Gaussian blur

I’m thinking I might want to devote Monday posts to math topics. Maybe these posts should be called Math Mondays. Today seems like a find day to start.

I remember in my early twenties wondering why things always blur in a Gaussian function e-x2. Then one day it occurred to me that there is no other possibility.

What I realized is that if you blur something horizontally, and also blur it vertically, then the blur needs to be circular. If you got any other result, it would not really be blurring.

And the Gaussian function is the one function that does exactly that, because when you multiply two functions ab and ac, you are really just adding their exponents ab+c.

Which is why Gaussians (and only Gaussians) make a circular blur shape when you blur in x (horizontally) and also blur in y (vertically):

      e-x2   *   e-y2   =   e-(x2+y2)

If you look at the resulting exponent, you realize that the blur is circularly symmetric. It drops off as the square of distance. And the Gaussian function is the only “drop off with distance” function for which this is true.

As Pascal might have said, et voila!

Aptly named

Here are 50 nicknames, and 50 professions.
Can you match the name to the profession?

Art
Bart
Bill
Brad
Cal
Cam
Chick
Chuck
Cliff
Court
Drew
Dot
Doug
Emmy
Eve
Flora
Gene
Gig
Gil
Hattie
Jean
Jimmy
John
Josh
Kit
Lolly
Mark
Matt
Millie
Mort
Ollie
Oscar
Pat
Penny
Rich
Rod
Rose
Rusty
Sandy
Shel
Sherry
Sue
Stu
Teddy
Tony
Trix
Van
Wade
Will
Woody
Nightgown salesman
Theater actor
Modelmaker
Painter
Liquor salesman
Undertaker
Wrestler
Skateboarder
Judge
Machinist
Session musician
Comedian
Millionaire
Pointillist
Botanist
First lady
Grave digger
Organic chemist
Arborist
Draftsman
Poultry farmer
Levi's salesman
Balloonist
Metallurgist
Plumber
Masseuse
Garbageman
Candy store owner
Carpenter
Locksmith
Beachcomber
Milliner
Deliveryman
Dietician
Movie actor
Legislator
Lawyer
TV actor
Berkeley train conductor
Mountain climber
Estate planner
Conchologist
Ichthyologist
Photographer
Coin collector
Lifeguard
Fisherman
Chef
Magician
Penman

Protecting the Jews

Today the NY Times reported that hundreds of students and faculty and staff members at the University of Pennsylvania signed a petition this week in support of their university’s refusal to turn over to the Trump administration names, phone numbers and physical addresses for some Jewish employees. The administration sued the university on Tuesday, arguing that the Ivy League institution has “refused to comply” with a subpoena from the Equal Employment Opportunity Commission, which is investigating antisemitism on the Philadelphia campus.

The subpoena seeks contact information for employees who have filed complaints about discrimination based on Jewish faith, those who belong to Jewish clubs or groups on campus, and anyone who works in the university’s Jewish studies program, according to the lawsuit filed in the United States District Court for the Eastern District of Pennsylvania. The information is “relevant to the EEOC’s investigation of potential unlawful employment practices, namely religious, national origin, and race-based harassment,” the E.E.O.C. says in a court filing.

A day after the suit was filed, a petition began circulating in the university community aimed at offering “our strongest support for the University of Pennsylvania’s decision to refuse to collect and share lists of names and personal contact information of Jewish students, faculty, and staff with the federal government.”

Amanda Shanor, an associate professor at Wharton, the university’s business school, who helped organize the petition, said the administration’s request was “terrifying.” “The history of creating lists of Jewish people for the government is one of the most frightening in world history,” Ms. Shanor said in an interview on Friday. “And the idea that this is being done in the interest of the Jewish community is particularly frightening.”

