On 1/20/2024 5:12 PM, Physfitfreak wrote:
> The rest of the story:
>
> Needless to say, after more than 13.5 years of climbing, Physfit's age
> had taken him to a stage in life that he could not even think of going
> back down and going home. So he dropped his last National Cup tea-bag
> into the hot water and began thinking to himself, "Now when I look down
> I can only see the lower parts of this mountain; no sign of an Earth
> underneath it; so I will spend the rest of my life here at the summit,
> inside my sleeping bag, watching all these stars above me ..."

Thus the story continues...:

Soon after such thoughts, Physfit got comfortable inside his sleeping
bag and began watching the amazing stars. He gradually fell into sleep,
dreaming that ... dreaming what? Things got confusing, then settled and
he found himself not at the summit of the magic mountain but inside a
strange structure of some sort, with high ceiling and a large narrow
slot across it. A facility of some sort. Before he began slowly walking
around, he noticed his shoes and dress looked weird, like belonging to
centuries back in Iran. Then he noticed the large device inside, which
pointed towards stars from that opening in the high ceiling. Rapidly,
his mind opened up, and he remembered where he was and who he was!

He was no Physfit.

From the magic mountain, he had stepped straight into the 13th century
Maragheh Observatory in northwest Iran, run by Nasiredding Tusi, right
inside the rein of Holaku Khan, the grandson of Chengiz!...

Now he knew who he was; in fact, who he'd always been. The sole pupil of
the master Tusi, Ghotbeddin Shirazi, who also worked in the observatory.
Not even a faint single memory of the magic mountain had left in him.

On that early morning hour, close to sunrise, Nasireddin Tusi and
Ghotbeddin Shirazi had called it a day an hour earlier, and had wrapped
up their works and were ready to leave.

Ghotbeddin turned to Tusi who was still at his large, long desk and with
a smile and a confident tone told him:

"Tonight I found two unique and special integers! They're in a
marvelous and unique way related to the date of Holaku's most beautiful
daughter's birthday :)"

Tusi who knew the date of that birthday from Ghotbeddin's previous
episodes of similar wishful and foolish mushy talk, without even lifting
his head answered,

"In what way?"

Ghotbeddin said,

"Each integer is made of three non-repeating digits and when you
divide the integers by the products of their own digits they give
exactly the month and the day of birthday of Holaku's beautiful
daughter, respectively! :)"

Tusi stayed silent for a few moments, then stood up and got ready to
leave. By the time the two made it to the gate of the observatory
compound to leave the premises and go home, Tusi turned to Ghotbeddin
and in a mildly teasing tone said,

"Sorry to disappoint you Shirazi, but there's nothing unique about
those three-digit integers of yours :)"

Ghotbeddin who knew Tusi enough to get a little nervous by such comments
quickly asked,

"What do you mean?"

Tusi right away gave him two other three-digit numbers that had exactly
the same properties! One would lead to the month (like Farvardin = 1,
Ordibehesht = 2, etc) and the other would lead to the day of the month
corresponding to the daughter's birthday by the same rules Ghotbeddin
had described a few minutes back. So the little personal party that
Ghotbeddin / Physfit had imagined for himself that night was, so soon,
over :)

What was the date of Holaku's daughter's birthday?

(sci.physics added)

On Sat, 27 Jan 2024 17:22:47 -0600, Physfitfreak wrote:

>
> Tusi right away gave him two other three-digit numbers that had exactly
> the same properties! One would lead to the month (like Farvardin = 1,
> Ordibehesht = 2, etc) and the other would lead to the day of the month
> corresponding to the daughter's birthday
>
> What was the date of Holaku's daughter's birthday?
>

Month = 8 (Aban)

Day = 18

The corresponding integer pairs:

128, 672 --> 8

216, 432 --> 18

On 1/28/2024 6:31 AM, Farley Flud wrote:
> On Sat, 27 Jan 2024 17:22:47 -0600, Physfitfreak wrote:
>
>>
>> Tusi right away gave him two other three-digit numbers that had exactly
>> the same properties! One would lead to the month (like Farvardin = 1,
>> Ordibehesht = 2, etc) and the other would lead to the day of the month
>> corresponding to the daughter's birthday
>>
>> What was the date of Holaku's daughter's birthday?
>>
>
> Month = 8 (Aban)
>
> Day = 18
>
>
> The corresponding integer pairs:
>
> 128, 672 --> 8
>
> 216, 432 --> 18
>

Damn you. Dont' give the codes yet :) Give others a chance.

You didn't solve it by hands, did you!... I think a program will do that
much faster, at least for me. For doing it by hand I'd have to go back
to my college algebra again :-)

But do at least tell us you did it by hand or by a program.

On Sun, 28 Jan 2024 16:44:22 -0600, Physfitfreak wrote:

>
> But do at least tell us you did it by hand or by a program.
>

I used a small C program to "brute force" the solution.

There may be a way to solve it with number theory, but I
don't know very much about number theory.

Anyway, for three-digit, non-repeating integers (also with
no digit being 0) there are 9*8*7 = 504 possibilities. Only
a crazy person would do it "by hand."

On 2024-01-29 08:28:55 +0000, Farley Flud said:

> On Sun, 28 Jan 2024 16:44:22 -0600, Physfitfreak wrote:
>
>>
>> But do at least tell us you did it by hand or by a program.
>>
>
> I used a small C program to "brute force" the solution.
>
> There may be a way to solve it with number theory, but I
> don't know very much about number theory.
>
> Anyway, for three-digit, non-repeating integers (also with
> no digit being 0) there are 9*8*7 = 504 possibilities. Only
> a crazy person would do it "by hand."

Hard to believe it now, but 65 years or so ago, when I was about 15, I
was that crazy. I read somewhere that the factors of 11111 were 41 and
271. I wondered if 1111111 had any factors, and if so what were they? I
found 239 and 4649, _by hand_! No computers then (not ones I had access
to, anyway) and I don't think I had access to a mechanical calculator.

