Some talk too much, others don’t dare to – but too many without a clear intention in mind.

The central sentence that stuck with me, when saying something is:

“Every minute you talk, equals N minutes of your N listeners..”

That means, on the one hand, that your time speaking is extremely costly: Don’t waste the time of others!
That means, on the other side: Your opinion is incredibly cherished, as the others give you the chance to be heard.

Therefore, I always ask myself initially: Does my part help? Do I contribute something new?
Do I just repeat something said? Is it important that I share my opinion here?

And from this, immediately a goal follows: What do I need to say, that my contribution makes sense? What can I leave out? How do I reach my goal?

With this, the spoken word becomes directly more focussed and also more meaningful.
For this, I want to share a last quote from the book Imperium about the life of Cicero:

“Speak up. Make them laugh, make them cry. And when you are done, sit down again.”

The difficulty in finding the “right thing” in “real world problems”

In my opinion, there exist in real world problem almost never a right way, but always clear wrong. With this, I don’t mean that all ideas of others are bad :), instead that no solution will ever be perfect.

And I think this increasingly influences public discourse, when less and less understanding and willingness to compromise is shown, to understand the other side.

Most solutions to a problem are a balance between ambition (will this actually make a difference?), legitimacy (Do the end justifies the means?) and practicability (Can we actually do this?). It is immensely difficult to find a solution that satisfies all fields, never mind answering all questions with “yes”. There are, however, ideas that are “wrong” in any regard – e.g. when answering all questions with “no”.

The way to compromise lies now in several aspects:

On the one hand, one also has to listen to their reasoning for their solution. On the other hand, one needs to share, where the other’s idea lacks. Afterwards, both should try to constructively find a (not necessary good) solution acceptable by all parties.

But most often, the discourse ends much earlier – I sometimes have the impression: Half of discussions are about semantics (the meaning of words) and the other half, because both sides are using different meaning of words (so because they didn’t discuss semantics ).

Probably, I oversimplify here (I think if you switch the word semantics with assumptions, it would be more correct), but this shows the important second part for constructive discourse: Both sides must agree on the same language and their interpretation.

And this language is different in comprehension than in the literal expression, because only last is unambiguous. A good example is following article/ reddit post. These show a depiction of a distribution, on how people understand the qualitative words from abysemal to perfect. In this, it becomes apparent that all words aren’t rigid to a single value, but encompass several values, or even ambigously several maxima. If now the other person in a discussion has a different perception of the same words, an agreement will become immensely more difficult.

The same, one has to accept also for the truth value of some statements: Some assumptions are not entirely true, but also not entirely wrong. This is a fact captured in the concept of fuzzy logic.

But this doesn’t mean, that no one can state assertions, or that all compromise should capture imprecisely different opinions without agreeing in a final decision. On the contrary, one should use these tools to distance from clearly wrong solutions and find true solutions in a common language.

Dimensions for qualitative properties –
A maths algorithm transferred to general purpose

Often, I have the impression that a mathematical concept would be incredibly helpful here – Especially in discussions outside of maths. And don’t worry: I don’t mean everyone should be an expert in maths – on the contrary: Let me share here an idea, in a way that may help a lot of people.

The problem

Let’s look at complex, multilayered problem. E.g someone (in this case gemini) wants to discuss the “The Digital Divide” and notes several facets:

Economic: The cost of access to high-speed internet and digital devices varies significantly across different socioeconomic groups, creating a digital divide between those who can afford it and those who cannot.  

Geographic: Rural and remote areas often have limited access to high-speed internet infrastructure, further exacerbating the digital divide.

Social: The digital divide can contribute to social inequality by limiting access to education, employment opportunities, and social services.

Cultural: Different cultural groups may have varying levels of familiarity and comfort with digital technologies, which can further widen the digital divide.

Ethical: The digital divide raises ethical concerns about the distribution of information and resources in the digital age, as well as the potential for further marginalization of already disadvantaged groups.

But the question that comes up is: Is the problem so well discussable, the parts clearly determinable? Or otherwise, do these criteria help us to describe it? Not really. Because, somehow, all seem to be dependent on each other …

What we would need are well-chosen dimensions, or criteria, which make it tangible. Ideally, these would be independently describable and adjustable (mathematically called, orthogonal). But how would we find those?

The idea

The Gram-Schmidt orthogonalization transforms a set of linearly-independent vectors into a orthonormal basis – Or in proper English: How do you determine from some criteria, the most differentiating dimensions to describe it (better).

The Gram-Schmidt procedure goes through following steps:
1. Select a first dimension.
2. Select another dimension.
3. Remove the common features between the new and old ones.
4. (Norm it) and back to step 2.

How could we transfer this to our example?

We would start with a first (cardinal) dimension. In principle, this can be done arbitrarily. But most helpful is to select the most central dimension.
I select Economic.

As next, we could take Geographic. Now the question occurs, what have the categories in common – or most different? Rich and poor regions shouldn’t be needed to discussed separately here. Most interesting is discussing, something that is independent from this: e.g. rural/ remote areas vs. urban areas. Those exist in richer and poorer variants.
Let’s name this dimension Urbanization/ Remoteness.
The forth step to normalize the dimension is in this context perhaps unnecessary, but perhaps, we removed so much that it becomes insignificant and would need to be amplified/ extended.

No go to the next one: Social.
Common with our existing dimensions, is social inequality in economic regards. As well as social background based on rural or urban localization. Before mentioned job opportunities social services have to be removed from the urban context.
As independent dimension, one could focus on Educational and professional background.

As you do this more often, there is more and more overlap to the existing dimensions to consider. It could instead be useful to just try to imagine new dimensions from the remaining ones, that are independent from the existing ones. E.g. I could read from the last two dimensions something like Digital experience – Although this is still possibly influenced by your education…
As an exercise for the reader, you could try instead to come up with two remaining useful dimensions.

Some final remarks

For those, who find this interesting and want to learn more:
It is further useful to think about what kinds of dimensions we are using. E.g. there are categories that are partitioned into discrete cases and some that are describable in a continuum, so fluidly/gradually changing.
For these dimension also some are clearly measurable, some very subjective and less graspable.

Also, this topic is a smooth transition to data science, where very complex topics are described by a lot of data with different values in several categories (dimensions). Not a surprise that this hand-in-hand connects to orthogonalization in linear algebra, and is, in turn, a necessary step in the optimization of nodes in neural networks, which analyse the data…