In ancient times, the Greek philosophers, including Aristotle, believed that Matter was a function of Life. In modern times, this position is reversed. Life is now considered to be a function of Matter.
Why the about face? The scientific community conquered the realm of material behavior with a deterministic mathematics. This mathematical approach could only see quantifiable features of Matter. Unable to quantify anything else, they assumed that Matter was all there is.
However, abundant experiential evidence indicates that Life has the possibility of interacting with Matter. For instance, we flex our muscles to move our bodies to obtain both food and sexual partners in order to survive as a unit and reproduce our gene pool. We exert our will to stay focused long enough to accomplish our goals.
Life does have a material component that, of course, obeys all the deterministic mathematical laws. Life has another component that inanimate Matter does not have –Attention/Awareness. There is a general scientific consensus that inanimate objects, e.g. hydrogen atoms or tables, are not aware. In contrast, all cells are more or less aware of their surroundings. In fact, there is a general agreement that evolutionary processes operate in such a way as to increase Attention. As to be expected, heightened Awareness1 provides a survival advantage.
It is safe to conclude that Attention differentiates Life and Matter. One has it; the other doesn’t. According to our model, Matter operates in time’s horizontal (linear) dimension, while Attention operates in time’s vertical (cyclical) dimension. Life exists at the intersection of time’s two dimensions. Under this perspective, Life is the interaction between Matter and Attention.
Life = Matter x Attention
The laws and such in each of time’s dimensions are entirely different. For instance, Matter inhabits a closed energy system, where energy is conserved; Attention belongs to an open energy system, where energy is consumed. Also Matter reacts to information, while Life via Attention interacts with info.
Attention’s vertical dimension is generated by an information digestion system that is shared by all living systems. The ID system also determines the laws and rules of the Realm of Attention (vertical time). This system also connects time’s two dimensions, i.e. the 2 realms that are inhabited by Matter and Attention.
We delineated some of the prime tenets of our model in the preceding chapter. According to one of our tenets, the engine of Life’s open energy system is what we call the ID Synergy. The next few chapters are devoted to explaining the inner workings of the Synergy.
The ID Synergy consists of 4 components. But to be honest, these elements don’t actually exist in a mortar and bricks location or anywhere else for that matter. Rather they are convenient markers – nodes and tendencies that assist in understanding the operation of the Synergy. That being said for ease of communication, we will pretend that they really do exist.
It is highly probable that there are other ways of explaining and interpreting the Synergy. These perspectives are dependent upon point of view or reference frame. However, regardless of the interpretation, the system remains the same.
The ID Synergy’s four components are linked via an Image Overlay Process (IOP), of which the LA is the mathematical realization. All life forms, including the ‘lowly’ bacteria employ the IOP to digest information – transform ‘raw’ data into a useable form.
Matter might also participate in an image overlay process. But the opacity between the overlays is 100% - no record/sense of the past. Miraculously, along with Attention came a reduction in opacity – a translucency between overlays. With this reduction came an awareness of time passing – an experience of the past, no matter how slight. Between images came an opportunity to adjust to circumstances.
But the ID’s Image Overlay Process is a tool that requires an operator. By itself, this abstract process is like a car without a driver. This is where the Synergy’s 4 components enter the picture. Each of the components are necessary.
1) Feelings/Life Force/jing provides the motivation to go somewhere;
2) Attention senses the environment – sees the road;
3) Mind analyzes the incoming data from Attention via the IOP and makes informed choices as to the best way to satisfy Feeling’s innate urges, e.g. which is the best route to take.
4) Intention executes Mind’s decisions regarding Attention’s sensory input to satisfy Feeling’s appetites.
Without Intention, Mind is helpless – like a paralyzed human on the driver’s seat – knowing where he wants to go, but no way to start and steer the car. Intention is the ability to deliberately flex muscles, both physical and mental, with a distinct purpose - to satisfy Feelings’ desires.
There you have it. The four underlined terms are the ID Synergy’s four components.
This brief overview provides an introduction to the workings of the Synergy. In the following chapters, we will discuss these terms and others (all familiar from everyday parlance) in more detail. 1) Feelings, 2) Attention, 3) Intention, 4) Mind, 5) Image Overlay Process, 6) Images, 7) Mental Energy, 8) Moments/Instants, and 9) Experience.
