irchans

Certainly most universities now have a very strong liberal bias. I think most science departments were left leaning in the 1950s, but it is stronger now. (I think colleges and universities have always been more progressive than the general populous.) The administrations of universities are now very strongly Democrat leaning. I think that Trump just sees a lot of Democrat run institutions and thinks, "Why should the government support these institutions run almost entirely by Democrats."

I'm retired. I hope to get a 3% per year income from my savings every year after inflation and taxes. If my state implemented a 1% wealth tax on savings each year, I would go bankrupt in 20 years. I am hoping that I will live 20 years.

I also "had an Iron Man moment last week" as a mathematician. I've been doing joint math research with two friends (professors) on a project for several years. Last week, I decided to explore part of our research using chat GPT. 1) I would have a thought. 2) Present it to GPT. 3) Ask GPT to write theorems that were easy to prove and put those proofs into LaTeX. (I always have to check the proofs carefully.) 4) Then I would ask it to generate code (I mostly use Mathematica the language.) 5) Running the code would help verify the proofs. It would also inspire more thoughts and I would go back to step 2). This worked very well, but at one point I could not bound a particular expression and I was not understanding it well, so I got out the pencil and paper and redid the derivation myself which helped a lot. This whole process worked about 10 times faster than doing it without GPT. At the end of a couple of hours I had around 20 pages of correct proofs and all the code needed to do numerical simulations related to the proofs.

ikrima, Do you have any links to your research or paper titles?

How about:

(* Mathematica Notation, Assume x>0 ) If[ x < 10^(-10), 1+ x/2, ( order x^2 error ) If[ x> 10^10, Sqrt[x], ( order 1/Sqrt[x] error ) (else) Sqrt[x +1] ] ] ( I guess the If statements take too much time. *)

Us humans do have difficulty with safety. Sometimes we are able to overcome that problem to an extent. Here are some the few examples where humans have done well with safety: FAA commercial airlines, Soyuz, ISS, Shinkansen trains, US Nuclear power post 3 mile island, Vaccines, and the Falcon 9.

I think that finding proofs for open mathematical questions should count as critical thought. (See https://medium.com/%40cognidownunder/three-erdős-problems-fe...)

AI makes it possible for someone who has never written code to generate a program that does what they want. One of my friends wanted to simulate a 7,9 against a dealer 10 upcard in the card game blackjack. GPT was able to write the simulation for him in javascript/html. So it took a 0.001x coder and turned him into a 0.2x coder.

This morning a person posted a question to the Reddit group r/Mathematica (https://www.reddit.com/r/Mathematica/comments/1s1fin2/can_ho...).

I asked GPT to write code to address their question and the code was quite acceptable drawing the circle and finding the correct intersection point. It would have take me about 40 minutes to write the code, so I would not have done it myself.

Currently, GPT is great for writing short programs. The results often have a bug or two that is easy to fix, but it's much faster to have GPT write the code. This works fine for projects that are less than 100 lines of code where you just want something that works.

Type "Polar plot 6 curves of the form r = (1 + Sin[2^(k - 1) t]/2^(k - 1)) where k =1, 2, .., 6 and t=0 to 2 Pi each curve should be a different color" into ChatGPT5.

https://chatgpt.com/share/690f675d-c340-8013-b598-41fe487b4e...

It has the nice properties that you can do any number of sets (in theory) and all the boundary intersections are either osculating or perpendicular.

I think this 6 set Venn Diagram is nice because I made it. :)

http://162.243.213.31/wp-content/uploads/2012/08/Ven3.png

I became a mathematician. From this childhood exposure, entropy was the first mathematical "concept" beyond arithmetic that I understood.

Very cool.

So, I think that I can avoid a lot of the data leak problems.

There might be a simple way to do this with a crypto-currency. If possession of a credit card is considered proof of age, then possession of cryptocurrency should also be considered proof of age. Maybe the user could play $0.01 to the porn site using crypto currency to prove that he is over 18. If done properly, no one, not even the government, would know who the user was.

Here is another idea.

You have independent stores where the clerks can sell proof-of-age certificates to people. These certificates are essentially just 20 random Base64 characters. By law, the independent stores are not allowed to identify the customer (who pays with cash). The store clerk is only permitted to issue certificates to people who appear to be over the age of 18, no id required. The store keeps a list of every certificate that they have sold along with the month in which the certificate was sold so that the certificates can expire after several months.

Now I claim that it is possible to create open source zero knowledge proof software that runs on a server for each store, a few government certifying authorities, the porn websites, and on the users computer so that as long as the stores don't identify the users, no one will be able to identify the user. The government will not be able to tell which certificate was used to access the porn. The government will not have access to the certificates. It will not be able to tell which store issued the certificate. The porn site will not learn the certificate of the user nor will it know his identity.

Also, the number of lines of code needed for each program of the five needed open source programs will be less than 1000 lines, maybe less than 100 lines.

I think that all of this could be done at a cost of about $50,000 to develop the software plus the cost of running the servers. I feel like I could write all the code for less than that.

