Then you would have loved the HyperCard Smut Stack, the first commercial HyperCard stack ever released!
I've begged Chuck to dig around to see if he has an old copy of the floppy lying around and upload it, but so far I don't know of a copy online you can run. Its bold pioneering balance of art and slease deserves preservation, and the story behind it is hilarious.
Edit: OMG I've just found the Geraldo episode with Chuck online, auspiciously titled "Geraldo: Sex in the 90's. From Computer Porn to Fax Foxes", which shows an example of Smut Stack:
DonHopkins on Feb 10, 2020 | parent | context | favorite | on: HyperCard: What Could Have Been (2002)
Do you have the first commercial HyperCard stack ever released: the HyperCard SmutStack? Or SmutStack II, the Carnal Knowledge Navigator, both by Chuck Farnham?
SmutStack was the first commercial HyperCard product available at rollout, released two weeks before HyperCard went public at a MacWorld Expo, cost $15, and made a lot of money (according to Chuck). SmutStack 2, the Carnal Knowledge Navigator, had every type of sexual adventure you could imagine in it, including information about gays, lesbians, transgendered, HIV, safer sex, etc. Chuck was also the marketing guy for Mac Playmate, which got him on Geraldo, and sued by Playboy.
>Smut Stack. One of the first commercial stacks available at the launch of HyperCard was Smut Stack, a hilarious collection (if you were in sixth grade) of somewhat naughty images that would make joke, present a popup image, or a fart sound when the viewer clicked on them. The author was Chuck Farnham of Chuck's Weird World fame.
>How did he do it? After all, HyperCard was a major secret down at Cupertino, even at that time before the wall of silence went up around Apple.
>It seems that Farnham was walking around the San Jose flea market in the spring of 1987 and spotted a couple of used Macs for sale. He was told that they were broken. Carting them home, he got them running and discovered several early builds of HyperCard as well as its programming environment. Fooling around with the program, he was able to build the Smut Stack, which sold out at the Boston Macworld Expo, being one of the only commercial stacks available at the show.
>This staunch defender was none other than Chuck Farnham, whom readers of this column will remember as the self-appointed gadfly known for rooting around in Apple’s trash cans. One of Farnham ’s myriad enterprises is Digital Deviations, whose products include the infamous SmutStack, the Carnal Knowledge Navigator, and the multiple-disk set Sounds of Susan. The last comes in two versions: a $15 disk of generic sex noises and, for $10 more, a personalized version in which the talented Susan moans and groans using your name. I am not making this up.
>Farnham is frank about his participation in the Macintosh smut trade. “The problem with porno is generic,” he says, sounding for the briefest moment like Oliver Wendell Holmes. “When you do it, you have to make a commitment ... say you did it and say it’s yours. Most people would not stand up in front of God and country and say, ‘It’s mine.’ I don’t mind being called Mr. Scum Bag.”
>On the other hand, he admits cheerily, “There’s a huge market for sex stuff.” This despite the lack of true eroticism. “It’s a novelty,” says Farnham. Sort of the software equivalent of those ballpoint pens with the picture of a woman with a disappearing bikini.
>“Chuck developed the first commercial stack, the Smutstack, which was released two weeks before HyperCard went public at a MacWorld Expo. He’s embarrassed how much money a silly collection of sounds, cartoons, and scans of naked women brought in. His later version, the Carnal Knowledge Navigator, was also a hit.
The Muller’s Recurrence is a mathematical problem that will converge to 5 only with precise arithmetics. This has nothing to do with COBOL and nothing to do with floating and fixed point arithmetics as such. The more precision your arithmetics has, the closer you get to 5 before departing and eventually converging to 100. Python's fixed point package has 23 decimal points of precision by default, whereas normal 64bit floating point has about 16 decimal points. If you increase your precision, you can linger longer near 5, but eventually you will diverge and then converge to 100.
# Long version
What's going on here is that someone has tried to solve the roots of the polynomial
x^3 - 108 x^2 + 815 x - 1500,
which is equal to
(x - 3)(x - 5)(x - 100).
So the roots are 3, 5 and 100. We can derive a two-point iteration method by
x^3 = 108 x^2 - 815 x + 1500
x^2 = 108 x - 815 + 1500/z
x = 108 - (815 - 1500/z)/y
where y = x_{n-1} and z = x_{n-2}. But at this point, we don't know yet whether this method will converge, and if yes, to which roots.
This iteration method can be seen as a map F from R^2 to R^2:
F(y,z) = (108 - (815 - 1500/z)/y, y).
The roots of the polynomial are 3,5 and 100, so we know that this map F has fixed points (3,3), (5,5) and (100,100). Looking at the derivative of F (meaning the Jacobian matrix) we can see that the eigenvalues of the Jacobian at the fixed points are 100/3 and 5/3, 20 and 3/5, 1/20 and 3/100.
So (3,3) is a repulsive fixed point (both eigenvalues > 1), any small deviation from this fixed point will be amplified when the map F is applied iteratively. (100,100) is an attracting fixed point (both eigenvalues < 1). And (5,5) has one eigenvalue much larger than 1, and one slightly less than 1. So this fixed point is attracting only when approached from a specific direction.