--
athel -- biochemist, not a physicist, but detector of crackpots

On 1/29/2024 2:28 AM, Farley Flud wrote:
> On Sun, 28 Jan 2024 16:44:22 -0600, Physfitfreak wrote:
>
>>
>> But do at least tell us you did it by hand or by a program.
>>
>
> I used a small C program to "brute force" the solution.
>
> There may be a way to solve it with number theory, but I
> don't know very much about number theory.
>
> Anyway, for three-digit, non-repeating integers (also with
> no digit being 0) there are 9*8*7 = 504 possibilities. Only
> a crazy person would do it "by hand."
>

By saying "by hand" I meant to go like this: There are 8 unknowns and 16
inequalities :)

And take that approach, and choose only integers in the solution areas.
It could be neat to try.

I haven't solved it either way. This is from years back, so I've
forgotten how I solved it. As soon as I get time I'll give it a try.
Then I can say for sure if your solution was good enough or not.

At this point I'm not even sure the problem is well-posed. I know that
years ago when I made this problem I was under the impression that it
was well-posed.

On 1/29/2024 2:28 AM, Farley Flud wrote:
> There may be a way to solve it with number theory, but I
> don't know very much about number theory.

Come to think of it, I may have concocted this problem from a math
number theory discussion in Scientific American. For sure, it was many
years ago. That's the only thing about it that I'm sure of :)

When I get time (for some reason these days various unusual chores are
popping up on me - each requiring a good part of a day's work), I'd like
to solve this both with a program and "with hand" the way I described
it. I would enjoy doing it, but deadlines are coming up and I got other
bullshit stuff to do on top of them.

Le 28-01-2024, Physfitfreak <Physfitfreak@gmail.com> a écrit :
> On 1/28/2024 6:31 AM, Farley Flud wrote:
>
> You didn't solve it by hands, did you!...

Of course he didn't. He solved it by either google or stackoverflow.

--
Si vous avez du temps à perdre :
https://scarpet42.gitlab.io

On 1/29/2024 4:53 AM, Athel Cornish-Bowden wrote:
> On 2024-01-29 08:28:55 +0000, Farley Flud said:
>
>> On Sun, 28 Jan 2024 16:44:22 -0600, Physfitfreak wrote:
>>
>>>
>>> But do at least tell us you did it by hand or by a program.
>>>
>>
>> I used a small C program to "brute force" the solution.
>>
>> There may be a way to solve it with number theory, but I
>> don't know very much about number theory.
>>
>> Anyway, for three-digit, non-repeating integers (also with
>> no digit being 0) there are 9*8*7 = 504 possibilities.  Only
>> a crazy person would do it "by hand."
>
> Hard to believe it now, but 65 years or so ago, when I was about 15, I
> was that crazy. I read somewhere that the factors of 11111 were 41 and
> 271. I wondered if 1111111 had any factors, and if so what were they? I
> found 239 and 4649, _by hand_! No computers then (not ones I had access
> to, anyway) and I don't think I had access to a mechanical calculator.
>

But you didn't divide 1111111 by _each_ number, did you. Using just a
table of prime numbers you could divide it only by the prime numbers
beginning with 2, until you find its factors, if any. In this case you'd
find 239 times 4649 by just 52 divisions, and since the prime number
table has 4649 also as a prime number, you'd know that there would be no
other factor for 1111111.

I hope you did this, otherwise...

S

On 1/27/2024 5:22 PM, Physfitfreak wrote:
> Tusi right away gave him two other three-digit numbers that had exactly
> the same properties! One would lead to the month (like Farvardin = 1,
> Ordibehesht = 2, etc) and the other would lead to the day of the month
> corresponding to the daughter's birthday by the same rules Ghotbeddin
> had described a few minutes back. So the little personal party that
> Ghotbeddin / Physfit had imagined for himself that night was, so soon,
> over :)

Thus the story continues...

The two scientists got out and locked the gate and left.

That day, in the evening, a party was to hold in Holaku's Summer
residence not that far from Maragheh. And the two were both invited!

Ghotbeddin got home and hit the sack fast and early to wake up fully
rested before attending the party. He couldn't be contained inside his
own skin, when thinking about the prospect of seeing Holaku's daughter
again within that same day...

As he slowly drifted off into sleep he dreamed that wherever he was, he
was actually already in that party but had just noticed it! He didn't
get time to think how it happened and why he'd only now realized where
he'd been all this time. Holaku was sitting on a throne across the huge
room and some of the vazirs were here and there chatting. But he knew
that he had not yet seen the daughter, so he made himself sure he'll
stay until she shows up. Also, he knew that he and Holaku both were
waiting for Tusi to arrive, because Holaku had something to ask from him.

But there was no sign of Tusi. At his home, he had come up with an idea
which needed the use of some tables of numbers kept at the observatory,
and he had chosen to go to the observatory in the evening, not even to
Hulaku's party where he was invited!

So after some time, at some point Holaku signaled to have a talk with
Ghotbeddin. A servant and one of the vazirs immediately came over to
Ghotbeddin and together walked to where Holaku was sitting.

Holaku to Ghotbeddin:

"They tell me you are a very smart man to be in the observatory,
helping someone like Tusi. Do you think you are as smart as Tusi?"

Ghotbeddin made a faint smile and said:

"Your Majesty, I am not blessed with as much talent as God has
bestowed upon Your Majesty _or_ Tusi."

Holaku:

"I have a task for Tusi to accomplish, but in his absence I want you
to do it."

Ghotbeddin:

"Your Majesty's wish is my utmost desire."

Holaku:

"In each of my parties, a session is always included in which a
chessboard is placed on the floor, with no chess pieces on it. There is
a contest, and the winner is blindfolded and given two random chess
pieces of same color - but not any pawns - out of my pocket, to place
somewhere on the chessboard by the winner, in two of the squares. Then
the blindfold is removed and the winner will look at the chessboard and
counts the number of different moves he can make with the chess pieces
from the squares that they are in. The winner will get as many gold
coins from me as that count is. If I know in advance which two pieces
will be given to the winner, I need to know how many gold coins I should
bring with me to the party, so I could never find myself with not enough
coins to give to the winner, and never carry with me even one gold coin
that would never be needed to be given to the winner. Find how many
coins I should bring with me to the party."

