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Numbers are fascinating

Numbers fascinate me. What the heck are they? They seem to have an intimate relationship with the “real world”, but are they part of it? If I heave a rock at you, I heave a physical object at you. If I heave two rocks at you, I heave real objects at you. It’s a different physical experience for you, though.

If I heave a third rock at you, again, it’s a different qualitative experience. It’s also a different qualitative experience from having one rock or two rocks thrown at you.

Numbers come in three “shapes”. There are cardinal numbers, which answer questions like “How many rocks did I throw at you?” There are ordinal numbers, which answer questions like “Which rock hit you on the shoulder?” Finally there are nominal numbers, which merely label things and answer questions like “What’s you phone number?”

As another example, in the recent 10km walk which I took part in, I came sixth (ordinal) in my age division. That sounds good until I admit that there were only seven (cardinal) entrants in that division. Incidentally, my bib number was 20179 (nominal).



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Cardinal numbers include the natural numbers, the integers and the rational numbers and the real numbers (as well as more esoteric numbers). For instance the cardinal real number π is the answer to the question “How many times would the diameter fit around the circumference of a circle?”

It’s a bit more difficult to relate ordinal numbers with real numbers, but the real numbers can definitely be ordered – in other words a real number ‘x’ is either bigger than another real number ‘y’, or vice versa or they are equal. However, there are, loosely speaking, more real numbers than ordinals, so any relationship between ordinal numbers and real numbers must be a relationship between the ordinal numbers and a subset of the real numbers.

English: Example image of rendering of ordinal... — English: Example image of rendering of ordinal indicator º Italiano: Immagine esemplificativa della resa grafica dell’indicatore ordinale º (Photo credit: Wikipedia)

Subsets of the real numbers can have ordinal numbers associated with them in a simple way. If we have a function which generates real numbers from a parameter, and if we feed the function with a series of other numbers, then the series of other numbers is ordered by the way that we feed them to the function, and the resulting set of real numbers is also ordered.

So, we might have a random number generator from which we extract a number and feed it to the function. That becomes the first real number. Then we extract another number from the generator, feed it to the function and that becomes the second real number, and so on.

The random map generator provides a limitless ... — The random map generator provides a limitless supply of colourful terrains of various themes. Open island maps, like this one, allow players to use airstrikes. Cavern maps have an indestructible roof which cannot be passed. (Photo credit: Wikipedia)

What we end up doing is associating a series of integer ordinal numbers with the generated series of real numbers. These ordinal numbers are associated with the ordered set of real numbers that we create, but the real numbers don’t have to be ordered in terms of their size.

Nominal numbers such as my bib number are merely labels. They may be generated in an ordered way, though, as in the case of my bib number. If I had registered a split second earlier or later I would have received a different number. However, once allocated they only serve to show that I have registered, and they also show which event I registered for.



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On the occasion that I took part there were two other events scheduled : a 6.5km walk and a half marathon. My bib number indicated to the marshals and officials which event I was taking in and which way to direct me to go.

I’m not a mathematician, but it seems to me that ordinal numbers are more closely aligned to the natural numbers, the positive integers, than to any other set of numbers. You don’t think of someone coming 37 and a half position in a race. Indeed if two people come in at the same time they are conventionally given the same position in the race and the next position is not given.

There’s a fundamental difference between natural numbers or the integers, or for that matter the rational numbers and the real numbers. The real numbers are not countable : they can’t be mapped to the natural numbers or the integers. The rational numbers can, so can be considered countable. (Once again, I’m simplifying radically!)

Natural numbers and integers are related to discrete objects and other things. The number of dollars and cents in your bank account is a discrete amount, in spite of the fact that it is used as real number in the bank’s calculations of interest on your balance. If I toss two rocks at you that is a discrete amount.

English: Causal loop diagram (CLD) example: Ba... — English: Causal loop diagram (CLD) example: Bank balance and Earned interest, reinforced loop. Diagram created by contributor, with software TRUE (Temporal Reasoning Universal Elaboration) True-World (Photo credit: Wikipedia)

Even I tip a bucket of water over you, I douse you in a discrete number of water molecules (plus an uncertain number of other molecules, depending on how dirty the water is). However the distance that I have to throw the water is not a discrete number of metres. It’s 1.72142… metres, a real number.

At the level at which we normally measure distances distances don’t appear to be broken down into tiny bits. To cover a distance one first has to cover half the distance. To cover half the distance one must first cover one quarter of the distance. It is evident that this halving process can be continued indefinitely, although the times involved are also halved at each step.



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This seems a little odd to me. Numbers are at the basis of things, and while numbers are not all that there is, as some Greek philosophers held, they are important, and, I think, show the shape of the Universe. If the Universe did not have real numbers, for example, then it would be unchanging or perhaps motion would be a discrete process, like movements on a chess board.

If the Universe did not have any integers, the concept of individual objects would not be possible, since if you could point at an object you would have effectively counted “one”. In other words we need the natural numbers so that we can identify objects and distinguish one from one another, and we need the real numbers so that we can ensure that the objects don’t all exists at the same spot and are, in fact separated from one another.

