graycat

One case: VERY much, FULLY, wanted home and family with love and emotional and financial security.

Tried. Never could. The reason:

ECONOMIC!!!!! For higher education and jobs, had to keep moving, Indiana, Maryland, Ohio, NY. The moving was EXPENSIVE in all of time, money, effort. Couldn't put down roots.

Worst part: NEVER could make money enough for a house, so always RENTED, which, long term, is a financial disaster.

Due to the financial stresses, my wife, back with her mother on her childhood farm home, killed herself.

For me, the sheriff came with several assistants and guns and dragged from my rented house all my belongings and left them on the grass. Lost my large professional library -- math, physics, computing -- piano, furniture, clothes, etc.

The shame and humiliation -- my brother's family, with 4 houses, made a place for me.

Looking back, the families that owned nice houses or even just one house, ALL were founders and owners of small-medium BUSINESSES and were NOT "employees". They were financially able to have children and DID.

Education? Wife was Valedictorian and then PBK, Summa Cum Laude, Woodrow Wilson, NSF, and Ph.D. My Ph.D., applied math and computing. These educations took time and money and made us welcome only as university research professors, and the ones I knew who had a house and children (darned few children) were all poorly paid and had other income, e.g., one was in the USAF, got a Ph.D., retired, became a professor.

Net, the US had kids from 1940 to 1960, and after that kept losing to the present where, literally, the birth rate is so low we are going extinct. Why? For good family formation, the US is a big LOSER.

Why? The US economy moved from farms to cities. The city business owners did well, but their employees didn't. So, e.g., Dad grew up in a small, country town. His father ran the general store, and his step father ran the feed and grain mill. They did well financially. Nearly everyone else in the area was a FARMER living on a FARM or working for farmers, e.g., a blacksmith, carpenter, etc. Once we visited, and I saw cows being milked and hay being loaded into the hayloft. Dad's family supported him well in college. After college, he got a job as an employee and never again did nearly so well. Wife's father? Farmer but on the side head of the local REMC (rural electric membership cooperative). Families broke up and scattered

Am still good at math and computing, so doing a startup: Hopefully from my work the children in my brother's family will have plenty of money for a good, private, college, good marriages, nice houses, close enough to keep the family together. But I don't know what they will do to be successful financially on their own.

So far it looks like in the US we need to have the population shrink by 50-75%, have people leave the big cities, have plenty of farm land per person, and live on farms, rely on the Internet and small businesses with much of the needed production automated and with the physical distribution and retailing as in Amazon.

In all those books I listed, and more, e.g., on axiomatic set theory and other foundations, never saw definition or mention of codomain. So, the term is obscure. Readers are supposed to guess at the meaning of obscure terms?

What I did was follow, as in the references, long established convention, that for a function to be a vector at least it had to be in a vector space where (1) can multiply a function by a number (e.g., reals or complex) and (2) add two functions and still get a function in the vector space. To be general, I omitted metrics, inner products, topologies, convergence, probability spaces, and more.

Or, as in the references I gave, math talks about vector spaces and vectors, and each vector is in a vector space. The references are awash in definitions of vector spaces with (1) and (2) and much more.

Computing is awash in indexes for data, e.g., B-trees, SQL (structured query language) operations on relational data bases, addressing in central processors, collection classes in Microsoft's .NET, REDIS, and calling all such also functions confuses established material, conventions, and understanding.

"Functions Are Vectors"?

Let's see: Let A be a non-empty set, N the set of positive whole numbers, and X the set of all functions f

f: A --> N

with usual notation.

Assume as is common, the scalars are the set of real numbers, but the set of complex numbers will also do.

So, is X a vector space and, thus, each f in X a vector?

No, since -f is not in X. Neither is (1/2)f.

Some references (with TeX markup):

Paul R.\ Halmos, {\it Finite-Dimensional Vector Spaces, Second Edition\/}

linear algebra treated as functional analysis.

Walter Rudin, {\it Real and Complex Analysis\/}

with Lebesgue integration and, then, Banach and Hilbert vector spaces.

