My generation learned about the googol (10100) and the googolplex (10googol) from Carl Sagan on Cosmos. The story was that a mathematician asked his son for the largest number and that's what the kid came up with -- Wikipedia dates that at 1920 and that the kid named it "googol" after Barney Google ("with the goo-goo-googly eyes").
A couple years ago I wrote a web page about number names, Number Names. For example, a value which is close to a googol is 1099 which is a duotrigintillion (short scale) and a sedecilliard (long scale). But the largest number name I list is for one millinillion (short scale) for 103003. Those entire number naming systems, short and long, should make high school students appreciate having to use scientific notation since it lets them avoid the names.
The long scale/short scale issue is why when I write "billion" I always add (109) to indicate which billion I'm talking about (CosmicChimp, who lives in Germany, should understand that, while members in the UK won't because they switched to the short scale back in 1974, at least for billions).
BTW, ain't no such things as jillions, zillions, or even bazillions.
I remember a sci-fi short story from high school (so it pre-dated the late 60's, most likely from the 40's or 50's) where a mathematician is kidnapped. The kidnapper had been injured or disfigured because of an industrial accident caused by a mathematician having made a mistake, so now he wants to take revenge on mathematicians. He'd kidnap one mathematician after another and present him with a problem. If he can solve it, then he can go free, but if not then he dies. The protagonist is the first one.
The problem is to guess a number, n, with particular properties. All I remember is one clue and maybe a second:
Adding any value to n results in n -- ie, n + x = n, for x non-zero.
Subtracting n from n results in any number -- ie, n - n = x, for x non-zero.
According to the short story's author, the value of n is infinity. That first clue was your observation that if you add 1 to the largest possible value then you get the largest possible value:
∞ + 1 = ∞ .
Edited by dwise1, : ABE: "most likely from the 40's or 50's"
a / b is a ratio, therefore its value is a rational number.
π is not a rational number, but rather is irrational (ie, cannot be expressed as the ratio of two integers).
Therefore π ≠ a/b
Like I said, I had to blink a couple times before I got it.
ABE:
Latest joke I tell everybody now:
The newest arrival to Heaven asks God the question that had vexed him his entire life: "What's the meaning of the universe?" God: "Well if I have to explain it, then that ruins the joke."
Edited by dwise1, : ABE
Edited by dwise1, : making pi (π) larger and hence more apparent
A while back I investigated whether it was possible to open such attachments safely. I no longer remember the details of what I learned, but the short answer is no.
Here's how I would always handle attachments and how it led me to two disturbing discoveries.
Having been a DOS-er for years, I never took to double-clicking a file but rather only application icons on the desktop. Even now in File Explorer I'll do a right-click "Open With ... " on a file rather than double-clicking on it (but then some of the filetype-to-app mapping is a bit wonky so I'd have to do it most of the time anyway).
So when I'd receive an email with an attachment, I would save the attachment to a directory by opening the content menu with a right-click and selecting the save attachment menu item and then open the associated app and open the file within the app. No, I wasn't born paranoid, but rather an attached file was something that I would want to save for future use so saving it was the logical first step.
One day I received an email with an attached Word document file (or Excel -- it's been decades) which seemed pertinent to things that I was involved in at the time (it had something to do with Scouting). So I saved it and opened it in Word, which refused to open it as being an invalid file format. I took a closer look at that file in Windows Explorer and the icon and stated file type didn't match. I went to DOS to look at the file's hex dump and that's when I saw its actual file extension for the first time: it wasn't a .doc file, but rather some kind of executable file.
So the two disturbing things that I learned from that:
I had encountered my first Trojan attachment. The file's name wasn't campgrounds.doc, but rather something like campgrounds.doc.exe, an executable! Double-clicking on it would run it and it would perform its nefarious function. But why didn't my computer warn me by displaying the actual file extension?
That was the second far more disturbing thing that I learned: Windows was set up by default to hide that vital information from us! In Windows Explorer's View there's an option to hide known filetype extensions and it's turned on by default!
So I turned that stupid thing off! But then after a while (triggered perhaps by a patch) it would be turned back on again, whereupon I would immediately turn it off again. Stupid! Stupid! Stupid!, but they have never fixed it! Stupid!
But now my emails no longer offer the choice of right-clicking on an attachment. The only way I can save an attachment is by clicking on it. Which means that I have to have a very good feeling about the authenticity of that email.
Similarly, when I would get a spam email on my phone I used to be able mark it as spam and get rid of it. Now on my new phone the email reader requires me to first open that email before it gives me the option to declare it spam. So I have to go to my computer where I still can declare them to be spam and get rid of them there.
Another story about Windows hiding file extensions by default. My Java class was held in an auditorium with the instructor using a school Windows box with a large-screen projection of the monitor. He would create a .java source file and compile it to create a .class file. But the computer wouldn't tell you which was which! Sure, they had slightly different icons, but nobody had any clue what a .java or a .class file icon was supposed to look like. So I would have to raise my hand and walk him through turning off that damned hide file extensions option so we could see the file extensions. Unfortunately, that box being a school computer meant that any setting changes you would make would go away when you logged off. So we had to go through that same evolution every single lecture. What a pain!
