Aggregate Quotes

“We must consider what we mean when we say that the spiking activity of a neuron 'encodes' information. We normally think of a code as something that conveys information from a sender to a recipient, and this requires that the recipient 'understands' the code. But the spiking activity of every neuron seems to encode information in a slightly different way, a way that depends on that neuron's intrinsic properties. So what sense can a recipient make of the combined input from many neurons that all use different codes? It seems that what matters must be the 'population code' - not the code that is used by single cells, but the average or aggregate signal from a population of neurons.
In a now classic paper, Shadlen and Newsome considered how information is communicated among neurons of the cortex - neurons that typically receive between 3,000 and 10,000 synaptic inputs.They argued that, although some neural structures in the brain may convey information in the timing of successive spikes, when many inputs converge on a neuron the information present in the precise timing of spikes is irretrievably lost, and only the information present in the average input rate can be used. They concluded that 'the search for information in temporal patterns, synchrony and specially labeled spikes is unlikely to succeed' and that 'the fundamental signaling units of cortext may be pools on the order of 100 neurons in size.' The phasic firing of vasopressin cells is an extreme demonstration of the implausibility of spike patterning as a way of encoding usable information, but the key message - that the only behaviorally relevant information is that which is collectively encoded by the aggregate activity of a population - may be generally true.”
― Gareth Leng, The Heart of the Brain: The Hypothalamus and Its Hormones

“In the second place, however, history is made in such a way that the final result always arises from conflicts between many individual wills, of which each in turn has been made what it is by a host of particular conditions of life. Thus there are innumerable intersecting forces, an infinite series of parallelograms of forces which give rise to one resultant — the historical event. This may again itself be viewed as the product of a power which works as a whole unconsciously and without volition. For what each individual wills is obstructed by everyone else, and what emerges is something that no one willed. Thus history has proceeded hitherto in the manner of a natural process and is essentially subject to the same laws of motion. But from the fact that the wills of individuals — each of whom desires what he is impelled to by his physical constitution and external, in the last resort economic, circumstances (either his own personal circumstances or those of society in general) — do not attain what they want, but are merged into an aggregate mean, a common resultant, it must not be concluded that they are equal to zero. On the contrary, each contributes to the resultant and is to this extent included in it.”
― Friedrich Engels, On Historical Materialism

“If the exchange act may thus be regarded as a creation of society, it is
no less true to say that both society and the individual become aware of
this only after exchanges have been completed. The work of an individual
is, first and foremost, his own individual endeavour, motivated by his
own self-interest. It is his personal labour, not the labour of society.
But whether or not it conforms with the requirements of the total
circulation of goods, of which his labour is necessarily a component
part, can be determined only when all the component elements have been
compared and the aggregate requirements of that circulation have been
completely satisfied.”
― Rudolph Hiferding, Finance Capital: A study in the latest phase of capitalist development