January first. Clean slate. Fresh start. Happy New Year.
Comments
Open thread 1/1/2025 — 32 Comments
Thank you, Neo, and back at ya!
Happy New Year !!
My accountant daughter has informed me that 2025 is probably the only year in our lifetimes that we will be living in a year that is a perfect square. By golly, she’s right — unless anyone here is going to make it to year 2116.
So have a happy and fulfilling 45 × 45, one and all!
* [45 × 45 = 2025 and 46 × 46 = 2116; was anyone here born in 1936 or earlier?]
I’m seeing more and more news items about China’s dire financial situation, including massive layoffs.
One report even told how a bank gave out bonuses last year, and was now clawing back those bonuses to such an extent that it was, in effect, paying its employees negative salaries.
M J R, that’s quite interesting. I have a taste for numeric patterns like that. Do you think 5/5/25 would be a really great date on which to do something nice, or could the 45 aspect be utilized somehow? There’s no month with 45 days, unfortunately, so it’s harder for me to see. Maybe 5:45 on April 5th?
(Alas! Perfect-cube years are even harder to come by… 2197!)
[P. S.: well, the forty-fifth day of the year is Valentine’s Day, so there’s that.]
Philip Sells (1:26 pm), good stuff there. I like the 45 days to Valentine’s Day.
I can’t say much about 5/5/25, but I can offer what an old friend sent me just this morning, to wit:
2025 is also the sum of the first nine cubes . . .
“….was anyone here born in 1936 or earlier?” – MJR
Yep, 1933. Soon to have made 92 orbits of the sun.
The mathematical facts about 2025 are interesting. Hope they are indicative of something good/special about this year.
Whatever happens, I’ll try to keep up with it here and be thankful every day that it’s not yet my time to fly West.
Happy New Year!
M J R, thanks for that – I think I have something new for my Fun Fact at work. 🙂
As to pipes, I wonder if there’s a non-nicotinic equivalent, like nonalcoholic beer.
( 1936 = 44 × 44 )
Y’know, it occurs to me that, since the sum of the first nine integers is 45
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
[This is easily seen by rearranging (1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5]
Let the sum of the first nine integers be SUM(n),
and
let the sum of the first nine cubes be SUM(n^3).
Then (SUM(n))^2 = SUM(n^3), a somewhat curious equality.
Actually, I think that the equation
(SUM(n))^2 = SUM(n^3)
applies to *any* integer “n”, but I’m not 100 percent sure.
Any number theorists lurking out there?
(It should be provable using mathematical induction.)
M J R:
I set ChatGPT on the problem. It kept using SUM(n^3) = (SUM(n))^2 as a known identity for proof, which obviously is circular.
I kept pressing it and I had to ask it explicitly to use mathematical induction, which it did and better than I could, given how rusty my induction is.
They use sum of first n integers and sum of first n squares and some algebra, and have a nifty geometric illustration from Wikipedia.
(Wikipedia is usually reliable on math and physics without political implications, but pitched at too high a level for questions of this kind. Stack Exchange is full of students trying to get help on their homework, and somebody usually walks them through it. In this case the one who asked the question didn’t know how to read sigma notation, and someone still helped out.)
Currently I am exploring Chat’s abilities. I am impressed by what Chat can do with math and programming.
I was surprised that Chat twice made the mistake of assuming the identity which it was trying to prove.
But with a bit of coaching Chat popped out a proof using mathematical induction. Furthermore, Chat formatted the proof using advanced markdown — which means close to typeset quality.
I do wonder how colleges are teaching math and computer science these days, when AIs are practically grad student smart and can come close to doing your homework for you.
@huxley:when AIs are practically grad student smart and can come close to doing your homework for you
They are plausible, I don’t grant “smart”, and they have no way to know if what they are telling you is true, so there’s a hard upper limit on the kind of help they can give. They’re still hallucinating references and mischaracterizing real references. If you’re lucky you’ll get an answer you’ll know how to check.
Niketas Choniates:
I see the glass half-full and getting fuller. AIs still have a ways to go, but damn …
Compared to thinking everything through oneself, using an AI is a great timesaver. Though, depending on one means depending on one.
Just as calculators doomed arithmetic mastery for many people, AIs will inevitably become a crutch.