Walter Rudin, {\it Functional Analysis\/}

with Fourier theory.

Jacques Neveu, {\it Mathematical Foundations of the Calculus of Probability\/}

with random variables, that is, functions from a probability space to, usually, the set of real numbers with convergence results, building on the work A. Kolmogorov building on the work of H. Lebesgue.

The number of people served varies, but a guess is 4: It has 4 pieces of bread, about 80 C (calories) per person. The 1 cup of cheese would be 1/4 C per person, and 1/4 cup of that cheese is enough to be noticed. The 3 heads of Romaine is 3/4 a head per person, and that's plenty for a salad. Could add up to ~300 calories, which is a lot for just part of a meal, just a salad, and not a full meal or even a main dish. So, might follow it with something with a lot of protein, a grilled T-bone steak, grilled/roasted chicken, etc.

But, the dressing yields about 3 cups with 2 cups of oil (plus the oil with the anchovies). The 2 cups is 32 tablespoons at 125 calories per tablespoon, ..., might feed 32 people. In that case, leave the dressing as is and increase the lettuce, bread, and cheese.

Some years ago tried Caesar salad many times and settled on the recipe below.

The Caesar dressing is in the family of oil and vinegar mixtures with flavorings and emulsifiers.

The salad also has croutons (pieces of toast flavored with some of the dressing) and grated hard, dry cheese, Parmesan or Pecorino Romano (and I prefer the second).

The lettuce is Romaine. If separate the leaves, rinse them, shake dry, wrap in some clean kitchen towels, refrigerate for several hours, then the lettuce usually will be crisp, which is desirable. Just before combining all the ingredients to make the actual salad, tear the leaves into irregular pieces.

For the egg, boil it the 10 seconds not to cook the egg but to sterilize the outside before cracking the egg.

=====

Note:

This oil/vinegar mixture has close to the usual (by volume) 3 parts of the oil to 1 part of vinegar. For a brighter flavor, might use more vinegar, maybe as high as a ratio of 3 to 2.

And the other measurements here are also subject to change.

One issue is, some of the ingredients, e.g., basil, oregano, parsley, fresh versus dried, can vary in flavor by a lot. Some garlic is mild and some very strong. And the flavors of the red wine vinegar and olive oil vary.

So, the results tend to vary, between two cooks a lot and even between two trials by one cook.

So for each trial, it's good to have good notes on what did so that can repeat the trial if it was good or adjust the trial if it was not.

So, the notes here are from some trials that seemed good but are subject to adjustment.

=====

Abbreviations (common in the US)

     T -- tablespoon

     t -- teaspoon

     C -- cup

=====

Good to have three bowls, 1 quart plastic or stainless, 5 quart stainless, ~3 quart wooden.

The wooden bowl is for style and the serving, and the large volume of the 5 quart bowl is to ease tossing the croutons and lettuce to coat them with the Caesar dressing.

=====

Caesar Dressing.

In a one quart bowl, combine

     1 egg boiled 10 seconds

     1 T Worcestershire sauce

     2/3 C red wine vinegar (what you pay
     for wine vinegar can vary
     significantly)

     1 1/2 T finely minced garlic

     3 T Dijon mustard (what you pay for
     the mustard can vary significantly)

     1/2 T basil (fresh or dried)

     1/2 T oregano (fresh or dried)

     2 T parsley (fresh or dried)

     1/2 t salt

     1/2 t freshly ground black pepper

     One 2 ounce can flat anchovies packed
     in oil, minced, with the oil

     2 C olive oil (what you pay for olive
     oil can vary significantly)

Combine all but the olive oil. Whip to start the emulsification of the oil and vinegar with the egg and mustard emulsifiers.

Add olive oil slowly with whipping. Seek good emulsification of the oil with the vinegar and the rest.

Makes about 3 C.

=====

Grated Cheese.

Grate some solid Parmesan or Pecorino Romano hard, dry cheese to yield ~1 C of grated cheese.

=====

Toast for Croutons.

