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OT: Mathematicians Discovered Something Mind-Blowing About the Number 15
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Judith Latham
May 4, 2023, 3:34:29 PM5/4/23
to
A duo of mathematicians just solved a 15-year-old problem.
They found an answer to how many numbers you need to fill an infinite
grid under specific conditions.
The answer: a simple 15.
15: That’s the answer to an incredibly complicated math problem
recently solved by a two-person team at Carnegie Mellon University
(CMU). Usually, big, complicated math problems that are hard to solve
have big, complicated answers that are almost equally hard for the
layperson to understand. But not this one. This one is just … 15.
The question, originally posed in 2008, went as such: If you had an
infinite grid of squares—like a sheet of graph paper that went on for
eternity—and you wanted to fill it with numbers that had to be
more-than-that-number squares apart, what is the minimum number of
different numbers you would need? This is called the “packing
coloring” problem.
And it had this caveat—repeating numbers’ distance “apart” refers to
something called their “taxicab distance,” meaning you only squares
between numbers in straight lines along paths made of right angles.
So, for example, two 1s could not be right next to each other, because
their “taxicab distance” would only be one square. But they could be
diagonal from each other, because their “taxicab distance” would be
two—one to the side and one up or down. The same rule goes for all the
other numbers. Their “taxicab distance” from their nearest repeat had
to be one more than their value.
Confused yet?
If so, it’s fair. After all, the problem took top mathematicians over
a decade to solve, and it wasn’t possible without a lot of computing
power and a fair amount of creativity.
According to a Quanta Magazine article, the duo who solved the
problem— CMU grad student Bernardo Subercaseaux and CMU professor
Marijn Heule—originally managed to narrow the list of potential
answers down to just 13, 14, or 15. But that group of answers had
already been achieved by another team a few years before, and
Subercaseaux and Heule wanted a true answer, not a range of
possibilities. So, they turned to powerful computers. Especially
because, in order to rule out a potential answer, they had to make
sure they tried every single combination of number placements.
Unfortunately, that takes a lot of time to do, even for a highly
advanced and extremely powerful computer. So, the researchers got
creative. They figured out that, for the sake of this problem,
symmetrical answers are the same. Mirroring the whole grid wouldn’t
change the result, but it would double the amount of work the computer
had to do. So, they implemented the “don’t worry about symmetrical
results” rule and were able to rule out 13, leaving just 14 and 15 on
the table.
But every time the number tested got bigger, the computer process took
a whole lot longer. So, even with the “don’t worry about symmetrical
results” rule in place, the computation to test 14 was going to take
too long for the satisfaction of Subercaseaux and Heule. In addition,
University of Colorado mathematician Alexander Soifer told Quanta
Magazine that the duo didn’t just want to brute-force the problem, but
wanted to “solve it in an impressive way.”
Subercaseaux and Heule eventually realized that if they had the
computer examine chunks of space together instead of each individual
square, the calculation became a lot more efficient. So, they divided
the space up into plus signs built from 5 squares, and had the
computer check each plus sign for red flags instead of each square.
And in just a little while, the computer ran it’s experiment and threw
a flag on 14. Leaving only 15 as an option and 15 as the answer. All
that work, and all that programming, and all that creativity for a
simple 15.
You’re probably not going to run into an infinite grid that needs
filled under very specific conditions in real life, but solving
problems like this isn't always about making the most
real-world-applicable discovery. Sometimes, it really is more about
the journey than the destination.
https://www.msn.com/en-us/news/technology/mathematicians-discovered-something-mind-blowing-about-the-number-15/ar-AA1aK0kC?ocid=msedgdhp&pc=U531&cvid=fbfc3f38c2414fdb8a91e9217890fba7&ei=25
They found an answer to how many numbers you need to fill an infinite
grid under specific conditions.
The answer: a simple 15.
15: That’s the answer to an incredibly complicated math problem
recently solved by a two-person team at Carnegie Mellon University
(CMU). Usually, big, complicated math problems that are hard to solve
have big, complicated answers that are almost equally hard for the
layperson to understand. But not this one. This one is just … 15.
