# Annotations

## perceptual origin of math

https://perceptualoriginsofmath.wordpress.com/chapter-3

> One reason why this amodal percept is so easily overlooked, is that it is not really a visual experience as such, even though it is often informed by a visual stimulus. When I encounter a box in pitch darkness, or with eyes closed, and feel it with my palms, I get the same amodal experience of a rectangular volume in a specific location in my space, and I perceive the whole box, through to its rear surfaces, even though I palm only selected faces or corners of the box at a time. And when I turn on the lights, or open my eyes, the tactile texture of the box felt by my palms is experienced on the very same rectangular volume as are its color and brightness that I perceive visually.

very bubble world-y

Apr '25

> In other words, the spatial structure that is our amodal experience of the world is the common ground, or lingua franca, that unites all sensory experience in a modality-independent structural representation of the world, and that amodal structure represents our perceptual and cognitive understanding of the world.

hmmmmm, but what about stuff that isnt amodally spatially perceived? like hearing words

Apr '25

> Amodal perception is the earliest, most basic form of mental imagery, one that we certainly share with almost all visual creatures. But amodal perception is also the door that opened perception to cognition and free-wheeling mental imagery, and true human intelligence, connecting the world of direct experience to the world of imagination.

hmmm, this is analogous to the invention of language but for our visual field. neat. symbols in our spatial field to represent concepts and not just sensations

Apr '25

https://perceptualoriginsofmath.wordpress.com/chapter-1

> But the concept of numbers runs much deeper than a simple one, two, three. Before you can even think of counting, you have to understand the concept of countable things. Whether you are counting people, coins, or pebbles on a beach, you must decide on the set of things you want to count, and what requirements you should establish to qualify for inclusion in that set. How big can a pebble be before it counts as a rock instead of a pebble, and how small before it counts as a grain of gravel or sand? The answer depends on why you are counting them, that requires a fine mathematical judgment. Counting requires that all the members of the set can be considered equivalent, interchangable, they each count for exactly one. This is so natural and obvious an assumption (to us humans) that we don’t even realize that we are making it. But it is an artifact of the human mind, not of the natural world, that things come in identical countable units. In reality pebbles are not at all identical, each one has its own unique size and shape and color, and the distinctions between rock and pebble and gravel are overlapping and indefinite. The fact that we can make ourselves see a set of pebbles as identical units is itself a conceptual feat that is a prerequisite to learning to count them.

good point. even our math is so anthropomorphic

Apr '25

> The schema is the framework that gives meaning to the math. It is what poses the question in the first place, and what interprets the meaning of the results at the end. That is the real mathematical thinking beyond mere arithmetic, the framing of the problem to be solved, the selection of the algorithm to be used to solve it, and understanding the significance of the results after the counting is done. The counting itself is the simplest part of the problem – so simple that even a stupid computer can do it. But conceptualizing the situation and seeing the schema in it, is in fact the real mathematical part of the task. The rest is merely arithmetic.

Apr '25

> Real mathematical thought is an embodied process, one that cannot be meaningfully separated from our direct experience of our body located in the world.

Apr '25

> And yet the digital computer is totally incapable of even the most primitive mathematical thought. The computer is completely incapable of conceptualizing a schema, or understanding the significance of the quantities that it calculates. It seems that there are two starkly contrasting aspects of math, one which is thoroughly understood, which can be performed by stupid machines even better than by humans, the other that we all do unconsciously and instinctively virtually every waking moment, but have no idea how we do it or even what it is we are doing.

i think the "building schemas" is nothing but our consciousness, given to us by the medium of language

Apr '25

https://perceptualoriginsofmath.wordpress.com/chapter-2

> And yet at the same time I do see a totally invisible mental image of a table in that same empty space, or at least in a space that is somehow superimposed on my normal visual space. I can both see the mental image, in an invisible ghostly way, and at the same time I don’t see anything at all. Furthermore, what little I see of the imagined table does not always have a specific location, nor a specific size or scale, nor a specific viewing angle, nor a specific color or furniture style. The “image” of the table (if it can be called such) often appears either fleeting and unstable in location, scale, and orientation, or it appears totally abstract, non-spatial, as if expressed only in some symbolic non-spatial code, like a node in a neural network model that is labeled “table”. It is this fleeting evanescence and instability of the mental image that allows so many to deny its very existence as a spatially extended image in our imagination.

Apr '25

> The fact that it is possible to form a mental image with a specific location and specific dimensions, and to mime its morphology with your palms, is proof that mental images can exist as stable three-dimensional structures, and that they can carry a specific information content. And the mental image can be formulated to have a specific location and spatial extent, even if it is not usually specified so precisely, but often remains in an indeterminate state. The fleeting evanescence and instability of many mental images should not be viewed as counter-evidence for their existence as images, but is merely evidence of a fleeting and unstable imaging system, one that is capable of representing multiple possibilities all superimposed, much like a quantum particle that can exist in multiple states simultaneously. Like a quantum particle, the mechanism or principle underlying the mental image can apparently flip or morph continuously into different forms, unless it is held to a stable state by an act of will.

hmmm where is he going with this

Apr '25

> has called this kind of vision “amodal” perception, because it is perception in the absence of a particular visual modality, such as color or brightness. We see a square in our imagination, but it is in a kind of invisible outline form, like a figure in a geometry text, without color or substance, just a shape.

the modality is actually the electromagnetic storm brewing in your head

Apr '25