BRK salary is 100k; the corp pays for the private jet ("the Indefensible"). Aside from Berkshire, he also has a personal stock portfolio worth 9 digits or so [in essence due to investment work prior to Berkshire]. He is able to compound that at high rates and is tax savvy so almost all returns are long-term cap gains (or at dividend rates); this is what he's pointed out when stating how low his overall tax rate is vs say typical administrative staff.
Evidently neither you nor the person you're arguing with actually knows much about this topic. It seems like you already have an extremely strong opinion on the man and are trying to back-fill it with "facts". Oh well.
The point of my reply was to point out that having a modest home was not necessarily an indication of character (hence the Scrooge comparison), and that even Warren Buffett - who is seen by some as the best of the wealthy - has come under criticism by the press for his motives and methods having been less than ethical (although they may have been perfectly legal).
One of the sources was anti-capitalist, but the journalists who wrote a a couple of those articles for business news sources undoubtedly were supporters of capitalism, and are likely to be know much more about the financial issues than most us do.
Although there are larger questions of whether anyone should be in a position to hoard so much wealth, what 'cost' that wealth comes at for the rest of us, and whether the accompanying power he exercises (even if indirectly) is good for society.
Those are larger philosophical and ethical queries, that do often come with strong opinions for good reason. Those on the right worry that regulating wealth may come with an affect on some other freedoms, those on the left worry that such wealth comes with a risk to the integrity of the democratic process and comes at a high societal cost.
Most of the defences of Buffett against this criticism have seemed to have been: "he is just a money geek who doesn't get into those details", "at least he is planning to give a lot of it away", and "you are in no position to judge him." I, like many others, do not feel he is beyond criticism or that those are sufficient answers.
Yea. Most of the media reporting on Buffett is... sloppy to put it politely. The guy lives with Astrid (and some body guards) in a 5 bed house that he sentimentally likes. He also has a couple nice houses in CA (and possibly other states) and a private jet. If someone reads any biography on him they'd know this. (IIRC it also came up when he was advising Gov Arnold on re-doing real estate taxes and he wrote some OP-eds.)
What's more surprising to me is how well he's doing (physically and cognitively) in his 90's as someone who eats at McDonalds every single day and I think is largely sedentary. The other side of the coin is his dad barely made it to 60 though his mom died in her 90's.
...interestingly enough, they have been publishimg this same "story" every few years for a long time now. He seems to be very carefully maintaining the image of a frugal billionaire. Either that or making sure to initiate every new generation to the personality cult of granpa-genius/uncle/frugal investor/ Warren Buffet.
if you read Johnson's work, it's typically both. Direct fructose consumption as well as the polyol pathway being on and your body converting 'extra' glucose into fructose.
excess fructose (in particular in ultra-processed forms) causes metabolic derangement but consuming too much of those other 3 esp from ultra processed foods, also activates the "switch" leading to endogenous fructose production and more derangement.
The role of sedentarism in all this is somewhat under-explored though.
It seems misleading to call this "symmetry" because what you wrote is not a group.
The only idempotent element in a group is the identity. And in abelian groups where the binary operation is given by "+" the identity is denoted by "0". Yet you have "1" being idempotent, so conclude that this is not a group (or that this is a sleight of hand because you've made the identification that 1 = 0).
and you can actually use up all the various desaturase and elongase enzymes in the process so that 10% upper bound drops markedly as you consume more ALA. Put differently long chain n-3's production definitely isn't linearly dependent on short chain n-3s like ALA and stearidonic acid.
I wish him being alive at 94 was proof of something but afaik my smoking grandmother with no exercise doing nothing particularly healthy lived that long...
However, she also wasn't doing novel research at age 86. Wow.
Steele's The Cauchy-Schwarz Masterclass is actually quite good and seemingly designed for self study. (A lingering result of this book is I heavily use inequalities even outside of analysis.)
Artin's Algebra probably has had the most impact on my math thinking. The development of groups and rings while tightly linking them to linear algebra was rather brilliant.
It's interesting. My first instinct was to disagree with this post, but on reflection I think I mostly agree with it. A couple useful mental models are (i) deliberate practice and (ii) train-validation-test(/out of sample) sets from machine learning
Your point (2) about compiler/interpreter in programming giving you rapid objective feedback is spot on and a vital component for deliberate practice that most people don't think on. You can kind of get this in math, in particular when you have some familiarity with the subject matter so the machinery isn't "too abstract" for you to sort through. (I.e. you should be able to confirm whether your proof/answer is accurate the vast majority of the time.) This is much trickier for first exposure to a subject though and the checking effort is on you, not the compiler.
The biggest issue I've seen with people self studying or in small math groups is your final (non-aside) paragraph which is perhaps more a psychological problem than and aptitude problem. When things get tough there's an enormous temptation to delude yourself to think you understand something that you are clueless about. The typical, schoolroom, way of mitigating this is via a final exam and you can check your grade at the end of the class; this gets typically gets short circuited in self guided study. Exams, btw, are essentially validation data sets you compare your math knowledge/model against. (We can call them 'test' sets if you prefer). The most important step really is repeatedly seeing how your knowledge works out of sample i.e. on 'new' stuff that comes out of the wood works and math.stackexchange is a perfect place for this when dealing with undergrad to mid-grad level problems. I do this all the time to get a sense of my understanding of a new subject I've recently acquired. But most people refuse this final step. People will tell me its 'too hard' and 'takes too much time' (meanwhile they start a new math book) but I strongly suspect it's in large part due to cognitive dissonance. (Another kind of out of sample test comes up when working on a subject matter that uses something you just "learned" as a pre-req, though there's a recursive element here and at some point they basically need to interact with 3rd parties.)
I suppose my relatively minor quibble is how much effectiveness depends on being "very gifted" [in some sort of math specific sense] vs understanding the basics of self-learning and being psychologically aware (astute?) enough to not go into denial. Insert quote from Feynman or whomever about how easy it is to fool yourself.
My understanding of one guess around e.g. annual flu shots is not so much protection from infection as frequent stimulation of the immune system being beneficial in particular for Apoe4 carriers.
E.g. from p. 329 of Lieberman's Exercised:
> Although Westerners who carry the two copies of a gene called Apoe4 (a protein that transports fats in the bloodstream) are three to fifteen times more likely to get Alzheimer's in old age, elderly Tsimane with the same ApoE4 gene are less likely to show declines in cognitive performance if they suffer from many infections.
------
I have heard something similar about ApoE4 carriers in Nigeria though don't have a source on hand. Basically a lot of variations of the hygiene hypothesis and possibly compatible with "angry immune cells". Definitely not a "mystery solved" though.
Evidently neither you nor the person you're arguing with actually knows much about this topic. It seems like you already have an extremely strong opinion on the man and are trying to back-fill it with "facts". Oh well.