Toast four slices of bread (might use some bread other than US lunch box white bread). Stack the four slices and cut in two parallel cuts, rotate 90 degrees and repeat so cut each slice of toast into 9 pieces.

=====

Dress the Lettuce.

In 5 quart stainless steel bowl, tear three Romaine hearts into irregular pieces.

Add 3/4 C of the dressing (right, will have plenty of dressing left over for more salads).

Toss.

Goal is to flavor the lettuce with the dressing but still keep the lettuce crisp, not wet or 'soggy'; so try to use the least dressing for the needed flavor.

Notes:

A nice way to present and serve is with a stylish wooden salad bowl full of the salad with croutons and grated cheese on top.

Thus the stylish wooden bowl is too small for tossing; use the 5 quart bowl for tossing and the wooden bowl for presenting and serving.

For the serving, might also use some stylish wooden salad tongs or fork and spoon.

=====

Toss Croutons.

Add the cut toast to the 5 quart bowl and toss with some of the salad dressing.

Goal is just to flavor the toast but keep it crisp, not soft or soaked.

Add the toast on top of the dressed lettuce in the wooden salad bowl.

=====

Sprinkle the grated cheese over the toast.

=====

Serve.

=====

With the egg, bread, cheese, and oil, it's filling.

Tell me more: At my PC, the weather URL

https://forecast.weather.gov/MapClick.php?lat=35.90615740000...

still works.

Taylor Swift did well understanding the emotions of teen girls, so well that lots of teen girls, not just in the US, begged their fathers and got ~$1000 for a ticket to a Swift concert, and Swift ended up worth ~$1 billion.

It also helped that with good makeup and a good photographer, she had one of the prettiest faces of any human female. She also had a near perfect figure. So, her audience could identify with those. Likely even more important, were her stories of love gained/lost.

I'm a man and so don't much like Swift's art, but the ~$1 billion got me to try to explain her success.

For any men here slow to figure this out and take it seriously, a lot of teen girls and young women have some strong emotions, and art that communicates and interprets those emotions to those teens/women can be very welcome, so welcome to generate ~$1 billion.

I did spend enough time with teen girls and young women to understand a little about their strong emotions.

On key changes in music, the Bach piece in the URL I gave starts in D minor, has central section on D major, and has the final third a lot like the first section and also in D minor.

When I was playing it on violin, I liked the D major section the best. There are some triplets, and I played them insistently, maybe not the best interpretation -- the URL doesn't do that. Maybe I tried the interpretation from a Heifetz performance.

The piece is also sometimes played on guitar. Waiting for a concert to start, a guitarist sat next to composer Mario Castelnuovo-Tedesco and said "The Bach Chaconne sure is difficult to play." The composer, a man of few words, said nothing until the end of the concert and then replied "The Bach Chaconne is the greatest piece of music ever written."

Oh, the URL I gave is a full orchestra arrangement of the Chaconne.

If pop music is that good, I'll be glad to listen to it!

> Bach lacks the skill and emotional depth to write a song about that lonely feeling

For a wide range of such feelings, some can regard as "lonely", as they develop, achieve a triumph, a catharsis, and finally a recapitulation and a comforting, secure resolution -- communication, interpretation of human experience, emotion, i.e., art.

https://www.youtube.com/watch?v=NEUYq5t-cCM

Bach wrote it for solo violin, but it's been arranged for solo piano, full orchestra, etc.

> "Chappell Roan"

Just now listened to some of her music, two of her pieces

Good Luck Babe

https://www.youtube.com/watch?v=1RKqOmSkGgM&pp=ygUcY2hhcHBlb...

and

Pink Pony Club

https://www.youtube.com/watch?v=GR3Liudev18&pp=ygUOcGluayBwb...

So, with the definition of art as the "communication, interpretation of human experience, emotion" what I saw in those two pieces was that they were intended for some teen girls and young women -- single, lonely, generally afraid of their circumstances, don't understand what they see of reality, eager for sex but afraid of it, lost, i.e., missing any good cultural, social, or intellectual foundation for understanding reality or facing life, ....