Ghotbeddin:

"Your Majesty's wish will undoubtedly get fulfilled."

How many gold coins should Holaku Khan take with him to his parties?

On Sat, 3 Feb 2024 04:00:30 -0600, Physfitfreak wrote:

>
> Thus the story continues...
>
> How many gold coins should Holaku Khan take with him to his parties?
>

I'll pass. I don't know how to play chess. I think that, like all
games, chess is stupid and boring.

It reminds of the time I enrolled in a computer science class at
the university. Our very first assignment was to write a program
that kept score of a bowling game.

Bowling? I don't fucking know how to bowl. I never fucking went
bowing in my entire fucking life.

So now I first gotta learn the rules of the game of bowling and
then write the program. I said: "Fuck that!" I just dropped the
course. I'll enroll with an instructor who is progressive and sane.

On 2/3/2024 10:19 AM, Farley Flud wrote:
> On Sat, 3 Feb 2024 04:00:30 -0600, Physfitfreak wrote:
>
>>
>> Thus the story continues...
>>
>> How many gold coins should Holaku Khan take with him to his parties?
>>
>
> I'll pass. I don't know how to play chess. I think that, like all
> games, chess is stupid and boring.
>
> It reminds of the time I enrolled in a computer science class at
> the university. Our very first assignment was to write a program
> that kept score of a bowling game.
>
> Bowling? I don't fucking know how to bowl. I never fucking went
> bowing in my entire fucking life.
>
> So now I first gotta learn the rules of the game of bowling and
> then write the program. I said: "Fuck that!" I just dropped the
> course. I'll enroll with an instructor who is progressive and sane.
>

Hahhahah :) Makes sense.

I get that feeling when in public media somebody who's supposed to
explain something for the general people uses "football" terms in his
words. Imagine Biden, while at the podium speaking, turning sideways and
beginning peeing on the floor, then turning back towards the audience
and continuing the talk as if nothing inappropriate was done. Or, ...
suddenly throw in a sentence in Mayan language... then continue in
English. Hahhahah :)

It amounts to being on the left side of the intelligence curve, where
half of the Americans happily reside. RIP Carlin... I hear you.

I used the chess game in this story cause it is a much, much more
universal pastime, and very ancient. So ancient that terms associated
with it in German and Persian are almost the same! It goes that far back.

And I used only the movement types of its pieces, and nothing else. No
other rules whatsoever. And I assumed everybody knows that chessboard is
an 8 squares by 8 squares board, consisting of 64 squares on which these
pieces can move in their own ways if not blocked by another piece.

This story gives an opportunity - for the code monkeys really - to try
their use of loops within loops to solve clear but involved logical
situations. Several arrays are involved.

I intended to later add one more piece to the two! :-) And then one
more, and then one more... Then one would get very close to do what
computer chess developers do.

But if it has to stop in this forum, before even it started, then so be it.

If my memory serves me right, that's how Ken Thompson, the other of the
duo with Dennis Ritchie, who together developed Unix, became expert in
programming and OSs. I think he wanted to make his chess program faster
and faster. I think that was the whole deal for him behind all that work
:) He won some chess computer competitions too, I think.

But I still challenge everybody in this forum other than Farley, to
salvage their fucked up images as "programmers", by writing the baby
program that solves this problem in its most simple form, which is two
chess pieces. It is simple enough to be done by any code monkey, and yet
involved enough to be too time-consuming to do it "by hand".

So, each of you in COLA, are you even a code monkey? Farley says you
are, but I even doubt that. I think you're just foolish little loud
mouths as far as programming is concerned. So far, only Farley has
proved himself as a real programmer.

Speaking of a computer science class, the only one I took was in Summer
1979 to learn PL/I. No other languages were being taught in that Summer.
It was actually a graduate course in computer science, so a lot of
programming knowledge in the students were assumed by the professor in
its covering of that language. But for me it was the first touch of a
programming language. Thanks god the text was excellent. A dictionary
size big black book of almost 1000 pages. That was my source really, not
what was being discussed in the classroom. My understanding of the
verbal English hadn't matured yet and I'd muss most of what the prof was
so elaborately explaining. I suspect that the aim of that course was to
prepare the students on _creating_ better languages. But the text chosen
was very comprehensive, covering every programming skill, all the
sensitive areas, all the usual mistakes, all the important concepts
associated to programming in general and in that language. I read and
understood that book from begin to end!

There was also a 13 or so year old kid in the classroom sitting with his
father, and asking most of the questions! One of those who even in
middle school knew how to program well and had a talent for it.

The course was 5 semester hours! A heck of a lot of material packed into
a month and a half Summer term.

Le 03-02-2024, Farley Flud <ff@linux.rocks> a écrit :
> On Sat, 3 Feb 2024 04:00:30 -0600, Physfitfreak wrote:
>>
>> Thus the story continues...
>>
>> How many gold coins should Holaku Khan take with him to his parties?
>
> I'll pass. I don't know how to play chess.

That's easy to believe.

> I think

I don't believe that.

> So now I first gotta learn the rules of the game of bowling and
> then write the program. I said: "Fuck that!" I just dropped the
> course.

I believe you were unable to find the solution on Internet and found an
excuse to drop without confessing the request was beyond you capacities.

--
Si vous avez du temps à perdre :
https://scarpet42.gitlab.io

On 2/3/2024 4:00 AM, Physfitfreak wrote:
> "In each of my parties, a session is always included in which a
> chessboard is placed on the floor, with no chess pieces on it. There is
> a contest, and the winner is blindfolded and given two random chess
> pieces of same color - but not any pawns - out of my pocket, to place
> somewhere on the chessboard by the winner, in two of the squares. Then
> the blindfold is removed and the winner will look at the chessboard and
> counts the number of different moves he can make with the chess pieces
> from the squares that they are in. The winner will get as many gold
> coins from me as that count is. If I know in advance which two pieces
> will be given to the winner, I need to know how many gold coins I should
> bring with me to the party, so I could never find myself with not enough
> coins to give to the winner, and never carry with me even one gold coin
> that would never be needed to be given to the winner. Find how many
> coins I should bring with me to the party."

