graycat

(1) Didn't see anything on the math of probability or stochastic processes, e.g., nothing from Dynkin, Neveu, Breiman, etc.

(2) That it's important to study carefully that computing is about "switches" is something like knowing the details of the amazing work in the chemistry of rubber tires is crucial for truck driving or we should all early in our education achieve good mastery of each of the proteins in our DNA.

(3) After working through all those books, cancelling nearly everything else in life for some years, just what is the result, the payoff, the reason? Academic research or something in the mainstream economy, technology, etc.?

Ah, never had anything to do with LaTeX.

Now, TeX, that's one of my favorite things!

Ah, just today used TeX on a paper in anomaly detection that exploits the Hahn decomposition!

In the paper of the OP, was there a place where it claimed it had a subset of a set when it was really an element of the set. Don't be careful about the difference between elements and sets and can get back to the Russell paradox.

Also, for some positive integer n, e.g., n = 3, we can have an n-tuple, e.g.,

(A,B,C)

but, guys, so far we've said nothing about the components of the n-tuple being numbers, e.g., for error correcting codes, elements of a finite field, multiplying an n-tuple by a number, adding n-tuples, taking inner products, so, so far, with just some n-tuples we a bit short of a vector space or vectors.

An important and well plowed subject. Can consider also for the coding theory

W.\ Wesley Peterson and E.\ J.\ Weldon, Jr., {\it Error-Correcting Codes, Second Edition,\/} The MIT Press, Cambridge, MA, 1972.\ \

and for the abstract algebra, e.g., field theory

Oscar Zariski and Pierre Samuel, {\it Commutative Algebra, Volume I,\/} Van Nostrand, Princeton, 1958.\ \

Addition: Omitted the reports that Swift is worth $1B from her singing.

Early on, with a good technical background, I guessed that, of course, the key to success in technology was some good technology but soon discovered that VCs just want to make money, a lot of money, quickly, and otherwise will hear from the investors in their fund.

Just heard of Palmer Luckey. Hmm! Money? No big staff, not much equipment, essentially just one person?? $1B+, quickly? Example: Taylor Swift. Did she ever hear of Linux???

Okay, "logistics optimization"???

In the US there have been a few, i.e., apparently less than 20, universities with an applied math program up to date in and teaching optimization.

Sooooo, anyone at all seriously interested, long, for decades, would, could, should visit some of those math programs, meet some of the profs, get recommendations for their former students, call them, chat, and offer a job better than their current lawn mowing, fast food restaurant kitchen cleaning, or car washing. Instead of just the US, might also consider Waterloo in Canada. Actually the Chair of my Ph.D. orals committee specialized in optimization in logistics. After sending 1000+ beautifully written resume copies and hearing back nothing, can begin to conclude that optimization is not a hot field and for highly dedicated optimizers who want to sleep on a cot in a single room, forgo bathing, most days eat bread, other days peanut butter, have no children, wife, or family contact, don't own a car, and must get any needed medical care from some of the last resort special clinics. Ah, real optimization!

Easier: At the best, cheap in-state college, major in math, science, or tech. Do well, and then for an Ivy, etc. college, go there as a grad student which can be even better for meeting people than being a ugrad student at an Ivy. Going as a grad student might be for free.

Maybe teach some ugrad courses -- a way to meet people, especially girls 1-3 years younger. Generally do a lot of the obvious things to meet people -- much of the reason for an Ivy is to meet people. If you want an academic career, then a top research university can be a HUGE help, i.e., may have several world class research professors any one of whom could get you a good start on an excellent research direction.

As a ugrad, to help getting into the college you want as a grad student, be sure to work hard and do well. E.g., any free time you might have, get and study the books of courses you plan to take. Then in such courses you will have a head start that can make you look MUCH smarter. For some of the profs that taught courses you did well in, get them to help you with suggestions of courses, texts, papers. You will want one or more such profs to recommend you for the grad program you want. To do well, maybe write an honors paper.

For the square covering problem, answer, 2.

> "C?"

Forgy was Charles Forgy.

For a "rules engine", there was also IBM's YES/L1.

"Rules"?

An earlier effort at AI was based on rules and the C. Forgy RETE algorithm. Soooo, rules have been tried??

> Classes are divorced from the practical applications of learning. Apprenticeships train in exactly the situation you’d want to apply the skill.

Hmm .... Something like in the movie "The Hunt for Red October", the US Navy wanted:

(1) Start with recordings by US submarines of underwater sounds, and write software to estimate the power spectra using the FFT (Fast Fourier Transform) and the Blackman and Tukey, "The Measurement of Power Spectra".