A primary focus of my entire opus of some 2000+ pages is Life’s relationship with the information contained in data streams. This particular volume explores Life’s information digestion system.
To be clear, when employing the terms, Life, living systems, life forms, organisms, etc., we are only referring to cellular life – everything from the single celled bacterium to humans with their 75 billion cells, each composed of between 5 million to 2 trillion molecules. We are not referring to the life-like behavior of artificial intelligence or even inanimate matter. We are also not referring to disembodied organisms such as culture, countries or groups, although these collections of living systems share some of the properties of insular life forms. Our analysis only applies to cellular life.
Life = Cellular Life ≠ Life-like: Artificial Intelligence
Cellular Life ≠ Disembodied Organisms: Countries
Cells = Building Blocks of Life
The scientific community all agree that cells are the building blocks of Life. As the building blocks, cells have everything contained in them that they need to build humans. Humans, of course, have many emergent properties that an individual cell does not have, for instance a sense of self or the ability to feel emotions. Some of these features arise from the increased connectivity and shared awareness of the 75 billion cells that cooperate to create our body.
Every life form regardless of its relatively simplicity or complexity shares certain features in common. For instance, they all share the same basic physiological systems. As noted Stanford biologist, Bruce Lipton states in his book, The Biology of Belief:
“The biochemical mechanisms employed by cellular organelle systems are essentially the same mechanisms employed by our human organ systems. Even though humans are made up of trillions of cell … there is not one “new” function in our bodies that is not already expressed in the single cell. Virtually every eukaryote (nucleus-containing cell) possesses the functional equivalent of our nervous system, digestive system, respiratory system, excretory system, endocrine system, muscle and skeletal systems, circulatory system, integument (skin), reproductive system and even a primitive immune system.” (Bruce H. Lipton: The Biology of Belief, Hay House, Inc., 2008, p. 7)
Rather than qualitatively different, cells are functionally like little humans.
Physiological Systems (Cells ≈ Humans)
The functional similarities don’t end here. In addition to these physiological systems, our model suggests that cells also have an Information Digestion System (IDS) complete with Synergy. This Synergy consists of Feelings, Attention, Intention, and Mind. These four components are tied together by an Image Overlay Process (IOP).
Info Digestion System (Cells ≈ Humans)
Most, if not all, biologists would agree that all life forms definitely exhibit Feelings and Attention – the Synergy’s first two components. They would also agree that even single celled bacteria seem to exhibit the deliberate behavior associated with Intention and Mind – the Synergy’s second two components. They seem to learn from experience, for instance avoiding toxic environments after repeated exposure.
Noted neuroscientist Antonio Damasio reflects the position that cells possess ‘will and desire’ in his acclaimed book, Self comes to Mind.
“Single cells had what appeared to be a decisive, unshakable determination to stay alive for as long as the genes inside their microscopic nucleus commanded them to do so. The governance of their life included a stubborn insistence to endure and prevail until some of the genes in the nucleus would allow the cell to die.
I know it is difficult to imagine that the notions of 'desire' and ‘will’ are applicable to a single lonely cell. How can attitudes and intentions that we associate with the conscious human mind, and that we intuit from the workings of big human brains, be present at such an elementary level? But there they are, by whatever name you may wish to call those features of the cell’s behavior.” Self comes to Mind, Antonio Damasio, Vintage Books, New York, 2010. p. 37
These symmetries between the biological consensus regarding the single cell and the components of the ID Synergy are certainly suggestive. Due to many patterns of correspondence (metaphorical compatibility) between the intrinsic logic of the biology of the Cell and the Information Digestion System, the physical Cell could easily provide the material substrate for the ID System, as well it should.
Cell Biology ≈ ID System
Cell Biology = Physical Substrate of ID System
Accordingly, we will look at the discoveries of cell biology to better understand the terms and processes associated with our Information Digestion System. Are there any more affinities between the two systems, one biological and the other based in the digestion of information? For instance, what do biologists and neuro-scientists have to say about Feelings and Attention, two of the Synergy’s prime components?
To pose some plausible answers to these questions, let us first establish Life’s cosmic context. This foundation will set the stage for the scientific facts regarding cellular biology.
To better appreciate how special Life is, let us look at the development of the Cell. Here is my version of the story. Hold onto your hats. We are going to cover a lot of territory very rapidly.