Looks like for the sub-"code monkeys" a bit of more explanation is due.

Holaku will give one gold coin for every different first move that the
winner can make on the board.

Example. If the two pieces happen to be two bishops, and if the
blindfolded winner happened to place one at the first square on the left
of the bottom row, and the other on the last square on the far right of
the bottom row, then winner will get 14 gold coins.

On 2/3/2024 4:00 AM, Physfitfreak wrote:
> Ghotbeddin:
>
>    "Your Majesty's wish will undoubtedly get fulfilled."
>
>

The rest of the story:

Ghotbeddin forgot that a daughter of Holaku even exists, and immediately
went home to work on the problem. Got his chessboard and placed it down
on the floor, on top of the fine Persian carpet woven in that same area,
according to Azarbayjan's styles which both colorwise and patterns were
distinct in Iran. He placed two same color pieces on the board and began
thinking...

Worked on it all night. By morning, his hopes of giving the tabulated
answers to Holaku on that morning had disappeared into thin air. It
would take some time to finish this job! So he went to bed tired and
beaten, and soon fell asleep. But shortly after he felt unusually cold.
Opened his eyes and found himself in his sleeping bag at the top of the
magic mountain!

Still remembering the dream, he stretched his hand into his backpack and
pulled out his Aspire One mini laptop dedicated to DOS, with qbasic on
it, prepared hot water to make tea, and as he gave out a good voluminous
fart he loudly said, "To you Pope The Penis X!" Then began coding the
now simple and totally under control problem. He got the answers,
tabulated them nicely, then hoped he would travel back to 13th century
next time he went to sleep, to give the table to Holaku Khan, and see
the beautiful daughter.

On 2/5/2024 1:51 AM, Physfitfreak wrote:
> On 2/3/2024 4:00 AM, Physfitfreak wrote:
>> Ghotbeddin:
>>
>>     "Your Majesty's wish will undoubtedly get fulfilled."
>>
>>
>
>
> The rest of the story:
>
> Ghotbeddin forgot that a daughter of Holaku even exists, and immediately
> went home to work on the problem. Got his chessboard and placed it down
> on the floor, on top of the fine Persian carpet woven in that same area,
> according to Azarbayjan's styles which both colorwise and patterns were
> distinct in Iran. He placed two same color pieces on the board and began
> thinking...
>
> Worked on it all night. By morning, his hopes of giving the tabulated
> answers to Holaku on that morning had disappeared into thin air. It
> would take some time to finish this job! So he went to bed tired and
> beaten, and soon fell asleep. But shortly after he felt unusually cold.
> Opened his eyes and found himself in his sleeping bag at the top of the
> magic mountain!
>
> Still remembering the dream, he stretched his hand into his backpack and
> pulled out his Aspire One mini laptop dedicated to DOS, with qbasic on
> it, prepared hot water to make tea, and as he gave out a good voluminous
> fart he loudly said, "To you Pope The Penis X!" Then began coding the
> now simple and totally under control problem. He got the answers,
> tabulated them nicely, then hoped he would travel back to 13th century
> next time he went to sleep, to give the table to Holaku Khan, and see
> the beautiful daughter.
>
>
>
>
>
>

So the story continues...

Days came and passed. None of the night sleeps resulted in a dream to
take him to the 13th century with the now ready table. So at night, when
warming himself with a little fire and getting ready to go to his
sleeping bag, he thought to himself, "If I don't travel back to Maragheh
observatory tonight, I'll just burn the one page table in the fire and
forget about it."

The night became morning, and Physfit still in his sleeping bag openned
his eyes and realized something was not right. There were clouds above
him! "At this altitude?..." he asked himself. He turned his head left
and found he was looking at urban areas of Dallas, with the Reunion
Tower over there standing by downtown! Turned his head right and saw
that he was lying down in his sleeping bag at the top of a 100 yard
mountain, with his house in the view, within a short walking distance!
He quickly, before anything get changed again, got up and put on his
mountain shoes and dress, and got ready to climb down fast before the
mountain gets bigger again.

By the time he reached the ground level, it was 4:45 pm and the sun was
setting, and in another 15 minutes he was home, at his computer, going
through the news.

He read somewhere that at least half of the Americans' missiles to hit
Houthi targets would only hit the adjacent areas, not the targets
themselves, but each time Houthis lauched a missile, it came down dead
correct and hit the target. Physfit wondered about it for a few moments.

There were a few related news pieces as well. In one of them, from a
Pakestani press outlet, they explained in detail how the missiles
automatically calculated the coordinates of the target. A reconnaissance
drone beforehand would get near enough to target to see it, then using
laser would fly on a straightline towards the target and record its own
coordinates at two different points on that straight line.

Then using such information, back home, the distance of the target to
the missiles launching site would accurately get calculated. Then they'd
launch the missiles.

Everything calculated were in two dimensions only. Just height and the
distance.

If the drone calculated coordinates of the two points on that line of
sight as (x_1, y_1) and (x_2, y_2), with x being the distance and y the
height, then the distance of the target to launch area would have any of
the two forms below:

x . y - x . y
1 2 2 1
x = -----------------
y - y
2 1

or:

/x - x \ . y
\ 2 1/ 1
x = x - --------------
1 y - y
2 1

And the Americans in charge being cro-magnons (and Nazi), seeing that
one of the above formulas can be derived from the other one, were
assuming it didn't matter which one to use for calculating x-intercept
for their missiles to hit Houthis targets. But Houthis, being Modern
Humans, always chose one of the above, and never the other.

So Physfit found out why about half of American missiles narrowly miss
their targets, while Houthis missiles always hit the targets.

