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Some of the most basic features of brains can be found in bacteria because even the simplest motile organisms must solve the problem of locating resources and avoiding toxins. They sense their environment through a large number of receptors, which are protein molecules embedded in the cell wall. Action is taken in response to the inputs such as the gradient of the chemicals (see Figure 02). Thus memory is required to compare the inputs from different locations. The strength of the signal is modulated by immediate past experience. This in turn regulates the strength of the response sent by chemical messengers to the flagellar motors. Thus even at the unicellular level, the bacteria have already possessed the ability to integrate numerous analog inputs and generate a binary (digital) output of stop or go. |
Figure 02 E. coli's Response to Chemical Gradient [view large image] |
Therefore even at such primitive level, the brain would modify the signals from the environment and generates a response, i.e., its survival does not directly depend on perceiving the real thing. It doesn't care about reality so cherished by philosophers. |
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In multicellur organism, cells specialized for receptor function are located on the surface. Other cells specialized for the transmission and analysis of information are located in the protected interior and are linked to effector cells, usually muscles, which produce adaptive responses (Figure 03). As do unicellular organisms, neurons integrate the diverse array of incoming information from the receptors, the resultant my induce the firing of an action potential (when the summation is above a threshold level) to initiate a response. Once the threshold for generating an action potential is reached, the signal is always the same, both in amplitude and shape (a nerve consists of many neurons, it does not obey the all-or-none law, see "Neurons and Nerves"). |
Figure 03 Neurons and Nerve |
Phyla | Brain Structure |
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Sponges | None. But have nervous components such as synapses and neuro-transmitters. See "Origin of Nervous System". |
Cnidarians | They have nervous network connecting outer and inner layers of cells; also possess light-sensitive cells. ![]() |
Flatworms | There is a small brain and two lateral nerve cords joined by cross branches. ![]() |
Roundworms | The brain is in the form of ganglia. There are nerve cords along the body connected by commissures. ![]() |
Cephalopods | They have the most complex brains of any invertebrates, very good eyesight. ![]() |
Annelids | There is a ventral nerve cord and lateral nerves. The brain is just a ganglion. ![]() |
Arthropods | The nervous system includes a dorsal brain and nerve cords, ... - similar to the Annelids' but more advanced. ![]() |
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must invest a great deal of effort in raising their infants. Young reptiles function as miniature versions of adults, but baby mammals and birds are dependent because of their poor capacity to thermo-regulate, the consequence of their need to devote most their energy to growth. Most mammals solve the problem with maternal care (Figure 05), shelter, warmth, and milk. In most birds, both parents cooperate to provide food and shelter to their young. The expanded forebrain and parental care provide mechanisms for the extra-genetic transmission of information from one generation to the next. This transmission results from the close contact with parents during infancy, which provides the young with opportunity to observe and learn from their behavior; the expanded forebrain provides an enhanced capacity to store these memories. The expanded forebrain and the observation of parents are probably necessary for the establishment of |
Figure 05 Maternal Care |
successful care giving behavior itself, as the young mature into adults that will in their turn have to serve dependent young. During the period of infant dependency, baby mammals and birds play, behavior that may be essential for the development of the forebrain. The baby's playful |
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The human brain can be divided into three parts: the hindbrain, which has been inherited from the reptiles; the limbic system, which was first emerged in mammals; and the forebrain, which has its full development in human. Different views of the human brain are shown in Figures 06, 07, and 08. Table 02 lists the functions of the different parts of the human brain. The brain is separated into two hemispheres. Apart from a single little organ -- the pineal gland in the centre base of the brain -- every brain module is duplicated in each hemisphere. The left brain is calculating, communicative and capable of conceiving and executing complicated plans -- the reductionistic brain; while the right one is considered as gentle, emotional and more at one with the natural world -- the holistic brain. |
Figure 06 |
Figure 07 Human Brain 2 |
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The cerebral cortex is covered in a thin skin of deeply wrinkled grey tissue called the grey matter (densely packed neurons for information processing). Each infold on the surface is known as a sulcus, and each bulge is know as a gyrus. While the white tissue inside are axons -- tentacles which reach out to other cells (to relay information). The cortex can be broken down into many functional regions, each containing thousands of cortical columns (oriented perpendicular to the cortical surface). Columns are typically about half a millimeter in diameter and contain about one hundred thousand neurons. They are the units of cognition (the mental process of acquiring knowledge by the use of reasoning, intuition or perception). |
