Another puzzle worth investigating (if it has not been done already) is this:
What percentage of young children, when learning to count, leave out the number Four, and if this really is a common thing, WHY so? And then, whether this digit is the same or different for different languages? (I invite parents to share their experience).
I believe, since children are taught rudimentary Arithmetic early on by rote learning (1) reciting a sequence of number as it were no more than a mere rhyme and riddle, and (2) restricting things to addition for very long, that adults may have failed to recognise some universal (if not genetic) aspect, one which children might be attempting to point out to adults about numbers (with their limited lexis).
Why do we even assume that children need to learn that 1 comes before 2, and then by adding these get 3 and so, (as if this wasn’t clear to even a baby what one is or even 3 ones) and without listening to how our ‘little angel’ (as mothers will call their child) are already getting it?
To this end I think that it just may be that Arithmetic, as taught today, is a useless, if not a counterproductive, way of teaching children, who may see the world beyond Newtonian dimensions, than those of our educational system degenerate.
Let not pedantry perturb and pedagogy get in the way of other possible logics.
Do let children contemplate the meaning of ONE, of ZERO, and of TWO, but leave them to take the liberty of calculating for themselves the rest, and perhaps learn according to another way of seeing things. If anything, teach them Prime Numbers; teach how numbers are related to sound.
Now here’s just one other possible logic, for instance:
(1) One is only one as long as there exists an other, extra one (in play), otherwise it is (still) ‘zero’.
(2) According to the above-said then, one and one therefore make One, not two, one being nothing without (at least) one other.
(3) Two, then, is ‘perfect’ as it attracts and bonds and, as like attracts like,
(4) Two is only a potential duality once a ‘one extra’ One is involved (or what we might call ‘THREE is a crowd’).
(5) Two is then still only One until an extra third one defines it as being Two.
(Each one dependant on the next for it to be called anything).
But back to my question of how come Four might often be skipped when counting upwards:
If not the highest digit, Four is perhaps a redundancy, but another Two; Five would be then just two Ones plus another One. Or Six means either 2 or 3, and that 7 gives Six meaning by its having an extra One. Children, on mentioning 8, will revel.
If I’m losing you, I ask that you look more than just superficially, or linearly, at the digits themselves; why not search deeper into the meaning of a number in relation to a ‘bigger picture’ behind what each can represent: Namely within the context of sound and of spirals and other natural phenomenon (we so like to disconnect from).
To paraphrase Dr Len Horowitz (YouTube): Eight (8) represents divine femininity and God. (Who dares mention that word in a Maths class, right?) When you put a 6 on top of a 9 (or vice versa) it looks like an 8. Moreover, when you put a 3 and another 3 reversed, and put these together, you also get an 8. God aside for the moment, why not at least look at numbers in their symbolic value, as well. [Dr Len Horowitz sees English as but a ‘alphanumerical’ coded language which corresponds to Hebrew in reverse].
Or here’s another way of looking at numbers, following Marko Rodin:
Form a circle with 9 at the top, and 8 and 1 at each side. Below these 7 and 2, 6 and 3, and 5 and 4 (all adding up to 9 by the way) so that on the left you’ll have 8, 7, 6 and 5; and on the right 1, 2, 3 and 4 in a circular fashion. Geometrics.
There are nine core creative frequencies, or the Perfect Circle of Sound:
174, 285, 396, 417, 528, 639, 741, 852, 963 (Hertz)
And within this circle you have 3 triangles.
For starters, let’s take the 3 and 6 (with 9 at the top of the circle, forming a triangle);
In music, primarily indication of harmonic intervals (either major or minor).
The other two triangles are 5-2-8, or 2-8-5, or 8-5-2; and 1-4-7, 7-4-1, or 4-1-7.
The Nine (9), in Chandrakantha Tabla technique, represents a ‘silent’ beat. Nine comes after 8 (completion), and before 10. When 0 is between 1 and 8 (which when put together make 9) you get the ‘auspicious’ 108.
(Why 108 is auspicious is perhaps another story, but it does represent 9). Anyhow…
231 – 123 (6) = 108 (9). Move 8 to the left and you get 810. 810 – 108 = 702 (9).
Back to 3s, 6s and 9s:
639 – 396* = 243 (move 3 to the left to get 324)
852 – 528* = 324 but so does 741 – 417 = 324 (9)
Now move 4 right to left and you get 432.
618 – 186 = 432 (9)
Take 528 and move 8 to the left to get 852. (Jamie Buturff (on YouTube) will explain it another way)
Incidentally, the speed of light is 432 squared. 432 Hertz (sound pitch) is a representation found everywhere in nature and in the cosmos, mentioned in works by Vernon Jenkins, Pythagoras, Joseph Puleo and Marko Rodin, among others.
So too is 528 argued to be significant (i.e. corresponds to the heart chakra).
In relation to 432 Hz, the tones of the Chakras (and Tibetan bowls) are tuned:
A= 216, 432, 864 (Crown)
D= 144, 288, 576 (3rd eye)
G = 192, 384, 768 (throat)
C = 128, 256, 512 (heart) * see also Pythagoras tuning
F# = 182, 364, 728 (solar plexus)
Eb = 303, 606, 1212 (sacral)
Bb = 228, 456, 912 (root chakra)
Traditional Solfège in equivalent Hertz are: 256, 288, 324, 344, 384, 432, 486, 512
But these are said to be a false representation of music, since these numbers are not meant to represent frequencies, or pitches, though they do represent number family groups. The fact remains that music in Western culture is suppressing the Music of Creation (by having the standard concert pitch tuned to 440 Hz). 528 Hz is said to be equivalent to Chlorophyll (Horowitz).
Well, in any case, we need to consider dearly why it is we still want to teach arithmetic the way we’ve done.