The system is not perfect. You have to trust the stores to not identify the customers and to do a decent job of identifying who is over the age of 18. Some kids will get certificates by copying their parent's code or copying the code of an older friend. Some 16 year olds will look like they are 18 and they will be able to buy proof of age certificates. But, over 80% of kids under 17 will not be able to view porn.

Despite the low cost and effectiveness of the idea above, I am not sure that it is a good idea. I don't like the government censoring content.

Even after reading the article, I think there are reasonable ways to set up a low cost system that uses zero-knowledge proofs to "prove" your age without disclosing your identity. I do think that you will need trusted entities and the system will only stop most, maybe 80 or 90 percent of children under 18 from seeing porn. But, if you do this, then maybe 99% of kids under the age of 14 will have a lot of difficulty viewing porn which is a good thing. There may be valid a slippery slope argument for not setting up the age validation system even if everything I said above is true.

My son accidentally brought a knife to school at age 12 -- maybe a 4 inch blade. When he realized that he had a knife in his backpack, he told his teacher. He was suspended from school for about 3 days and we had a fairly pleasant conversation with the principal after the suspension.

When I was in eighth grade my advanced algebra teacher said "I wonder if you always did your homework in pen, would you make fewer mistakes." That was 45 years ago. Now I am a mathematician and I have done 95% of my math in pen since then. I'm not sure how much it helped, but as you said maybe I think a bit more before I write because I don't like scratching out mistakes.

This might be the best article that I have read this year. It might change the way that I program. I really want to write up examples for each of the ideas presented: Monotonicity, Pre- and post-conditions, Invariants, Isolation, Induction, and Proof-affinity as a quality metric. I think it's easy to find these ideas in my code, but I want to try to practice writing proofs "in my head" as I code to make my code better. It is not apparent to me now how this will work, but if I write up some examples, I imagine it will become clearer.

Forth :) It's been like 30 years since I the last time I wrote a Forth program that was more than 10 lines long---fond memories.

I believer there is an error in

"Readers comprehend “the boy hit the ball” quicker than “the ball was hit by the boy.” Both sentences mean the same, but it’s easier to imagine the object (the boy) before the action (the hitting). All brains work that way. (Notice I didn’t say, “That is the way all brains work”?)".

It should be, "the SUBJECT (the boy) before the action (the hitting)." (I added caps for emphasis.)

I also wrote a brute force, kinda dumb, depth-first Suduoku solver. I think it took me a few hours in C or C++. At every node in the search tree, I just checked to make sure no constraints were violated. If I remember correctly, it would run in less than 30 seconds and it would always find a solution if a solution existed. (It might have been a lot less than 30 seconds. I only remember thinking, "That was quick".)

The article is a very enjoyable history of how Cuneiform was deciphered by a small group of often competing scholars.

Oh yes, I also will listen to NPR and other radio news when I'm driving.

I forgot. I also watch NBC Nightly News and "What about it?" on YouTube.

Mostly I read Slashdot, HN, and the Wall Street Journal. I read the Economist when I feel like paying for it (sometimes I get a deal like $50 for the digital version for a year). I did Ground News for a year.

What kind of chocolate ? :) (humor)

Interesting "fact" - The total amount of lead in the universe is a somewhat less than a cubic light year.

I liked the article and I hope that I can understand it more with some study.

I think the following sentence in the article is wrong "Applying Noether's theorem gives us three conserved quantities—one for each degree of freedom in our group of transformations—which turn out to be horizontal, vertical, and angular momentum.”

I think the correct statement is "Applying Noether's theorem gives us three conserved quantities—one for each degree of freedom in our group of transformations—which turn out to be translation, rotation, and time shifting.”

I think translation leads to conservation of momentum, rotation leads to conservation of angular momentum, and time shifting leads to conservation of energy (potential+kinetic). It's been a few decades since I saw the proof, so I might be wrong.

I'm an applied mathematician (Ph.D. in math but never a professor) and I did not want to try to understand the description of schemes in the obituary. I thought that the obituary was too technical for me. On the other hand, if I thought that schemes were useful for my work, then I would dig into them and try to understand them.

I think that researching pedagogy is very difficult, and, like many scientific fields, it is hard to reproduce results found in papers. (I am not an expert in this area -- I am just a former teacher with around 10 years teaching experience.) One of the main things I notice is that standardized test scores are not really improving. I think that high school students today would score about the same as high school students in the 1980's if they were given the same multiple choice tests. This implies to me that the field has not advanced a lot. I do think that LLMs and other computer based teaching could help.

I think that it would be fairly easy (meaning that I think I could do it in 8 hours) to build a Turing Machine that prints 10^1000 1's on its tape and then halts. We would not be able to construct and run physical Turing machine that could do every move physically (by moving electrons) within 100 billion years, but we can still write the proof that it halts, probably with less than 3 pages. (In fact, we could probably tell you which state it is in for any i in the set {1, ...., halting step} without ever constructing and running a physical machine.)

On the other hand, if the "shortest" proof of halting is more than 10^20 pages long, then we would have major problems "writing" it.