The question, originally posed in 2008, went as such: If you had an
infinite grid of squares—like a sheet of graph paper that went on for
eternity—and you wanted to fill it with numbers that had to be
more-than-that-number squares apart, what is the minimum number of
different numbers you would need? This is called the “packing
coloring” problem.
And it had this caveat—repeating numbers’ distance “apart” refers to
something called their “taxicab distance,” meaning you only squares
between numbers in straight lines along paths made of right angles.
So, for example, two 1s could not be right next to each other, because
their “taxicab distance” would only be one square. But they could be
diagonal from each other, because their “taxicab distance” would be
two—one to the side and one up or down. The same rule goes for all the
other numbers. Their “taxicab distance” from their nearest repeat had
to be one more than their value.
Confused yet?
If so, it’s fair. After all, the problem took top mathematicians over
a decade to solve, and it wasn’t possible without a lot of computing
power and a fair amount of creativity.
According to a Quanta Magazine article, the duo who solved the
problem— CMU grad student Bernardo Subercaseaux and CMU professor
Marijn Heule—originally managed to narrow the list of potential
answers down to just 13, 14, or 15. But that group of answers had
already been achieved by another team a few years before, and
Subercaseaux and Heule wanted a true answer, not a range of
possibilities. So, they turned to powerful computers. Especially
because, in order to rule out a potential answer, they had to make
sure they tried every single combination of number placements.
Unfortunately, that takes a lot of time to do, even for a highly
advanced and extremely powerful computer. So, the researchers got
creative. They figured out that, for the sake of this problem,
symmetrical answers are the same. Mirroring the whole grid wouldn’t
change the result, but it would double the amount of work the computer
had to do. So, they implemented the “don’t worry about symmetrical
results” rule and were able to rule out 13, leaving just 14 and 15 on
the table.
But every time the number tested got bigger, the computer process took
a whole lot longer. So, even with the “don’t worry about symmetrical
results” rule in place, the computation to test 14 was going to take
too long for the satisfaction of Subercaseaux and Heule. In addition,
University of Colorado mathematician Alexander Soifer told Quanta
Magazine that the duo didn’t just want to brute-force the problem, but
wanted to “solve it in an impressive way.”
Subercaseaux and Heule eventually realized that if they had the
computer examine chunks of space together instead of each individual
square, the calculation became a lot more efficient. So, they divided
the space up into plus signs built from 5 squares, and had the
computer check each plus sign for red flags instead of each square.
And in just a little while, the computer ran it’s experiment and threw
a flag on 14. Leaving only 15 as an option and 15 as the answer. All
that work, and all that programming, and all that creativity for a
simple 15.
You’re probably not going to run into an infinite grid that needs
filled under very specific conditions in real life, but solving
problems like this isn't always about making the most
real-world-applicable discovery. Sometimes, it really is more about
the journey than the destination.
https://www.msn.com/en-us/news/technology/mathematicians-discovered-something-mind-blowing-about-the-number-15/ar-AA1aK0kC?ocid=msedgdhp&pc=U531&cvid=fbfc3f38c2414fdb8a91e9217890fba7&ei=25
alan_m
May 4, 2023, 3:53:10 PM5/4/23
to
On 04/05/2023 20:34, Judith Latham wrote:
> A duo of mathematicians just solved a 15-year-old problem.
>
> They found an answer to how many numbers you need to fill an infinite
> grid under specific conditions.
>
> The answer: a simple 15.
Greater analysis may give the true answer as 42.
> A duo of mathematicians just solved a 15-year-old problem.
>
> They found an answer to how many numbers you need to fill an infinite
> grid under specific conditions.
>
> The answer: a simple 15.
--
mailto : news {at} admac {dot} myzen {dot} co {dot} uk
Hank Rogers
May 4, 2023, 5:10:11 PM5/4/23
to
alan_m wrote:
> On 04/05/2023 20:34, Judith Latham wrote:
>> A duo of mathematicians just solved a 15-year-old problem.
>>
>> They found an answer to how many numbers you need to fill an
>> infinite
>> grid under specific conditions.
