A tetrafoo is four times the size of a barbaz. Tetrafoos are pretty big things, about the size of a washing machine.
Now I've said nothing specific about either these things, besides size.
Can you tell me if a barbaz fits through a door? Probably.
Can you see that you can reach that anwser without doing any math about how big doors and washing machines are, but just with implicit knowledge?
The source of truth here is not visualization, it's knowledge. In fact, whatever you visualized, I gave you too little details so that your visualization would have to make up extra things that aren't true. You don't even know if the shape of those things is square or circular.
So even if you can't do it without visualizing, you should see that visualization is really just pulling from some other source (abstract knowledge). You can bypass that step and just get to know the result, without visualizing it.
Possibly with numbers. Can you properly visualize a tennis ball next to a baseball and tell which is larger? I was never much of an athlete (in the sports ball sense, at least) and have insufficient experience with either to tell you definitively which is larger (I looked it up, my guess was baseball and that turned out to be correct). The fact is that a small but still standard sized baseball is only 5mm larger than a large but still standard sized tennis ball. That is near enough that my memory (I played baseball last as a kid) could not distinguish between the size of the two objects.
But now I know the fact, a standard baseball is larger than a standard tennis ball (now, don't ask me in a few weeks what the actual sizes are, I will probably forget, though I will probably remember that the baseball is larger).
Another way is just having knowledge of relative sizes and the ability to perform rudimentary logic. A tennis ball feels about the same in my hand as a door knob (in terms of size and ability to wrap my hand around it, bigger than most but not by too much). A keyhole fits into a doorknob. I'd have to be really drunk to not realize the logical implication of that: A tennis ball won't fit into a keyhole (assuming both are standard sized and we're not talking about a comedian's prop key and keyhole).
If you think of a bowling pin vs a baseball bat, do you have such a specific visual image in your mind that you could compare their sizes?
I'm particularly curious about a bowling pin because we often only see them from far away, so size is harder to gauge in the first place. I can't form detailed images of anything in my mind, but those images are also all "normalized" to an extent - e.g. in my head, both bowling pin and baseball bat seem to be similar in size. Even though that's very much not true. So to me, visualization and size comparison are totally different faculties.
Even though I've never held a bowling pin or been close to one, I know how big a bowling pin is because I've seen the ball hit the pin at the end of the lane and I've held the ball in my hand.
A bat is definitely longer than a bowling pin, but not by much. I don't see either in mind when doing this referencing.
These ideas are linked through memories of spatial relatedness, not imagery.
I once had an interesting discussion with someone who had participated in unique treatments for PTSD. The councilors advised the patients, when they saw disturbing imagery in mind, to place the imagery on a poster. They indicated that most patients could do this task. They then proceeded to have the patient put the poster on the wall "across the room". The image "shrunk" in mind by forcing it into spatial perspective. They then had the patient put the poster on a telephone pole "across the street". This shrunk it even more. A diminishment in the strong feelings (stress) related to the imagery was reported in some patients. So, the smaller something appears, the less some appear to react to the imagery. Small monsters vs. large ones, I guess.
When you do mental arithmetic, say 48 added to 73, do you visualize 48 objects and 73 objects and then count them? Do you visualize a page like a 1st grade arithmetic homework sheet and draw out the numbers with a mental pencil and do all the carrying by mental hand? Or do you “just” add them and end up with 121 in your head?
I don't assign numbers when mentally comparing things. I compare them relative to each other. I think that's why it's hard to compare things that have a large difference in size.
Now I've said nothing specific about either these things, besides size.
Can you tell me if a barbaz fits through a door? Probably.
Can you see that you can reach that anwser without doing any math about how big doors and washing machines are, but just with implicit knowledge?
The source of truth here is not visualization, it's knowledge. In fact, whatever you visualized, I gave you too little details so that your visualization would have to make up extra things that aren't true. You don't even know if the shape of those things is square or circular.
So even if you can't do it without visualizing, you should see that visualization is really just pulling from some other source (abstract knowledge). You can bypass that step and just get to know the result, without visualizing it.