Visualisation of the (countable) field of alge... — Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate degree of the polynomial the number is a root of (red = linear, i.e. the rationals, green = quadratic, blue = cubic, yellow = quartic…). Points becomes smaller as the integer polynomial coefficients become larger. View shows integers 0,1 and 2 at bottom right, +i near top. (Photo credit: Wikipedia)

The Search for the Fundamental

Motion of gas molecules Español: Animación mos... — Motion of gas molecules Español: Animación mostrando la agitación térmica de un gas. Cinco partículas han sido coloreadas de rojo para facilitar el seguimiento de sus movimientos. Русский: Хаотическое тепловое движение на плоскости частиц газа таких как атомы и молекулы (Photo credit: Wikipedia)

When does it stop? This screen that I am looking at, the keyboard that I am typing on, the invisible air between my eyes and the screen, even my body, all are composed of atoms, I told and believe. Apart from atoms, all there is is radiation, of various sorts.

The ancient Greek philosophers didn’t know about atoms so proposed various theories, which today seem quaint, but eventually they came around to atomism, and abandoned the other theories. In particular the theory of the four classical elements, earth, fire, water and air was dropped.

As I said, the theory now sounds quaint, but, given that the ancient Greek philosophers were not of an experimental frame of mind, the four classical elements could explain much of what could be observed. Everything could have been a mixture of these elements in various proportions.

After all, it appeared to work for colours – all colours that can be displayed on a computer screen can be specified in terms of the amount of the three primary colours of red, green and blue that a single pixel or dot on the screen emits. Why shouldn’t this scheme work for other things than light?

However Greek philosophers (and of course, philosophers in other cultures) noticed that, while some things could be broken down into component parts – sugar could be melted and burned, water could be driven off to leave the salts behind, and more importantly alcohol could be evaporated off and collected to make spirits, some things could not be broken down.

Gold, sulphur and phosphorus stubbornly refused to separate into earth, air, water or fire. Of course such stubbornness could be explained by the classical element theory – after all some things are easier to break down than others, but the Greeks eventually dropped the theory in favour of atomism. (This and what follows is highly simplified and condensed).

(Click here for rotating model) (Photo credit: Wikipedia)

This is the belief that everything is made up of small indivisible particles which differ from element to element. The lump of gold contains billions of gold atoms, while the sulphur block contains sulphur atoms.

From about the start of the scientific revolution, people started to work out the rules of chemistry, and the ‘why’ of chemical reactions. Why did carbon in coal burn away and leave an ash? We know that the carbon in the coal burns using the oxygen in the air and creates oxides of carbon which are gasses and not easily detectable, but the experiments which led to this knowledge were preformed in the era of the scientific revolution.



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So, matter is composed of atoms. That seemed to be the end of the story, as the vast majority of chemical experiments could be explained in terms of atoms, but exactly why atom A reacts in fixed proportions with atom B, but won’t have a bar of atom C. These relationships were noted but not really explained.

By the middle of the 19th century scientists began to detect problems with the “atoms as billiard balls” model. Electrons were discovered and soon related to chemistry, answering the above question. The new model, “atoms as small planetary-like systems”, had a small positively charged, and solid nucleus surrounded by a swarm of negatively charged electrons, with the electrons taking a major role in determining the chemistry of the atom.



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It was discovered that many elements behaved as if each atoms of the element weighed the same, but some elements broke this rule. The gas Chlorine for example has an atomic weight of 35.45. In other words each atom weighed about 35 and half times as much as a Hydrogen atom.

It was eventually discovered that not all Chlorine atoms weighed the same. Most had an atomic weight of 35 but some (about half) had a weight of 36. To cut a long story short it was discovered that the supposedly solid nucleus was composed of a collection of other particles called protons and neutrons.

While the number of protons and electrons determine the chemistry of an atom almost completely, the number of neutrons contribute mass to the atom and barely affect the chemistry.

While electrons appear to be truly fundamental particles and cannot be broken down further, the protons and neutrons are composed of particles called quarks. For reasons mentioned in the Wikipedia article quarks cannot be found in isolation, but are only found in other particles.

In addition to protons and neutrons, quarks make up other sub-atomic particles such as mesons. Scientists have discovered or postulated bosons which are particles that bind quarks and other fundamental particles together. From then on, things get complicated!

I haven’t mentioned the photon, which is bosonic, or the neutrino which is a fermion. All fundamental particles fit into one of these two families, and all sub-atomic interactions are the result of the rather incestuous exchange of these particles in their various groups and a strict set of rules. So far so good.

English: Enrico Fermi (Photo credit: Wikipedia)

However, there are still questions to be answered. Are these particles truly fundamental or do they have components, which may or may not be particles in the classical sense? What are the sizes of these particles, if such a concept is appropriate at this level? Have we found them all? What about dark matter?

Scientists have abandoned the first question. They don’t generally refer to particles as fundamental. They have seen a long list of fundamental particles turn out to be not so fundamental after all.



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Sizes of the particles may not make sense at the particle level, but the various theories may indicate sizes for some of them. There are difficulties over the size of the electron for instance. If it were a point object rather than having something that equates to size, then that causes difficulties with some theories.

As for the third and fourth questions, it appears that scientists may have found all the particles that explain ordinary matter, but naturally cautious, they don’t rule out other forms of matter such as the so called “dark matter” and “dark energy“. Dark matter and dark energy apparently interact with gravity and (from the Wikipedia article) and the Weak Nuclear Interaction.

My original question was “When does it stop?” By this I meant, which particles are truly fundamental and which have components that determine their properties? This question remains open, but if you have followed through my exposition, you will probably see that this is a question without an easy answer.