1- Verify that the two formulas are correct, and algebraically related.

2- Assuming the drone calculated (x_1, y_1) as (1.31, 4.76) kilometers,
and (x_2, y_2) as (1.93, 3.24) kilometers, and assuming that for
shortest computation time, numbers are rounded to three digits in the
codes imbedded in drones and missiles, then calculate the x-intercept in
both ways.

3- Explain which of the two methods is being used by the Houthis, and why.

On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:

>
> If the drone calculated coordinates of the two points on that line of
> sight as (x_1, y_1) and (x_2, y_2), with x being the distance and y the
> height, then the distance of the target to launch area would have any of
> the two forms below:
>
> x . y - x . y
> 1 2 2 1
> x = -----------------
> y - y
> 2 1
>
> or:
>
>
> /x - x \ . y
> \ 2 1/ 1
> x = x - --------------
> 1 y - y
> 2 1
>
>
> And the Americans in charge being cro-magnons (and Nazi), seeing that
> one of the above formulas can be derived from the other one, were
> assuming it didn't matter which one to use for calculating x-intercept
> for their missiles to hit Houthis targets. But Houthis, being Modern
> Humans, always chose one of the above, and never the other.
>
> So Physfit found out why about half of American missiles narrowly miss
> their targets, while Houthis missiles always hit the targets.
>
> 1- Verify that the two formulas are correct, and algebraically related.
>
> 2- Assuming the drone calculated (x_1, y_1) as (1.31, 4.76) kilometers,
> and (x_2, y_2) as (1.93, 3.24) kilometers, and assuming that for
> shortest computation time, numbers are rounded to three digits in the
> codes imbedded in drones and missiles, then calculate the x-intercept in
> both ways.
>
> 3- Explain which of the two methods is being used by the Houthis, and why.
>

1)

Multiply first term of second expression by 1 = (y2 - y1)/(y2 - y1):

x1 ⋅ (y2 - y1) (x2 - x1) ⋅ y1
────────────── - ──────────────
y2 - y1 y2 - y1

Combine fractions:

x1 ⋅ y2 - x1 ⋅ y1 - x2 ⋅ y1 + x1 ⋅ y1
─────────────────────────────────────
y2 - y1

Cancel terms:

x1 ⋅ y2 - x2 ⋅ y1
─────────────────
y2 - y1

They are equivalent.

2)

Using exact rational arithmetic based on the values given
(e.g. 1.31 = 131/100), the x-intercept for both expressions
is:

x = 3089/950 = 3.25

For an image of this, see this link:

https://postimg.cc/2LS0KRHr

3)

Because of potential catastrophic cancellation in distance coordinates,
the first expression is preferable due to the absence of subtraction
(i.e. x2 - x1) in the numerator. For the record:

x1 ⋅ y2 - x2 ⋅ y1
─────────────────
y2 - y1

On 2/6/2024 3:00 PM, Farley Flud wrote:
> On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:
>
>>
>> If the drone calculated coordinates of the two points on that line of
>> sight as (x_1, y_1) and (x_2, y_2), with x being the distance and y the
>> height, then the distance of the target to launch area would have any of
>> the two forms below:
>>
>> x . y - x . y
>> 1 2 2 1
>> x = -----------------
>> y - y
>> 2 1
>>
>> or:
>>
>>
>> /x - x \ . y
>> \ 2 1/ 1
>> x = x - --------------
>> 1 y - y
>> 2 1
>>
>>
>> And the Americans in charge being cro-magnons (and Nazi), seeing that
>> one of the above formulas can be derived from the other one, were
>> assuming it didn't matter which one to use for calculating x-intercept
>> for their missiles to hit Houthis targets. But Houthis, being Modern
>> Humans, always chose one of the above, and never the other.
>>
>> So Physfit found out why about half of American missiles narrowly miss
>> their targets, while Houthis missiles always hit the targets.
>>
>> 1- Verify that the two formulas are correct, and algebraically related.
>>
>> 2- Assuming the drone calculated (x_1, y_1) as (1.31, 4.76) kilometers,
>> and (x_2, y_2) as (1.93, 3.24) kilometers, and assuming that for
>> shortest computation time, numbers are rounded to three digits in the
>> codes imbedded in drones and missiles, then calculate the x-intercept in
>> both ways.
>>
>> 3- Explain which of the two methods is being used by the Houthis, and why.
>>
>
> 1)
>
> Multiply first term of second expression by 1 = (y2 - y1)/(y2 - y1):
>
> x1 ⋅ (y2 - y1) (x2 - x1) ⋅ y1
> ────────────── - ──────────────
> y2 - y1 y2 - y1
>
>
> Combine fractions:
>
> x1 ⋅ y2 - x1 ⋅ y1 - x2 ⋅ y1 + x1 ⋅ y1
> ─────────────────────────────────────
> y2 - y1
>
> Cancel terms:
>
> x1 ⋅ y2 - x2 ⋅ y1
> ─────────────────
> y2 - y1
>
>
> They are equivalent.
>
>
> 2)
>
> Using exact rational arithmetic based on the values given
> (e.g. 1.31 = 131/100), the x-intercept for both expressions
> is:
>
> x = 3089/950 = 3.25
>
> For an image of this, see this link:
>
> https://postimg.cc/2LS0KRHr
>
>
> 3)
>
> Because of potential catastrophic cancellation in distance coordinates,
> the first expression is preferable due to the absence of subtraction
> (i.e. x2 - x1) in the numerator. For the record:
>
> x1 ⋅ y2 - x2 ⋅ y1
> ─────────────────
> y2 - y1
>
>

Hmm... But you need to show with actual numbers why in the 3rd part, one
of the expressions is better to use.

Put yourself in the shoes of a computer (inside the drones and missiles)
that rounds every number off (not just the result! But every number it
comes upon in computing the results) to keep only three significant
digits. Follow what happens from begin to end of the computation for
each expression. Then argue why one computed result is better than the
other computed result. Lot's of math lines to write, but all are needed
to see for sure why one result is better than the other.

