cheesy TV shows like “I Love Lucy” or contrived  “reality” shows. After all, that’s what we have been broadcasting.

 

Fox Reality Channel
Fox Reality Channel (Photo credit: Wikipedia)

All of the above is moot as is my previous post if the LGM do not exist. The most famous attempt to estimate the likelihood of there being other civilisations other than ours out there is the Drake Equation. As I mentioned in my previous post, this equation irritates real mathematicians, since it is not derived from anything, but is merely a string of terms strung together to look like an equation. Plausible values for the components of the equation can give answers ranging from almost zero (there are no other civilisations other than ours in our galaxy) to 38 million or more.

 

"Where is Everybody?", or "Why ...
“Where is Everybody?”, or “Why am I so Lonely?”: Fermi’s Paradox / the Drake Equation, Logocentrism and Gabriel Garcial Marquez (Photo credit: timtak)

The SETI Institute concludes that “The importance of the Drake Equation is not in the solving, but rather in the contemplation”. Certainly the values of most of the terms of the equation are not really known, though estimates can be made. Investigation of one term may throw up information which throws some light on the other terms.

 

Drake Equation
Drake Equation (Photo credit: Merritt Boyd)

The crucial term is, I feel, “L”, the length of time that a civilisation will be able to and desire to make radio signals. Looking at how we have used radio waves, there seems to be a trend from the low end to the high and very high end of the broadcast spectrum. Early experiments and usage was in the VLF (very low frequency) band, but the frequencies used for most radio broadcasting moved to medium frequencies. TC, both digital and analog use VHF (Very High Frequencies) and UHF (Ultra High Frequencies). Satellite broadcasts use even shorter wavelengths (higher frequencies). So our radio usage has changed over the 100 years or so that we have had radio receivers and transmitters.

 

Aerials
Aerials (Photo credit: ettlz)

All in all I think that it is unlikely that we will contact LGM. We may stumble over some, if we ever manage to go Interstellar, and it may be that some as yet unknown technology might enable us to easily spot advanced civilisations from a distance, so that we can signal or visit, but although I applaude the SETI effort I don’t think that the search will be fruitful.

 

SETI@home logo
SETI@home logo (Photo credit: Wikipedia)

It may be that we can never visit other stars because no way exists for us to do so. In a story that I once read, but can no longer remember the name of, one character referred to star systems as “God’s test tubes”. I recall that at the end of the story the human race had just found a way to escape its “test tube”.

 

A,B,C - test tubes
A,B,C – test tubes (Photo credit: Wikipedia)
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