Computers and cells

English: "U.S. Army Photo", from M. ...
English: “U.S. Army Photo”, from M. Weik, “The ENIAC Story” A technician changes a tube. Caption reads “Replacing a bad tube meant checking among ENIAC’s 19,000 possibilities.” Center: Possibly John Holberton (Photo credit: Wikipedia)

(Oops! One day late this week!)

A computer has some similarities to living organisms. Both produce something from, well, not very much. A computer program has data input from various sources, and produces output to various sinks or targets. A living organism takes in nutrients from various sources, and produces branches, leaves, fur, bones, blood and other organs.

Of course there are differences. A computer is much, much simpler than a living being, even single celled organism. A computer in general only has a relatively small number of parts, but the “parts” in a living organism number in the billions. And of course, living organisms reproduce, but that may change in the foreseeable future.

English: The heterolobosean protozoa species A...
English: The heterolobosean protozoa species Acrasis rosea Olive & Stoian. Photographed at the Biology of Fungi Lab, UC Berkeley, California. (Photo credit: Wikipedia)

Some animals are sentient, but I’m not going to discuss that here. Maybe in another post.

A computer has hardware, software and operates on data. The data is either part of the software or read from buffers in the hardware. It stores its calculations in “memory”, which is special hardware with particularly fast access speeds.

English: 1GB SO-DIMM DDR2 memory module
English: 1GB SO-DIMM DDR2 memory module (Photo credit: Wikipedia)

The computer produces results by placing data into buffers in the hardware. This results in things happening in the real world, such as printing a letter or number on paper, or more frequently these days, on some sort of screen. It may also do many other things, such as control the flow of water by moving a valve or other control mechanism.

Computers communicate with other computers, by placing data in an output piece of hardware. The hardware is connected to a distant piece hardware of the same sort which puts the data into a buffer accessible to another computer. This computer may be a specialised computer that merely passes on the data. Such computers are called routers (or modems, or firewalls).

Railway network in Wrocław
Railway network in Wrocław (Photo credit: Wikipedia)

Computers, specialised only in their usage, are found in washing machines, cars, televisions, and we all these days have multi-functional computers in our pockets, our cellphones. It would be hard to find a piece of electronic equipments these days that doesn’t have some sort of computer embedded in it. Very few of these computers are completely isolated – they chatter to one another all the times by various mechanisms.

Internet
Internet (Photo credit: Wikipedia)

(Incidentally, I came across a bizarre example of connectivity of things the other day – a wifi teddy bear. Say you are sitting in the lounge and you want to send a message to your child who is in her bedroom. You pick up your tablet and send a message to a “cloud” web site. This sends a message to your child’s tablet which is in her bedroom with her. The teddy bear, which is connected to the child’s tablet by wifi, growls the message to the child. No doubt scaring her out of her wits.)

So in the current technological world everything is connected to everything else. Much like all the cells in a living being are connected to all the other cells in the organism, directly or indirectly. So how far can we take this analogy, where the organism is the network and the individual cells as the computers. (Caveat emptor – I am not a biology expert, so don’t take what I might say from here on as gospel).


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A computer consists of hardware, software, and operates on data. A cell is sort of squishy, so “hardware” can only be a relative term, but a cell does have a relatively small number of organelles, such as mitochondria. The nucleus, which contains most of the genetic material, acts as the control centre of the cell, much as the CPU is the control centre of a computer.

The function of the nucleus is to maintain the integrity of these genes and to control the activities of the cell by regulating gene expression—the nucleus is, therefore, the control center of the cell.

In the cell, the genetic material is in some sense the software of the cell. It contains all the necessary information to create the cell itself or more interestingly the information needed to cause the cell to split into two identical daughter cells. This information is generally encoded in the DNA of the chromosomes.

Information flows between DNA, RNA and protein...
Information flows between DNA, RNA and protein. DNA -> protein is another special transfer, but it is not found in nature. (Photo credit: Wikipedia)

The cell also contains, within the nucleus, an organelle called the nucleolus. This organelle (which is part of the nucleus organelle) seems from my reading to mostly relate to RNA, while the rest of the nucleus mostly relates to DNA, very roughly. RNA and DNA perform a complex dance called protein synthesis in organelles called ribosomes.

Cells produce chemicals, which can be consider analogous to computer outputs and receive chemicals from other cells, and so cells communicate, in a sense, with each other. Since all cells are equal genetically, it follows that a cell’s type, liver, skin, lung or brain neurone is determined by factors in its environment.

