What is a good way of conceptualizing intelligence in the sense that lay people use the term?
It is mostly an ability to think - rather than an amount of knowledge (much knowledge is, rather, a result of intelligence), intelligence is quantitative (people can be more or less intelligent)...
High intelligence is (I would say) a combination of two attributes: thinking rapidly about a large number of things simultaneously
Intelligence could therefore be reduced to a combination of fast processing speed (i.e. 'g'), and a large working memory.
So, how do people think (intelligently)?
I envisage intelligent thinking as going on within a 3D space - and the subject matter of thought being something like complex 3D shapes in this space.
But all thinking must be done in a finite time-frame - say 5 seconds (just to clarify the explanation).
(This 5 seconds represents that the neurons which do the thinking can only be activated (and interact) for a finite time - and that thinking therefore occurs in a time window. Thinking can only be done over about 5 seconds because after that time the earlier information will fade and be lost. That is, only a finite number of things can be 'held in mind simultaneously" - and the "simultaneously" therefore actually boils-down to the period of time in which an idea can remain active while other ideas are added to the 3D space.)
The number and size of 3D shapes is constrained by the size of the space (ie. the size of working memory) and the stuff that can be done with them is constrained by the speed with which manipulations can be performed.
So, there is a maximum of 5 seconds in which to manipulate the ideas (3D shapes) - and higher intelligence means that either more manipulations of ideas can be done in those 5 seconds (because the processing speed is faster), or else that more ideas can be manipulated in 5 seconds (because working memory space is larger) - or both of these (more rapid simultaneous manipulation of more ideas).
What results from this thinking is
So, what is the role of experience and knowledge?
I envisage learning as a matter of chunking.
Chunking is the process by which ideas are summarized or condensed - so that instead of memorizing 1 2 3 4 5 6 as six pieces of information, it could be remembered as (say) two chunks of 123 and 456, or a a single chunk which abstractly represents "the first six digits".
In other words, by chunking we 'encode' information, in a smaller and briefer form. In effect, chunking takes many 3D shapes and encodes them into one 3D shape which can later be decoded to yield the many shapes which made it.
When a person is learning, they are (in effect) taking large amounts of information and encoding them into 3D shapes - so that each shape can be decoded to yield a lot of information.
So a trained and experienced mathematician is able to think using ideas that could be understood as highly-encoded 3D shapes. And indeed, mathematical learning could be imagined as an iterative or cyclical process of chunking, then chunking these chunks into new chunks; by which more-and-more complex ideas are encoded.
(Many ideas are encoded into one chunk - then many of these encoded chunks are combined into one chunk - and so on.)
The basic 'intelligence' is still constrained by the number of ideas which can be held in mind 'simultaneously' (i.e. over a 5 second timespan) and by the speed of manipulation which constrains the number of manipulations possible in 5 seconds.
In other words, intelligence remains constrained by the fixed values of WM size and 'g'/ processing speed.
But after the manipulations are finished, after the thinking has been done; each 3D shape (or the resulting combinations of shapes) can (in effect) be decoded (and the products of decoding themselves be decoded, perhaps many times) to yield potentially a very large amount of information.
So, this model explains how people may suppose that 'intelligence' (in a lay sense) is increased by education, training, knowledge, experience etc - while the real underlying intelligence (consisting of 'g' reducible to processing speed, and Working memory) may be innate, fixed, mostly inherited.
And the cyclical, iterative chunking produced by education and experience, may disguise declining intelligence - either in ageing individuals whose processing speed is slowing, or in a society subject to dysgenic decline of 'g' with a generation upon generation slowing of processing speed.
What this means is that an increasingly specialized and prolonged education can result in exactly this kind of multi-cycle iterative chunking, so that within a specialized field the use of more complex chunks can disguise the decline in processing speed.
In other words, declining 'g'/ processing speed, means that less processing can occur in the constraint of the 5 second time window - but the ideas being processed (within the specialist domain of a specialized education and experience) may be more-complexly encoded. And this may superficially disguise the decline in processing speed.
BUT if an average modern person (with slower processing speed) had the same education and training as the average person of 150 years ago - and was thinking at the same level of generality - then there the average modern would display a very clear inferiority in terms of the maximum complexity of function.
AND THIS IS WHAT WE FIND - modern intellectual life is characterized by what I have termed microspecialization
(See the chapter "No such thing as ‘Science’ anymore" in http://corruption-of-science.blogspot.co.uk )
So, a human geneticist may function intellectually at a high levels within his microspecialism - but will be utterly incompetent at thinking in terms of genetics as a whole, or natural selection, or biology generally; so intellectual life is necessarily fragmented into 'autonomous' micro-units - when when the average intellectually sluggish modern person tries to think in general terms about general issues, they reveal an often embarrassing degree of simple-minded incompetence.
Because processing speed has declined, the average modern person simply cannot do much manipulation of ideas within the '5 second' temporal constraint of working memory - when compared with what was normal 150 years ago.
Except on familiar territory, modern people therefore cannot follow complex (several step) explanations which were comprehensible to previous generations - in effect because the beginning of the explanation has long since faded and gone before they can get to the end of it!
(More exactly, when the 3D space of WM has been filled with ideas, not much in the way of manipulation can be done with these many ideas in the brief time available before these ideas fade and are lost, and need to be re-loaded afresh.)