Generalization accross time?

[daylen]

Let generalization level refer to the measure of how spread someones accumulated knowledge is. Let A = ( lifetime , generalization level ) be a 2-dimensional space where lifetime is the independent variable.

A simple example would be a line with positive slope representing a constant progression towards being more generalized as someone gets older.

What is the optimal curve in A for ERE? (you can also think about the derivative of generalization level with repect to time)... Is it harmful to generalize too much early in life? When should one start to generalize? How do you quantify generalization?

Clearly specialization correlates with pay, but specialization also correlates with spending (need more outsourcing). This is covered in the ERE book, but I am looking to go more into depth. My guess is that the curve would be a third order polynomial where around college generalization is reversed in favor of specailization until early-middle age when generalization starts to increase again.

Also, a somewhat related question... In your 20's your mind is at its peak iq. What is the best way to utilize this time in order to maximize ability to generalize in the future? My guess would be to invest time into understanding math and logic to build a solid base from which all other knowledge is derived, but how far should one go in their mathematical specialization? Math is a big subject and could be studied for many lifetimes.

[Ego]

Interesting question. Back in the 80s the Maestro (Something From Nothing thread) was very much anti-tech. At the time, computers and technological pursuits were for specialists. My recent interactions with him have opened my eyes to just how fast a person can miss the boat and how vulnerable they can become when they do not have a basic understanding of a wide variety of fields.

I was once rather proud of the fact that I was not tethered to a cell phone. Never again.

So, to answer your question, I am not so sure if I would worry about specializing early on or even later in life. I would worry more about the things I refuse do. The glaring gaps in knowledge and abilities will cause the greatest problems. If these gaps are the result of spending too much time as a specialist, then yes, cut back on the specialization and focus on maintaining a basic understanding of the things those crazy young people are doing.

While I won't be swiping left (or right), I will try to maintain an understanding of what it means to swipe left.

[enigmaT120]

While I won't be swiping left (or right), I will try to maintain an understanding of what it means to swipe left.

I had to Google it when I saw it in a Dilbert cartoon.

[chenda]

I don't think it's been clearly established that IQ necessarily peaks in your 20s.

Though I expect specialisation more typically follows a Bell Curve, increasing then decreasing.

[daylen]

I don't think it's been clearly established that IQ necessarily peaks in your 20s.

Maybe not, but there is a general trend throughout history that mathematicians do their best work in their late 20's. Perhaps this relates to creativity.

[daylen]

So, to answer your question, I am not so sure if I would worry about specializing early on or even later in life. I would worry more about the things I refuse do. The glaring gaps in knowledge and abilities will cause the greatest problems. If these gaps are the result of spending too much time as a specialist, then yes, cut back on the specialization and focus on maintaining a basic understanding of the things those crazy young people are doing.

Actually, I was worried about generalizing too much. At this point, I am qualified for several entry level jobs with decent saleries, but I lack the specialization necessary to make a great entry level salary.

[George the original one]

Actually, I was worried about generalizing too much. At this point, I am qualified for several entry level jobs with decent saleries, but I lack the specialization necessary to make a great entry level salary.

I'd probably be described as a generalist who specialized. Many skills, much knowledge, mainly used for putting together the right specialist resources or troubleshooting for the unknowledgeable. As a generalist in a specialized field, it meant I was flexible and could put things together that no one else recognized as going together.

[7Wannabe5]

I agree with Ego.