So in the music, the costumes and stage shows are rapidly changing, outrageous, meaningless, fantasy, scary, i.e., are communication, interpretation of those women's experience, emotions, rapidly changing, outrageous ....

In simple terms, those women have circumstances that yield strong emotions that the music communicates.

"Communicates"? Why? As common, to the audience comfortingly confirms that they are not alone and instead like many others.

How could this be? In the past the women lived in a culture based on strong social, practical, economic, religious, parenting forces. Now (1) for millions of those women the culture is weak or gone and (2) the Internet permits getting confirming, reinforcing communication, interpretation of their scary circumstances from the loss of the culture.

In short, the music really is communication, interpretation of the experience and emotions of those women.

To me it seems that Taylor Swift did much the same, i.e., similar audience, but Chappell Roan is stronger, louder, more outrageous for an audience with stronger emotions.

As a young man, the teen girls I knew, right, had the anxieties from their circumstances but much more constrained and less scary than now.

The music, for me, a man: Get rid of the sets, costumes, dancing, and words and take just the background music (a lot of drum beating) and the singing. In places, the singing is pretty good, i.e., expressive, but really the singing, as art, is all nearly the same, that is, the same vocal content for the same communication, interpretation of experience and emotion.

I expect that even the current devoted audience will soon, a year or so, give up on the current Chappell Roan -- for a cruel joke, "A one trick pony.".

From Vivaldi and Bach through Beethoven and Brahms ... Wagner, Tchaikowsky, ..., Barber there is a lot of effective communication, interpretation of a wide range of experiences, emotions, that is, really good art.

For level 101, a major key is glad and a minor key, sad. Then changing keys, selected chords within keys, pitch, volume, variety of sounds from the variety of instruments, combinations, ..., give a lot more tools for expression than used by Chappell Roan and, thus, permit a lot more music, art.

Next, the tools were just means, and Bach, Wagner, Tchaikowsky, ..., were really good in the artistic content, that is, again, communication, interpretation of human experience emotion.

For abstract algebra, there is the polished

I.\ N.\ Herstein, {\it Topics in Algebra,\/}

(markup for TeX word processing).

For Galois theory, took an oral exam on what was in Herstein.

For linear algebra where the field is any of the rationals, reals, complex, and finite fields there is

Evar D.\ Nering, {\it Linear Algebra and Matrix Theory,\/} John Wiley and Sons, New York, 1964.\ \

As I recall, Nering was an Artin student at Princeton.

Some of the proofs for the rational, real, or complex fields don't work for finite fields so for those need special proofs.

Had a course in error correcting codes -- it was applied linear algebra where the fields were finite.

Linear algebra is usually about finite dimensional vector spaces with an inner product (some engineers say dot product), but the main ideas generalize to infinite dimensions and Hilbert and Banach spaces.

NP-hard is really hard, but it is hard for (a) polynomial running time, (b) for exact solutions, (c) on worst case problems.

One might suspect that fast enough on specific problems for approximate solutions that still make/save a lot of money might also be welcome. Ah, perhaps not!

E.g., in NYC, two guys had a marketing resource allocation problem, tried simulated annealing, and ran for days before giving up.

They sent me the problem statement via email, and in one week I had the software written and in the next week used the IBM OSL (Optimization Subroutine Library) and some Lagrangian relaxation. In 500 primal-dual iterations with

600,000 variables

40,000 constraints

found a feasible solution within 0.025% of optimality.

So, I'd solved their problem (for practical purposes, the 0.025% has to count as a solving) for free.

They were so embarrassed they wanted nothing to do with me. We never got to where I set a price for my work.

The problem those two guys had was likely that, if they worked with me, then I would understand their customers and, then, beat the guys and take their customers. There in NYC, that happened a second time.

If a guy is in, say, the auto business, and needs a lawyer, the guy might want the best lawyer but will not fear that the lawyer will enter the auto business as a powerful competitor. Similarly for a good medical doctor.

