[jimsimmons]

That’s not better notation. Programming uses equals and it’s fine. Symbol salad is the problem. One needs to control the number of symbols. Using a symbol for frequently used operations is better. For everything else being explicit is better even if it means repeating it a few times or being verbose.

And you’re wrong about abstraction. It only works if the abstractions are solid and non leaky. Most abstractions aren’t. If I gave you education at a high level of abstraction you wouldn’t know much. Human ability is to move between abstractions and create new ones. Not parsing things at an arbitrary level of abstraction. One needs to build abstractions. Not hand over high level ones.

[simion314]

Sorry dude but you don't really know true Math. In Math all is precise, all abstraction is precise, there is no place for interpretation.

When you read a physics book you will see stuff like

F = m * a

this are defined somewhere , you can't just jump at the middle of the book and understand. Is the same with terms, you get teh concepts explained at the beginning where for example it will tell you that mass != weight and what it really represents , a physics paper does not need to get verbose because some random person wants to understand it but at the same time wants to skip the requierments.

Sure, there could be somewhere some bad book/article/paper that is confusing maybe for everyone but that is an exception>

I am still waiting for some proof or example on how this no symbols Math should like? Do we repat the terms definiont all the time , do I need to explain all the time what a natural and real number is ?,what a set and function is ? do I need to explain what PI and e is every-time I use it ? If not do I ask you what you level is and everything you personally don't understand is the thing that I must defined even if I don't target you?

But if you are a dev you should start cleaning up the software side too, like let's stop naming stuff functions what they are not functions, let's stop naming shit int if they are not the real Integers, let's stop using +, * and / because this are not the real thing(they do not respect all the laws in all conditions)

[jimsimmons]

Words are also symbols. When you say it’s defined somewhere means it’s defined in natural language somewhere. Things ultimately get defined in natural language and it’s unavoidable. You cannot take a kid and shower him with symbols and expect him to understand. One needs examples that elucidate the situation and pointers to understand the factors under analysis. You need to write down assumptions like “frictionless surface” or “isolated system”. Sure you can rigoursly try to define them too but eventually they’ll still be defined in terms of other words and sentences which are inherently ambiguous. Euclid’s theorems used an axiom that wasn’t known until 18th century. It’s not due to lack of rigour. It’s due to leaky abstractions.

I’m not arguing for no symbols. Surely the quantity of symbols used is less in Physics relative to math or geometry relative to algebra. Just like a well written physics textbook, there is a middle ground between verbose description and symbolic manipulation. They both have their place and neither can substitute one another.

You have a middle school interpretation of science. Things may seem rigours to you because it’s written in a language that’s a lot more precise than the day to day language we use. That doesn’t mean they are ultimately precise. Even mathematics hasn’t been automated or formalised in a computer. That’s not due to lack of trying. It’s insanely hard to precisely codify mathematical concepts. So imagine, when math and geometry are hard to formalise, how hard physics would be. All fields or models of reality are precise in answering the questions they consider. But they sweep hide swaths of ambiguity under the rug even before the proposing the first formal statement. That is what you need to realise.

[simion314]

I know what I am talking about, I graduated Math, I studied the Fundamentals of Math theory and all the fundamental branches.

You fail to understand that the symbols and terms are defined, the reason you don't understand an equation when you go to wikipedia is either the article is bad or you are not prepared to read that equation.

If we dumb down Math/science articles we will get a similar issue with biology, there are not many symbols in biology so any random dude (including some big ego HN-ers think they are now COVID experts just by reading wikipedia or worse some click farm article linked from social media).

Btw have you read a rigurous book on logic, sets and numbers? a university level one? Is there any ambiguity there so if you have 10 non retard readers you get 10 different Mathematics because some term or operation was not ambiguous?

Computers and software are limited, they are missing the creativity a human has, you can teach software to follow some steps but it will never create any original step so at best you might get computers to verify someone.

[jimsimmons]

You don’t know who I am yet you assume I’m unable to read math. I’ll ga have you know I’ve published original proofs and derived efficient algorithms from doing very delicate math. I’m employed to do this which is something most math graduates can’t say.

I’m not advocating for dumbing down —- rather the exact opposite. People have superficial understanding of things and think they know the subject deeply because they can write a bunch of symbols. But wannabe proofs written by such people lack predictive power or explanatory value. Logic, sets and numbers are precise about the things they address just like a board game can be precise about it’s rules and outcomes. This is not the case for mathematics at large. Doing exercises in the textbook will be unambiguous because the content of the textbook grounds the meaning of objects well enough using verbose natural language. The problems are also small in size. However there is a difference between reading a law textbook vs reading the constitution. Definitions and semantics at the frontiers of mathematics are under flux and consensus among mathematicians is slow. Proofs are large and contain a lot of holes. Without the kind of verbose grounding you have in textbooks, meaning can be quite ambiguous. What is a set by the way? Since it’s a fundamental construct, can you define it unambiguously? Again I’m not asking for the notation of a set. But rather the definition of it. If you were asked to present it to a tribal person with no formal education, do you think the definition you thought of would have the same explanatory value to them? If this constraint made you rethink your definition you see my point.

I’m not talking about any creative aspect. I’m just talking about formalisation. Geometry is notoriously hard to formalise for computers. Take a look at the Lean theorem prover and how hard it has been to formulate large sections of math despite repeated attempts over decades. The creativity you suggest is actually rooted in the pattern processing machine that is the brain which fills in large blanks left out from formal representation and which many mathematicians take for granted without realising the extent of ambiguity it brings.

Your language and usage of R word suggests you’re in an Ivory tower just because you understood a few problems in your textbook at some point.

[simion314]

Can you just give me an example? Like link to your work or someone else(preferably a mathematician) that does rigorous proofs using natural language. Maybe i do not understand exactly your point, you want some symbols so what is the rule what symbols are allowed and what not.

Not sure what you mean about defining a set, as I mentioned in Math fundamentals you have no choice then to define a few initial primary terms and axioms to bootstrap things.