I can also, perhaps, offer some bit of insight into your specific question about mathematics. I am an absolute rogue generalist, dilettante, jill-of-all-trades-mistress-of-none, but somehow, more than a quarter century ago, I wound up graduating from college with a B.S. in mathematics and a minor in general science. I think math was my 5th or 6th declared major at the third university I attended. My favorite class was Abstract Algebra. The professor gave me an A even though I didn't complete all the assignments (I had to care for a breastfed infant who was hospitalized with post-surgical complications that term in addition to my usual slacker tendencies.) because he said that I had demonstrated that I understood the theory better than the Chinese students. The semester after that, I wanted to hurry up and graduate due to my maternal responsibilities, so I switched to actuarial track. One professor told me that it was necessary to study for 200 hours to do well on the exams, so after cooking dinner, I left my son with his too-young father (drinking beer, blasting Henry Rollins), and sat in a booth at the McDonald's across the street from our apartment, and logged almost exactly 200 hours studying. I passed the first exam which covered all math through the calculus with a 10 (highest score) and the second exam on probability and statistics with a 6 (passing score) at the same sitting. Then I got knocked up again, so I didn't take any more actuarial exams, but a couple years later I sat for the GRE and received scores of 800 Verbal/780 Analytical/790 Quantitative. I don't recall the exact percentiles, but my Verbal and Analytical scores were relatively much more rarefied than my Quantitative score, so I knew I shouldn't waste my time specializing further in that direction.

Anyways, at one point in my 40s, I thought I wanted to study economics, but I didn't have enough under-grad credits, so I had to pretend like I wanted to get a dual-degree Masters in mathematics. So, I had to go back and re-learn almost all the same material I had to study in order to pass the first actuarial exam when I was in my 20s. The conclusion of this short point made into long story is that, IMO, it is NOT decline in IQ and CERTAINLY NOT decline in creativity that is the problem with doing mathematics as you age. The problem is that your brain simply will not process and retain all the information you are not deriving on the spot at the same rate or volume. IOW, it very quickly became apparent to me that if I were to attempt the exact same challenge of passing the actuarial exams, I would have to log 300 or 400 hours rather than 200.

Just the other day I was discussing the topic of crappy schools with a new friend who is in his mid-70s and likely wealthier than anyone on this forum. He said that he didn't think even basic high school level algebra should be required, but kids should be made to read philosophy and practice home economics. I agreed that knowledge of mathematics beyond the most rudimentary was not necessary to succeed financially, but totally disagreed for other reasons. A couple years ago, after I read "Anti-Fragility", I decided to attempt Taleb's practice-towards-erudition which is something like read/study challenging/varied materials for 30 hours/week feeling free to stop/drop any book/topic in accordance with your druthers in the moment. So, I kept downloading more and more free books into my kindle app and reading at random, but along linked threads, and eventually I came upon a book on the topic of surreal numbers, and it answered a question that had been bothering me ever since I studied abstract algebra almost 3 decades earlier, and that was a truly delightful experience.

Of course, I would also recommend reading at least 50 of the 100 novels on the Modern Library, or similar, Best Ever list, if you want to have a full, rich, interesting life. Remember, your brain is the one toy or tool they can't take away from you. Okay, okay, they can take that too, but then you would arguably no longer be you, so ...? Also, although I constantly whine about the cruelty of requiring a single pull-up from one so aged, kewpie doll armed, and back-bottom-loaded as myself, I would note that your body is the second least likely thing they can take away from you, and it is likely that a similar rule-of-thumb regarding decline in function with age would apply.

[fiby41]

Specialize in one generator. Generator is any income producing activity. Usually it is one job that we all have.

Generalize in everything else. MVP (minimum viable product) passable skills in everything else- stocks, DIY skills, etc.

[daylen]

My favorite class was Abstract Algebra.

Mine too!

I still think it is because of creativity though. As our minds get older and more experienced, we become slower learners (like you said) but also less able to think about our fields in an entirely different way (which is often required for original research). The problem older mathematicians (or any researchers) face is not learning but thinking differently than they have been thinking most of their lives. It is hard to rewire a mature neural network, just as it is hard to repave a city's road network.

Specialize in one generator. Generator is any income producing activity. Usually it is one job that we all have.

Generalize in everything else. MVP (minimum viable product) passable skills in everything else- stocks, DIY skills, etc.