For an optimization guy saving, say, 5% of the operating costs of a big business, say, $billion in revenue a year, all the management suite will be afraid of the guy getting too much power and work to get him out -- Goal Subordination 101 or just fighting to retain position in the tribe.

After having some grand successes in applied math where other people had the problem but then being afraid that I would be too powerful, I formulated:

If some technical, computing, math, etc. idea you have is so valuable, then start your own business exploiting that idea -- of course, need a suitable business for the idea to be powerful.

I derived some math, new at least to me, based on my pure math background, e.g., Rudin in measure theory some functional analysis, probability based on measure theory from Neveu, tightness in probability once used in some statistics for computer science, presented at NASDAQ, some optimization via the Kuhn-Tucker conditions, some stochastic optimal control, etc.

> How can a person become so good at researching ?

My time in my Ph.D. program and some of the work in my career (getting paid) suggest that I was "good at researching". But I left such research due to wanting to get paid more, and settled on starting a business, owning it, and making it valuable. If some research can help the business, fine, but the real goal is just the money from a successful business.

On (academic) research, one lesson no one ever mentioned to me but eventually I formulated: Pick a field of research. Then in that field a lot about what is expected, respected, intended, valued or not, ..., is not much spoken about and not made clear -- clear that have fertile ground for politics. Then, for such questions, the answers you guess or get in some one field will likely be quite different in another. In some fields can get reminded of the old quip: "Haydn wrote 101 symphonies or one symphony 101 times?" Or at times can believe that with high probability, a paper gets read by just two people, the peer reviewer and the author; as a result of that case, the only accomplishment of papers, good or bad, are that they get counted as in someone with 50 papers is regarded as better than someone with only 4. Ah, tough to prove that the paper will never get 1000 readers!

For research, one approach is to study a (assume an academic) field, crawl down some narrow alley or rabbit whole, see a question with no answer, consider the broad status of the field, then if making progress on the question seems not obviously impossible, give it a try. By a few days or weeks should have an answer, a partial answer, or hints that by continuing you might get something.

Another approach is to pick a problem mostly on your own and not from, trying to extend, published research. You might follow some instance of personal curiosity or something from some other field, e.g., do some math, optimization, statistics, ... research from problems in the environment (why the ups and downs of lobsters in east Canada?), medical testing, the supply chain, some engineering problem, some business problem, etc.

Do note that in the US, after radar, the proximity fuze, submarine acoustics, code breaking, jet engines, the "bomb", the US military had plenty of both money and problems, and that funded a lot of US research. Now there seems to be a general view: We don't know what research directions will yield powerful results, but since we can't afford to miss out on some big results or fall behind, we will continue to fund research. Non-military research seems less eager for results and to have less money.

Ah, be good at the politics, e.g., even follow "Always look for the hidden agenda." If working in an organization, beware of "goal subordination", i.e., others working to have you fail.

Clearly "Section 174" is now, currently, an issue.

And vaguely I seemed to remember some Trump campaign statements that in taxes some business spending could be deducted instead of amortized (spread over several years) or some such.

I'm deliberately no expert on taxes or business taxes.

Some of the Internet discussions seemed to suggest that some of the worst of 174 were to be implemented, continued, canceled, whatever, so for more information on the background, status, future, etc. of 174, did a little Google search and came up with the discussion I posted here. That discussion seems to say that the "Big Beautiful Bill" may get rid of 174, and that would seem to be in the collection of deduction changes Trump discussed.

About the economy, growth, the Fed's Prime rate, deficit spending, interest payments on Treasury bonds, tariffs, inflation, the balances of trade and payments, R&D, AI, foreign investment in the US, 174, etc., to me the MSM (mainstream media) is short on enough credible information for me to have much in opinions.

In addition, for politics, mostly it looks like noise for some manipulation, effect, or other and a reason to follow "Always look for the hidden agenda."

So, about 174, the information I have looks no more credible and a lot less fun than an old Bugs Bunny cartoon! But maybe Bugs Bunny or Elmer Fudd would guess that getting rid of 174 would help R&D, new businesses, factories, business revenue, and even, net, tax revenue. Or did Elmer repeat "To make money, have to spend money."?

