As I was being interviewed by an IBM branch manager in Chicago (my wife had started grad school at the University of Chicago), it was explained to me:

"Some people think that IBM is a technology company or a computer company. It's not. IBM is marketing company. IBM would be in the grocery business if they thought there was any money in it."

For a marketing company they invest way too much in developing fundamental technology. The number of (useful) patents and Nobel prizes they have is quite impressive.

Such a cube, i.e., a set, is closed, right? Sooo, there exists a function on the space that is 0 on the cube, strictly positive otherwise, and infinitely differentiable.

For garbage collection and the idea of assigning storage requests to different categories of (dynamic) storage ....

Apparently part of the algorithm is based on the size of the storage being requested.

Hmm. So, we have historical data of storage requests and for each (i) the size of the request, (ii) how long until the storage is freed, (iii) etc. ....

Guessing about a bizarre case: It might be that on Monday many storage requests of certain small sizes have lifetime just a little longer than the decision to move the request to another category, i.e., the moving effort was inefficient, wasted.

So, in simple terms, for an optimization, for each of the variables have both in the history and real time, make the variable values discrete, altogether may have for some positive integer n a few thousand different n-tuples of variable values; then for each n-tuple pick the best decisions (policies, etc.). Uh, unless this idea has already been tried.

> ridiculously tiny and fragile my little life

Naw!!! We are rare, so rare that we might be unique in our solar system, galaxy! We don't look little and instead the reason for the whole show! "Where is everybody?" -- easy, we're it. Soooo, what's the reason??

The whole event is likely to be an exponential, and the last, ah, after Newton, Maxwell, Einstein, Schrödinger, biochemistry, ..., computers, we look like we're at -- a standard for exponential growth, e.g., the question P v NP -- the unique big turn up out of the atmosphere ... blowing past Andromeda at 0.5 c and accelerating.

It can appear that some famous companies pursue pure research as a source of public luster.

> random delay

A Poison process. Just specify the expected value. E.g., if the expected value is 5 seconds and have gone some hours without an event, then the expected time is still 5 seconds.

E.g., like the time to some radio active delay and whatever its expected value to decay is.

Likely are also making a probabilistic independence assumption.

Got an iPhone 16 Plus:

Apparently somehow needed to have an "Apple account." Don't want one -- don't want to be subservient, subordinate to, dependent on Apple or hurt my privacy -- but relented and applied -- refused!!!!!

The phone rang, apparently with someone from Apple Help who somehow noticed that my frustration (wasting time) was about to explode with some gigatons of TNT, enough to level everything from me to CA on to Hawaii. Soooo, apparently Apple HQ is somehow always online -- outrageous privacy threat. Since I was trying to make the phone work for even the simplest things, I could not receive the call.

Heck, could not even get an Apple account.

Super, semi-quasi, pseudo bright: The phone isn't working so to help call the phone that isn't working.

Apple, to communicate with a new user, use some REAL computing, including email. Understand???

New user? That iPhone is my first cell phone, first Apple product, and hope my last.

Using some computing that has a real keyboard, 30" screen, an 8 core AMD processor, and Windows and actually works, eventually got to Apple online help. Was advised to press the "Down Volume" button. I asked which one of the five was that button, and the help staff didn't know. Soooo, not even the Apple help operation knows what the buttons do. Disney with Donald Duck could make total riot out of this disaster!

I declared the iPhone 16 Plus a disaster, expensive, useless, worthless, at best a puzzle box, and will return it to Xfinity.

Actually, of course, the iPhone is a grand triumph of electronic engineering, optics, software, etc. -- still for new users is useless and worthless as a phone, i.e., won't make or receive calls, just won't; several hours a day of absurd mud wrestling in the dark for several days yielded no utility at all.

Useless? First big problem: Apple, apparently with rock solid, ironclad determination, deliberately, totally refuses to DOCUMENT, say, with an easy to find, COMPETENTLY, BEAUTIFULLY, EFFECTIVELY written PDF of D.O.C.U.M.E.N.T.A.T.I.O.N. Go bankrupt, maybe. Write documentation for new users, NEVER. Won't do it.

Me? Can I read tricky material from good documentation? Hold a Ph.D. in applied math with plenty of pure math where learned lots of tricky stuff, but from well-written books.

Apple, shut up, sit down, and listen up -- until you DOCUMENT, for new users your expensive phones are worse than worthless junk. Sure, maybe high school girls form little groups and share some of the basics they discovered somehow, but I'm out of high school.

One word Apple -- DOCUMENT.

Here’s the first time setup documentation: https://support.apple.com/en-us/105132

And the general iPhone documentation: https://support.apple.com/guide/iphone/welcome/ios

Sometimes, I wish this documentation was a bit more technical, but it’s not bad at all.

The film on the front of a new iPhone, that you remove to reveal the screen during unboxing, provides pictorial icons of what each button on the phone does. For volume down, you can see a minus in a circle. It’s the bottommost button on the left.

I’m not sure why you had so much trouble creating an Apple ID, but you can still skip that when it prompts you to do so. I believe it’s under “Forgot password or don’t have an account”.

Very strange comment.

Literally hundreds of millions of people have set up an Iphone, it's trivial if your aren't cognitively impaired and/or very elderly.

I don't understand how you could have trouble finding the volume down button.

It's quite obviously placed, and is one google search away if not...

> I don't understand how you could have trouble finding the volume down button.

Read again: It was Apple Online Help that didn't know where the Volume Down button was.

I wasn't asking them; in a 'chat' session as part of an effort to get the phone working, they were asking me, asking me to press that button, and not for sound volume; to be sure, I asked them just where the button was, and they didn't know.

In simple terms, I unpacked the phone, read the documentation, plugged it in to charge its battery, tried to use it to make and receive calls, and it didn't work. "Just work"? No, didn't work.

Whatever, this was one HORRIBLE end-user experience, and I'm way past putting up with it, returning the iPhone, and going to look at something from Samsung. Before spending any money, I will want to see their DOCUMENTATION.

Bell Labs was part of AT&T which had in effect a government approved monopoly -- nearly all of the US telephone system, so was awash in earnings for transistors, lasers, information theory, the Fast Fourier Transform, etc. Xerox PARC was part of Xerox that was also "awash in earnings" from photocopying machines and for more whatever else, e.g., more in personal computing.

So, for a high school student, the lesson there was not just to do great science but to join or start a business that is or soon can be "awash in money" and then do whatever you want, e.g., Jim and Marilyn Simons, including "great science".

In more detail, now in practice, one of the main motivations of a company "awash in money" is to pursue research for luster, e.g., AI, quantum computing.

Ah, Lesson 101 in US life and money!