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Mainframes were different

IBM System 360/65 Operator's Panel The IBM Sys... — IBM System 360/65 Operator’s Panel The IBM System/360 Model 65 first shipped in 1966 This photo was taken by Mike Ross of corestore.org . He has given permission via email “Feel free to make use of … my pictures under the GNU license. All I ask is that they are credited & linked…”. –agr 19:07, 17 Aug 2004 (UTC) (Photo credit: Wikipedia)

Mainframes were … different. Today we have devices that have orders of magnitude more processing power than the old mainframes. The old mainframes were big machines that performed business tasks for large organisations and that cost millions of dollars. The phone in your pocket shows you your email, let’s you Facebook or tweet your friends where ever you might be and what ever you might be doing. You can even use it to phone people!

Arguably we fritter away most of the enormous amount of processing power and storage that our hand held devices provide. We watch videos on them, yes, even porn, and play endless silly games on them. And cats. Cats have taken over the Internet and thereby our connected devices.

The fundamental concept of the mainframe is one single powerful(!) computer with all devices, such as card readers, terminals (screen and keyboard, no mouse), printers, tape units and other devices, more or less directly and permanently connected to the computer.

Interestingly, when you typed something into a terminal using the keyboard, it wasn’t sent immediately to the mainframe but was recorded in a buffer in the terminal. When one of a number of keys was hit the whole buffer was sent to the mainframe. These special keys were “Return”, which is similar to the “Enter” key, a “PF Key”, which is similar to a function key, and a few others.

This meant that you could type and edit stuff at your terminal and it would only be sent when you were finished. That is different from the model used by PCs and other modern devices, where every single key press that occurs is sent to the target computer, including typos and correction to typos.

Of course, when you press a key on your PC keyboard, the computer that is the target is the one that the keyboard is connected to, and what you type in goes into a buffer, but the principle still applies. The effect is more obvious if a lot of people are connected to a multi-user computer and are using it heavily, when the response to hitting a key takes a second or so to echo back to the screen.



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Multi-user computers are not common these days as they are not trivial to set up, and computers and networks have become so fast that it is generally easier to change the model and access applications over the network rather than use the direct connect model that was used in the early days.

A lot of the features of modern computing devices originated in mainframes. Mainframes originally ran one job or task at a time, but soon they became powerful enough to run many jobs at the same time. Mainframe operating systems were soon written to take advantage of this ability, but to achieve the ability to run multiple jobs, the operating systems had to be able to “park” a running job while another job got a slice of the processor.

To do that the operating system had to save the state of the process, especially the memory usage. This was cleverly achieved by virtualising memory usage – the job or task would think that it was accessing this bit of memory but the memory manager would make it use that bit of memory instead. The job or task didn’t know.

For instance the job or task might try to read memory location #ff00b0d0 (don’t worry about what this means) and the memory manager would serve up #ffccbod0 instead. Then a moment of so later another job or task might try to read that memory location. It would expect to find its own data there not the first task’s data, and the memory manager would this time serve up, say, #ffbbb0d0.

SVG Graph Illustrating Amdahl's Law — SVG Graph Illustrating Amdahl’s Law (Photo credit: Wikipedia)

The key point is that the two tasks or jobs access the same address, but the address is not real, it is what is known as a virtual address, and the memory manager directs the request to different real addresses. This allows all sorts of cunning wheezes – a job or task can address more memory than the machine has installed and memory locations that have not been used in a while can be copied out to disk storage allowing the tasks in the machine to collectively use more memory than physically exists!

Exactly the same thing happens in your phone, your tablet, or your PC. Many tasks are running at the same time, using memory and processors as if these resources were dedicated to all the tasks. (Actually not all tasks are running at the same time – only as many tasks as there are processors in the processor chip can be running at the same time, but the processors are switched between task so fast it appears as if they are. The same is also true of mainframes).

Of course, there’s a downside to the mainframe model and that is that if the mainframe goes down, everyone is affected. In the early days of the PC era, every PC was independent and if it went down (which they often did) only one or two people, those who actually used the computer were directly affected. So if the Payroll computer crashed it didn’t affect Human Resources.

Soon though the ability to connect all the computers over a network became possible and computing once again became centralised. Things have changed, but the corporate server or servers now fulfil the role that once belonged to the mainframe.



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All the advantages of centralisation have been realised again. Technical facets of the operation of computers have been removed from those whose job was not primarily computing, much to the relief of most them I’d suspect. Backups and technical updates are performed by those whose expertise is in those fields, rather than by reluctant amateurs in the field.

However, the downside is that a centralised computing facility is never as flexible as the end users would like it to be and, somewhat ironically, that as an outage of the old mainframe used to affect many people, so will an outage of a server or servers in the current milieu.

Ganglia report showing editing outage, when Wi... — Ganglia report showing editing outage, when Wikipedia server srv156 stopped responding (Photo credit: Wikipedia)

Too Much Sweetness

Sugar is a the name given by chemists to a family of compounds comprised of Carbon, Hydrogen and Oxygen in various configurations. Generally there are the same number of Carbon and Oxygen atoms and twice as many Hydrogen atoms, but this is not always true.

So far as I know all living things contain sugars, which supply the body with energy through a complex series of chemical reactions which function to slow down the release of energy from the sugar, which would otherwise be released in an unusable burst of energy.

The end result of these reactions is the release of water and carbon dioxide. The cycle of reactions needs as many Oxygen molecules as there are sugar molecules, more or less, assuming the the sugar is fully broken down, and that is why all living things need to take in Oxygen and why we breath out carbon dioxide.

We don’t normally notice the sugar that we take into our bodies as it is largely contained in the foods that we eat. With the exception of the sugar in our tea and that we may scatter on our cereals, it is invisible to us. We actually take in a lot of sugar when we eat things.