Figure 08 Human Brain 3 |
Table 02 below lists the location and functions of the major components in the human brain. |
Structure | Location | Functions |
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Hindbrain (Reptilian Brain) |
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Medulla | at the top of the spinal cord | controls breathing, heart rate, and blood pressure. |
Pons | above the medulla | regulates sensory information and facial expressions. |
Cerebellum | at the lower rear | controls movement, coordination, balance, muscle tone, and learning motor skills. |
Reticular Formation | a network of nerves extends from the medulla to the cerebrum | monitors the general level of activity in the hindbrain and maintains a state of arousal; essential for the regulation of sleep and wakefulness. |
Midbrain (superior & inferior colliculus) | above the pons between the hindbrain and forebrain | relays sensory information from the spinal cord to the forebrain. |
Pineal Gland | on top of the midbrain behind the thalamus (the third eye¤ for fishes, amphibians, reptiles, and some birds) | involves in circadian and circannual rhythms; possibly involves in maturation of sex organs. |
Limbic System (Mammalian Brain) |
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Thalamus | in the middle of the limbic system | relays incoming information (except smell) to the appropriate part of the brain for further processing. |
Hypothalamus, Pituitary Gland | beneath thalamus | regulates basic biological drives, hormonal levels, sexual behavior, and controls autonomic functions such as hunger, thirst, and body temperature. |
Optic Chiasm | in front of the pituitary gland | left-right optic nerves cross-over point. |
Septum | adjacent to hypothalamus | stimulates sexual pleasure |
Hippocampus | within the temporal lobe | mediates learning and memory formation. |
Amygdala | in front of the hippocampus | responsible for anxiety, emotion, and fear |
Mammillary Body, Fornix | linked to the hippocampus | have a role in emotional behavior, learning, and motivation. |
Basal Ganglia (Striatum): Caudate Nucleus, Putamen, Globus Pallidus | outside the thalamus | involves in movement, emotions, planning and in integrating sensory information |
Ventricles and Central Canal | from tiny central canal within the spinal cord to the enlarged hollows within the skull called ventricles | fills with cerebrospinal fluid for mechanical protection. |
Cingulate Gyrus | above corpus callosum | concentrates attention on adverse internal stimuli such as pain, contains the feeling of self. |
Corpus Callosum | under the cingulate gyrus | is a bundle of nerve fibers linking the cerebral hemispheres, involve in language learning. |
Forebrain (Human Brain) |
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Frontal Lobe (Conscious Brain) |
in front of the head | controls voluntary movement, thinking, and feeling. |
Prefrontal Cortex | in front of the frontal lobe | inhibits inappropriate actions, forms plans and concepts, helps focus attention, and bestows meaning to perceptions. |
Parietal Lobe | in top rear of the head | contains the primary somatosensory area that manages skin sensation. |
Occipital Lobe | in the back of the head | contains the visual cortex to manage vision. |
Temporal Lobe | on each side of the head above the temples | contains the auditory cortex to manage hearing and speech. |
Stage | Age | Event(s) | DO | DON'T |
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1 | 0 - 10 months Gestation |
* Growing neurons and connections * Making sure each section of the brain grows properly and in the right place |
Mother should: * be stress-free, eats well * take folic acid and vitamin B12 * stimulate the young brain with sounds and sensations |
* Mother should stay away from cigarettes, alcohol and other toxins |
2 | Birth - 6 Childhood |
* A sense of self develops as the parietal and frontal lobe circuits become more integrated. * Development of voluntary movement, reasoning, and perception * Frontal lobes become active leading to the development of emotions, attachments, planning, working memory and attention * Life experiences shape the emotional well-being in adulthood * At age 6, the brain is 95% of its adult weight and at its peak of energy consumption |
* Parents should provide a nurturing environment and one-on-one interaction |
* Parents should beware of the emotional consequence of neglect or harsh parenting |
3 | 7 - 22 Adolescence |
* Wiring of the brain is still in progress * Grey matter (neural connections) pruning * White matter (fatty tissue surrounding neurons) increase helps to speed up electrical impulses and stabilize connections * The prefrontal cortex (involving control of impulses, judgment and decision-making) is the last to mature |
* Teenagers should learn to control reckless, irrational and irritable behaviors * Do learn a skill to support life in the future |
* Teenagers should avoid alcohol abuse, smoking, drug and unprotected sex. |
4 | 23 - 65 Adulthood |