I'd scream at the junk -- drama -- in the MSM, but it won't do any good.

Summary: For the main issues here in the US, I just don't have good information. The stuff I posted above seems to suggest that the future of 174 is still in doubt.

Your Honor, here printed on paper is what the Prosection calls "software". Actually as anyone can see on the paper, what is there is just ordinary typing A-Z and 0-9 with a lot of the typing in English. Businesses have been doing typing for many decades. E.g., this typing is much like instructions to a delivery truck driver to deliver goods to customers. And it's the same if a drone reads those instructions and makes the delivery. Prosecution has yet to show what of this paper is other than business typing ~100 years old.

On "Section 174" and more on taxes from Hill, Barth & King LLC

at

https://hbkcpa.com/insights/proposed-tax-bill-addresses-trum...

is in part:

     Jobs Act. The bill also addresses the
     “big three” business tax provisions:
     deducting research and development
     expenses, 100% bonus depreciation,
     and loosening the rules for the
     deductibility of business interest.

with

     deducting research and development
     expenses

For more there is (with my reformating of the text):

HBK

Home / Insights / Proposed Tax Bill Addresses Trump Campaign Promises and Expiring TCJA Provisions

Proposed Tax Bill Addresses Trump Campaign Promises and Expiring TCJA Provisions

Date May 15, 2025

Earlier this week, the House Ways and Means Committee released details of a multi-trillion-dollar tax-cut bill. The legislation closely follows President Donald Trump’s campaign promises of no tax on tips and overtime, tax breaks for seniors and car buyers, and extension of much of the expiring 2017 Tax Cuts and Jobs Act. The bill also addresses the “big three” business tax provisions: deducting research and development expenses, 100% bonus depreciation, and loosening the rules for the deductibility of business interest.

Key Provisions

(1) Permanent extension of individual income tax rates (no new millionaire’s tax rate)

(2) Permanent extension of the higher standard deduction with temporary increases for 2025 through 2028

(3) Additional $4,000 standard deduction for seniors (subject to income limitations)

(4) Estate and gift exemption increased to $15MM

(5) State and local tax deduction is increased from $10,000 to $30,000 (subject to income limitations)

(6) Child tax credit of $2,000 made permanent with an increase to $2,500 for 2025 through 2028

(7) Return of the $300/$600 above-the-line deduction for charitable contributions

(8) 100% bonus depreciation for assets placed in service after 1/19/25 and before 1/1/2030

(9) Full expensing of Section 174 domestic research and experimental expenses for 2025 through 2029

(10) Increase in the Section 179 deduction to $2.5MM with the phaseout beginning at $4MM

(11) Qualified business income deduction made permanent and increased to 23%

(12) Addition of a special deduction for “Qualified Production Property” which allows 100% depreciation for manufacturing buildings

(13) Eliminates many business, home and vehicle energy tax credits

(14) Creating a new round of Qualified Opportunity Zones with investor tax benefits

There is still substantial debate to come as this bill moves through Congress. We will continue to monitor developments and keep you updated on any changes that may affect your tax situation. Please contact HBK with any questions or to discuss how these potential tax changes might impact your specific financial circumstances.

So items (8) and (9) seem to have to do with deducting "depreciation for assets" and "Section 174".

> vector instructions

Gee, for the polar decomposition, Gauss-Seidel, etc., looked really hard for those in my IBM PC/XT and couldn't find any!!!

Fast matrix transpose? Agree for a transposed matrix, just change the indexing arithmetic that converts row i and column j to an offset in the storage for the matrix and then remember that this is a transposed matrix. Some software object semantics could make this easy for other software to use.

> What does “Undecidable” mean, anyway

A big and relatively recent example is to take (1) the axioms of Zermelo-Fraenkel set theory and (2) the axiom of choice and ask if (1) can be used to prove or disprove (2). The surprising answer is "No", i.e., (1) cannot be used either to prove or disprove (2). So, can work with (1) and, whenever convenient, assume (2), continue on, and never encounter a problem.

