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What are some useful logical/math/cs operators or textual tools for thinking

I notice programming stuff leaks into my thinking and writing often but I actually enjoy the various constructs that help clarify thinking. I don’t have any formal background in logic tho :(

What are some useful and accessible logical tools/operators/symbols that help in thinking+“pseudocode” Edit: definitely useful math/cs/logical symbols are particularly interesting

If you can, please copy/paste the actual unicode symbol or whatever

turkalino ,
@turkalino@lemmy.yachts avatar

Knowing the difference between exclusive and inclusive OR is pretty helpful. XOR is super useful in programming and is even the basis for one of the few “perfect” encryption systems

Exclusive OR is usually just written as XOR, but if you’re dying to use a symbol: ⊕

aDogCalledSpot ,

I like noticing when something is the derivative/integral of something.

Often using a derivative helps break something down and an integral might show an end result.

For example, a software product is the sum of its commits.

cheese_greater OP ,

Whats the symbol?

∑

?

aDogCalledSpot ,

I use the term rather loosely so it’s hard to say because it depends on the setting and how pedantic you want to be.

In a continuous setting (time, for example), you will usually see the derivative of a function f(t) being denoted as a df(t)/dt. In some cases it would also be written as f’(t). Engineers are pretty much always dealing with functions across time so they added another notation which is simply a dot over a variable. E.g. if x is your position in space then ẋ is your velocity (the derivative over time). You can add another dot if you want your acceleration (the second derivative over time = the derivative of the velocity).

The counterpart of a derivative is the integral which is always denoted by ∫f(t)dt.

The discrete case is a bit more tricky because these things arent that well defined in these cases. People dont seem to mind if you go with the next best thing. The derivative is the difference between steps (Im not aware of a notation for this) and for the integral you would use a sum ∑.

Note that even this wall of text doesnt cover all of it but I hope it gets the point across.

saigot ,

Well maybe this is too basic but here are the most important to me:

formal implication:

X ⇒ Y (X implies Y)

means that if X is true, Y is also true. Note that the reverse is not necessarily true, Y being true does not mean X is true (or that X is false). There is truly a staggering number of people who make this mistake in thinking all the time. And If X ⇒ Y and Y ⇒ X then X ⇔Y (X if and only if Y).

Understanding ∀ (for all) and ∃ (there exists) is also very valuable.

Understanding these concepts is enough to understand the basic notation of a lot of math, with it you can start reading basic math papers and really expand your horizons.

chumbalumber ,

You might find the discipline of systems engineering of interest.

cheese_greater OP , (edited )

Can you give a couple quick rudimentry exemplars to illustrate?

Edit: whats that thing that concerns bottlenecks in business and manufacturing systems/processes?i remember something about sufficient/necessary dichotomy or sumfing

agamemnonymous ,
@agamemnonymous@sh.itjust.works avatar

Are you thinking of Lean methodologies? Part of Lean is to try to streamline your processes so you don’t have a bunch of raw material/intermediate product/final product just sitting around in a warehouse doing nothing. Or you might be thinking of something along the lines of the Pareto Principle (80/20 rule), wherein chasing perfect efficiency yields diminishing returns.

cheese_greater OP , (edited )

No there’s something else. Its not quite scientific but its this pop-business study of bottleneck condtions and how to structure processes and organizations to remove bottlenecks/optimize for particular outcomes by resolving strategic bottlenecks.

Don’t know why I can’t remember.

> Something something neccessary but not sufficient

There’s a famous book, something about an auto plant…i dunno its gone from me

Theory of constraints

Thats what I was thinking of

agamemnonymous ,
@agamemnonymous@sh.itjust.works avatar

Ah! ToC does synergize very nicely with Lean Six Sigma principles.

It sounds like some study of Systems Engineering, Process Improvement, and Project Management would help you in your goal. Not so much in the way of the kind of dense and precise operative symbology you get out of formal Logic, but in the form of less rigorous but still useful analysis and problem-solving methodologies. Just formally mapping dependencies alone can be a powerful tool.

cheese_greater OP ,

I just like the idea of certain symbols: conventions as a leverage for more systematic or explicit thinking. I like my coding stuff has helped give me some tools I wouldn’t generally have based on background and I wanna collect them in the same way MentalModels are aggregated/referenced

agamemnonymous ,
@agamemnonymous@sh.itjust.works avatar

It’s math instead of coding for me, but same. That’s what pushed me to SE/PI/PM. Formal Symbolic Logic is going to be where you find pretty much all of the explicit symbols you’re looking for. General System Theory also makes frequent use of differential equations, and if you understand DE than it can provide a helpful framework, but Logic is going to be most of what you want.

cheese_greater OP ,

What about LaTeX or whatever? Would that be of any use to me?

agamemnonymous ,
@agamemnonymous@sh.itjust.works avatar

Eh, I haven’t really used it personally but from what I can tell it’s more about formatting than anything else. It would probably be useful if you want to type up any analysis that uses less common symbols, but as far as I know it doesn’t really present symbols which don’t originate elsewhere.

chumbalumber , (edited )

For sure. Systems engineering is a way of trying to apply more rigid thinking to what are known as ‘wicked’ problems. There’s a whole bunch of tools that come under the discipline, but to pick one specific example, causal loop diagrams are often used to help understand why complex phenomena happen. An example:https://lemmy.blahaj.zone/pictrs/image/7fdfe983-e87e-4f2e-b085-8767e0db1617.jpeg

This shows a causal loop diagram for an energy network. The pluses indicate positive causation in the direction of the arrows, the minuses negative causation. If you were tasked with coming up with all the causes and impacts of fluctuations in energy demand, you might find it difficult to show (e.g.) positive and negative feedback loops

cheese_greater OP ,

Theory of constraints

Thats what I was thinking of

shapesandstuff ,

I like the inline if/else notation

(condition) ? (action if condition applies) : (else condition)

Not sure if that’s the kind of thing you’re looking for

cheese_greater OP , (edited )

ternary expressions?

Ya, its not out of place here or anything.

That too and also initially I was thinkngmore referring to using symbols in place of words like

∴ == therefore

But I’m just as open to those too 🤠

Edit: I love ternary expression, such an elegant shorthand

shapesandstuff ,

Ahhh gotcha.

Yeah I’m shit with vocabulary, despite coding for a long time now :'D

It can reaaally clean up the thought process as well as the code

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