Today 82% of professional programmers are using AIs for their work. Sure, they check the AI output and make sure it plays nice with the rest of their system. But it’s a big win for productivity.
And the AIs will keep getting better.
@huxley:Compared to thinking everything through yourself, using an AI is a great timesaver. Though, depending on one means depending on one.
I didn’t understand how to make sense of the Butlerian Jihad until the rise of AI and algorithms in the last ten years.
To expand your comment… In Dune computers were replaced by a class of intellectuals called mentats using a drug to surpass ordinary human mental abilities
___________________________
It is by will alone I set my mind in motion. It is by the juice of Sapho that thoughts acquire speed, the lips acquire stains, stains become a warning. It is by will alone I set my mind in motion.
It is by caffeine alone I set my mind in motion. It is by the beans of Java that the thoughts acquire speed, the hands acquire shakes, the shakes become a warning. It is by caffeine alone I set my mind it motion.
___________________________
Been there, done that. Still do. 🙂
@huxely:In Dune computers were replaced by a class of intellectuals called mentats using a drug to surpass ordinary human mental abilities….
Yes, for this reason:
Once men turned their thinking over to machines in the hope that this would set them free. But that only permitted other men with machines to enslave them. “Thou shalt not make a machine in the likeness of a human mind.”
Even before the LLMs I was disturbed by the number of people willing to think and act on what came out of magic boxes. We’re getting closer to Morlocks and Eloi every day (to mix science fiction references).
2025: happens to be the size of my HVAC filter (20×25), so I guess that counts, too.
@M J R
Yes, it is true. Do S(n+1)^2 – S(n)^2, to get (n+1)^3. You could call that the induction step, or just make the substitutions for the cubes and note the cancellations.
Butlerian Jihad before Dune: Jeeves and his colleagues overtly replacing Wooster and his pals.
Hey, thanks one and all for the mathematical conversation today!
M J R
Thanks Charles. I noticed that each sum in the series was a perfect square but the relationship wasn’t obvious.
Between the Biden Administration–“my word as a Biden”–the MSM–“Biden has never been better,” “Sharp as a tack,”– and Academia–men can be women and women men–we’ve had a near perfect Empire of Lies.*
Here’s gaslighting Joe Scarborough disgracing himself big time at
Snow on Pine: “Here’s hoping that this incoming Trump Administration can make a good start at dismantling this Empire.”
Strictly speaking, that is not their job. It is ours.
We need to reverse Gresham’s Law for speech.
@ R2L – I did not know what Gresham’s Law said (need to update my economic education!), and discovered I was actually familiar with the maxim itself, but not its meaning.*
You made a good, and rather subtle point, that we need to allow the good (true) speech of the new government/populace to drive out the bad (false) speech of the current administration/elites.
“Gresham’s law is a monetary principle stating that “bad money drives out good”. For example, if there are two forms of commodity money in circulation, which are accepted by law as having similar face value, the more valuable commodity will gradually disappear from circulation.” — because people hoard the currency with a higher intrinsic value, IOW undebased coinage, for the most part.
An interesting corollary – even Agnew got some things right!
“The principles of Gresham’s law can sometimes be applied to different fields of study. Gresham’s law may be generally applied to any circumstance in which the true value of something is markedly different from the value people are required to accept, due to factors such as lack of information or governmental decree. [AF: or collusion of government with media, as we have seen too much of]
Vice President Spiro Agnew used Gresham’s law in describing American news media, stating that “Bad news drives out good news”, although his argument was closer to that of a race to the bottom for higher ratings rather than over- and under-valuing certain kinds of news.”
Leave a Reply
HTML tags allowed in your
comment: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>
Thank you, Neo, and back at ya!
Happy New Year !!
My accountant daughter has informed me that 2025 is probably the only year in our lifetimes that we will be living in a year that is a perfect square. By golly, she’s right — unless anyone here is going to make it to year 2116.
So have a happy and fulfilling 45 × 45, one and all!
* [45 × 45 = 2025 and 46 × 46 = 2116; was anyone here born in 1936 or earlier?]
I’m seeing more and more news items about China’s dire financial situation, including massive layoffs.
One report even told how a bank gave out bonuses last year, and was now clawing back those bonuses to such an extent that it was, in effect, paying its employees negative salaries.