So, given (1), (2) is undecidable.

The work was by Paul J. Cohen as at

https://en.wikipedia.org/wiki/Paul_Cohen

The field of research about what is undecidable also goes back to Kurt Gödel as at

https://en.wikipedia.org/wiki/Kurt_G%C3%B6del

Another example, starting with (1), of an undecidable statement is the continuum hypothesis:

     There is no set whose cardinality is
     strictly between that of the integers
     and the real numbers.

In simple terms, "cardinality" means that there is no set X that is too large to be put into 1-1 correspondence with the set of integers and too small to be put into 1-1 correspondence with the set of real numbers.

> Trump administration halts Harvard's ability to enroll international students

Sounds catastrophic!

Ah, at no risk are the books and papers, the famous research professors, and their late grad students, and apparently in simple terms (except for just money), that's about all such a university cares about.

So, not much of a catastrophe! Only partially sarcastic!

Five rules:

(1) Financial Security.

Since tough to get financial security when have a boss, instead start a business, make it successful, and sell it. Usually at the beginning, tough to know if some business direction is good, and good/bad can change over time. So, keep in mind new directions.

The business should yield at least enough for a good family, a house for self and family in a good neighborhood, and significant savings.

(2) Health. Do well on diet and exercise. Don't smoke, drink, or take illegal drugs. Don't try to climb Mount Everest or anything similar.

(3) Family. Enabled by the other rules.

(4) Education. K-12, 4 year college, advanced degrees should yield good ability at selecting good from bad.

     “It ain't what you don't know that
     gets you into trouble. It's what you
     know for sure that just ain't so.“ –
     Mark Twain

Some of the good content may help with financial security. Friends made can be crucial for financial security and parts of family formation. Never stop learning and for much of education pick some good and relevant material and largely teach yourself. For your children, help them with their education.

(5) Socialization. Understand people and how to interact. So, special cases include friends, family, leadership, media, politics.

More is important, but these five 'rules' are a start.

And for the people who get that money, guess who they will be voting for and donating to political campaigns for, etc.

"Always look for the hidden agenda."

"noisy news"

> some billionaire via tax cuts

The current noisy news is taxes for the rich the same or higher, not "cuts".

The story includes some skipping class yet getting a Fields Medal.

At least here in the US:

In academics, a grade of A is better than the rest yet still some independent or from outside school results can mean more than grades and even make poor grades irrelevant.

Some examples:

E.g., for getting into a selective college, SAT Math scores (from outside of school) the highest in my high school class made everything else irrelevant. E.g., overlooked my F in Typing!

Actually, the Typing class was very worthwhile and learned touch typing, but the class was nearly all girls, GORGEOUS, who buzzed away with perfect accuracy at maybe 30 characters a second!

E.g., in graduate school, found a problem and in two weeks got a solution accepted right away by Mathematical Programming. Suddenly had an impenetrable shield and all grades and everything else were irrelevant.

E.g., before grad school thought of a problem and had a first solution; in grad school wrote a first draft; wrote and ran the related software; and wrote the document, all independently. Stood for orals and graduated.

Again, course grades are not everything, and good independent work can make everything else irrelevant.

Try to make some sense out of the OP. Start with some examples:

Google: As I recall, two guys in a garage, literally, until they had a good start on a good business, offered to sell out for $1 million.

Amazon: Bezos and a few programmers.

FedEx: I was there early on and saw a lot of stuff about the BOD (board of directors), Founder-CEO, executives, General Dynamics, visitors from big NYC banks, funding of the airplanes, deals with Memphis to get space on/near the airport, the worker bees, etc. Was close to the action, office next to the Founder--CEO F. Smith, reported to a Senior VP with office across the hall but really reported just to Smith, was close to the BOD ("you just keep doing what you are doing until someone tells you to stop"), twice in work for the BOD enabled crucial investment and literally saved the company, etc.

Plenty of Fish: One guy, three old Dell servers, Microsoft's .NET with ASP.NET and ADO.NET, on-line romantic introduction site, sold out for $575 million.