The model of an artificial neuron as the activ...
The model of an artificial neuron as the activation function of the linear combination of weighted inputs (Photo credit: Wikipedia)

This only loosely true as each cells is the daughter of another cell and inherits its type, but in the early days of an organism’s life, before organs are formed cells do differentiate. Just as when computers were new, they were all very similar, keyboard, monitor, and beige case.

As the computer-sphere evolved, special types of computer evolved, such as routers and modems, and firewalls. Not to mention phones. Computers became specialised. Similarly cells become differentiated, some going on to become liver cells for example, and others brain cells (neurones).

English: Front side of a Juniper SRX210 servic...
English: Front side of a Juniper SRX210 service gateway Deutsch: Vorderseite eines Juniper SRX210 Service Gateways (Photo credit: Wikipedia)

When an organism is young and a cell divides both cells are the same type, but when the organism is very young there is no differentiation. The DNA in the cell contains the necessary information to determine the cell type and tissues and organs are created in the more complex animals.

This process obviously can’t be random, otherwise cells of the various tissue types would be all mixed up. It seems to me, maybe naively, that while the “program” for creating cells is in the DNA, some factors in the environment convey such information as how old the organism is, and what type of cell needs to be created.

an example of a Program
an example of a Program (Photo credit: Wikipedia)

We know from investigations into fractals that a simple equation can result in the creation of an image that looks very much like a tree or grasses and that small changes to the equation can lead to different tree or grass shapes. It is tempting to think that a similar process takes place in organisms – a general rule is given which results in the right sort of cells being produced in the right places.

The problem with the fractal idea is that it only creates simple shapes. An arm with fingers, skin and so on is beyond the capabilities of a fractal process so far as I know. Fractals don’t stop. Again, so far as I know there’s no way to iteratively create a tree structures with leaves.


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So the “software” of the cell, the “program” embedded in the DNA doesn’t appear to be analogous to a simple computer program that draws fractals. Of course that doesn’t mean that we can never describe a simple organism completely in fractal terms, and create analogous distinct individuals.

It seems that a long as the analogy is not pushed too far, computers in a distributed network are reasonably similar to living organisms. Please note I am note referring to the fractal type computer programs, but am talking about the way that computers themselves in a network are somewhat analogous to living organisms. Primitive ones!

Sample oscillator from hexagonal Game of Life.
Sample oscillator from hexagonal Game of Life. (Photo credit: Wikipedia)

Why Pi?

Based on Image:P math.png
Based on Image:P math.png (Photo credit: Wikipedia)

If you measure the ratio of the circumference to the diameter of any circular object you get the number Pi (π). Everyone who has done any maths or physics at all knows this. Some people who have gone on to do more maths knows that Pi is an irrational number, which is, looked at one way, merely the category into which Pi falls.

There are other irrational numbers, for example the square root of the number 2, which are almost as well known as Pi, and others, such as the number e or Euler’s number, which are less well known.

Illustration of the Exponential function
Illustration of the Exponential function (Photo credit: Wikipedia)

Anyone who has travelled further along the mathematical road will be aware that there is more to Pi than mere circles and that there are many fascinating things about this number to keep amateur and professional mathematicians interested for a long time.

Pi has been known for millennia, and this has given rise to many rules of thumb and approximation for the use of the number in all sorts of calculations. For instance, I once read that the ratio of the height to base length of the pyramids is pretty much a ratio of Pi. The reason why this is so leads to many theories and a great deal of discussion, some of which are thoughtful and measured and others very much more dubious.

Menkaure's Pyramid
Menkaure’s Pyramid (Photo credit: Wikipedia)

Ancient and not so ancient civilisations have produced mathematicians who have directly or indirectly interacted with the number Pi. One example of this is the attempts over the centuries to “square the circle“. Briefly squaring the circle means creating a square with the same area as the circle by using the usual geometric construction methods and tools – compass and straight edge.

This has been proved to be impossible, as the above reference mentions. The attempts to “trisect the angle” and “double the cube” also failed and for very similar reasons. It has been proved that all three constructions are impossible.

English: Drawing of an square inscribed in a c...
English: Drawing of an square inscribed in a circle showing animated strightedge and compass Italiano: Disegno di un quadrato inscritto in una circonferenza, con animazione di riga e compasso (Photo credit: Wikipedia)

Well, actually they are not possible in a finite number of steps, but it is “possible” in a sense for these objectives to be achieved in an infinite number of steps. This is a pointer to irrational numbers being involved. Operations which involve rational numbers finish in a finite time or a finite number of steps. (OK, I’m not entirely sure about this one – any corrections will be welcomed).