14 billion years ago: the Big Bang occurred, at least according to the current scientific consensus – which is pretty stable – until it isn’t. The concentrations of subatomic energy/information became so dense that it materialized as the first protons and neutrons, atoms, molecules and stuff. The superposition of the electrons, photons et al became material reality. Hydrogen atoms with their proton nucleus and orbiting electron became the seed atom of all future atoms and molecules.
This is a huge transition, as it generates a new realm of existence. Before the beginning, there was only Energy – the superposition of the Subatomic Realm. No space or time. Now there is a Universe, where Matter moves through space and time. Rather than only a potential Subatomic Realm, now there is also a real Molecular Realm. Previously one, now two. Subatomic potentiality interacts with Molecular actuality.
For the next 10 billion years, Matter began accumulating into larger and larger chunks due to the attractive force of gravity. Small proto-particles became objects, which gradually merged into larger and larger concentrations of mass. Some of these accumulations, i.e. stars, began imploding so intensely that they generated light and energy. After some supernova explosions and neutron star collisions, a stellar cloud of cosmic debris began spinning around itself – eventually coalescing into a solar system – with planets circling around a sun.
4.1 billion years ago: the Earth had finally hardened into a full-fledged planet - complete with core, mantle, surface and more importantly liquid water and an atmosphere. Then a relatively short 600 million years later, Cellular Life made its first appearance.
3.5 billion years ago: the initial cell somehow came into being – the seed beginning of all cellular Life. Perhaps the concentrated complexity and connectivity of Matter passed a threshold and Life emerged from the random chaos of molecular collisions. Or perhaps some divine force gave the molecular concentrations a nudge to create the first life forms. It doesn’t really matter. Both the initiation of Big Bang and the creation of Life remain scientific mysteries – probably never to be solved.
Whoa! This is another huge transition. At first (before the beginning), there was only the Subatomic Realm – consisting of Energy, but no Matter. Then the Big Bang added the Molecular Realm – filled with both Matter and Energy. The creation/emergence of Cells added yet another realm of existence – the Realm of Attention. The Universe is now filled with Matter, Energy and Life.
Accompanying Cellular Life are many new features that were entirely absent from the Material Realms. Although too many to enumerate, a few come to mind. Perhaps the most significant is the urge to survive as a unit. Rather than merely remaining intact like a mountain or a rock, this survival instinct entailed organizing a revolving door of molecules into amino acids, proteins, cell membrane, and cytoplasm – features that are essential for survival.
Along with these physiological features, the cell also has an information digestion (ID) system that allows these earliest of life forms to persist as an organic collection of atoms and molecules. Life’s ID system employs an image overlay process. This process that is exclusive to Life generated a second dimension of time based in cycles and spirals. This so-called Vertical Time, the second dimension, is the basis of meaning, context, and memory. Matter only participates in Space and Horizontal Time, not Life’s Vertical Time. So with Life came another new dimension of time that had not existed before.
For the next 2 billion years, Prokaryotes, the name of the first cells, were the only life form on our planet. Tiny Bacteria are in this family. These microscopic cells must have been an incredibly successful evolutionary strategy as this so-called most primitive of life forms has successfully self-replicated for billions of years. Further, they show no sign of going away. Pretty good success rate.
Incredibly enough, these long-lasting Prokaryotes only consist of a cell membrane that encloses cytoplasm. Prokaryotes have neither nucleus nor organelles. Those features were later evolutionary innovations.
1.5 billion years ago: a new type of cell evolved from the Prokaryotes. They are called Eukaryotes. What is the difference?
In addition to a membrane enclosing cytoplasm, Eukaryotes also have a nucleus and organelles, all covered with a thin membrane. According to legend, some colonies of bacteria got trapped inside a larger bacterium, made themselves useful, and decided to stay in the interior forever. More appropriately, these bacteria got sealed inside as an organelle with a specialized task. The mitochondria, the cell’s powerhouse, is in this category.
These organelles began performing essential duties in the cell’s interior that were previously done on the surface. This specialization freed the membrane up for increased awareness. This mind-expanding experiment proved to be a successful survival strategy, as this new cell with the heightened attention, the eukaryotes, has self-replicated ever since.
There is one other major difference between the two types of cells. This difference only became apparent about a billion years after the first nucleated cells appeared on the planet.