Giving the attachment a .exe file extension shouldn't mean anything to a Mac, which, as I understand, uses metadata attached to a file to figure out what to do with it when you double-click on it. Windows uses the file extension, which you can associate to whatever application you want to.
It appears to depend on how the HTML was written. I used to be able to right-click on the attachment and save it. Now they've "improved" the page so that I have to click on it; when I try to use the attachment's context menu to "Save As ... " it only allows it to be saved as an HTML file (I suspect that the context file is for the entire page).
Though clicking on the attachment pulls down a menu which shows the progress of downloading the file and then offers options (including opening it). But that still doesn't feel right, kind of like having to provide your SSN for access to services (eg, Medicare before they issued us new numbers). Or being expected to walk around with an RFID credit/ATM card in your pocket.
Peter Schickele would say that he taught musicology at the University of Southern North Dakota at Hoople. However, Hoople (pop. 242) is in the north-eastern part of the state, north of Grand Forks.
About 20 years ago Schickele had a radio show on public radio, which I would listen to on San Diego's KPBS late Sunday afternoon once a month on my drive home from reserve duty. One of the things he said was:
quoteThose who can, do. Those who can't, teach. Those who can't teach become musicologists.
The instructor for my music appreciation class in 1972 had attended school with Peter Schickele, as I recall. My first exposure to him was when she played the sports coverage of Beethoven's Fifth for the class.
Most of the jokes are based on musicology lore. For example, Bach's music being rediscovered because a fish monger was using it to wrap fish in became PDQ Bach's music being used as the filter in the coffee pot -- that turned out to be the "Sanka Sonata", a play on Bach's Coffee Cantata, a miniature comic opera which he had written for the grand opening of a friend's coffee shop in c. 1734 and which used caffeine addiction as a plot device ("If I couldn't, three times a day, be allowed to drink my little cup of coffee, in my anguish I will turn into a shriveled-up roast goat.").
And Concerto for Piano versus Orchestra (Schickele 88) is a play on the concerto form in which a solo instrument plays contra an orchestra.
Reminds me of a small Windows programming exercise. In the window is a button labeled "The Answer to Life". When you try to move the mouse cursor to the button to click on it, the button changes location, always moving away from the mouse cursor. You can never catch it and click on it, so it can never give you the answer that you seek (which it's not programmed to do anyway). Which in itself is the answer to life.
In the various new series, it's become a thing for each captain to have his/her own signature command to engage. They even hang a lantern on it in the Season Two trailer for Strange New Worlds when Spock takes the con (at 1:15): failed to embed; link at https://www.youtube.com/watch?v=HN-d7dHNDqo
It seemed to have become a fan-driven thing with Picard's dramatic delivery of "Engage!", similar to the "Picard Maneuver" (ie, upon standing after having been seated pulling down on your tunic to straighten it out).
Now in Star Trek: Strange New Worlds they have CAPT Pike give the order of "Hit it!", whereas the original CAPT Pike (Jeffrey Hunter in the first pilot, The Cage) gives the order as "Engage", the same as Picard would decades later (though in the original German* the order he gives is "Beschleunigen!", "Accelerate."). Again, I assume that it was Patrick Stewart's dramatic flair or British accent (typical for a Frenchman) that made it stand out and then made it a "thing" with the fans.
I'm trying to remember what Kirk's command was and it keeps coming to me as "Engage." Though when timing of the order of execution was important, I recall him using "On my mark ... now!"
What do others recall?
FOOTNOTE *
Watching Star Trek in the original German.
While I am actually doing that on Paramount+, it refers to an old joke that had gotten retread in the last TOS movie, Star Trek VI: The Undiscovered Country in which Klingon General Chang keeps quoting Shakespeare to which Chancellor Gorkon remarks: "You have not experienced Shakespeare until you have read him in the original Klingon."
The source of that reference could be as old as two centuries, though that movie's Wikipedia page refers to a Nazi propaganda campaign to claim Shakespeare as German as their source (now that I know about it, I tend to concur). Still, Shakespeare had been translated into German starting in the 18th Century and has long been popular in German-speaking lands. A common truism is that at any given time there are more productions of Shakespeare being performed in German than in English.
For some reason, the YouTube algorithm recommended to me this film from 2016. It's by Brian Keith Dalton, AKA "Mr. Deity", Phat's favorite ex-Mormon and alumnus of PragerU ("Go Devils!"); The Bourne Again Identity:
It was fun seeing Lucy in front of the camera again.
Share and enjoy!
ABE:
Synopsis (spoiler avoidance attempted) --
A couple take in a stranger with amnesia whose identity seems tied to a crucifix he was wearing when they found him. He remembers nothing about religion so they try to explain it to him, but nothing they tell him makes any sense.
