strain on the mind when illogical

[trevorjohnson83]

2 x 3 = 4 or 2,3,4 the former fills your mind with rationalizations and patch work, your mind attempts to joke in ridicule. The latter is easy logic strainless thought of numbers in succession.

What you’re pointing at is a difference between forcing coherence and recognizing structure.

• “2 × 3 = 4”
  This violates an internal pattern we already carry. The mind immediately tries to repair the break: rationalize, argue, joke, ridicule, or patch it with exceptions. That effort is cognitive strain. Humor and mockery are common reflexes because the brain is signaling “this doesn’t fit.”
• “2, 3, 4”
  This is pattern-following. No repair is needed. The mind simply tracks succession. There’s no tension, no justification, no defense—just recognition. That’s low-resistance cognition.

So the contrast you’re describing isn’t really about arithmetic correctness—it’s about mental load.

In simpler terms​

• False structure → mind works hard to explain, defend, or reject
• Natural sequence → mind glides, no commentary needed

This lines up with a broader principle you’ve touched on in other discussions:

Truth (or coherence) feels quiet; error feels noisy.

Noise is not always wrong—but unnecessary noise is often a sign of patchwork logic rather than emergent order.

 

[scruffy]

It's hard in math because the symbols have different meanings. Sometimes you have to unlearn the old meaning. Like "dx" in calculus, once you learn differential geometry it becomes a basis vector in the tangent space, and when you get to stochastic calculus there's yet another meaning. So if you're looking at a random journal article you have to figure out which meaning they're using.

 

[trevorjohnson83]

scruffy I was being much more simple, justifying the equation 2+3=4 you would have to change the symbols, act real dumb, or create idiosynchratic rules, but if you take out the symbols and just leave it as 2,3,4 you can feel your mind stress less, sort of the way computers should measure confidence in what they are saying.

 

[scruffy]

scruffy I was being much more simple, justifying the equation 2+3=4 you would have to change the symbols, act real dumb, or create idiosynchratic rules, but if you take out the symbols and just leave it as 2,3,4 you can feel your mind stress less, sort of the way computers should measure confidence in what they are saying.

Well, you're touching on the most important principle in information geometry, it's called KL-divergence, it means the distance between representations. Intuitively, things that are similar should be closer together. Table and chair should be closer than table and car. And within the cluster called chair, you have big chair, blue chair, upside down chair, and so on.

So without the operators you just have a sequence of numbers, and numbers are a cluster containing examples of numbers, so 2, 3, 4. So you're really only activating one cluster, it doesn't cost very much.

On the other hand, operators might be unclustered because their meanings are so different. Each one has a different function, much more so than numbers which are just copies of themselves. You're right, it takes work to infer the meanings.