750 million years ago: Multi-cellular organisms first appeared. They evolved from Eukaryotes, not Prokaryotes. Eukaryotes are the building blocks of multi-cellular organisms. Bacteria and the rest of their family do not form multi-cellular organisms.
Bacteria did join together to form colonies. These collectives remained together in part for heightened awareness. This grouping tendency eventually led to the evolution of nucleated cells, the eukaryotes, with even greater awareness.
When Eukaryotes joined as multi-cellular organisms, this enabled a greater specialization of tasks, which again multiplied the capacity for awareness exponentially – by orders of magnitude. When bacteria join as colonies and nucleated cells become multicellular organisms, their collective awareness transcends the awareness of the single cell, whether prokaryote or eukaryote. The whole is greater than the parts.
In addition to physical characteristics, e.g. speed and height, it seems that evolutionary forces also choose for mind expansion. In fact, this seems to be a primary, not secondary, feature that enhances survival.
What is the connection between, the Cell Membrane and Attention – the former a thin cellular skin that differentiates inside from outside and the latter a mysterious talent shared by all life forms?
According to our model, Attention is one of the four components of Life’s Info Digestion System. If Life really employs the ID system to digest data streams, there should be some reflection of Attention in the actual physical content of Cells, the undisputed building blocks of all life forms.
What does the microbiology of the Cell have to reveal about the Attention? Does Attention even have a biological manifestation in the single Cell? If so, how does this jive with the ID System? Are the intrinsic logics of the two systems (biological and informational) compatible? Are they headed for the divorce court or a permanent union?
Cell ≠ or ≈ Attention?
The only features that all Cells share in common are their membrane and cytoplasm. As prokaryotes/bacteria are the common ancestor of all cells, it makes sense that the structure of their membrane is the same. The membrane is where Attention occurs. Let us see how.
The membrane is so thin (7 millionths of a millimeter) that it can only be seen through an electron microscope. As this tool was only discovered in the 1950s, early biologists were not even aware that cells had a membrane, much less any kind of meaningful role.
“With the aid of microscopes, biologists learned that all living cells have membranes and all cell membranes share the same basic three-layered structure.” (Lipton, p. 46)
Every cell has a membrane that is composed of phospholipid molecules. These unusual molecules consist of three layers. The two outer layers consist of polar molecules (water loving: oil hating), while the inner layer consists of non-polar molecules (water hating; oil loving). Just as oil and water don’t mix, neither do the layers. But more importantly, this triple layer insulates the interior of the cell from the outside world. Two layers prevent water from entering the cell’s interior and the other layer prevents oil-based compounds from entering the inner sanctum. As it is both water-proof and oil-proof, the membrane maintains the cell’s integrity. Us and Them are clearly differentiated.
However, the cell must interact with the environment in order to survive. For instance, the cell must have a way of transporting nutrients from the outside to the inside and waste from the inside to the outside. Integral Membrane Proteins (IMPs) perform this task. Thousands of these IMPs are imbedded in the cell’s 3-layer membrane.
How do these IMPs enable the transfer of ‘information’ across the cell membrane?2 What is their MO?
Cells contain over 100,000 proteins. Thousands of these proteins change shape every second. The protein’s shape-changing is what allows living systems to move about, e.g. procuring food and avoiding enemies.
“The constant, shape-shifting movements of proteins – which can occur thousands of times in a single second – are the movements that propel life.” Lipton, p.29
All proteins, including IMPs, are composed of amino acids. There are 20 types of amino acids. Some are polar molecules – i.e. water loving, oil fearing, while the others are non-polar molecules – water-fearing, oil loving.
IMPs are bi-polar in that they consist of both types of amino acids, polar and non-polar. Their split personality allows them to wend their way through the membrane’s three layers, which also alternates polar and non-polar. Rather than just inside the membrane, these IMPs also extend beyond into either the interior or exterior of the cell.
IMPs consist of 2 functional classes: 1) receptors and 2) effectors. The cell’s receptors are the functional equivalent of our sensory nerves. They allow the cell to ‘monitor’ the environment. The effectors are like our motor nerves. They allow the cell to ‘adjust’ to environmental circumstances.
The receptors could be considered the cell’s sense organs. They are akin to microscopic nano-antennas that monitor the internal and external environment. Cells have receptors that are tuned to every circumstance necessary for survival. For instance, they have insulin receptors that are tuned to insulin molecules. Some of these IMP receptors can also read energy fields, e.g. magnetic or even mental.