In fact we are told that we take in far too much sugar in a modern diet. People drink tea and coffee with sugar, or drink copious amounts of sugar filled soft drinks and we know that this is bad for us. It rots our teeth and makes us fat. It predisposes us to diabetes and other metabolic problems.

The reason that it makes us fat is because early humans (and other animals) had a life which saw feasts and famines as the food supply fluctuated. The body evolved to take advantage of the feast phases by storing energy for the famine times by converting the excess sugars that were ingested to fat. Fat is harder to break down to release its stored energy, and the body preferentially uses any sugars circulating in the body (in the form of glucose).

The aldehyde form of glucose (Photo credit: Wikipedia)

As a species we have a taste for sugar. The body wants to take in as much as it can, in order to keep itself running, and to store up energy as fat for the lean times. However, these days, there are rarely any truly lean times for most people, so they take in more sugars than they need and store it as fat.

There is debate sometimes as to whether or not our desire for sugar amounts to an addition. Personally I don’t feel that it is truly an addiction, just a very strong desire to eat as much sugar containing food as possible. People don’t suffer intense reaction to the withdrawal of sugar from their diet as they would if it were an addition.

Generally they don’t suffer hallucinations, pains, or other mental or physical symptoms. Quite often they even feel better. Quite often they lose weight. Diabetes symptoms may abate, they may sleep better, and other physical problems may disappear.

It seems a no brainer that we should reduce the amount of sugar that we consume in our food and drink, yet we continue to consume it to excess. In my opinion there are at least three reasons for this.

Firstly, the body itself makes us crave sugary foods, as it has evolved to make us feel pleasure when eating something that it can use for fuel and additionally store up for the leaner times that never come. We are predisposed to like sweet things, and our experience tells us that a chocolate bar is sweet.

Secondly, we have been given sweet things as a treat from the time that we are small, and we expect our treats to be sweet. In a restaurant the main course is about protein, usually with some meat or other as the star, but desserts are treats and therefore must be loaded with sugar.

Thirdly, it is absurdly easy to obtain sugar these days. The confectionery aisle of the supermarket has the most shelf space. Cakes and desserts take up shelves of their own, as do soft drinks which are laced with sugar.

That’s a big issue. Everything has sugar in it these days. In the past there was sugar in many things, but I believe that the quantity of sugar was lower. These days there is a large slug of sugar in almost everything.



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It’s even crept into the main course. Glazes and marinades have always had sugar in them as the sugar caramelises on the meat as it cooks, and gives it a nice colour, but many pouring sauces and dressings also contain copious amounts of sugar. Even the humble meat pie contains sugar or so I heard. Something to do with giving the right consistency to the gravy, I believe. So what was wrong with the original ways of thickening it?

This has all led to an issue, so far as I am concerned. I can see all the health benefits of reducing one’s intake of sugar, but so far as others are concerned their bodies are their own responsibility. If they wish to make themselves fat and ill, that is up to them.

English: This is a graph showing the rate of o... — English: This is a graph showing the rate of obesity in adults and the rate of being overweight in both children and adults in the United States from 1960 – 2004. (Photo credit: Wikipedia)

What really annoys me about the sugar in everything trend is that almost everything tastes of sugar! I gave up sugar in tea many decades ago, and I didn’t miss it, but now I hate the taste of tea with sugar in it. I can’t drink it. I also gave up sugar on my morning cereal, which was harder, but I now don’t miss it. There’s already some sugar in it of course so why add more?

But everything else? Everything that you touch at the supermarket is laced with sugar, from the white stuff they call bread to the pickles and sauces you put in your sandwich. As a result, you can’t taste much of anything under the overpowering sweet taste.

Someone once commented when I complained about the overbearing sweet taste of everything, that I could just make my own. That’s fine, and I do do it as much as I can, but it’s not always possible, as the ingredients may already contain sugar, and sometimes i just wants the convenience of picking something off the shelf.

English: Organically produced blackstrap molas... — English: Organically produced blackstrap molasses produced in Paraguay. (Photo credit: Wikipedia)

Thus it was written….

1976 The beginning of flexible computing in pu... — 1976 The beginning of flexible computing in public health. Auditorium A at CDC, converted to a war room for the Swine Flu crisis, is filled with epidemiologists and a Digital Equipment PDP 11 minicomputer the size of a refrigerator. A program called SOCRATES, written in FORTRAN by programmer Rick Curtis, allowed an epidemiologist to define questions, enter data, and summarize the results in tabular form without the aid of a programmer. (Photo credit: Wikipedia)

Have you ever noticed that a computer program never does exactly what you want? Oh, it will process your data for you, and produce results that you can use, or it will move those files from here to here, but may move ones that you didn’t want moving or leave ones that you did want to move. But it won’t do exactly what you want, first time with no hassles.

Of course you can make it work for you, make it do what you want more accurately, but you have to work harder to make it do so, and programs are supposed to make things easier, right? Take this very editor that I am using to compose this post. I thought the bold words above as I wrote, but I needed to perform an action to make them come out bold and another to ensure that the text after the bold words didn’t also come out bold.

JWPce is a Japanese Word Processor, this softw... — JWPce is a Japanese Word Processor, this software is under GNU license. (Photo credit: Wikipedia)

Of course this is a very minor consideration and if I were to find a program that changed the font to bold for one word and then stopped, I’d probably find it irksome to bold two words in succession. Also, I’d bet the house that there would be something that the first program did automatically or easily that would be difficult to achieve using the second program.