(2) Given ships at sea and a war, how long would the US submarines last? Start with some WWII analysis of search and encounters by Koopmans and do a Monte-Carlo Markov process, generate many independent sample paths and average.

Gee, how could I do those without my academic courses in analysis and probability? And there are more examples, including the crucial, original core math in my startup.

My Ph.D., applied math, Johns Hopkins, supports my post.

Cairo may have a way out: Commonly the main criteria for a Ph.D. is: (1) Pass qualifying exams in several important topics in the field. (2) Do some research that is an "original contribution to knowledge worthy of publication" where the main criteria for publication is "new, correct, and significant".

No professor or university Dean can keep her from doing well on both (1) and (2). It looks like (1) would be easy enough for her. The work she has already done may satisfy (2). Once she has done well on (1) and (2), tough not to award her a Ph.D.

> collateral damage ...

Right.

One, maybe not the only one, hands off, automatic, 100% "all-natural", do nothing solution to the "housing crisis": Hope the birth rate, i.e., on average the number of babies born per woman, stays significantly under 2.0 or even 2.1, maybe 2.2.

So, the population will shrink but with some maintenance (roof, painting of exterior siding, kitchen/bath, HVAC, windows/doors) mostly the housing supply won't.

The Internet may reduce the time and money commuting to work and/or the need to be in high density, expensive housing areas for a job.

Microsoft?

For progress, one word: Document. For more, quit forcing on me stuff that hurts my work. One more, for a list of old problems, document and fix those.

Maybe since the Big Bang I'm the only one, but AM one, to be torqued at what I regard as media low credibility and undefined, obscure terminology.

Sorry guys but I (1) very much DO want solid information about a range of interests and (2) have a STEM field background that places great emphasis on solid evidence.

We don't have to dig into quantum mechanics: Instead there are some common high school standards for term papers that call for claims supported with data with references from credible, hopefully original, sources.

Instead I see various attempts at getting reader attention via emotional appeals.

Uh, "Breaking news, this just in, experts shocked": Now we have the Internet where before we had news writers with typewriters, typesetters, big rolls of paper, printing plants, distribution trucks, paperboys, etc., twice a day, morning and evening. With the Internet there are lots of sources, cheap means of distribution, ....

E.g., recently saw some news, scary drama, about suddenly too high prices for corn. Okay, HOW high are they? How do they compare historically? Can we have some good graphs of credible NUMERICAL data????

Well a little use of Google gave

     https://www.nass.usda.gov/Charts_and_Maps /Agricultural_Prices/pricecn.php

with a really nice graph -- numerical data, no drama -- from 2016 to the present. For a fast look at corn prices, nuff said.

Point: Commonly the old media pushes drama and is stuck in the past, and now the Internet offers ways to set aside the old media and get solid information. "Media, fun knowing you."

Yup: And stochastic dynamic programming and stochastic optimal control! Suppose a cargo plane is to fly from Kansas City to St. Louis, Chicago, Indianapolis, Dayton, Nashville, and Memphis and at each city pickup cargo. Suppose the cargo weights are known only in probability distribution from history and otherwise are probabilistically independent. Have weather reports for the winds and temperatures, but the actual values can vary from the reports. And suppose the fuel prices vary significantly among the stops but are known.

Then, how much fuel should the pilot buy at each stop to minimize expected cost for the trip? I.e., in simple terms, buy extra fuel where it's cheap and carry (tanker) it to where it's expensive but in so doing burn extra fuel from the extra weight of the extra fuel.

Solution: Stochastic dynamic programming.

Hint: In Canada, the solution is illegal!

Was meeting with Nemhauser (see references below); my cab back to the airport was waiting; and he gave me a 15 second lecture. On the plane thought about his lecture, ..., and stood for my Ph.D. orals and passed (extra credit for guessing my employer).

Some references (with TeX markup):

Stuart E.\ Dreyfus and Averill M.\ Law, {\it The Art and Theory of Dynamic Programming,\/} ISBN 0-12-221860-4, Academic Press, New York.\ \

Dimitri P.\ Bertsekas, {\it Dynamic Programming: Deterministic and Stochastic Models,\/} ISBN 0-13-221581-0, Prentice-Hall.\ \

George L.\ Nemhauser, {\it Dynamic Programming,\/} ISBN 0-471-63150-7, John Wiley and Sons, New York\ \

E.\ B.\ Dynkin and A.\ A.\ Yushkevich, {\it Controlled Markov Processes,\/} ISBN 0-387-90387-9, Springer-Verlag, Berlin.\ \