M J R, that’s quite interesting. I have a taste for numeric patterns like that. Do you think 5/5/25 would be a really great date on which to do something nice, or could the 45 aspect be utilized somehow? There’s no month with 45 days, unfortunately, so it’s harder for me to see. Maybe 5:45 on April 5th?
(Alas! Perfect-cube years are even harder to come by… 2197!)
[P. S.: well, the forty-fifth day of the year is Valentine’s Day, so there’s that.]
Philip Sells (1:26 pm), good stuff there. I like the 45 days to Valentine’s Day.
I can’t say much about 5/5/25, but I can offer what an old friend sent me just this morning, to wit:
2025 is also the sum of the first nine cubes . . .
1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 = 2025.
Put that in yer pipe ‘n’ smoke it [ smile ] . . .
“….was anyone here born in 1936 or earlier?” – MJR
Yep, 1933. Soon to have made 92 orbits of the sun.
The mathematical facts about 2025 are interesting. Hope they are indicative of something good/special about this year.
Whatever happens, I’ll try to keep up with it here and be thankful every day that it’s not yet my time to fly West.
Happy New Year!
M J R, thanks for that – I think I have something new for my Fun Fact at work. 🙂
As to pipes, I wonder if there’s a non-nicotinic equivalent, like nonalcoholic beer.
( 1936 = 44 × 44 )
Y’know, it occurs to me that, since the sum of the first nine integers is 45
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
[This is easily seen by rearranging (1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5]
Let the sum of the first nine integers be SUM(n),
and
let the sum of the first nine cubes be SUM(n^3).
Then (SUM(n))^2 = SUM(n^3), a somewhat curious equality.
Actually, I think that the equation
(SUM(n))^2 = SUM(n^3)
applies to *any* integer “n”, but I’m not 100 percent sure.
Any number theorists lurking out there?
(It should be provable using mathematical induction.)
M J R:
I set ChatGPT on the problem. It kept using SUM(n^3) = (SUM(n))^2 as a known identity for proof, which obviously is circular.
I kept pressing it and I had to ask it explicitly to use mathematical induction, which it did and better than I could, given how rusty my induction is.
Interesting.
Try Stack Exchange for stuff like this.
They use sum of first n integers and sum of first n squares and some algebra, and have a nifty geometric illustration from Wikipedia.
(Wikipedia is usually reliable on math and physics without political implications, but pitched at too high a level for questions of this kind. Stack Exchange is full of students trying to get help on their homework, and somebody usually walks them through it. In this case the one who asked the question didn’t know how to read sigma notation, and someone still helped out.)
Currently I am exploring Chat’s abilities. I am impressed by what Chat can do with math and programming.
I was surprised that Chat twice made the mistake of assuming the identity which it was trying to prove.
But with a bit of coaching Chat popped out a proof using mathematical induction. Furthermore, Chat formatted the proof using advanced markdown — which means close to typeset quality.
I do wonder how colleges are teaching math and computer science these days, when AIs are practically grad student smart and can come close to doing your homework for you.
@huxley:when AIs are practically grad student smart and can come close to doing your homework for you
They are plausible, I don’t grant “smart”, and they have no way to know if what they are telling you is true, so there’s a hard upper limit on the kind of help they can give. They’re still hallucinating references and mischaracterizing real references. If you’re lucky you’ll get an answer you’ll know how to check.
Niketas Choniates:
I see the glass half-full and getting fuller. AIs still have a ways to go, but damn …
Compared to thinking everything through oneself, using an AI is a great timesaver. Though, depending on one means depending on one.
Just as calculators doomed arithmetic mastery for many people, AIs will inevitably become a crutch.
Today 82% of professional programmers are using AIs for their work. Sure, they check the AI output and make sure it plays nice with the rest of their system. But it’s a big win for productivity.
And the AIs will keep getting better.
@huxley:Compared to thinking everything through yourself, using an AI is a great timesaver. Though, depending on one means depending on one.
I didn’t understand how to make sense of the Butlerian Jihad until the rise of AI and algorithms in the last ten years.
Very interesting article about Milei. https://www.theamericanconservative.com/the-argentine-miracle/
Re: Butlerian Jihad
Niketas Choniates:
To expand your comment… In Dune computers were replaced by a class of intellectuals called mentats using a drug to surpass ordinary human mental abilities
___________________________
It is by will alone I set my mind in motion. It is by the juice of Sapho that thoughts acquire speed, the lips acquire stains, stains become a warning. It is by will alone I set my mind in motion.