I may have accidentally chosen the coordinate numbers that don't quite
show the difference, I don't know. I haven't solved this yet (just
concocted it last night). If that's the case, then I'll find coordinate
numbers that will show the difference.

But so far, I'm assuming just about any coordinates measured might work
to show the difference in the results of computations. So I'm asking
that you do that and show it here.

On 2/6/2024 3:43 PM, Physfitfreak wrote:
> On 2/6/2024 3:00 PM, Farley Flud wrote:
>> On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:
>>
>>>
>
> Put yourself in the shoes of a computer (inside the drones and missiles)
> that rounds every number off (not just the result! But every number it
> comes upon in computing the results) to keep only three significant
> digits. Follow what happens from begin to end of the computation for
> each expression. Then argue why one computed result is better than the
> other computed result. Lot's of math lines to write, but all are needed
> to see for sure why one result is better than the other.
>
> I may have accidentally chosen the coordinate numbers that don't quite
> show the difference, I don't know. I haven't solved this yet (just
> concocted it last night). If that's the case, then I'll find coordinate
> numbers that will show the difference.
>
> But so far, I'm assuming just about any coordinates measured might work
> to show the difference in the results of computations. So I'm asking
> that you do that and show it here.
>
>
>

I shouldn't have said, "three significant digits". Significant digit
concept is somewhat different.

Ok, let's talk more accurately.

Machine numbers are in binary form. But these machine numbers can be
expressed in decimal machine numbers like:

0.d_1d_2 ... d_k x 10^n

, where d_1 digit is _not_ zero, and d_2, d_3 ... d_k digits can each be
an integer from zero to 9.

Since this example has k digits after the decimal point, it is called
k-digit decimal machine number.

The decimal machine number form is not exactly equal to the binary form
that machine handles, and the difference has to do with the machine
epsilon. But nevertheless, the two form are very closely the same number.

In this problem, I'm assuming the computers on missiles work on such
binary numbers that have 3-digit decimal machine numbers. And forget the
binary form of them, cause this problem is not about the machine
epsilon. Just assume that the computers deal with decimal machine
numbers and k=3. So for example the number

0.0033169 x 10^4

is rounded off to

0.332 x 10^2

So depending on how your code computes the two given expressons, any
time the computer handles a number, if it is not already in 3-digit
decimal machine number form, it converts it to 3-digit machine number
before using it for computations.

On 2/6/2024 3:00 PM, Farley Flud wrote:
> On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:
>
>>
>> If the drone calculated coordinates of the two points on that line of
>> sight as (x_1, y_1) and (x_2, y_2), with x being the distance and y the
>> height, then the distance of the target to launch area would have any of
>> the two forms below:
>>
>> x . y - x . y
>> 1 2 2 1
>> x = -----------------
>> y - y
>> 2 1
>>
>> or:
>>
>>
>> /x - x \ . y
>> \ 2 1/ 1
>> x = x - --------------
>> 1 y - y
>> 2 1
>>
>>
>> And the Americans in charge being cro-magnons (and Nazi), seeing that
>> one of the above formulas can be derived from the other one, were
>> assuming it didn't matter which one to use for calculating x-intercept
>> for their missiles to hit Houthis targets. But Houthis, being Modern
>> Humans, always chose one of the above, and never the other.
>>
>> So Physfit found out why about half of American missiles narrowly miss
>> their targets, while Houthis missiles always hit the targets.
>>
>> 1- Verify that the two formulas are correct, and algebraically related.
>>
>> 2- Assuming the drone calculated (x_1, y_1) as (1.31, 4.76) kilometers,
>> and (x_2, y_2) as (1.93, 3.24) kilometers, and assuming that for
>> shortest computation time, numbers are rounded to three digits in the
>> codes imbedded in drones and missiles, then calculate the x-intercept in
>> both ways.
>>
>> 3- Explain which of the two methods is being used by the Houthis, and why.
>>
>
> 1)
>
> Multiply first term of second expression by 1 = (y2 - y1)/(y2 - y1):
>
> x1 ⋅ (y2 - y1) (x2 - x1) ⋅ y1
> ────────────── - ──────────────
> y2 - y1 y2 - y1
>
>
> Combine fractions:
>
> x1 ⋅ y2 - x1 ⋅ y1 - x2 ⋅ y1 + x1 ⋅ y1
> ─────────────────────────────────────
> y2 - y1
>
> Cancel terms:
>
> x1 ⋅ y2 - x2 ⋅ y1
> ─────────────────
> y2 - y1
>
>
> They are equivalent.
>
>
> 2)
>
> Using exact rational arithmetic based on the values given
> (e.g. 1.31 = 131/100), the x-intercept for both expressions
> is:
>
> x = 3089/950 = 3.25
>
> For an image of this, see this link:
>
> https://postimg.cc/2LS0KRHr
>
>
> 3)
>
> Because of potential catastrophic cancellation in distance coordinates,
> the first expression is preferable due to the absence of subtraction
> (i.e. x2 - x1) in the numerator. For the record:
>
> x1 ⋅ y2 - x2 ⋅ y1
> ─────────────────
> y2 - y1
>
>

Your reasoning is correct of course, but if you had numerically
calculated the relative errors and compared them to each other, it would
be more convincing.

The second expression, as you said, has a potential problem. If the
drone when recording its own coordinates two times, is very far from the
launch site, then x_1 and x_2 will be represented in 3-digit decimal
machine numbers by two numbers very close to each other, and their
difference when rounded produces a number with lower than 3 significant
digits. If we calculate the relative error compared to case of using
exact numbers (no rounding off), we see that it is much larger than same
relative errors for closer distances to launch site.

So, subtracting two large numbers that are very close to each other is
like asking for failure if you have it done by a machine.

But using the first expression, the closeness of the numbers x_1 and x_2
gets to a good degree ineffective because each is multiplied by the
other point's associated height _before_ subtraction is performed. So,
the difference between first and second terms in the numerator gets much
larger, causing it to lose fewer significant digits when rounded.