Wendell H.\ Fleming and Raymond W.\ Rishel, {\it Deterministic and Stochastic Optimal Control,\/} ISBN 0-387-90155-8, Springer-Verlag, Berlin.\ \

Michael Athans and Peter L.\ Falb, {\it Optimal Control:\ \ An Introduction to the Theory and Its Applications,\/} McGraw-Hill Book Company, New York.\ \

Dimitri P.\ Bertsekas and Steven E.\ Shreve, {\it Stochastic Optimal Control: The Discrete Time Case,\/} ISBN 0-12-093260-1, Academic Press, New York.\ \

E.\ B.\ Lee and L.\ Markus, {\it Foundations of Optimal Control Theory,\/} ISBN 0471-52263-5, John Wiley, New York,

Hmm. (1) An article from WSJ. From their reputation, not good. (2) Article about Pig Butchering? Obscure, undefined terminology, really bad writing. That's too much -- refuse to read or pay attention.

AGI???? Again, once again, over again, yet again, one more time:

(1) Given triangle ABC, by means of Euclidean construction find point D on line AB and point E on line BC so that the lengths |AD| = |DE| = |EC.

(2) Given triangle ABC, by means of Euclidean construction inscribe a square so that each corner of the square is on a side of the triangle.

Come ON AGI, let's have some RESULTS that human general intelligence can do -- gee, I solved (1) in the 10th grade.

The topic was about Federal budget cuts for the STEM fields. My point was, budget cuts or not, if want to work in the STEM fields, 'bout have to pursue work and funding for national security. I gave some "autobiographical" examples.

Moreover, in WWII we had Turing's code breaking, England's radar, the US proximity fuse, and "the bomb, the ATOMIC bomb".

Then Garwin and Tukey talked, and we got the FFT (fast Fourier transform), talked about the test ban treaty and detecting underground tests.

GPS is nice, but the first version, with the relativity considerations, was done at the JHUAPL for the US Navy missile firing submarines.

Then, as I recall, some people in the US concluded

"Never again will US science operate independently of the US military"

or that since WWII nearly all the reason for all the science funding -- Los Alamos, Oak Ridge, Lawrence-Berkeley, Stanford Linear Accelerator, Fermi, Brookhaven, Hanford, JHUAPL, NASA, along with DOE and NSF funding of academic research in the STEM fields at Berkeley, U. Chicago, Carnegie-Mellon, Harvard, Princeton, Johns Hopkins, etc. -- was intended for US leadership in the STEM fields and, thus, US national security.

Bluntly put.

Right, Simons funds a lot. And Hopkins has the Whiting School of Engineering from the widow of Whiting of Whiting-Turner Construction, etc.

Sorry about war, but I do like the science.

(1) "Tab Pickup". I've never used it, don't want to use it, doubt if I will ever use it, but when I'm in the middle of my work, moving fast, lots of windows open, then bring a window to the top of the Z-order and get "Tab Pickup" and an INTERRUPTION of my work. If I had a gun and if it would do any good, I'd SHOOT the computer. I HATE "Tab Pickup". PLEASE, in Settings, make "Tab Pickup"

       =====>>> Optional <<<=====

hopefully with default OFF.

(2) Again, in the middle of busy work, I move the mouse and, presto, bingo, again, if a gun would do any good, another INTERRUPTION in my work as Firefox has a POPUP that covers what I'm trying to look at. Sometimes the popup is of a URL, a LONG URL with ~10 lines of text, and covers a LOT of the screen. Sometimes so, ASAP I have to get rid of the popup. I hate interruptions, "Tab Pickup", popups, changes I didn't ask for.

Budget cuts?

Want to get paid, by the US Federal Government, for pursuing science or technology?

From experience, in simple terms, a word: Have the work for and the funding from the US DOD, department of defense, military, for some work they really care about.

This sounds like a joke, but it's 90+% real.

For years early in my career in applied math and computing, far and away the best parts, funding, technically advanced work, growth in expertise, and working conditions were on US military work, e.g.:

(1) The FFT (fast Fourier transform) and power spectral estimation (as in the book by Blackman and Tukey) for analyzing ocean audio, close to parts of the movie The Hunt for Red October. Also, the movie uses magneto hydrodynamics (MHD), and the specialty of the guy I was working for was MHD.

(2) Some optimization using Lagrangian relaxation for nuclear war.

