What’s amazing, Aaron, is that you guys – and it is general – have a virtual cognitive deficit here -
a complete inability to recognize that regular units are fundamentally
different from irregular units, and general (regular) units are fundamentally
different from individual (irregular) units – and that science which depicts
general classes and what they generally have in common, is fundamentally
different from the arts which depict individuals and what makes each one
different and distinctive. Generalizations about “human beings” are
fundamentally different from individual portraits of “Hamlet” and “Falstaff”
and “Holden Caulfield” and “the Mona Lisa.”
You can’t boil down the one to the other – they are opposite and
**complementary**. But there is an absolutely mad egocentricity esp. in this
field, but also in the whole of science, that refuses to understand or even
look at the opposite position.
Formally it comes down to this – and it is no abstract philosophical issue –
but the centre of AGI -
there is no formula for :
There is no formula for a group of irregular units – there is only a formula
for a group of regular units.
This is a simple truth. And y’all cannot either disprove it or deal with it.
The common mistake you all make over and over - and it’s painful – is to say:
“but I can reduce that shape there to a geometrical definition.”
Yes, you can reduce ONE shape to a geometrical definition, but you can’t reduce
ALL of them – the whole group.
But the human mind CAN reduce all the above irregular units to one common
SCHEMA of “blob[s]”.
Not a common formula, but a COMMON SCHEMA.
And that is the central unsolved problem of AGI.- to give machines that
capacity to **schematise diverse irregular units** – which is fundamental too
to creativity generally, not just object recognition and conceptualisation.
Frankly, this field may well be the most creatively unimaginative in the
history of technology.
Faced with a major creative problem – *how does the brain schematise irregular,
diverse objects?” – all this field can do is to plug the same old technologies
over and over – and just utterly refuse to think of anything new. Which is
simply WRONG – it never has worked or will work.
You are all esp trying to plug maths when it is failing utterly in terms of AGI
-
all trying to think inside the same old boxes.
Well, this is both literally and creatively, an area where the solution lies in
thinking outside the [geometric] box. Moving into a whole new formal field.
One way or another, you will never find a formula for those blobs/islands/cells
above. And I can present the same old problem in different guises to you over
and over, and you will all always run away from it.
I’ve also presented the solution to you – at a philosophical level. And that
level is translatable into mechanical terms.
From: Aaron Hosford
Sent: Tuesday, November 06, 2012 4:38 AM
To: AGI
Subject: [agi] Randomness: Mathematics as Perceptual Bias
Mike, here's something for you to chew on:
I like to think of the term "random" as meaning the absence of a detectable
pattern, due to biases and/or blind spots of the observer or perspective. Under
this definition, it is implicit that anything can be seen as random or
non-random given an appropriate observer or perspective.
I think our minds are simply filters for reality, designed to pluck out the
most common and useful patterns through appropriate biases. We look for the
patterns we do because they help us accomplish our evolutionary purpose. When
something looks random to us, it simply means we can't identify a pattern, not
that there isn't one.
Mathematics is a language for representing the sort of patterns the human mind
tends to perceive. It is, in other words, a language for representing reality
in terms of our intrinsic human perceptual biases. We have integer arithmetic
because we perceive discrete, countable units in the universe. We have calculus
because we perceive continuous phenomena such as curves, areas, volumes, and
flows in the universe. We have geometry and topology because we perceive shapes
and invariances of shape in the universe. We have logic because we perceive a
mapping between situations and their descriptions (language, including math) in
the universe. And we find commonalities and relationships between the various
branches of mathematics, described in the terms of logic because logic is the
language we use to talk about languages, including those of mathematics.
Much of the confusion and failure generated by Boolean logic, the most commonly
used and least versatile form of "fully functional" logic, arises from the
failure of Boolean logic to recognize the distinction between different kinds
of false statements (pieces of language). Boolean logic only recognizes
statements that are false because their opposites are true. But it completely
disregards the existence of statements which cannot be mapped to reality to
verify their truth. These sorts of statements are not false because their
opposites are true, but because they are meaningless. This lack of distinction
(a bias towards perceiving truth and falsehood but not meaninglessness) is the
source of many mathematical and logical paradoxes.
As for your "irregular forms", Mike, what all this boils down to is that if the
regularity of some aspect of the world isn't visible to mathematics, it isn't
visible to people. Mathematics simply codifies what our brains already do. When
we notice a regularity in reality, we create a branch of mathematics to
describe it. If we don't see a regularity in a portion of reality, we call it
random and mentally disregard it. I am identifying concepts themselves as
human-perceivable regularities in the world, in case that isn't readily
apparent. Thus if we can conceptualize something, it must be regular in our
minds, and either a branch of mathematics exists to describe those
regularities, or we can create one. (These new branches of math always start
out as human language and become steadily more formalized as we become more
certain about what the regularities are and how to more effectively describe
them in language.)
So, in summary:
1) A concept is a human-perceivable regularity.
2) Mathematics is a highly refined language for describing human-perceivable
regularities.
Therefore:
3) Mathematics is a highly refined language for describing concepts.
Mathematics (and language in general) is how we tell each other about the
world. If something can't be described in terms of mathematics, it's because it
either can't be perceived, or we have identified a new branch of mathematics
that needs to be created. Eventually, we will have covered all the filtering
biases evolution has built into our minds, and mathematics will be sufficient
to describe all concepts the human mind can perceive without further additions
to the language.
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