That's why Houthis kicked ass :-)

On 2/6/2024 9:55 PM, Physfitfreak wrote:
> On 2/6/2024 3:00 PM, Farley Flud wrote:
>> On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:
>>
>>>
>>> If the drone calculated coordinates of the two points on that line of
>>> sight as (x_1, y_1) and (x_2, y_2), with x being the distance and y the
>>> height, then the distance of the target to launch area would have any of
>>> the two forms below:
>>>
>>>       x  . y  - x  . y
>>>        1    2    2    1
>>> x = -----------------
>>>            y  - y
>>>             2    1
>>>
>>> or:
>>>
>>>
>>>            /x  - x \ . y
>>>            \ 2    1/    1
>>> x = x  - --------------
>>>        1       y  - y
>>>                 2    1
>>>
>>>
>>> And the Americans in charge being cro-magnons (and Nazi), seeing that
>>> one of the above formulas can be derived from the other one, were
>>> assuming it didn't matter which one to use for calculating x-intercept
>>> for their missiles to hit Houthis targets. But Houthis, being Modern
>>> Humans, always chose one of the above, and never the other.
>>>
>>> So Physfit found out why about half of American missiles narrowly miss
>>> their targets, while Houthis missiles always hit the targets.
>>>
>>> 1- Verify that the two formulas are correct, and algebraically related.
>>>
>>> 2- Assuming the drone calculated (x_1, y_1) as (1.31, 4.76) kilometers,
>>> and (x_2, y_2) as (1.93, 3.24) kilometers, and assuming that for
>>> shortest computation time, numbers are rounded to three digits in the
>>> codes imbedded in drones and missiles, then calculate the x-intercept in
>>> both ways.
>>>
>>> 3- Explain which of the two methods is being used by the Houthis, and
>>> why.
>>>
>>
>> 1)
>>
>> Multiply first term of second expression by 1 = (y2 - y1)/(y2 - y1):
>>
>> x1 ⋅ (y2 - y1)   (x2 - x1) ⋅ y1
>> ────────────── - ──────────────
>>      y2 - y1          y2 - y1
>>
>>
>> Combine fractions:
>>
>> x1 ⋅ y2 - x1 ⋅ y1 - x2 ⋅ y1 + x1 ⋅ y1
>> ─────────────────────────────────────
>>                 y2 - y1
>>
>> Cancel terms:
>>
>> x1 ⋅ y2 - x2 ⋅ y1
>> ─────────────────
>>       y2 - y1
>>
>>
>> They are equivalent.
>>
>>
>> 2)
>>
>> Using exact rational arithmetic based on the values given
>> (e.g. 1.31 = 131/100), the x-intercept for both expressions
>> is:
>>
>> x = 3089/950 = 3.25
>>
>> For an image of this, see this link:
>>
>> https://postimg.cc/2LS0KRHr
>>
>>
>> 3)
>>
>> Because of potential catastrophic cancellation in distance coordinates,
>> the first expression is preferable due to the absence of subtraction
>> (i.e. x2 - x1) in the numerator.  For the record:
>>
>> x1 ⋅ y2 - x2 ⋅ y1
>> ─────────────────
>>       y2 - y1
>>
>>
>
>
> Your reasoning is correct of course, but if you had numerically
> calculated the relative errors and compared them to each other, it would
> be more convincing.
>
> The second expression, as you said, has a potential problem. If the
> drone when recording its own coordinates two times, is very far from the
> launch site, then x_1 and x_2 will be represented in 3-digit decimal
> machine numbers by two numbers very close to each other, and their
> difference when rounded produces a number with lower than 3 significant
> digits. If we calculate the relative error compared to case of using
> exact numbers (no rounding off), we see that it is much larger than same
> relative errors for closer distances to launch site.
>
> So, subtracting two large numbers that are very close to each other is
> like asking for failure if you have it done by a machine.
>
> But using the first expression, the closeness of the numbers x_1 and x_2
> gets to a good degree ineffective because each is multiplied by the
> other point's associated height _before_ subtraction is performed. So,
> the difference between first and second terms in the numerator gets much
> larger, causing it to lose fewer significant digits when rounded.
>
> That's why Houthis kicked ass :-)
>
>
>
>

The error in computation of second expression is bad enough when two
large and very close numbers are subtracted. In this particular case
this error is yet magnified by a factor of y_1 ... making it much larger.

On 2/6/20966666624 6:19 PM, Physfitfreak wrote:
> Machine numbers are in binary form. But these machine numbers can be
> expressed in decimal machine numbers like:
>
> 0.d_1d_2 ... d_k x 10^n
>
> , where d_1 digit is _not_ zero, and d_2, d_3 ... d_k digits can each be
> an integer from zero to 9.

By the way, can FriCAS show the above math expression correctly in
pretty print? Diagon cannot! At least I don't know how to use it to
write that number in the familiar way.

Diagon seems to treat each digit as a separate number, and therefore
requires a math operation inbetween them! Hehe :) What a flaw. I just
noticed it.

But perhaps friCAS is like that too.

On 2/5/2024 7:39 PM, Physfitfreak wrote:
> And the Americans in charge being cro-magnons (and Nazi), seeing that
> one of the above formulas can be derived from the other one, were
> assuming it didn't matter which one to use for calculating x-intercept
> for their missiles to hit Houthis targets. But Houthis, being Modern
> Humans, always chose one of the above, and never the other.
>
> So Physfit found out why about half of American missiles narrowly miss
> their targets, while Houthis missiles always hit the targets.

Suddenly Physfit heard a loud scream. Opened his eyes and realized one
of the male cats had surprized the other. It was calm again. He turned
his face left and tried to read the time from the pendulum clock on the
wall without eyeglasses.

Whatever the time was, it was too early to get up; this much, he could
discern from it. So Physfit made himself comfortable and let himself
dive back into sleep.

But something wasn't right.

