If no one asks me, I know what it is. If I wish to explain it to her/him who asks, I do not know.
As the case of St Augustine with the time, memory is also a difficult thing to understand.
It's meaning, function and infrastructure is different in biology (see the role od DNA, RNA), in neurophysiology (synaptic potentiation), IT settings (flash memory, external HDD-s) or history, archaeology, other sciences - and ultimately at the level of the whole society.
Can we find such a definition for memory, which would be universally valid?
Memory is a cognitive state (occurring now!) that we infer must have occurred before given what we believe to be true now.
Guillaume and Jonathan: yes, memory has a definite transtemporal character, which respects the arrow of time: memories formed in the past are used now or in the future, and the memories formed at the present could be available in the future – but never in the past. This should be a commonplace observation – although since the winners are those who are writing history, it's not so simple.
As Christopher emphasized, our memories can be related to what we believe true now (which is a quite remarkable formulation) – and this aspect is relevant for the memories related to the conscious processes.
In my oppinion the memory is an aptitude, a capability which is present in some of the unconscious sytems also – free from these cristopherian limitations of the conscious systems.
Let me try to demonstrate an attempt to classify memories, based on some supraiacent layers
I. Unconscious Systems
I.1. Genome: DNA chain>genetic code>proteins
I.2. Neurophysiology: sensorial inputs> synaptic potentiation in neural circuits > ideas, concepts
I.3. IT settings: data>ASCII code or other alphabet> remanent electron configuration (flash), writings, books, etc
II. Conscious Systems
II.1. Sciences: facts, observations>christopherian truth
II.2. Society: perceived reality>governing Memes
The main point is, that on these levels data or raw information are encoded according to that level's specific rules and preserved to act later to steer the behaviour of the whole system.
Our personality, our endeavours and activity are coded in these five levels of memories, which determines us.
That's why we are our memories. And our friend's memories and of the neighbour's and of our acquintance's and so on (with the christopherian limitations in the latter cases, of course :-).
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