Cell's Receptors ≈ Sense Organs
Every time there is a match – a fit between signal and receptor, the IMP protein changes shape. This change opens the membrane. When there is no match, the protein remains in the ‘off’ position – closed to the environment. When the signal matches, the protein changes shape to the ‘on’ position – open to the environment.
Effector IMPs respond to signals (sensory input) from receptors IMPs. If the appropriate sensation occurs, they change shape. This shape change initiates a motor response. When there is no sensory input, the effector protein remains in the ‘off’ position, no motor response. When there is sensory input, the protein changes to the ‘on’ position, which initiates a motor response, no matter how slight.
A relevant aside: Generally speaking, IMP proteins are in one of two states – on or off. As such, each IMP generates a binary data stream over time. These data streams are the food/fuel of our ID system.
While the IMPs provide the data streams, the fuel of the ID System, they are not a functional part of the ID system. The IMPs’ information must be digested before it becomes useful. Similarly, food must be digested before it becomes a functional part of an organism.
The Receptor/Effector complex turns environmental signals into cellular behavior. Sometimes this complex initiates motor movement. Other times, these protein switches might turn on genes.
Genes don’t necessarily operate automatically. Frequently, they must be activated to run their program. That is one of the functions of the cell membrane’s IMPs. In other words, environmental signals turn on genes. By controlling or regulating these signals, we can influence our behavior independent of genetic programming.
The receptor-effector IMPs work as a team. One senses and the other acts in response to these sensations. However, there is no choice on this individual level. The intricately coordinated movements of the cell’s many proteins behave like the cogs of a mechanical clock – automatically – deterministically.
“Taken together, the receptor-effector proteins are a stimulus-response mechanism comparable to the reflex action that doctors typically test during physical examinations.” (Lipton, p.54)
It seems that the receptor/effector synergy is a mechanistic operation. No thinking involved. Sheer reflex. Some believe that this is all there is – just a bunch of IMPs turning off and on. Stimulus-Response (SR). It certainly could be. But this model is unable to account for hoards of evidence. A serious flaw, by most standards.
Despite the automatic nature of the bulk of the operations necessary for survival, sometimes all the billions, even trillion of molecules in the cell must cooperate as a unit. For instance, the cellular muscles, the effectors, must coordinate firing in order to move the entire organism towards food and away from enemies.
The receptor/effector proteins in the cell membrane, sense and then act deterministically for small time operations, such as regulating waste. However, the entire cell also operates a unit. Something monitors and then deliberately adjusts to environmental conditions based upon a ‘memory’ of past experience. While behavior on the individual level is reflexive (stimulus response), the collective level requires at least a minimum level of deliberate behavior (monitor and adjust.)
In other words, cellular behavior is not like a billiard ball – bouncing randomly from location to location. Nor is it like gas molecules whose behavior can be approximated to any level of precision by employing the laws of probability on the accurate assumption of random behavior by individual molecules. Rather cells exhibit intentionality – deliberate behavior that is not random at all.
Some source is analyzing data and making ‘intelligent’ choices based upon ‘memory’ of past experiences. This mysterious life force must decide what to do with the information contained in the millions of data streams that are constantly bombarding the systems. The function of these choices is to serve the entire cell - the good of the whole. While individual parts, e.g. the IMPs, behave deterministically, these collective decisions have a sense of urgency that demands a degree of intentionality.
How is that individual IMPs behave deterministically, while the collective behaves intentionally? What is responsible for this intentional behavior? Where is the ‘intelligence’ located that holds a revolving door of molecules together as an integrated organism for a substantial period of time? Where is the ‘brain’ of the cell?
Experiments have shown that cells can exist for up to two months without a nucleus containing their DNA3. Parts break down more rapidly without the DNA assembly instructions, but life goes on until crucial replacements aren’t forthcoming. Even though lacking the DNA’s instructions, cells continue to exhibit the ‘intelligent’ behavior that enables them to survive.