What about minimizing risk by having multiple incomes? At some point I would like to make money by serveral types of freelancing and self employed work. Though these things take time to develop. I guess the best course of action would be to work on one product/service at a time until it matures (..and working for someone in the meantime).

I do not want to be managed by someone else, and I get bored focusing on a skill for too long unless it is highly theoretical (..and therefore not profitable).

[7Wannabe5]

I think the difficulty in re-booting or making room for creativity at mid-life might have more to do with ego-maintenance or sunk-cost-fallacy than stiffening of neural network. I mean, if you already invested 20 years of your life-energy on writing papers on the topic of phlogiston, you aren't going to be super open-minded about the next paradigm shift.

Tiny low level example. I passed the AP Biology exam in high school, so I never had reason to take a college level course, but I had always been interested in genetics and read a lot of books at the Stephen Jay Gould level on the topic over the years. One idea that somehow got stuck in my mind was that siblings could either share all the same genes or none of the same genes, depending on a sort of lottery at the time of conception. Then on one occasion over brunch, my DD25 who studied biology at a very good university, informed me that my model was insufficient, the process of meiosis is actually much more complex than I knew, and simple math can't be applied. So, my ego had to relax and allow me to become stupider for about 15 minutes before I could become smarter for a lot longer. I kind of think it is good to keep your ego exercised in both directions if you want to stay creative. Like half the time you march around and loudly sing "I am great! I am GREAT!! I am the smartest, the cutest, the toughest, the nicest, and the best!!I LIKE ME!!!" and then half the time you softly chant the mantra "I have nothing. I know nothing. I have nothing. I know nothing. " to yourself. As always, YMMV.

[fiby41]

I think the difficulty in re-booting or making room for creativity at mid-life might have more to do with ego-maintenance or sunk-cost-fallacy than stiffening of neural network. I mean, if you already invested 20 years of your life-energy on writing papers on the topic of phlogiston, you aren't going to be super open-minded about the next paradigm shift.

This is the first 7w5 post that I understood completely. Phlogiston was used to explain combustion before oxygen and hydrogen were discovered. Meiosis is a process of cell division. Random facts learned in 10th finally came to use.

This relates to the question posed in the title.

[7Wannabe5]

fiby41 said: This is the first 7w5 post that I understood completely.

lol- My DS28 (INTP) keeps telling me that my brain has turned to rot since I allowed myself to start reading self-help and psycho-babble around 10 years ago. Maybe I need to put myself on a Fine Arts and Hard Sciences ONLY input diet. Also, I know that I need to reduce the ratio of words, hyphens and exclamation marks to periods, paragraph breaks, and semi-colons in my output. I plan on embarking on a hobby career as a garden essayist in either 2036 or 2043, so I need to keep my gray matter in reasonably good timber and polish my skills.

This plan relates to the question by the OP, because another point I would make is that lifespan planning is extremely difficult and prone to accumulation of error, change and chance. You will be recognizable to yourself and those who know you well 20 years from now, but your circumstances will likely have changed in many ways that you could never have predicted. Therefore, I am currently setting my major goal posts at 7 year intervals with complete freedom to change future major goals, current minor goals, and means of achieving any goals.

[daylen]

I plan on embarking on a hobby career as a garden essayist in either 2036 or 2043, so I need to keep my gray matter in reasonably good timber and polish my skills.

This plan relates to the question by the OP, because another point I would make is that lifespan planning is extremely difficult and prone to accumulation of error, change and chance. You will be recognizable to yourself and those who know you well 20 years from now, but your circumstances will likely have changed in many ways that you could never have predicted. Therefore, I am currently setting my major goal posts at 7 year intervals with complete freedom to change future major goals, current minor goals, and means of achieving any goals.

Yea, I am definitly not a long term planner (in the sense that I try to control my future path in life), but I do like to imagine possible future timelines and prepare for contingencies (typical for Ne dominate personalities). I find it bizarre that people think they can control their lives to such an extreme extent, and it is even more bizarre that people would want to.