Those who are not programmers seem to have an ambivalent attitude to programs. On the one hand, if they are using a program and they can’t get it to work, they blame themselves. “I must be doing something wrong!” comes the impassioned plea. So the technophile in the household has to interpret what helpful statement “It doesn’t work!” really means and what how the program expects in the way of input. Problem fixed. Until the next time.

On the other hand, the non-programmer will accept it without question when the hero/heroine of the film briefly types something at the computer and the world is saved! Hooray! The sentient virus destroying humanity is defeated! Hooray again!

However these issues with programs are not bugs. The program is not doing something wrong. The issue is with our expectations of how things ought to work. It may well be that the program is designed to do things differently to those expectations, either because the programmer assumes that the way that he codes it is the way that people will expect things to work.



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If the programmer gets a lot of issues with a particular feature of his program, he may decide to change it to fit more closely with the expectations of the users, and then send out an update. It is likely that he will then get a lot of issues from those people who have been using the program for a while and have come to expect it to behave the old way. The programmer can never win.

I’ve done quite a bit of programming over the years, thankfully mostly for myself. Every program that is written these days usually fits into what might be called an ecosystem. There are programs to gather data, programs to crunch data, and programs to display the results, but there are many programs to perform each of these three tasks.

For example, the results may be printed on a printer, either as a table of data, or as graph or pie chart, or in these days of 3-D printing, a physical object, or it may be displayed on a screen, or in any other way where the recipient can interrelate with it.

Data input may typed in, drawn in on a graphical input device, or it may be collected by some means or other from sensors or other devices. Your heartbeat may be collected from a number of sensors on your skin, read by a machine and be printed off on a roll or paper, while at the same time being displayed on a local screen. It may also be sent off to some remote location where specialists may peruse it.

In the middle, between input and output comes the processing or crunching of the data. This is what most people think of when they think of computer processing. Somewhat unfairly the input and output processes are relegated to only secondary interest. This is, however, what a program or system is written to do. Even so, input and output processes may be complex.

Data may be processed in several different ways in between input and output, and by several different programs. There are layers within layers. For example a program that takes advantage of a database uses many layers. The program which the programmer is writing will no doubt call programs (called APIs or interfaces) within the environment that he is working in which start the process of communicating with the database.

The API puts the programmers request into a form that the database expects and sends it to another process, not usually part of the programmer’s chosen system, which exists only to connect the programmer’s program (and any other similar programs) to the database.

At the database end the receiving part of the database system receives the request and passes it to the main database program, which checks it and executes it. During the execution process the database program makes calls to system programs which perform any necessary retrieval or writing of the data to the system’s file system, via the system’s hardware interface with the storage system.



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I’ve collapsed many layers in the explanation above. The main point is that the programmer’s program is the tip of the iceberg, and there are many layers which are called into action during the execution of the program. To complicate things further, the system that the programmer uses to perform his work is also a program and has its own layers on top of layers.

This explains why programs don’t ever do exactly what you want. The programmer has to use utility programs which, while flexible can’t do everything. The utility programs are also flexible, but are interfacing with other programs, which while flexible also can’t do everything. And so on.

English: TM-database (Photo credit: Wikipedia)

The more flexible a program is, the bigger it is, as it has be programmed to enable the flexibility. So, this forces constraints on it, which impose constraints on the programmer, whose program therefore imposes constraints on the user of the program. And those constraints are why the program can’t do exactly what you want, but usually, it’s close enough that the program is useful to the end user. Most of the time.

Water, the cause of surfing.

I came across one of those pages on the Internet which state something like “At least a few molecules of the water in your body probably passed through the kidneys of Julius Caesar“. They generally use statistics to show that what they are saying is true.

Only those who believe in homeopathy should be disturbed by this. To anyone else, a molecule of water is a molecule of water, and the fact that it had once been contained in a stream of urine is irrelevant. In any case it is too late. 60% of our body is made up of water, so water from Caesar’s urine is already in us.

Water is a fascinating chemical. It carries stuff around as it is the basis for blood and lymph and all the other fluids of our bodies. It carries nutrients up the stems of plants. It wears away mountains and builds rocks, it cools lava to form other rocks. It brings nutrients to our crops and washes them away. It even sinks ships.

“You are water
I’m water
we’re all water in different containers
that’s why it’s so easy to meet
someday we’ll evaporate together.”
― Yoko Ono

It’s difficult to think of any occurrence in our familiar world which is not mediated or affected by water in some way. Shortage of water to a society is a disaster, as food cannot be produced, leading to famine and deaths.

Water is thought by most people to be liquid at usual temperatures, though there are some places where it is to be found in solid form. Actually there is a great deal of it around in the gaseous phase, or vapour. We measure this airborne water in terms of the humidity or wetness of the air.

Water is extraordinarily pervasive and can be found in all the nooks and crannies in the materials that we have around us. It acts as a lubricate, and if the water is driven off, by heating or chemical means things become stiff and fragile. Even so, water cannot be completely removed from things – even a diamond probably has a few entrapped water molecules.

Water molecules attaching to each other by hyd... — Water molecules attaching to each other by hydrogen bonds (Photo credit: Wikipedia)

Water plays a role in rotting things down. A corpse kept in a very dry environment desiccates and turns leathery and fragile. I guess that this is because the organisms that rot a body away cannot function in a water free environment.