It reminds me of a short story I found a couple decades ago on a British atheist site. Here's a synopsis of it from memory, though maybe one of our British members might know where to find it:
quote:A traveling preacher stumbles upon a village where nobody had ever heard of religion before, let alone Christianity. So he starts preaching to them and they all crowd around him eager to learn and listening intently. But nothing he tells them makes any sense, so they keep interrupting him with questions, pleading with him to please explain -- they sincerely want to understand what he's teaching them. But he keeps finding that he is unable to answer their questions and that once he started thinking about their questions himself even he couldn't understand what he was saying. The story ends with him fleeing the village (and the loss of his willful ignorance) with the villagers following him sincerely pleaing with him to answer their questions.
Now a bit of geek humor, though that requires a little background information.
Unix is a copyrighted computer operating system, though the Berkeley Software Distribution (BSD) is not copyrighted since it was given to UC Berkeley before the copyright. Then later Linus Tovald developed an open source version, the Linux kernel, under the GNU Project.
My understanding is that Linux got around the Unix copyright using the same "virgin programmer" reverse-engineering trick that led to the Phoenix Technologies cloning of the IBM PC BIOS (which enabled the massive IBM-clone industry). Basically, you hire one programmer to use the copyrighted source code (IBM literally distributed a copy of the BIOS source code with their first PCs; I had a copy at work) in order to write a specification for that code describing all the inputs, outputs, and processing. That programmer is now tainted so he's removed from the project, but then you get an untainted (AKA "virgin") programmer who has never seen the copyrighted source to use the spec in order to write code that would do the same things as the original. This process was reenacted in the first season of Halt and Catch Fire.
Unix comes with a library of utility programs that the user can use to perform various tasks through a user interface known as a shell (since it comprises an outer software layer encapsulating the OS kernel -- basically, you talk to the shell, the shell talks to the kernel, the kernel replies to the shell and the shell replies to you). Originally, shells would be command-line interpreters (CLI) that you worked with through your teletype terminal (called a "tty" in Unix/Linux) connected to the computer. Veteran PC users will recognize MS-DOS as that system's shell (and indeed the configuration files (¿CONFIG.SYS?; it's been a few decades) had a "SHELL=" line where you could specify a different shell (eg, "DR-DOS")).
Perhaps UNIX' most common CLI shell was written by one Stephen Bourne in 1979 ( so it predates both the 1980 book and 1988 TV movie with Richard Chamberlain, "The Bourne Identity"). Called the "Bourne shell", it is invoked through its file name, sh for "shell". Other shells would base their names on "sh" like the C shell (csh), Korn shell (ksh), secure shell (ssh).
Because of copyright considerations, utility names in Linux had to be changed slightly, often by prefixing them with "g" for GNU; eg, the C compiler (cc) became gcc. The same happened to sh which became bash for "the Bourne Again Shell".
That's the punchline: bash stands for "Bourne Again Shell".
zsh is a Unix shell, not Linux, but it works fine.
Apple is not my community (except for my iPod Nano), but from what I have read the kernel for Macs starting with OS X (ten) was BSD Unix (Berkeley Software Distribution) or at least based on BSD. Unix itself ended up being copyrighted, but BSD was still free.
Analogous to how speciation starts, Unix and BSD have started diverging. This would show up as new utilities (such as shells) would appear in one but not in the other, but mostly it appears as differences in how the utilities were used, such as differences in the command switches (AKA "command options"; ie, the options for a command which appear with a hyphen in Unix/Linux (eg, gcc -v to get the version of gcc) or with a slash in MS-DOS (eg, dir /s to include the directory listing of subdirectories)).
Indeed, in The Cuckoo's Egg Cliff Stoll working in the UC Berkeley computer center was able to determine that the hacker was coming in from the outside (it turned out from Germany, which also explained why he would come in at such weird hours) because he was using AT&T Unix syntax instead of BSD syntax which UC Berkeley was using as well as everybody at UC Berkeley.
The story was the subject of the 03 October 1990 episode of NOVA, "The KGB, the Computer, and Me", which is on YouTube:
PS
I always liked that opening title for NOVA which depicts a star going nova.
That book is also going into my keep pile. Though my favorite part was Stoll's oral exams for his PhD Astronomy in which he's asked "Why is the sky blue?" and it takes him two to three hours to answer that question completely.
It was in the book and not the NOVA episode that he mentioned the clue that this was an outsider because his syntax was not the native BSD.
Since it had been quite a while, I watched that NOVA episode again right after posting Message 1437. I'm going to watch it again a decade or so from now with my grandsons, mainly to show them what computers used to be like.
One of the comments for that video mentioned a German movie about the hackers in this case: 23 – Nichts ist so wie es scheint ("23 - Nothing is what it seems", 1998). It appears to be the first movie for the star, August Diehl, who in Inglourious Basterds played the SS Major in the tavern who catches Fassbender's character using our distinctly non-German hand gesture for "three". His character in 23 is supposed to be obsessed with that number, so it's interesting that in the NOVA story he always logs into Cliff Stoll's computer as terminal tt23 -- to my knowledge, a user logging into a system has no control over which device he connects through.
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