>>
>> The answer: a simple 15.
>
> Greater analysis may give the true answer as 42.
>
Did you use Pcalc to get that answer?
> On 04/05/2023 20:34, Judith Latham wrote:
>> A duo of mathematicians just solved a 15-year-old problem.
>>
>> They found an answer to how many numbers you need to fill an
>> infinite
>> grid under specific conditions.
>>
>> The answer: a simple 15.
>
> Greater analysis may give the true answer as 42.
>
Thomas
May 4, 2023, 7:00:30 PM5/4/23
to
Thomas Joseph
May 4, 2023, 11:51:56 PM5/4/23
to
alan_m wrote:
the mathematicians? How dare you question Judith's important
copy and paste report? We are talking about actual scientists
here. Harvard, Yale, the whole nine yards. These are important
studies. All of them are important if actual scientists are involved.
I myself am a scientist - an intuitive scientist. I made it to the top
of the ladder without graduating high school. I don't need the books,
man - science is in my soul. I believe you've got some natural
science in you as well, although not on my level. You are correct,
greater analysis is needed. Always. We can change the world,
make it a better place for all. Let's do it for the children.
Judith Latham wrote:
> The answer: a simple 15.
> Greater analysis may give the true answer as 42.
How dare you challenge the scientists? How dare you besmirch
> The answer: a simple 15.
> Greater analysis may give the true answer as 42.
the mathematicians? How dare you question Judith's important
copy and paste report? We are talking about actual scientists
here. Harvard, Yale, the whole nine yards. These are important
studies. All of them are important if actual scientists are involved.
I myself am a scientist - an intuitive scientist. I made it to the top
of the ladder without graduating high school. I don't need the books,
man - science is in my soul. I believe you've got some natural
science in you as well, although not on my level. You are correct,
greater analysis is needed. Always. We can change the world,
make it a better place for all. Let's do it for the children.
Davey
May 5, 2023, 5:07:22 AM5/5/23
to
On Thu, 4 May 2023 20:50:45 +0100
alan_m <ju...@admac.myzen.co.uk> wrote:
> On 04/05/2023 20:34, Judith Latham wrote:
> > A duo of mathematicians just solved a 15-year-old problem.
> >
> > They found an answer to how many numbers you need to fill an
> > infinite grid under specific conditions.
> >
> > The answer: a simple 15.
>
> Greater analysis may give the true answer as 42.
>
>
>
Of course, there is no doubt.
alan_m <ju...@admac.myzen.co.uk> wrote:
> On 04/05/2023 20:34, Judith Latham wrote:
> > A duo of mathematicians just solved a 15-year-old problem.
> >
> > They found an answer to how many numbers you need to fill an
> > infinite grid under specific conditions.
> >
> > The answer: a simple 15.
>
> Greater analysis may give the true answer as 42.
>
>
>
--
Davey.
Hank Rogers
May 5, 2023, 7:25:53 PM5/5/23
to
Thomas
May 5, 2023, 8:36:30 PM5/5/23
to
Brian Gaff
May 6, 2023, 5:40:32 AM5/6/23
to
Actually, and I hate to pour cold water on this, but this way of working was
just one of the ways to attempt to make search and travelling salesmen
problems faster and easier to do.
I wonder, did they actually look at these sort algorithms etc, before
reinventing the wheel?
Brian
--
--:
This newsgroup posting comes to you directly from...
The Sofa of Brian Gaff...
bri...@blueyonder.co.uk
Blind user, so no pictures please
Note this Signature is meaningless.!
"Judith Latham" <judith...@gmx.com> wrote in message
news:4o185i971obea5q85...@4ax.com...
> eternity-and you wanted to fill it with numbers that had to be
> Marijn Heule-originally managed to narrow the list of potential
just one of the ways to attempt to make search and travelling salesmen
problems faster and easier to do.
I wonder, did they actually look at these sort algorithms etc, before
reinventing the wheel?
Brian
--
--:
This newsgroup posting comes to you directly from...
The Sofa of Brian Gaff...
bri...@blueyonder.co.uk
Blind user, so no pictures please
Note this Signature is meaningless.!