–Mentat Mantra, “Dune” (David Lynch film, 1984)
___________________________
It has been parodied:
___________________________
It is by caffeine alone I set my mind in motion. It is by the beans of Java that the thoughts acquire speed, the hands acquire shakes, the shakes become a warning. It is by caffeine alone I set my mind it motion.
___________________________
Been there, done that. Still do. 🙂
@huxely:In Dune computers were replaced by a class of intellectuals called mentats using a drug to surpass ordinary human mental abilities….
Yes, for this reason:
Even before the LLMs I was disturbed by the number of people willing to think and act on what came out of magic boxes. We’re getting closer to Morlocks and Eloi every day (to mix science fiction references).
2025: happens to be the size of my HVAC filter (20×25), so I guess that counts, too.
@M J R
Yes, it is true. Do S(n+1)^2 – S(n)^2, to get (n+1)^3. You could call that the induction step, or just make the substitutions for the cubes and note the cancellations.
Butlerian Jihad before Dune: Jeeves and his colleagues overtly replacing Wooster and his pals.
Hey, thanks one and all for the mathematical conversation today!
M J R
Thanks Charles. I noticed that each sum in the series was a perfect square but the relationship wasn’t obvious.
2025’s getting off to a rocky start.
So let’s take change gears with this…
“A U.S. Marine And An American Hero”—
https://www.zerohedge.com/political/us-marine-and-american-hero
(With a shout-out to Rudyard Kipling.)
And another…
“Service dog helps boy with rare genetic disorder achieve ‘unbelievable’ progress;
“New York mother shares how her son, 4, and his golden retriever are a ‘match made in heaven’”—
https://www.foxnews.com/health/service-dog-helps-boy-rare-genetic-disorder-achieve-unbelievable-progress
Between the Biden Administration–“my word as a Biden”–the MSM–“Biden has never been better,” “Sharp as a tack,”– and Academia–men can be women and women men–we’ve had a near perfect Empire of Lies.*
Here’s gaslighting Joe Scarborough disgracing himself big time at
https://www.realclearpolitics.com/video/2024/03/06/scarborough_f_you_if_you_cant_handle_the_truth_this_version_of_biden_is_the_best_biden_ever.html
Here’s hoping that this incoming Trump Administration can make a good start at dismantling this Empire.
Not sure that Scarborough is capable at this point of “disgracing himself” any further than he already has (for years now).
He seems to truly enjoy his rather impressive perversity. Relish in it. Delight in it. It’s his default position, after all.
To be sure, he’s a hero to the usual suspects…and he has his reputation to consider…and maintain!
You need more Ann-Margret in your life.
==
https://www.youtube.com/watch?v=J2iBX_wGbkU
Snow on Pine: “Here’s hoping that this incoming Trump Administration can make a good start at dismantling this Empire.”
Strictly speaking, that is not their job. It is ours.
We need to reverse Gresham’s Law for speech.
@ R2L – I did not know what Gresham’s Law said (need to update my economic education!), and discovered I was actually familiar with the maxim itself, but not its meaning.*
You made a good, and rather subtle point, that we need to allow the good (true) speech of the new government/populace to drive out the bad (false) speech of the current administration/elites.
Well done!
* https://en.wikipedia.org/wiki/Gresham's_law
“Gresham’s law is a monetary principle stating that “bad money drives out good”. For example, if there are two forms of commodity money in circulation, which are accepted by law as having similar face value, the more valuable commodity will gradually disappear from circulation.” — because people hoard the currency with a higher intrinsic value, IOW undebased coinage, for the most part.
An interesting corollary – even Agnew got some things right!
“The principles of Gresham’s law can sometimes be applied to different fields of study. Gresham’s law may be generally applied to any circumstance in which the true value of something is markedly different from the value people are required to accept, due to factors such as lack of information or governmental decree. [AF: or collusion of government with media, as we have seen too much of]
Vice President Spiro Agnew used Gresham’s law in describing American news media, stating that “Bad news drives out good news”, although his argument was closer to that of a race to the bottom for higher ratings rather than over- and under-valuing certain kinds of news.”