A body of liquid water fills things from the bottom up. Gravity pulls the water down to the lowest parts of a container and water continues to layer the container. The surface appears to be flat, but that is an illusion. At a small scale, if a tiny bit of the water happens to be higher than the rest of the water, gravity will pull it down, while the other water molecules resist by being in the way.

Eventually as the water stills, the differences in level even out, and the water surface becomes as level as it can. However, at the molecular level, molecules of water, which are moving relatively fast on these scales, can pop out of the liquid and float away. Other molecules can also pop in to the liquid, so that on average the water is level.

Why doesn’t the surface appear blurry and ill defined then? Well we can’t see at the molecular scale, and also the water molecules form weak electrical bonds with each other. A water droplet is like a large crowd of people all milling about, holding hands much of the time. Those on the outside are not as tightly bound as those further in.



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Imagine now that the crowd is surrounded by a storm of people who are moving faster, and are more spread out so they rarely join hands. One of these gaseous people will now and then bump into the crowd. They may knock loose one of the crowd who will shoot off and become one of the gaseous people, while gaseous person who hit him may now be travelling more slowly and link up with the crowd.

Even in the macro world a water surface is rarely really flat. The dynamic nature of the flatness is apparent when a container is jolted slightly and tiny waves form on the surface as compression waves disturb it. Wind and rain also cause visible disturbances in a lake or pond.

Flowing water often forms a smooth, if not level surface. A submerged rock in a river or a weir or fall in a river can form persistent ripples of flumes as the water flows over them. Kayakers know to aim their craft at a flume to safely descend a rapid or waterfall, although downstream of flumes the river often forms “haystacks” where turbulent water is forced into humps which can prove difficult to navigate.

A little stream may be described as turbulent as it makes its way over and around boulders and small drops, but interestingly it is not random. It is not chaotic. A close look will reveal that the bow waves of stones in the flow may flutter and throw off little whirling vortexes, but the bow wave and the pattern of vortexes persists. The little waterfall over a small stone ledge persists, even though the shape of the waterfall may ripple a little.

In large bodies of water, such as lakes and seas, winds form waves which can travel many thousands of kilometres across oceans and seas. Water waves don’t represent the movement of water over those distances – the only thing that moves is the energy in the wave. Water molecules in a wave move mainly up and down and only a little forwards and backwards.

Circular water current in a wave (Photo credit: Wikipedia)

However when a wave travels over a beach or shoal, the movement in the vertical direction is curtailed, and the energy is transformed into a forward motion – the wave breaks. Water is transported forward, with the water higher up moving faster than the water at the sea bed which may be water draining off the beach from the previous wave and the wave steepens until it collapses. Hence surfing!



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Real or virtual caving? What’s the difference?

A bit less than a year ago I posted about caves virtual and real. I’m going to expand a bit on this today.

I worked for many years as a Linux Systems Administrator, a job which I loved and to a large extent brought home with me. I run a number of Linux systems at home, including the computer that I am writing this on. I have a system that I refer to as my “server” which I use for backups and for things that might get in the way on my desk computer.

Tux, the Linux penguin (Photo credit: Wikipedia)

When Minecraft was a craze some time ago I didn’t get involved at first but when my grandkids got into it I became interested. In Minecraft you can build elaborate structures, but to do so you need to find and extract the necessary materials, and, depending on the server that you are using, fight off automatic monsters (“mobs”) and other players.

I installed the Minecraft client, tried it out and liked what I saw. However, playing on other peoples’ servers soon became less than satisfactory. I didn’t like the unrealistic ability to “fly” (not fall down when unsupported by things) and the combative aspects of the game were found on many servers.



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So, I investigated and tried running my own Minecraft server. This is possible, and not particularly tricky, you still have to pay for the client. There’s nothing wrong with paying for things, of course, and I did pay for it, but being a Linux user I’m always interested in seeing if there is a free version out there. Not of the actual Minecraft naturally, but of a similar program.

Minetest is a very similar program to Minecraft, works in much the same way, but is free, and there were Linux packages available, meaning that the install was simple. So I installed the packages and started playing. (I later downloaded the source code and compiled it, but that is another story. The packages worked fine).

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Pretty much everything that you can do in Minecraft you can also do in Minetest. The differences are minor. So everything I say from here on will probably apply to either program.

The game is all about assembling resources to build things, and you assemble resources mainly by mining. You whack a block (say stone) with a tool (say a steel pickaxe) and it disappears and appears in your inventory. When you have enough blocks you can build a wall of them by taking them from your inventory and placing them appropriately. That is the start of your fortress or palace.

A plain stone building is boring, so you will want to acquire some fancy blocks to smarten it up and that is where the game shines. You can make fancy blocks to place on your building, but to do that you need to acquire resources and fabricate or “craft” them. The resources are found under the ground, which requires you to dig down to get them, which is of course where the “Mine” part of the name comes from.

If you dig downwards (on a slope, so that you can return to the surface eventually) you will sooner or later encounter a void or space where there are no blocks. Hopefully you will avoid falling to the bottom and dying. If you carefully climb down to the bottom of the void you are are the bottom of a virtual cave.

The cave may have blocks which look slightly different to the normal blocks. These blocks contain resources, usually ores, that can be collected and used to make other special blocks. For instance a block with iron ores in it can be used to make steel ingots, which can then be used to make steel pickaxes and other useful tools.

The game’s caves are similar in many ways to real caves. The topography of the caves is varied, with narrow passageways in some places, deep clefts in others, potholes, and sometimes openings to the surface.

Of course it is dark underground. That means that you need to manufacture torches and carry them in your inventory if venturing underground. A torch placed on the wall will illuminate a small area of the cavern leaving dark voids beyond the torchlight which might be interesting to explore!

