[leroyrandolph]

I don't really follow. Say, during the in-between step "10×3 + 6×3 + 5", how do you store and cognize the individual numeric and operator elements?

Surely, even if the arithmetics can be simplified and "lookup-table'd", you are still aware of the numbers in Arabic form or whatever equivalent you're using, right? Or do you somehow have 53 individual blobs swirling inside your consciousness?

[idiotsecant]

Not poster you replied to but it sounds like we might have a similar internal model.

I store numbers as pictures of numbers, or a geometric representation depending on how big or precise the number is.

Are you saying when you think of the concept of 'twelve plus twelve' you have the equivalent of someone in your head saying 'hmm, well twelve is 2 more than ten, so if I add up ten and ten and two and two I get twenty four?'

That's wild if so.

For your reference, I would follow the procedure above approximately, but visually with numbers that just do the thing that feels right. I think under the hood we're probably doing the same thing, just with a different interface layer

[jacomoRodriguez]

I can just speak for me, obviously, but yes, that is what's happening. But it's not someone, it is more like me explaining / telling it to myself. Depending on the complexity this can be more or less verbal - the more complex, the less verbal I would say.

[crooked-v]

In short, I just do. It's not a linguistic representation of the number 10, it's the concept of the number 10, the same way as (to extend on the mention of another comment) I don't need the word "cat" to know how to interact with a pet cat.

[wizzwizz4]

Language (human) and language (theoretical computer science) are different concepts.

[fc417fc802]

Not sure if it helps you make sense of it, but at least myself I only verbalize more complicated things. 10x3 for example I just "see" as 30 without needing to "think" or "speak" about it.

If you see a cat walking along the road, do you have to think to yourself "oh, that's a cat" or do you just know that it's a cat without verbalizing anything? It has its own abstract concept, right? Same thing with sufficiently simple numeric transformations.

> you are still aware of the numbers in Arabic form or whatever equivalent you're using, right?

Not sure if you're in a Fahrenheit or Celsius sort of place but if someone says that it's 70 degrees out do you really think in terms of numbers? Or do you just "know" what 70 degrees is without thinking about it?