OK, so that tells us something about Pi and irrational numbers, but my title says “Why Pi?”, and my question is not about the character of Pi as an irrational number, but as the basic number of circular geometry. If you google the phrase “Why Pi?”, you will get about a quarter of a million hits.

Animation of the act of unrolling a circle's c...
Animation of the act of unrolling a circle’s circumference, illustrating the ratio π. (Photo credit: Wikipedia)

Most of these (I’ve only looked at a few!) seem to be discussions of the mathematics of Pi, not the philosophy of Pi, which I think that the question implies. So I searched for articles on the Philosophy of Pi.

Hmm, not much there on the actual philosophy of Pi, but heaps on the philosophy of the film “Life of Pi“. What I’m interested in is not the fact that Pi is irrational or that somewhere in its length is encoded my birthday and the US Declaration of Independence (not to mention copies of the US Declaration of Independence with various spelling and grammatical mistakes).

Pi constant
Pi constant (Photo credit: Wikipedia)

What I’m interested in is why this particular irrational number is the ratio between the circumference and the diameter. Why 3.1415….? Why not 3.1416….?

Part the answer may lie in a relation called “Euler’s Identity“.

e^{i \pi} + 1 = 0

This relates two irrational numbers, ‘e’ and ‘π’ in an elegantly simple equation. As in the XKCD link, any mathematician who comes across this equation can’t help but be gob-smacked by it.

The mathematical symbols and operation in this equation make it the most concise expression of mathematics that we know of. It is considered an example of mathematical beauty.


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The interesting thing about Pi is that it was an experimental value in the first place. Ancient geometers were not interested much in theory, but they measured round things. They lived purely in the physical world and their maths was utilitarian. They were measuring the world.

However they discovered something that has deep mathematical significance, or to put it another way is intimately involved in some beautiful deep mathematics.

English: Bubble-Universe's-graphic-visualby pa...
English: Bubble-Universe’s-graphic-visualby paul b. toman (Photo credit: Wikipedia)

This argues for a deep and fundamental relationship between mathematics and physics. Mathematics describes physics and the physical universe has a certain shape, for want of a better word. If Pi had a different value, that would imply that the universe had a different shape.

In our universe one could consider that Euler’s Relation describes the shape of the universe at least in part. Possibly a major part of the shape of the universe is encoded in it. It doesn’t seem however to encode the quantum universe at least directly.

English: Acrylic paint on canvas. Theme quantu...
English: Acrylic paint on canvas. Theme quantum physics. Français : Peinture acrylique sur toile. Thématique physique quantique. (Photo credit: Wikipedia)

I haven’t been trained in Quantum Physics so I can only go on the little that I know about the subject and I don’t know if there is any similar relationship that determines the “shape” of Quantum Physics as Euler’s Relation does for at least some aspects of Newtonian physics.

Maybe the closest relationship that I can think of is the Heisenberg Uncertainty Principle. Roughly speaking, (sorry physicists!) it states that for certain pairs of physical variables there is a physical limit to the accuracy with which they can be known. More specifically the product of the standard deviations of the two variables is greater than Plank’s constant divided by two.

English: A GIF animation about the summary of ...
English: A GIF animation about the summary of quantum mechanics. Schrödinger equation, the potential of a “particle in a box”, uncertainty principle and double slit experiment. (Photo credit: Wikipedia)

In other words, if we accurately know the position of something, we only have a vague notion of its momentum. If we accurately know its velocity we only have a vague idea of its position. This “vagueness” is quantified by the Uncertainty Principle. It shows exactly how fuzzy Quantum Physics.

The mathematical discipline of statistics underlay the Uncertainty Principle. In a sense the Principle defines Quantum Physics as a statistically based discipline and the “shape” of statistics determines or describes the science. At least, that is my guess and suggestion.


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To return to my original question, “why Pi?”. For that matter, “why statistics?”. My answer is a guess and a suggestion as above. The answer is that it is because that is the shape of the universe. The Universe has statistical elements and shape elements and possibly other elements and the maths describe the shapes and the shapes determine the maths.

This is rather circular I know, but one can conceive of Universes where the maths is different and so is the physics and of course the physics matches the maths and vice versa. We can only guess what a universe would be like where Pi is a different irrational number (or even, bizarrely a rational number) and where the fuzziness of the universe at small scales is less or more or physically related values are related in more complicated ways.


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The reason for “Why Pi” then comes down the anthropological answer, “Because we measure it that way”. Our Universe just happens to have that shape. If it had another shape we would either measure it differently, or we wouldn’t exist.


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