The game’s caves often have, just like real caves, uneven floors and there will be much jumping over obstacles, and climbing up and down. Some caves do have flatter floors, as do many real caves.

English: Subglacial pothole on Pothole Dome. (Photo credit: Wikipedia)

Some game caves have sloping floor, much like a staircase, and the roof also may slope down, giving the impression of a sloping slit, as is often found in real caves. It is not advisable to skip down the slope into the darkness, of course, as the slope may end in a drop, as may also be found in a real cave.

Game caves are often elongated, just like real caves, and may form large interlinked caverns. Cross passages may start way up on the walls of the caverns, just as happens in real caves. It’s often possible to travel some distance more or less horizontally before one has to climb up or down to continue.



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Game caves do not often contain water, which is unlike most real caves, and when they do the water is either in the form of a waterfall or a lake. Long flowing river of water are not common in game caves. Sometimes a cave will contain a lake of lava, or a lava fall which often looks spectacular. Both lava and water may form short flows but will quickly “seep” into the rocks.

Some of the potholes are spectacular. As they are underground and dark, one cannot see the bottom. Often they can edged or mined around and descended that way. Looking back up one can see the torches that one placed on the way down as tiny lights, often to spectacular effect.

I’ve explored both real caves and game caves, there is a great deal of similarity in the experience. In both cases, one has only limited visibility around one, one has a sense of void, and a sense that one may fall. There’s the thrill of discovery as one explores, and a sense of achievement. Unfortunately in the game caves, there are no stalactites and stalagmites to decorate the cave, but perhaps someone will write some in some time.

About Mums, and a little about Dads too.

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.

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.



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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.

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.

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.



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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.

Time and time again

It is often said that Einstein considered time to be an illusion, and web sites which collect notable quotes often just claim that Einstein said “Time is an illusion“. This a classic case of taking a quote and posting it out of context. What Einstein actually said was more complex and more subtle.

He actually said:

The distinction between the past, present and future is only a stubbornly persistent illusion.

He did not claim that time is an illusion, but that the moment of “now” is an illusion. In fact his equations give time the same status as space. For instance, the square of the space time interval between two events is defined by combining the square of the space interval minus the square of the time interval interval. (Provided all values are expressed in the same units.)

Time dilation spacetime diagram06 (Photo credit: Wikipedia)

The details don’t matter too much here. The point is that time is treated equally with the space dimensions, and no one is claiming that Einstein was arguing that space does not exist. There are many references to be found on the Internet which explain Einstein’s ideas with variable clarity and accuracy.

I said above that Einstein argued that the instance of “now” is an illusion, but I was over simplifying. What I believe that he was saying was that while we experience a “now” now, we also experienced a “now” ten seconds ago, and one second ago, and one instant ago. There is nothing special about the “now” moment and all instants of time are “now” moments.



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This isn’t that surprising really. If you consider where you are at a particular place and at a particular time, not only is there a “now” moment, there is also a “here” place. When you move to another place, you have another “now” moment, and another “here” place. To experience an event you have to have both.

If we are taking a road trip we have no difficulty with the concept that the “here” place changes continually and that a place we have passed through was a “here” place when we passed through it, and that a place further on will later be a “here” place. Where ever we are we are “here”.



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You might argue that time is fundamentally different from space, in that we can see what is in front of us in space but we can’t see what is in front of us in time. This is true, but maybe we just don’t have the physical equipment to do so. We can use sight to look around as see what is not “here”, to some extent, but we don’t have complete visibility to things around us.

If we did we would not bump into things and fall off of things as much as we do. We use sight to build a picture of things around us, but we don’t have physical access to those things until we move up to them.

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Since we don’t have “time vision” we have use whatever abilities we can to work out what is in the future, such as reason and intuition, both of which have limited success. We do have some ability to fairly accurately guess the future, as evidenced by our abilities to catch a ball thrown to us. If you have ever watched a top table-tennis match, you will no doubt be amazed at how accurately we can so this, as the ball whizzes from end to end of the table.

Time is measured in seconds and space is measured in metres (or hours and yards or other equivalent units). This seems to be a difference between the space dimensions and the time dimension.

Time dilation spacetime diagram05 (Photo credit: Wikipedia)

However it is easy to show that there is little fundamental difference. Distances are often measured in terms of time – astronomers refer to a light year, which is the distance that light travels in one year. It is not often, however, that the opposite is true. Times could be measured in terms of light metres, or the time it takes light to move a given number of metres, but this is not usual, possibly because a light metre is such a very short period of time.

Interestingly some people claim to be able to “see” the future. They are claiming that they have a sense similar to vision which they use to determine what is going to happen in the future. While it is possibly conceivable to have such a sense, there appear to be no organs in the body which could be used to “view” the future.

Panoramic view of the future Phoenix-Lake from the observation deck of the Phoenix-Lake Infopoint (Photo credit: Wikipedia)

Such organs would have to have receptors which would have to receive information about the future just as the eyes receive information about things that are relatively distant, and that information would have to travel in time from the future to reach the receptors in the present. This appears to be counter to all known physics. Possibly “unknown physics” would allow this, but I suspect not.

In any case the human body doesn’t appear to have any receptors which could possibly serve this purpose, and although not everything is known about the human body, such organs, if such existed and could be used by some people, would be probably be apparent.