He noticed he was only _thinking_ that he was in bed, while actually,
when he'd look around him, it was obvious that he was lying down on the
back seat of his car. So he sat up and looked through the windows and
.... although for some reason it felt familiar, he could not recognize
exactly where he was. The car was parked inside a restaurant, it seemed,
with tables and chairs and a few people blabbering nonsense and eating
junk food. Why did that place feel familiar?

Physfit had just turned around to check the place some more, when he
realized who it was that was sitting all by himself at a table. There
could be no mistake. He was Pope The Penis X.

And on the ground, in front of the Pope, just three feet from his fat
feet, was RonB in prostration posture, flat on the ground with hands
stretched sidewise like a cross. In absolute submission. Worse than
that, The Pope's penis was hanging out! ...

"Enough of this crap," said Physfit to himself, and walked over to an
available table and sat down. Two monkeys were up there close to the
ceiling sitting by themselves, hand in hand, lauching at people down
around the tables.

"So this is COLA; I'm _inside_ it now, there's RonB flat on the floor,
The Jack Mormon and DFS up there hand in hand, laughing and screaming.
Where is Joel? ..."

A fly the size of the text character % was buzzing around a table in a
darker area of the restaurant. "That must be %", Physfit said to
himself, "and that's where Joel could be sitting as well."

A couple of strangers where here and there too, and other than these
people there were no one else in the shop.

Then a Garson appeared, walking with an inflated sense of
self-importance toward Physfit's table, and asked him what he would like
to have. Phyisfit said "strong coffee, no sugar", and as he looked up
and saw the Garson, he immediately realized who this fellow was. It was
that "true American" fellow, complete with a towel on his forearm, and
saddle-shaped spectator shoes. So before it was too late, Physfit
quickly changed his mind and said, "Never mind, I'm not having anything
today." He wouldn't know what crap the "true American" would add to his
coffee back inside the kitchen before serving it to him.

Physfit pulled his notebook out and opened it. Went for the last entry.
There they were, the two numbers in base e, to be added together. He had
presented the challenge earlier in the day for COLA frequenters when he
was outside of cyberspace, but having nothing better to do for the
moment, he went ahead and calculated the result in 14 significant digits.

What was the result he got, if the two numbers in base e were 2122 and
1212 ?

--
This email has been checked for viruses by Avast antivirus software.
www.avast.com

On 2/12/2024 1:39 AM, Physfitfreak wrote:
> Physfit pulled his notebook out and opened it. Went for the last entry.
> There they were, the two numbers in base e, to be added together. He had
> presented the challenge earlier in the day for COLA frequenters when he
> was outside of cyberspace, but having nothing better to do for the
> moment, he went ahead and calculated the result in 14 significant digits.

He closed and put his notebook back in his blue jean's backpocket, then
thought to himself, "How the hell do I get out of here and go home?...
Where the hell is this place located?" But he knew it must not be that
far from home cause he'd driven to here somehow, and he almost never
takes long trips. Perhaps getting outside and taking a look would help,
he thought. So he stood up and got ready to walk outside.

By now Pope The Penis X was on his feet, penis hanging out, and slowly
moving towards the opening of the restaurant from which an intense flood
of white light was pouring in. RonB was still flat on the ground, but
was now holding on to one of the Pope's ankles with both hands, and was
getting dragged along as the Pope slowly moved.

"What a repulsive, nauseating, 'true American' scene :( ... " Physfit
thought to himself. "45 fucking years of it and it's not anywhere close
to over. Fucking cro-magnons. Even AUSCHWITZ took only 4 years! _INANE_
fucking early human idiots, still walking the face of the Earth... "

As soon as Physfit began walking towards the entrance, one of the
monkeys up there screamed and jumped down and began running around the
shop howling and screeching while holding a piece of paper up. When the
monkey passed by Physfit, he noticed that there was a swastika band
around the monkey's left arm too!

"Now that's something that's not going to escape history," he said to
himself.

At last one of the COLA peers that Physfit didn't know well stood up and
stopped the monkey and snatched the piece of paper and began reading it.
The monkey was now jumping up and down panting while waiting for the
guy's reaction. A couple of others walked over to take a look as well.
The guy began reading the script from the paper for everyone to hear:

"Founder of the GuhNoo project Richard Stallman: 'necrophilia,
bestiality, possession of child pornography, and even
incest and pedophilia... should be legal as long as no one is coerced.'"

People there began muttering in disapproval. Physfit got curious and
stopped to think for a moment. Then confident why Stallman had said
that, he kicked the monkey out of his way and went outside. Area being
flat as fuck, he spotted the peculiar summit of the magic mountain from
afar and walked back to his car and drove the relatively short distance
home.

Why did Stallman say that?

--
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On Wed, 14 Feb 2024 12:50:13 -0600, Physfitfreak wrote:

>
> Why did Stallman say that?
>

I can't speak for the great Dr. Richard Stallman but I can
deliver some worthwhile observations.

Western society (i.e. USA/Europe) has gone backwards. Even
though such sexual indicators such as the age of menarche have
fallen in the West, the age of consent has paradoxically
increased.

Oh yes. A lot of girls at the age of 10 years can actually
become pregnant -- and that alone should define the age
of consent.

Unfortunately, the sexual maturity of males lags behind that
of females. The consequence of this is that some (a lot?)
of 10-year-old girls actually seek and seduce older men.
IOW, the older man does not seduce the 10-year-old girl,
but the 10-year-old-girl seduces the older man.

The fact is undeniable but the prudish West ignores the
truth and enacts insane legislation that defines the end
of childhood to be 18 years. Holy moley! Thus, a girl
who is 17 years, 11 months, 30 days, 11 hours, and 59 minutes
is still a fucking child! (And you'll be put in prison if
you get caught fucking that bitch.)

Hell, I was sexually active when I was 11-12. I remember
playing "spin the bottle" with a bunch of 6th-graders.
But most kids know how to keep a secret. So "child"
fucking goes on and is quite rampant everywhere.

The great Dr. Richard Stallman only states the obvious that
every progressive human understands.

Only the repressed prudes will screech like monkeys.