Compared with Plenty of Fish, how Google started, and the arithmetic in the post, a summary: For the invested money: (a) Too many big, powerful chiefs, and not enough working indians. (b) Big hats, too few cattle. Too much overhead for the work done, e.g., per line of code written and running.

So, one approach: Start cheap, dirt cheap. Sole, solo founder. Only an LLC and with lawyers and accountants like, say, a grass mowing business -- LITERALLY. Founder lives cheap, say, in an area with low cost of living, in a used manufactured house, that is also the office, old used car. Take advantage of the still exploding Internet and cheap, powerful tower case computers (assembled from parts) for development and servers, $60/month 1 Gbps Internet connection, etc. Find a market need can meet with this dirt cheap approach and can get to profitibility with rapidly growing revenue.

So, leave out the time, cost, botheration of: Investors, lawyers, accountants, rented high quality offices, investor meetings, Board meetings, a management tree, manager meetings, reports to investors and the BOD, 10+ employees with all the expenses, legalities, lots of plane travel, employee stock plans, vesting, etc.

For a while, tried to raise funding; time wasted. Lesson: In simple terms, most VCs won't look at a business idea or technology before there is rapidly growing revenue. Then nearly all the VC money is used for the lawyers, other overhead, etc.

Comparison: (A) Dirt cheap: Invest $50-K a year. (B) Angel, VC, private equity approach: $10+ million a year. Big difference.

Problem: Investors need the lawyers, accountants, and other overhead so go for approach (B) where %10- of the money goes for the real work of getting the business going.

Back to work!

> Maybe this misses the point slightly?

Maybe! My thoughts were, say, tangential or incidental.

A guess is that a central issue is how much in new features should we develop and use?

I see a dilemma: (A) I mentioned the old controls that go back to early Windows and even IBM's 3270 terminals. An advantage of these controls is that lots of software tools implement them and billions of people already understand them. (B) Being too happy with the old stuff or even the present risks progress that is possible and worthwhile.

Your post seemed to illustrate (B).

But generally in the industry, with smartphones, laptops, desktops, Apple, Google's Android, Windows, browsers, apps and extrapolating, we could have an explosion of new features that would complicate work for everyone and fragment the industry.

Ah, maybe Darwin would explain: Lots of mutations with only the best lasting??

For my work, I'm thrilled with the tools and technology available now that I get to exploit.

Uh, a guess is that 1+ billion people are already good at using "drop down menus" along with check boxes, radio buttons, single line text boxes, multiline text boxes, push buttons, links. So, when those user interface controls are sufficient for the purpose, using something else might reduce the collection of happy users. The Web site of my bank stays close to such now classic controls.

> What your wrote is ... not related to the topic of the article.

The article was: The Halting Problem is a terrible example of NP-Harder and I wrote:

> So, in this case can tell if the "program will stop" and, thus, solve "the halting problem".

> "Trivial"?

I never claimed the post was a significant contribution to computer science or complexity theory, and at most only a tiny fraction of posts at HN are such. Also, my post does not address the complexity theory question of P = NP.

If what I wrote was "new, correct, and significant", then I should have sent it to a good computer science journal. I've published enough papers in good math and computer science journals to notice that the checks take a long time to arrive. I'm not in academics and never wanted to be.

HN is not a journal of new, correct, and significant work in computer science.

From responses in this thread, the post has proven to be at least curious and interesting to some of the HN audience.

"administration"?

I avoided that. I was commenting in general terms.

"countries with truly dysfunctional judicial"

I suspect that much of how people get along in such a country is just to pay enough to the right persons. As a joke, that would often be faster and cheaper than following the US system fully honestly.

I'm reminded of the movie where, given a problem, someone could go to Vito and get a solution -- he had "all the judges and politicians in his pocket".

The role of Congress: The SCOTUS is from the Constitution, and all the rest are from Congress. If Congress sees a problem with those courts, it can fix it right away -- impeach a judge, cut off their funds, abolish their court, etc.

Just because our legal system is not the worst possible in the world does not mean that we should tolerate its faults.