(3) Given many ships at sea, some Red, some Blue, and some Blue submarines, war breaks out, and how long will the ships last, in particular, the Blue submarines? Sounds impossible or nearly so, but in WWII there were some cute derivations on search at sea and some Poisson process math by a guy Koopmans, and I did a little more on the math, in assembler wrote a random number generator starting with an Oak Ridge formula, and wrote some Monte Carlo code for the whole thing -- yes, used the speeds of the ships, their detection radii, and for each Red-Blue pair the probabilities of none die, one dies, the other dies, both die.

Surprisingly, a famous probability prof was flown in for a fast review. His remark was: "No way can your Monte Carlo fathom the huge sample space tree." Well, maybe, but so what?

"After some days, say 5, let X be the number of Blue submarines still alive. Then X is a random variable and is bounded, that is, is >= 0 and <= the finite number at the start. Then the law of large numbers applies, and can do 500 independent and identically distributed sample paths, add, divide by 500, and get the expected value for the 5 days, and each of the (times) days, within a gnats ass nearly all the time." The prof agreed but was offended by the gnats remark!

Sure, it was simple, but maybe not fully too simple -- was liked, passed the review, and helped my wife and I get our Ph.D degrees.

Also the military funding let me sit alone for some days learning PL/I that later, with a tricky feature of PL/I calling back into the stack of routines called but not yet returned, used to save IBM's AI product YES/L1! Ah, military worked again!

Ah, the military may (still) be interested in computer and communications security and reliability, system design and development methodology, system monitoring, and management, and now in AI, drones, etc. A commercial server farm or network doesn't expect to be attacked by long range missiles, but DOD systems have to be robust in a war!

Once I was at the David Taylor Model Basin (big tank of water to tow candidate ship hull designs), and they were seriously interested in the Navier-Stokes equations -- maybe they still are! Uh, do they have good solutions yet?

Maybe a related practice (what I do): Write actual proofs or good documentation that contains essentially proofs and combine that with Knuth's Literate programming.

For what is to be proved, try to use divide and conquor to make the whole proof consist of separate steps, each of which gets a short proof and each of those steps might become a subroutine (whatever the terminology and functionality of the programming language and environment).

> I don't understand what you mean.

I explained in (2). The main point in (2) is that ALL the people in the threatened area, right on the street they ARE, where they live, work, shop, walk, whatever, get LOUD SIRENS, REALLY LOUD, to warn them and also transportation OUT'A there.

Alerts on cell phones, TV, radio, newspapers, "water stream gauges", etc. leave HUNDREDS of people, including a camp full of girls and counselors, still ASLEEP and now "missing" or "DEAD". As in (2), we need to WAKE them, everyone, UP and get them OUT.

There may be proposals to install flashing lights, bells, whistles, sirens, etc. on phone poles, etc., but in the ~60 years to the next such flood such means will likely be rusty, broken, dead, etc. Sooooo, (2) just has people alive at the time of the flood THEN using the cars, trucks, horns, sirens available and working THEN to solve the problem.

Seeing Musk's announcement of his Grok 4, three questions:

(1) Is there a function from the plane to the real line that is 0 on the Mandelbrot set in the plane, strictly positive otherwise, and infinitely differentiable?

If so, then what function?

If not, then why not?

(2) In the Kuhn-Tucker conditions, are the Kuhn-Tucker and Zangwill constraint qualifications independent? For an answer, give a proof.

(3) Given a triangle ABC, using Euclidean construction, inscribe a square so that each corner of the square is on a side of the triangle.

I solved this one in the 10th grade.

Threads is for mobile? There's an app? Mobile, why do I care about mobile?

Mobile's for phone calls, right? And a mobile phone has a tiny screen, is short on electrical power, and has the worst substitute for a keyboard back before the first typewriter!!!

Instead, I type this using an excellent 32" screen and a really good keyboard got years ago with a Gateway computer!!!

A joke, folks!

Get a good system to alert, wake, get the attention of all the people at risk and on the way out'a there right away for $0?

(1) The weather center develops a warning directed graph of persons who spread the word to get the PAS at their work. You ask what is the PAS?

(2) PAS -- People's Alert System: Everyone in the weather center, fire, police, and everyone else ready and willing to help, etc. who has access to a car, better, a firetruck or ambulance, gets in and turns on the horn and/or siren and drives all the vulnerable streets and makes sure all the buildings are awake and know about the threat. Then the PAS people, with others as passengers, drive the heck out of the area of the threat. Should also work for hurricanes, etc.

Didn't see a way to try Grok 4 for free, so tried Chat GPT:

Given triangle ABC, by Euclidian construction find D on AB and E on BC so that the lengths AD = DE = EC.

Chat GPT grade: F.

At X, tried Grok 3: Grade F.