In theory sure, but in practice the internal complexity of organizations leave plenty of room for obfuscating that ideal. Throw in nepotism, favoritism, corruption, and an inflated valuation of upper management roles and you've got plenty of jobs that pay well past what they "bring in", which is itself nebulously defined at best, especially in white collar industries. Hell I know some companies that would've been better off just axing some of their c-level suite.
I totally agree but do think it's true in terms of averages and probably true more often than not that a given individual falls within the range. After all, you can't have an industry-wide average for most roles that's higher than the value they bring in. There's also a myriad of roles that don't produce directly and are either supportive, compliance, or simply unnecessary.
I've always adhered to the idea that "infinity" encodes "allness". For instance, to say that the sum of 1/2^n for all natural numbers n converges to 1 is not to say that we're actually adding up infinitely many numbers, but rather that I can always win a certain game: you give me an arbitrarily small epsilon > 0, I can give you enough terms in the sequence such that their sum (a finite sum) is within epsilon of 1. No, I can't actually add up infinitely many numbers, but you can never win my game, so certainly "infinity" exists in that sense.
So, while I can't "point" to an infinite number of things like I can point to 9 things or 3.62 things, I still think it exists.
I'm not sure how well this generalizes to all infinite cardinals, ordinals, or to transfinite induction/construction. It is certainly strange that Cantor's theorem (the cardinality of a set is strictly smaller than that of its power set) implies there are different sizes of "all" implicit in my usage of the word.
Never encountered this idea before, does it have a formal name? Most fractional-dimension spaces encountered refer to either the Minkowski or Hausdorff Dimension.
Here's a paper which discusses fractional degrees of freedom:
Effective degrees of freedom of a random walk on a fractal
by AS Balankin · 2015 · Cited by 42 — This allows us to define the fractional dimensional space allied ... number of effective dynamical degrees of freedom on the fractal
To hammer the relationship home, consider the holographic principle, which is based on observation of black holes, and states that our reality only needs 2 spatial dimensions instead of 3. Both Hawking and Susskind have eluded to this being the case solely because of the symmetries in the laws of physics. The symmetries cause a massive redundancy/pattern in the field values over the 3d space, such that we should theoretically be able to predict the state of the entire field given only the values at two-thirds of the volume.
Therefore, you can imagine a 2d surface which contains the state of our universe, and some kind of computational (possibly geometric/algebraic) projector, which understands the redundancies, reads the 2d surface, and renders a sparse 3d volume. In the case of our universe, the projection operation might be extraordinary complex, requiring a deep understanding of the laws of physics and the redundancies they induce into the underlying state that they operate on.
Math is more interesting, purely as math, as I get older. I found the same is true for history as well. The trick is to find good history authors for the particular time you are interested in. Same with math.
I graded very well in math through college, but later in life, I went back and explored more how all the concepts relate. In college, you are sort of fed calculus through a fire hose, and you just have to 'accept it' and move on. And you are left wondering, how were these ideas, these conclusions, reached? Until you go back through and see the long history of infinite series and see the various attempts to codify solutions. The problem is, as a student, you cannot possibly spend that much time deriving the whole solution from scratch and still hope to finish a degree in four years. As Carl Sagan said “If you wish to make an apple pie from scratch, you must first invent the universe.”
Which is why you can never stop learning. I am in my mid 60s, and I still learn something new regularly. Something big at least once a year, something smaller at least once a month. Never stop learning.
I meant that mathematics has been used for nuclear bombs, breaking cryptography, and other nefarious purposes. Physics is a sort of applied mathematics, where reality is the testing ground for models created on paper.
It was originally thought that Einstein's theory of special relativity was just a cool mathematical idea. But it was much much more. Mathematics has consequences that are so deep that even now it is rearing its head in AI..differentiable loss functions.
Pardon my ignorance, but when was it ever about technology? Seems technological progress has done nothing to alleviate the starve-if-you-don't-work condition. Higher industrial efficiency in the 19th/early 20th centuries came with the promise of less work and more leisure, but that never arrived. I'm not sure why, but I'm guessing it's an economic/sociological problem, not a technological one. Curious to hear what ideas you have enough.
I think we're in agreement. It's totally an economic/sociological problem.
I was just pointing out that technology's ability to reduce scarcity keeps increasing--so as time goes on, our obsession with scarcity as a motivator is increasingly embarrassing.
There's plenty of point in merely enjoying the moment. There is little one can do or say to combat the inherent meaninglessness of being, as every argument can be thwarted by a simple "we're all going to die anyways so what's the point?" I don't think there can even logically be a point to life.
That's not to say that goals such as bettering society, bettering one's self, or enjoying the moment aren't worthwhile. Nor does it imply that we should sink into abject hedonism and shoot heroin all day. It merely means that none of these things should be expected to subvert meaninglessness. In this sense, it's actually quite liberating. You can do anything you please, without the burden of wondering whether or not it will fill the perceived void in your soul. That void is an illusion, one which is unfortunately brought about often by depression, BPD, GAD, etc.
After lots of therapy I learned I had internalized a negative voice from an abusive relationship early in my development, which fucked up my sense of self-worth and my perception of life. It made me incessantly focused on "being the best", and if I couldn't achieve anything "great" then I had no choice but to hate myself.
If you're having suicidal thoughts, then it's time to seek professional help. I was at that point too. My doctor and I decided our best bet was to try 10mg of Lexapro for a couple months, and I've never felt better. Depression is a pernicious beast. It seeps in slowly subsuming all rational cognitive faculties, to the point where I was not merely sad, I was obstinately despondent, and refused to listen to reason. It emanated from a "feeling" of meaninglessness which I could never eliminate with mere rational thought. I guess my "chemicals" were just fucked up, and I needed a little help from the Lexapro.
So, what do you do if you're not successful? Anything else you want. The world is your oyster. Failure ultimately means as little as success. If you don't succeed at something you enjoy, then simply keep doing it, keep enjoying it, maybe you haven't struck gold yet but the journey is worth embarking on once you realize that contentment doesn't lie at the end of the journey, but within it's entirety. If you feel it's too late to start, there's still plenty of beauty left in life. Sometimes I find the following Kurt Vonnegut quote useful:
> "What is the purpose of life? To be the eyes, the ears, and consciousness of the creator of the universe, you fool!"
Now, I'm fairly young, I expect my opinions are biased by the fact that I personally feel like I still have a lot of time left to embark on journeys. I can understand if the perspective changes as you age, and feel as if you missed out or squandered your best years. Hopefully someone older can step in and share their thoughts.
I also hope I don't sound like I'm proselytizing. Just wanted to share my experience if it helps anyone.
