Hello my friend, it’s nice to see you again.

Nice to see you V. What are we talking about today?

It’s been almost a year since we talked about the hierarchy of ambigrams. I would like to talk more about this, now that we’ve explored a third horizon, filter ambigrams.

(By the way, if you’re relatively new here, you can take a look at the chapter I’m talking about here.)

I’ll give you a quick review of what we’ve discussed so far.

Ambigram categories fall into hierarchy. The mind category is the fundamental one, since mind ambigrams contain the elements that make ambigrams work. That is, they contain the most basic, primary and substantial tools of duality in reading. The geometric category builds upon the tools used in the mind category. Here’s the image we’ve used to display this relationship.

Let’s remind ourselves of the number hierarchy.

Natural numbers (N) are 1, 2, 3 etc. Those are the most basic, fundamental numbers that exist. Then integers (Z) build upon those, they introduce 0 and negatives, such as -1, -2, -3 etc. Rational numbers (Q) build upon integers, they are 1/2, 2/3, 1/4 etc. Each and every group above builds on the most basic ones. Only irrational numbers break the mold. But, let’s leave that aside for the moment.

The same rule applies in ambigram hierarchy as well. Mind ambigrams contain the fundamental tools of duality in reading. Geometric ambigrams build upon those, but also introduce geometric transformations as well.

Now, the question is… where do filter ambigrams fall in this diagram?

In order to find out, we must examine the relationship between filter-geometric and filter-mind ambigrams.

Actually, it would be wise to say that we should only examine the relationship between filter and geometric ambigrams. That’s because, if filter ambigrams contain geometric ones, then they must contain mind duality tools as well. But who knows? Maybe filter ambigrams are something like irrational numbers, totally unrelated. Let’s see…

  Filter – Geometric

Let’s take a look at some of the filter ambigrams we’ve already seen.

In Athens-Athena, we experience reflection.

In dot-opt, we experience rotation.

In fried-fired, we experience translation.

Voila! We’ve achieved geometric transformations just by using filters.

This means that filter ambigrams build upon geometric ambigrams.

So, let’s update the ambigram category relationship diagram.

This also means that filter ambigrams must build upon mind ambigrams as well, since geometric ambigrams build by definition upon mind ambigrams. Let’s take a closer look at the lens ambigram ‘Athens-Athena’ once again.

Let’s focus on the s-a glyph. The reason that this glyph works is that it’s based on the middle-form duality principle. This means that the artist has drawn the middle form of a reflected ‘a’ and an ‘s’, as shown below.

So, the duality mechanism in this piece is a middle-form glyph, that gets reflected when seen through a lens.

Did you notice the pattern? Let’s read again.

The duality mechanism in this piece is a middle-form glyph (mind),

that gets reflected (geometric)

when seen through a lens (filter).

This proves that filter ambigrams build upon mind ambigrams as well, since filter ambigrams build upon geometric ones, and geometric ambigrams build upon mind ones.

This means, that our relationship diagram is formed like this.

Let’s simplify this a little bit.

That’s better. What do you think my friend? I’ve been talking for too long, probably.

I’ve been all ears throughout, Vassilis. It’s good to have the hierarchy map expanding as well.

I agree. These coffee breaks help us explore the ambigram worlds at a deeper level. Moreover, this hierarchy diagram will help us invent new ambigram types in the future. Maybe it’s not so simple to understand why, but I promise, you’ll see. All I need from you is time. After all, all good things take time.

I am thankful having you besides me for once again, my friend. Happiness in life is found in moments that bring us joy. I hope this was one of those moments that gave you a smile today.

Have a wonderful and blessed day.

Did you smile today?

If so, please drop a message at [email protected], and I’ll smile as well. 🙂