* The brain reaches the peak power at around age 22 and lasts for about 5 years; thereafter it's downhill all the way * The last to mature and first to go brain functions are those involve executive control in the prefrontal and temporal cortices * Episodic memory for recalling events also declines rapidly * Processing speed slows down * Working memory is able to store less information |
* Stay active mentally and physically * Eat healthy diet |
* Avoid cigarettes, booze, and mind-altering drugs. |
5 | > 65 Old Age |
* Losing brain cells in critical areas such as the hippocampus where memories are processed |
* Exercise to improve abstract reasoning and concentration * Learn new skill such as guitar playing to attain the same effect * Practice meditation can promote neutral emotions |
* Avoid grumpiness by eating certain foods, such as yogurt, chocolate, and almonds to get a good dose of dopamine (for promoting positive emotions) * Don't stressed out as it is related to higher risk of developing dementia. |
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Figure 09 The Four Stages of Human Brain [view large image] |
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which the window of opportunity slams shut, and learning anything new in that realm becomes difficult, if not possible (Figure 10). For years, it is assumed that the brain's plasticity, or the ability to learn within the critical periods, was the work of excitatory neurons, which encourage neighboring neurons to fire. Recent study using inhibitory neurotransmitter (such as GABA) indicates that inhibition actually causes the onset of the critical period. It is found that termination of the mental process can be separated into two categories - structural and functional. The former involves physical structures such as neural network and is not easy to change; while the latter is just chemical compounds not difficult to administer. It may be very useful to reopen the critical period later in life. However, no one should |
Figure 10 Learning Curves [view large image] |
tamper the brain's critical periods casually. There is always the possibility of an adverse response, as we break the rule of nature. |
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as listed Table 04, while Figure 10a shows many types of receptors. When a receptor is stimulated, it generated nerve impulses that are transmitted to the spinal cord and/or the brain, but we are conscious of a sensation only if the impulses reach the cerebrum. It is immediately clear that reality of the external world is transformed to nervous impulses via various kinds of receptors. The brain then interprets the inputs as colors, sound, pain, ... These kinds of sensations |
Figure 10a Senses |
Figure 10b Cerebrum |
are one level away from the real things such as electromagnetic waves, sound waves, molecules in various states of motion, ... In other words, the brain just offers a very subjective experience. |
Receptor | Type | Sense | Stimulus / Limits |
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General | |||
Ruffini's endings, Krause end bulbs | Radioreceptor | Hot-cold | Heat flow |
Merkel's and Meissner's endings | Mechanoreceptor | Touch | Mechanical displacement of tissue |
Pacinian corpuscles | Mechanoreceptor | Pressure | Mechanical displacement of tissue |
Free nerve endings | Chemoreceptor | Pain | Tissue damage |
Proprioceptors | Mechanoreceptor | Limb placement | Mechanical displacement |
Special | |||
Eye | Radioreceptor | Sight | Light / wave of (370 - 730) nm, dimmest star at 10-14 watt/cm2 ~ 104 photons/sec-cm2, and resolution of ~ 1' (arc minute) |
Ear | Mechanoreceptor | Hearing | Sound / frequency range of (20 - 20K) Hz |
Olfactory cells | Chemoreceptor | Smell | Chemicals / 400 types of receptors, 109 different odours |
Taste buds | Chemoreceptor | Taste | Chemicals / 104 taste buds |
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Figure 11a |
Figure 11b Human Eye [view large image] |
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Figure 12a Retinal [view large image] |
Figure 12b Retina |
There are five layers altogether (see Figure 12b). Starting from the outermost layer: |
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Figure 13 Optic Pathway |
Light | Sound | |
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Velocity | c = 3x1010 cm/sec = ![]() ![]() it propagates in transparent medium as well as in vacuum |
v = (Ks/![]() where Ks is the bulk modulus, ![]() |
Frequency | Visible Range : (8 - 4)x1014 Hz, depends on E = h![]() |
Audible Range : (20-20k) Hz, same as the vibrating source |
Intensity | I = L/(4![]() |
Measured in dB = log10(I/I0), where I0 = 10-12 w/m2 is the hearing threshold for human |
Type | Transverse, polarizable ![]() |
Longitudinal ![]() |
Presence | Every where in day time, ubiquitous. Localized at night | Depend on space/time of the vibrating source, localized |
Imaging | Form vivid 3-D image instantly | Construct virtual image by sound pattern or language |
Vitalness | Most life form depends on light | Not essential for most life form |
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Figure 14a shows the range of loudness level for human. It appears that most of the sources are localized and monotonic. It requires the addition of patterns like singing or talking to convey more information. The measuring unit is in dB, dB = 0 means absolute silence for human ears. Figure 14b displays the audible spectrum for different species. The ranges for some natural |
Figure 14 Hearing Level and Range [view large image] |
