The unconscious ambiguity that defines our lives...

Alrite, this little idea, originally introduced to me by my brother, found its second life when I chanced on the following lines in a wonderful book, courtesy Ajit:

"No mathematician has ever seen an integer! When we read "1994", we read a word whose letters are called numerals."

Pause, think, and move ahead.

I shall mostly agree with you if you say that visualizing numbers doesn't really make too much sense in the first place. But even then, one can't help but feel a LITTLE duped, when learning that, that which had defined the basis of one's mathematical prowess, was little more than a derivative from language.
(A debate on whether mathematics is the father of language and all other sciences, or vice versa, is BEYOND the scope of this particular post!)

It would be instructive to consider another example. This time more easy relate-able.
You see a red rose. It is your brain that tells you that the shades of the delectable little creation in front of your eyes, are closest in its RGB mix, to that of Red.
But what is red in the first place?

Is it not the colour that your mom/dad/teacher/anywho called out, when pointing to apples, Manchester United memorabilia, and yes, roses, when you were 3.1 years old, and innocent to such boundaries of chrominance?
So, what is red to him/her?

Instead of embarking on that infinite loop, I'll take an unconditional jump, to:
What you perceive to be red, is ONLY what YOU perceive to be red. As of today, (to the best of my limited knowledge), there is NO way for you to confirm, that "your red" is the same as "your neighbour's red". That is, it is possible that you might be calling Team India's jersey "Blue", in spite of it seeming to be what your neighbour would call "Red".

Next, I shall proceed, as is rather straightforward, to generalizingly extrapolate to cover the remainder of the senses.
Partially ignoring the subjectivities of aesthetics:
1. it is possible that the audio filters present in my ears end up transforming what might be Yanni to you, into your Metallica, for me. And given my programming since my most impressionable childhood, I have grown to appreciate "that Yanni", as you appreciate "your Yanni".
2. it is possible, that I actually feel "your cold", when touched by a "your hot" pan, but I call it "F#$@ that was HOT!", given my programming since my impressionable childhood.
3. I needn't go on now. You can very well see how sight, sound and touch can be extended to smell and taste.

Enough for now!
Without further ado, I shall leave you and your self, to talk it over on whatever it is that you're thinking right now.

Cheers duniya!