"Judith Latham" <judith...@gmx.com> wrote in message
news:4o185i971obea5q85...@4ax.com...
>A duo of mathematicians just solved a 15-year-old problem.
>
> They found an answer to how many numbers you need to fill an infinite
> grid under specific conditions.
>
> The answer: a simple 15.
>
> 15: That's the answer to an incredibly complicated math problem
> recently solved by a two-person team at Carnegie Mellon University
> (CMU). Usually, big, complicated math problems that are hard to solve
> have big, complicated answers that are almost equally hard for the
> layperson to understand. But not this one. This one is just . 15.
>
> They found an answer to how many numbers you need to fill an infinite
> grid under specific conditions.
>
> The answer: a simple 15.
>
> 15: That's the answer to an incredibly complicated math problem
> recently solved by a two-person team at Carnegie Mellon University
> (CMU). Usually, big, complicated math problems that are hard to solve
> have big, complicated answers that are almost equally hard for the
>
> The question, originally posed in 2008, went as such: If you had an
> infinite grid of squares-like a sheet of graph paper that went on for
> The question, originally posed in 2008, went as such: If you had an
> eternity-and you wanted to fill it with numbers that had to be
> more-than-that-number squares apart, what is the minimum number of
> different numbers you would need? This is called the "packing
> coloring" problem.
>
> And it had this caveat-repeating numbers' distance "apart" refers to
> different numbers you would need? This is called the "packing
> coloring" problem.
>
> something called their "taxicab distance," meaning you only squares
> between numbers in straight lines along paths made of right angles.
> So, for example, two 1s could not be right next to each other, because
> their "taxicab distance" would only be one square. But they could be
> diagonal from each other, because their "taxicab distance" would be
> two-one to the side and one up or down. The same rule goes for all the
> between numbers in straight lines along paths made of right angles.
> So, for example, two 1s could not be right next to each other, because
> their "taxicab distance" would only be one square. But they could be
> diagonal from each other, because their "taxicab distance" would be
> other numbers. Their "taxicab distance" from their nearest repeat had
> to be one more than their value.
>
> Confused yet?
>
> If so, it's fair. After all, the problem took top mathematicians over
> a decade to solve, and it wasn't possible without a lot of computing
> power and a fair amount of creativity.
>
> According to a Quanta Magazine article, the duo who solved the
> problem- CMU grad student Bernardo Subercaseaux and CMU professor
> to be one more than their value.
>
> Confused yet?
>
> If so, it's fair. After all, the problem took top mathematicians over
> a decade to solve, and it wasn't possible without a lot of computing
> power and a fair amount of creativity.
>
> According to a Quanta Magazine article, the duo who solved the
> Marijn Heule-originally managed to narrow the list of potential
ARW
May 6, 2023, 8:28:19 AM5/6/23
to
often than any other number.
I was my call sign on the radio at work last week, the last 3
girlfriends lived at no 52 (different streets not the same house), it
was also the number on my prescription order when at hospital last week
plus countless other of times.
Thomas Joseph
May 6, 2023, 6:29:57 PM5/6/23
to
ARW wrote:
> For some reason the number 52 has followed me around and appeared more
> often than any other number.
>
> I was my call sign on the radio at work last week, the last 3
> girlfriends lived at no 52 (different streets not the same house), it
> was also the number on my prescription order when at hospital last week
> plus countless other of times.
How old are you? If you're older than 52 you can forget it. If you're
> For some reason the number 52 has followed me around and appeared more
> often than any other number.
>
> I was my call sign on the radio at work last week, the last 3
> girlfriends lived at no 52 (different streets not the same house), it
> was also the number on my prescription order when at hospital last week
> plus countless other of times.
51 you'll be dead within the year.
Vir Campestris
May 10, 2023, 11:10:32 AM5/10/23
to
On 04/05/2023 20:34, Judith Latham wrote:
> A duo of mathematicians just solved a 15-year-old problem.
Fascinating as this was to a geek like me what's it got do do with the
groups you chose?
Andy
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