What about the brain? Could the brain perhaps receive information about future events in some way? Well, the brain is an organ for processing information, not for receiving information from the future. There is nothing like a receptor in the brain, though it is connected via nerves to receptors which terminate those nerves and when stimulated excite the nerves which then pass the stimulation to the brain.

In my opinion, which of course could be wrong, there is no way that information from the future could be detected by the human body, and in particular by the brain acting as a receptor. That does not mean that time is in any way different from space as a dimension. What it does mean is that we are able to perceive the dimensions of space differently from the dimension of time.

Diagram of human brain (Photo credit: Wikipedia)

That doesn’t address the question as to why the space dimensions are accessible to vision and time is not. It only addresses the question of why we can “see” the space dimension, but cannot “see” the time dimension. Something links the space dimensions into one seeming whole, while the time dimension seem singularly different.



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Cuteness

If you saw a human being whose body was only three times the size of his/her head instead of the usual six times, who lacked the ability control his/her limbs and bodily functions, who was almost unable to communicate and who needed round the clock care, would you conclude that they were unfortunately seriously physically disabled, or would you lean in and say “What a cute baby!”

When the characteristics of a baby are listed like that, it makes it seem very unattractive, but, unless the baby is playing up in some way, most, but not all people, would find it appealing. There is something in our natures that is attracted to babies and young children.



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It’s not just the young of our own species that we find attractive. A small bumbling puppy or kitten very often causes us to go “Awww!”. We often have an urge to cherish baby animals, and this urge appears to extend to other species to some extent. It is not infrequent that a mother of one species will care for the young of another species, even species that would normally be prey for the mother.

That’s quite astounding when you think about it – the mothering instinct has completely suppressed the predatory instinct. Of course, if food were scarce, possibly the mothering instinct would not be as strong as the predatory instinct.



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Obviously the pleasure that people get from babies (and pets) outweighs all the negative aspects of looking after them. Babies can be demanding, annoying, frustrating and downright unpleasant to live with, if the truth be told. And they are expensive to look after!

Other people’s children will sometimes cause you to wonder why the parents didn’t practise birth control, and your own will frequently be an embarrassment to you, but overall society tolerates the anti-social behaviour of children to an amazing extent. Of course, parents tend not to take babies and small children to events where they would cause chaos and mayhem, such as a musical concert or a play.



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We could term this attractiveness of young children to adults “cuteness”. “Cuteness” invokes the parental instincts that can in some circumstances overcome the instinct of self preservation. In having produced offspring, a parent has performed almost all that is necessary for the propagation of the species, and the only task left is for the parent to ensure that the child gets the best start in life that is possible.

The cuteness of children allows such human institutions as fostering. A child can be looked after by a non-relative, if the parent (and all the child’s relatives) are unable to bring up the child for any reason. Sometimes, maybe often, a fostered child comes with “problems”. They may have been mistreated, for example, and have become reserved or disruptive.



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Foster parents are often special people, who take in unwanted children and do their best to sort out any problems and issues that they have, trying their hardest to break through any barriers that the child may have put up, earning the child’s trust if possible, and even their love.

That is important, because the parent/child bond is bidirectional. The parent loves the child, and the child loves the parent back. I suspect that the parent loves the child first and the child learns from this to love the parent back. When a child is born, it is barely aware of its surroundings and parents grow to love their child even before the child learns to and is capable of responding to the parents.

George and Barbara Bush with their first born ... — George and Barbara Bush with their first born child George W. Bush, while Bush was a student at Yale (Photo credit: Wikipedia)

It’s a tragedy that so many parents either don’t know how to love their children, or their love fades quickly over time. I guess it is not surprising that in a few cases parents don’t know how to love their kids, and I also guess that this can be the result of the parents’ parents not showing their kids much love.

However, that is pure speculation. It’s reasonable, I’d say, but not definite, so far as I am aware. Certainly, children who come from environments where the mutual affection in a family is apparent will most likely prove to be loving parents themselves.

English: Russian Family (Photo credit: Wikipedia)

It is hard to watch when a child goes wrong, or is caused distress by something external. Older children of even loving parents sometimes go “off the rails”. They may indulge in drugs, or alcohol, or indiscriminate sex, or may develop mental or physical illnesses. They may simply develop world views that are opposed to those of their parents. They may even vote for the wrong political party!

This wayward behaviour is often worst for parents who have rigid world views, such as those who are religious or are philosophically rigid. It may indeed be this very rigidity of viewpoint that has pushed their kids away. Most parents encourage their children to develop their own personalities, but sometimes these personalities clash with those of the parents.



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The innate tendency to find children and the young of pet animals cute serves as the glue to bind the parents to a very demanding entity in the child. The cuteness of a child is only partially visible to others though, and there may be conflict between parents and other adults in places like restaurants and planes and busses.

As children get older the cuteness factor tends to wear off. By the time that they leave the family home the bonds between parents and children have transitioned between child/parent and young adult/parent. Though the bonds are still there they are qualitatively different to the original bonds formed just after the birth.

Sometimes the cuteness idiom is probably taken too far, as in the Japanese quality of Kawaii. In Japan many older children and young adults dress and behave in ways which in younger children would be considered cute. In my opinion this is decidedly dubious, as the Kawaii quality is too easily linked with sexual attractiveness, and making oneself more attractive by acting younger than one’s age can possibly cause younger children seem sexually attractive.

In contrast, in Western cultures children will try to dress and act older than their age when they begin to feel that they need to be attractive to others. While this is not ideal, it does mean that sexual attractiveness is directed to older looking partners, and not, as in Japan, to younger looking ones.



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