phenomena represent the varying frequency as the wave propagates through medium of varying density (see "Properties of seismic waves"). |
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fibers along the organ of Corti to the main cochlear nerve, and then to the temporal lob of the brain for processing into the sounds that we perceive. According to the frequency of the sound wave, different parts of the basilar membrane along the organ of Corti are set into motion. In general, low-pitch sounds make the apex of the cochlea vibrate while high-pitched ones cause most vibrations near the base of the cochlea. Figure 15b shows such frequency distribution along the length of the cochlea for both the incoming and outgoing waves. The strength of nerve signals also depends on the volume of the sound. This is interpreted by the brain as loudness. It is believed that tone is an interpretation of the brain based on the distribution of hair cells stimulated. |
Figure 15a Cochlea |
Figure 15b Sound Wave |
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within a group (see "Prokaryotes"). Higher animals subsequently develop more elaborate mechanism to perform various functions (Figure 16a). Depending on its usefulness in a particular environment, different kinds of animals possess different number of receptors (Figure 16b). Some chemical message can elicit a specific reaction such as sexual arousal, it is called "pheromone". |
Figure 16a Smell Detection and Functions [view large image] |
Figure 16b Receptor #, Animals' |
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Figure 16c Sense of Smell [view large image] |
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Figure 17 Olfactory Bulb |
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Figure 18 Pathways |
combined effect when interpreted by the cerebral cortex. For example, some of the molecules may move from the nose down into the mouth region and stimulate the taste buds there. Therefore, part of what we refer to as smell actually may be taste. |
Smell | Taste | |
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Messengers | Gaseous molecules in surrounding | Usually organic molecules in food |
Input | From nose | From mouth (the 2 senses mix at the back of the mouth to create flavor) |
Range | Some distance away from the source, short range | In mouth, very close contact |
Processing | Dissolved in mucus, to receptor, to neuron, to brain | Same, but in different region of the brain (see ![]() |
Purpose | To access favorable and avoid harmful substance (evaluation, before reaching for it) | To consume yummy and reject poisonous food (already in mouth) |
Threshold | 200 - 0.0005 ppm (decline with age, see List) | 0.01 - 10-6 M (Molar = mol/L, decline with age, see List) |
Absence | The molecule does not induce the sense of smell (caused by no receptor, long exposure, illness, ...) |
The food is tasteless (caused by long exposure to the same food, illness, also see "Loss of Taste") |
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tongue (see Figure 19, also a 2010 version). Each detects a different class of chemical: sweet (sugars), sour (acids), bitter (complex organics), and salty (salts). The "hot" sensation of foods such as chili peppers is detected by pain receptors, not chemical receptors. But a report in 2006 reveals that contrary to popular belief, there is no tongue map. Responsiveness to the five basic modalities - bitter, sour, sweet salty and umami (a Japanese word meaning the savory or meaty taste of amino acids) is present in all areas of the tongue. |
Figure 19 Tongue |
Figure 20 Papillae |
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Figure 21 Sense of Taste |
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only become aware of them when other impulses are sent to the brain to "inform" what has happened. The path which impulses travel along during a reflex action is called a reflex arc. Not all the body parts receive the same attention of the brain. The relative importance is often represented by mapping over the length of the sensory or motor cortex. These cortical maps (Figure 22b) are not drawn to scale; instead they are variously distorted to reflect the amount the neural processing power devoted to different regions. This accounts for the grotesque appearance of the human body in the homun-culus, which is a translation of the body's sensory map into the human form. |
Figure 22a Propriocep-tors [view large image] |
Figure 22b Homunculus |
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Figure 23a Balance |
The vestibular nerve feeds its information chiefly to the cerebellum and to four structures in the medulla known as vestibular bodies. Using these data, as well as input from the other three sensory sources, the brain works out what to do, usually subconsciously. |
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It turns out that such structure of hair within gel to detect disturbance has been around hundred of million years in the shark and fish (Figure 23b). This is the neuromasts embedded in the skin of fish. They give the fish information about the flow of water. Amphibians and reptiles have a simple uncoiled inner ear. Jawless fish has only one semicircular canal instead of three in mammals (for detecting three dimensional movement). Ultimately, it is the Pax 2 gene that give rise to these structures. It is also known that the Pax 6 gene is responsible for the development of eye. The connection to ancient creatures goes even deeper when it is found that the box jellyfish carries a gene which is the combination of Pax 2 and Pax 6. |