“Enucleated cells [nucleus along with DNA removed] still exhibit complex coordinated life-sustaining behaviors, [for up to two months] which imply that the cell’s brain is still intact and functioning.” (Lipton, p.36)
Conversely, cells immediately die without their membrane, effector or receptor IMPs. They no longer exhibit the ‘intelligent’ behavior that enables them to survive. Without the membrane, cells fall apart, like a human without skin. Without the receptor IMPs, the cell has no way of knowing what is going on in the environment and is unable to respond accordingly. Without the effector IMPs, the cell is unable to act, even though it is able to sense what is happening in the surroundings.
“To exhibit ‘intelligent’ behavior, cells need a functioning membrane with both receptor (awareness) and effector (action) proteins.” (Lipton, p. 56)
Due to their widespread acceptance, these findings are considered to be scientific facts.
DNA = Not Crucial for continued Survival
Cell Membrane = Crucial for Survival
Receptor IMPs = Crucial for Survival
Effector IMPs = Crucial for Survival
Because of their crucial role in the cell’s ‘intelligent’ (survival-oriented) behavior, IMP Protein complexes are considered the fundamental units of cellular ‘intelligence’ or more technically ‘units of perception’.
“The definition of perception is ‘awareness of the elements of environment through physical sensation’.” (Lipton, p. 57)
Note that the ‘perception’ entailed by the IMP switch is not passive. Rather it includes a ‘motor’ response (an effector protein changing shape) – an automatic reaction to sensory input (matching the receptor protein’s feelers to environmental stimuli.) These switches act in tandem, not individually.
There are hundreds of thousands of IMP switches in the cell membrane. The mechanistic behavior of a single switch is relatively meaningless in terms of the overall behavior of the cell. Rather the switches somehow act collectively to generate behavior, e.g. approaching food or evading predators.
The switches belong to a holistic system – the cell. Their collective behavior is in relationship to the whole cell. The parts mean very little, if anything, by themselves. A single ant or bee is nothing to worry about. An ant colony or beehive is another story. The collective Awareness transcends the individual perception/response of the individual IMP switches.
In a previous article, we discussed how Life consists of a logical dualism, i.e. two systems that are logically incompatible. We suggested that Life’s material component is atomistic, while the informational component is holistic.
Could this IMP/Attention connection be the exact juncture that an atomistic system (Matter) generates a holistic system (Life)? The intersection is straightforward: from mechanistic IMPs, which as we shall see are the building blocks of our crucial sensory–motor network, to intentional collective Awareness, which is the purposeful interface between Life and Matter.
The moment that Atomistic IMPs generate Holistic Attention, this is the same moment that Matter becomes Life. Could this juncture be the source of the logical dualism that is inherent to Living Systems?
Life’s logical dualism is, of course, a significant feature of my ID model. The two types of systems, atomistic and holistic, require different mathematical systems. Calculus and Newtonian Dynamics provide the mathematical foundation for Matter’s atomistic system, while abundant evidence indicates that the LA and Data Stream Dynamics provide the same for Attention’s holistic system.
In addition to logical structure, there are other reasons that two types of math are required. The components, processes, and database of the two systems is qualitatively different. Further atomistic Matter is best depicted by its components, i.e. atoms and molecules, while holistic Attention is best depicted by processes, e.g. how images become Experience.
The mathematics of closed data sets works perfectly for Atomistic Matter. This classic mathematics generates eternal immutable relationships between variables. In contrast, Holistic Attention requires the mathematics of open data streams. This reflexive mathematics identifies contextual processes that, although transitory, have repetitive themes.
From atomistic IMPs to holistic Attention: could this be the biological foundation of Life’s logical dualism? Reiterating: while IMPs provide the material substrate, they as individual switches are not Collective Attention. While supplying the fuel, they are not part of the holistic Intentional Network. The IMPs are instead part of Matter’s atomistic network. Whoa! Heavy, man.
As seen, biological experiments have exhibited that cells can’t survive for long without the sensory-motor intelligence supplied by these receptor/effector proteins that are located in the cellular membrane. Are there any other indications of the importance of these IMP proteins to the organism?
I don’t know; let’s check out the next chapter.
1 In this article, nay opus, the two terms ‘Attention’ and ‘Awareness’ are employed as interchangeable synonyms. As such, utilizing one to define the other is akin to circular reasoning that goes around in circles without providing any new information.
2 Almost all the biology in this article is derived from Bruce Lipton’s Biology of Belief. The biological info in this section is extracted from page 54.
3 Some of the following comes from Lipton page 57.