Kahan [1, page 3] outlines a method to find sequences that converge to 5. We can choose beta and gamma freely in his method (Kahan has different values for the coefficients of the polynomial, though) and with lots of algebra (took me 2 pages with pen and paper) we can eliminate
the beta and gamma and get to the bottom of it. What it comes down to, is that for any 3 < z < 5, choose y = 8 - 15/z, and this pair z,y will start a sequence that converges to 5. But only if you have precise arithmetics with no rounding errors.
For the big picture, we have this map F, you can try to plot a 2D vector field of F or rather F(x,y) - (x,y) to see the steps. Almost any point in the space will start a trajectory that will converge to (100,100), except (3,3) and (5,5) are stable points themselves, and then there is this peculiar small segment of a curve from (3,3) to (5,5), if we start exactly on that curve and use exact arithmetics, we converge to (5,5).
Now that we understand the mathematics, we can conclude:
Any iteration with only finite precision will, at every step, accrue rounding errors and step by step end up further and further away from the mathematical curve, inevitably leading to finally converging to (100,100). Using higher precision arithmetics, we can initially get the semblance of closing in to (5,5), but eventually we will reach the limit of our precision, and further steps will take us away from (5,5) and then converge to (100,100).
The blog post is maybe a little misleading. This has nothing to do with COBOL and nothing to do with fixed point arithmetics. It just happens that by default Python's Decimal package has more precision (28 decimal places) than 64bit floating point (53 binary places, so around 16 decimals). Any iteration, any finite precision no matter how much, run it long enough and it will eventually diverge away from 5 and then converge to 100.
Specifically, if you were to choose floating point arithmetic that uses higher precision than the fixed point arithmetic, then the floating point would "outperform" the fixed point, in the sense of closing in nearer to 5 before going astray.
I've begged Chuck to dig around to see if he has an old copy of the floppy lying around and upload it, but so far I don't know of a copy online you can run. Its bold pioneering balance of art and slease deserves preservation, and the story behind it is hilarious.
Edit: OMG I've just found the Geraldo episode with Chuck online, auspiciously titled "Geraldo: Sex in the 90's. From Computer Porn to Fax Foxes", which shows an example of Smut Stack:
https://visual-icon.com/lionsgate/detail/?id=67563&t=ts
https://news.ycombinator.com/item?id=22285675
DonHopkins on Feb 10, 2020 | parent | context | favorite | on: HyperCard: What Could Have Been (2002)
Do you have the first commercial HyperCard stack ever released: the HyperCard SmutStack? Or SmutStack II, the Carnal Knowledge Navigator, both by Chuck Farnham? SmutStack was the first commercial HyperCard product available at rollout, released two weeks before HyperCard went public at a MacWorld Expo, cost $15, and made a lot of money (according to Chuck). SmutStack 2, the Carnal Knowledge Navigator, had every type of sexual adventure you could imagine in it, including information about gays, lesbians, transgendered, HIV, safer sex, etc. Chuck was also the marketing guy for Mac Playmate, which got him on Geraldo, and sued by Playboy.
https://www.zdnet.com/article/could-the-ios-app-be-the-21st-...
>Smut Stack. One of the first commercial stacks available at the launch of HyperCard was Smut Stack, a hilarious collection (if you were in sixth grade) of somewhat naughty images that would make joke, present a popup image, or a fart sound when the viewer clicked on them. The author was Chuck Farnham of Chuck's Weird World fame.
>How did he do it? After all, HyperCard was a major secret down at Cupertino, even at that time before the wall of silence went up around Apple.
>It seems that Farnham was walking around the San Jose flea market in the spring of 1987 and spotted a couple of used Macs for sale. He was told that they were broken. Carting them home, he got them running and discovered several early builds of HyperCard as well as its programming environment. Fooling around with the program, he was able to build the Smut Stack, which sold out at the Boston Macworld Expo, being one of the only commercial stacks available at the show.
https://archive.org/stream/MacWorld_9008_August_1990/MacWorl...
Page 69 of https://archive.org/stream/MacWorld_9008_August_1990
>Famham's Choice
>This staunch defender was none other than Chuck Farnham, whom readers of this column will remember as the self-appointed gadfly known for rooting around in Apple’s trash cans. One of Farnham ’s myriad enterprises is Digital Deviations, whose products include the infamous SmutStack, the Carnal Knowledge Navigator, and the multiple-disk set Sounds of Susan. The last comes in two versions: a $15 disk of generic sex noises and, for $10 more, a personalized version in which the talented Susan moans and groans using your name. I am not making this up.
>Farnham is frank about his participation in the Macintosh smut trade. “The problem with porno is generic,” he says, sounding for the briefest moment like Oliver Wendell Holmes. “When you do it, you have to make a commitment ... say you did it and say it’s yours. Most people would not stand up in front of God and country and say, ‘It’s mine.’ I don’t mind being called Mr. Scum Bag.”
>On the other hand, he admits cheerily, “There’s a huge market for sex stuff.” This despite the lack of true eroticism. “It’s a novelty,” says Farnham. Sort of the software equivalent of those ballpoint pens with the picture of a woman with a disappearing bikini.
https://archive.org/stream/NewComputerExpress110/NewComputer...
Page 18 of https://archive.org/stream/NewComputerExpress110
>“Chuck developed the first commercial stack, the Smutstack, which was released two weeks before HyperCard went public at a MacWorld Expo. He’s embarrassed how much money a silly collection of sounds, cartoons, and scans of naked women brought in. His later version, the Carnal Knowledge Navigator, was also a hit.