Figure 23b Neuromast |
The box jellyfish is an amazing animal with more than 20 eye pits and many eyes very similar to ours. They seem to double for ears as well. |
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Now we known that it is the senses and the brain to keep us informed about the external environment through many special setups. In addition, the process consumes a lot of energy and requires intricate wiring (of neurons), it has to impose limits beyond which survival is not at stake (Figure 23c). For examples : the sight is limited to the visible range of the electromagnetic spectrum, the senses ignore those frequent inputs bearing no threat to life, and it processes inputs in discrete intervals (there are blanks in between that we are not aware of, see "Saccades"). Therefore, the brain not only distorts |
Figure 23c Threshold of the Senses |
the reality to suit the requirement of survival, it also neglects lot of details in order to expedite the task. It is definitely that we are not perceiving the reality, which is always modified by the brain. |
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As shown in Figure 02, the ability to modify our behaviour in response to life's experiences is shared by all animals including the bacteria E. coli. Such feat requires the brain's willingness to learn. Learning results in the formation of memories and in humans this process reaches its most sophisticated form, allowing us creatively to associate different reflections on the past, to generate new ideas, and most importantly to acquire language as a medium of expression and communication. Memory requires the brain to be physically altered by experience and it is this remarkable property that makes thought, consciousness, and language possible. The basic mechanism of memory formation is highly conservative over billion years of biological evolution. The difference in humans is that we have a lot more of the stuffs. There are about 100 trillion synaptic connections in our brain. |
Figure 24a Memory Classification |
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There are many ways to classify the memory. The concept of explicit and implicit memory refers to whether or not the recollection is produced consciously and intentionally. While the scheme of declarative and nondeclarative memory depend on the retrieval that can be declared verbally or not. Associative memory is triggered by clues; nonassociative memory can be habitual or sensitive. There are also short term and long term memory. One of the classification schemes is shown in Figure 24a. Table 07 is an attempt to put them all together. In the table, the declarative, and the procedural memory are explicit with the rest of nondeclarative memories being implicit. Only the working memory belongs to the category of short term memory fading away in hours, while the others are long term, and available for retrieval in years. Figure 24b shows the components, locations, and pathways for many types of memory. |
Figure 24b Types of Memory |
Type | Location(s) | Function | Example(s) |
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Working Memory | |||
Phonological Loop | Left hemisphere | Rehearsing verbal information to keep it in the short-term memory | String of numerals and alphabets such as telephone numbers |
Visual-spatial Scratch Pad | Visual Cortex | Controlling visual imagery | Scanning text |
Central Executive | Frontal lobe | Controlling awareness of the information in working memory | Constructing sentence, comprehending speech |
Non-declarative Memory | |||
Procedural Memory | Cerebellum, temporal lobes | Managing "how to" | Riding a bicycle, kungfu exercise |
Classical Conditioning | Cerebellum | Forming habitual behaviour | Coffee break, afternoon tea |
Fear Memory | Amygdala | Emotional conditioning | Phobias, flashbacks |
Nonassociative Memory | Spinal cord | Habituation and Sensitization | Decreased or increased responsiveness to stimulus |
Remote Memory (Priming) | Scattered around the cortex | Foundation for new memories | Childhood memory |
Declarative Memory | |||
Episodic Memory | Cortex | Remembering past experience | Some enchanted evening |
Semantic Memory | Frontal lobe, temporal lobe | Registering facts | Meanings of words and symbols |
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held in short-term storage may be important enough to be remembered for a long time and must therefore be transferred to a more stable form of storage, which is represented by far more robust alterations in the brain's chemical and physical make-up in the form of synaptic connections. It is not necessarily for an important experience to trigger the formation of long-term memories, other factors such emotion, practice, and rehearsal also facilitate the transformation. Experiments show that in all cases the most important underlying distinction between the short- and long-term memory formation is that the latter requires a dialogue between synapses and genes and the former does not. |
Figure 25 Working Memory |
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Figure 26 Nondeclarative Memory |
Nondeclarative memory can be classified to five main groups : |
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Figure 27 Long-term Memory |
Semantic, and episodic memory are the subclasses of declarative memory: |
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Figure 28a Declarative Memory |
