You need to learn the distinction between a word (the symbol) and the concept (the meaning) of language. By your standard a Frenchman could never communicate with an Englishman but we know that is not the case.

Because unlike the lesser animals, for a human adulthood is not a biological, societal or a chronological question but an epistemological question. The answer is that you become an adult when you learn to think for and by your self. Most people are not adults by that standard.

I think the real issue is that MS doesn't view Windows primarily as an OS that should be invisible, out of the way -- with minimal "innovation" geared to sell MS products. The problem is that MS views Windows as a sales/marketing channel for their ads/apps/services.

The imaginary number i=SQRT[-1] is the base solution to the polynomial equation -y= x^2. If you read the history it was invented to solve certain types of cubic equations, i.e. as a heuristic of method. So not only is it not a number it is a bare contradiction. While i was useful to solve some subclass of all cubics it did not lead to a general solution to cubic equations. Nevertheless the mathematicians ran with it and added complex numbers to the definition of number so that the number system could solve all possible polynomial equations.

In my opinion imaginary numbers are a kludge and deadend and it is masking the real issues in math, i.e. the ghosts of departed quantities. In math some symbols stand for an infinite series but you can't just choose any arbitrary series for Pi or e or SQRT[2], they all have to be defined as part of a system of measurement with clearly defined and globally defined epsilon/delta (i.e. precision) of measurement to get valid results.

Not "most" but all real numbers are similar to Pi, i.e. they are symbols that stand for an infinite process to calculate a rational number. Both irrational numbers like Pi, e, etc. and reals exists and are legit and useful math concepts but infinite precision does not exist "in the wild" only in your mind as an abstraction. In any actual calculation or measurement your infinite series must stop and the dedekind cut must be made.

The ghost of departed quantities still haunts math. Is Pi 3.14 or 3.1416? Mathematically, it is neither and both because math intentionally abstracts from the precision of the ratio of the circumference to the diameter of a circle. These open-ended (infinite) processes are ultimately used to define a rational number, a ratio of integers.The finitist -vs- infinitist is a false binary which ignore that actual measurement must use rational numbers.

It is a subtle distinction but important. We define the exact value based on the context. If I am tiling my circular patio then 3.14 is fine to calculate how many tiles I need. If I going to the moon or mars then I need more decimals or I will miss the target.

Off to a bad start. Aristotle was not making a mathematical point but a metaphysical one. Infinities do not exist and is not a number. For example, Pi is not a number but a symbol that stands for an open-ended (infinite) process to calculate a rational number and is a perfectly valid mathematical concept that, I am sure, Aristotle would agree. On any computer, despite protestations by the mathematical platonists, Pi is ultimately a rational number in all use cases involving actual measurement or calculations.

The error is illustrated in the first image in the article.

https://www.quantamagazine.org/wp-content/themes/quanta2024/...

The third set in this example is an invalid and undefined set by including Pi since Pi is indeterminent and thus cannot be an object to be counted. All of Cantor's nonsense rests on this type of error, i.e. treating a mathematical process as a number. All of these errors are implicit in Newton's calculus and Berkeley's Ghost of Departed Quantities critique still needs to be answered. Hint; there is no such thing as infinite precision and epsilon/delta needs to be defined in a consistent way, not arbitrarily as it is now.

Specialized forum content, discussion and community suffered with the VerticalScope rollup that borged them all a few years back. They immediately upgraded the forum software to be phone app compatible (more eyeballs) and forum quality died soon after. No one is have good discussion, arguments, stories or history while phone posting on the can or in line at the DMV. It is all repetitive drive-by comments or questions that could be answered by a quick search of the forum so it is short attention span theatre now. I saw this across multiple forums that got rolled up by VS.

tldr; Vertical Scope and phone app use.

https://www.verticalscope.com/our-solutions/be-the-solution/

I always thought there was a connection between geometry and the math and physical constants. Once I was thinking about Einstein's equivalence principle between gravity and acceleration and his elevator-in-space argument. He claimed that there is no experiment that the man in the elevator could do to determine if he was in a gravity field or accelerating rocket. It occurred to me that all he had to do was wait because the rocket could not accelerate at 9.81 m/s forever. So I did the math lightspeed/acceleration of gravity = 30559883.59 sec = 353.7023 days for 86,400 sec/day or 96.9% of a year to get to c. Just a coincidence, they say.

I don't know if that would work but it is an interesting idea to me. However, it also illustrates that authentication and protecting user identity on the web without sacrificing anonymity is a _political_ problem not a technical problem. I have always been told that when thinking about security you have to define what threat are you trying to protect yourself from. I see discussions on security and virtually all of them ignore that the govt or govt controlled corps (i.e. fascism) is a much bigger threat to individuals and freedom than so called "hackers" or "terrorists" and other boogie men, etc.

So the trick is to set the rule [don't do X, do Y instead] and immediately stop thinking about X and move on to Y. Just shut down the "do X" thought and shift to Y. "Y" can be anything even the absurd like patting the top of your head 5 times because it breaks your subconscious programming. In fact, the absurd Y's seem to be more effective BECAUSE they a silly or ridiculous. Of course, as you gain skill at this method you can start using more productive Y's like doing 10 pushups or do a quick household chore, do a small task on your to-do list, etc. Once the subconscious program is broken then thoughts to do X will fade and you can move on to X2 that you want to change.

Can't wait for Windows 12 to have a mandatory S-Mode and a Microsoft account tied to your PII, for your protection. No anonymous writer can publish the 21st Century equivalent of the Federalist Papers and our tyranny is safe.

https://news.ycombinator.com/item?id=20052407

https://www.edge.org/conversation/clay_shirky-newspapers-and...

The reason you need to minor in philosophy is to understand the history of the field going all the way back to the Greeks. Most importantly, you need to clearly define a theory of concepts and apply it to fundamental concepts such as existence, consciousness, free will, space and time. Current physics (and math, btw) are vitiated by inconsistent fundamental concepts. In fact, Einstein's concept of spacetime is a denial of consciousness (an axiom) and a deadend. The fundamental concepts in physics should be lightspace and gravitytime to avoid this error. You won't learn much in modern philosophy courses in regard to these issues but you need to understand the history and read Ayn Rand's Philosophy:Who_Needs_It, Introduction_To_Objectivist_Epistemology and the title essay of her anthology For_The_New_Intellectual.

He has a math consulting business which seems very interesting a cool way to make a living. Maybe you can contact him and get some advice.