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A memory is a collection of huge number of inter-connecting neurons called "Cell Assembly". It is estimated that there are about 1 billion cells in a human hippocampus storing at least 10000 different concepts; therefore each one of them would involve 100000 hippocampi neurons. While the hippocampus plays an important role, memory in the cortex is an integrated part for handling action, thought, sensory perceptions, .... |
Figure 28b Memory Making |
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and principles involved in its formation of short- and long-term memories are conserved throughout the animal kingdom, including in humans. Aplysia exhibits a behaviour of protective reflex in which the sea slug withdraws its gill into the safety of the mantel cavity in response to a mild touch stimulus to another part of the body called the siphon (Figure 29a). If the stimulus is repeated a number of times, the gill withdrawal reflex becomes weaker until finally the animal ignores the touch stimulus. The waning of sensitivity to repeated stimulation is known as habituation and is a very simple form of learning found in all animals, including humans. Another type of learning is sensitization, when we are exposed to an unexpected or strongly unpleasant stimulus. Generally the sensitizing effect of a single alarming stimulus is short-lived, lasting perhaps for just a few |
Figure 29a Memory in Aplysia |
minutes. But if the alarming stimulus is repeated a number of times our senses may be heightened for days and now such sensitization becomes a form of long-term memory. |
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As mentioned earlier, repeated activation yields a lasting increase in the efficiency of synaptic transmission -- a process called long-term potentiation (LTP) -- which is thought to underlie memory formation. LTP depends both on enhanced insertion of receptors for the neurotransmitter glutamate at spines (the sites of synapses) and on spine growth. Figure 29b shows the molecular basis of LTP as described in a 2008 neuroscience article. Essentially, it reports that the process is driven by the myosin V proteins, which shuttling receptors and membranes to make synaptic junctions better detectors of incoming signals. |
Figure 29b LTP, Molecular Basis of [view large image] |
A brief description for each step of the process is outlined in the following (also see Figure 29b): |
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It is reported in 2007 that the seat of memory has been pinpointed in mouse. By monitoring 260 neurons in the hippocampus (Figure 29c), researchers have discovered that different experience is recorded in different area called "clique", which can be categorized from very general to very specific. Furthermore, such brain activities can be translated into binary codes (Figure 29d). Supposedly, we can read the mind from such codes and tell what it is thinking by the process of backward translation. |
Figure 29c Seat of Memory |
Figure 29d Memory Code |
The followings are steps to uncover the memory code: |
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In an article commemorates the 50th anniversary of the "New Scientist" magazine, Roger Penrose suggests that there are three kinds of reality: the physical, the mental and the mathematical, with something (as yet unknown) profoundly mysterious in the relations between them. According to this view, the various "Quantum Interpretations" are attempts to link the mathematical reality to the physical or mental reality. Figure 30 shows the mathematical reality as the patterns of interference computed from a mathematical formula, while the physical reality is in the form of photographic plate with the darker strip corresponding to the higher value of the curve. The mental reality is the image of dark and white strips formed in the retina and perceived by our consciousness (the brain). |
Figure 30 Reality | He expounds the same view 14 years earlier in the same magazine in 2020. Insisting that there is a profound mathematical truth hidden from us. He has not yet come to terms with different levels of reality. Anyway, the ultimate real thing could be forever beyond our comprehension - something called TAO (道) as explained in the following. |
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Figure 31
| Figure 31 is a painting of Lincoln by Salvador Dali, who tried to "resolve the contradictory conditions of dream and reality into an absolute reality, a super-reality, or surreality". He had success in crossing the boundary of the rather boring reality via his paintings at least. |
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Figure 32 Mathematical Reality
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Figure 33
| Its existence does not depend on the brain or any interaction to conjure up some sort of sensation; while the mathematical formulation offers only an approximate version. We may never know the exact nature of this objective reality (see illustration in Figure 33). |
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Now according to the above context of different reality levels, the "Tao" (道) can be identified to the knowledge about the cosmos. Both the subjective and mathematical levels do not offer a complete explanation (but can be told). The real explanation is in the level of objective reality, but cannot be fully expressed in words or mathematics --- this is the "Eternal Tao" as envisioned by 老子. |