The executive committee of Penn’s chapter of the American Association of University Professors has applauded the university for refusing to comply. Penn Hillel and MEOR Penn, two prominent Jewish groups on campus, issued a joint statement saying they supported the fight against antisemitism but were “deeply concerned” about the E.E.O.C.’s subpoena, adding that “the privacy, consent and safety of Jewish students, staff and faculty cannot be compromised. Collection of Jews’ private information carries echoes of the very patterns that made Jewish communities vulnerable for centuries,” the statement said.

Liz Huston, a spokeswoman for the White House, said the Trump administration would “always aggressively enforce the law, protect public safety and prosecute incidents of illegal discrimination. The University of Pennsylvania should comply with the straightforward subpoena and demonstrate their commitment to safeguarding their students.”

“But it’s ok,” she added, “We have an alternate plan in place. To better protect Jewish students and faculty at U. Penn, we are printing up yellow stars for them to pin to their chests. That way, as they go to their classes, everyone will know who they are, so nobody will be able to discriminate against them.”

Updating applets

I am about to engage in a year long project. I will be updating all of those many on-line Java applets on my NTU homepage.

I started creating those applets in 1996, the first year you could create an interactive Java applet and post it on-line. Over time I created various support libraries for them, including a pretty comprehensive 3D software renderer.

But then in January 14, 2014 it all came crashing down — that’s when Oracle officially declared that unsigned Java applets were not ok. From then on my little experiments no longer worked on the Web.

So for the next 12 months I am going to be rewriting as many of them as I can. On the surface they will hopefully look the same, but underneath they will all be Javascript.

Some will run with Canvas2D and others will run with WebGL — I will need to decide on a case by case basis. But the underlying ideas will remain the same.

And that’s the great thing about ideas. Unlike technology, ideas can last forever.

Acceptance speech

It’s hard to write a good acceptance speech. There are so many questions to consider. Here are just a few:

Who do you thank, and who do you leave out? Do you err on the side of inclusion, or of not boring your audience?

Do you talk at length about your own accomplishments — which are, after all, the reason you got the award? And if so, can you avoid sounding like an asshole?

Some questions have obvious answers: Don’t use the occasion as an opportunity to settle old scores. That sort of thing works only if you are a corrupt narcissistic man-child who likes to starve Americans while shamelessly lining his pockets. But I digress.

How do you start your speech? How do you end it?

My sense is that the most important thing is to create the feeling of a narrative arc. Your speech should convey some important lesson, but not too obviously.

And this is important: The take-away lesson should not be about yourself. It should be about some larger principle.

Oh, and one more thing. If you really must tell a joke, make sure it is actually funny. 🙂

The right decision

Today in NY City I had a visit with a doctor I had never met before. He was a bit older, quite distinguished looking, and he was wearing a yarmulke.

While he was sticking needles in me and fiddling with various equipment, he asked me whether my family name was Jewish. When I said yes, he asked whether we had had problems at NYU with the “Palestinian situation”. I said no, and that NYU had done an excellent job of diffusing tensions all around.

We then got onto the subject of how our respective families had migrated from Eastern Europe in the great mid-century wave of Jewish immigration to America. In the end he wished me a happy Hanukkah, and I wished him a happy Hanukkah.

During our chat, I decided not to bring up the topic of Mayor-elect Mandami. It seemed like the right decision, given that I was talking with a person who was sticking needles in my body.

An AI summary

For the last day or so I have been looking over my previous blog posts, going back many years, for an article that I am working on about the future of text. You could say that I am mining data from myself.

It has occurred to me that this process be also done by an AI. So, out of curiosity, I decided to ask Google Gemini what it thought my blog says on the topic.

Here is what Gemini had to say: “According to Ken Perlin’s blog, the future of text involves integration into immersive Extended Reality (XR) environments and augmentation by Artificial Intelligence (AI). This future envisions text moving beyond traditional screens, becoming part of shared, enhanced realities facilitated by ubiquitous mixed reality glasses, while AI enhances human communication and creativity rather than replacing it.”

It’s a pretty fair summary, albeit at a somewhat superficial level. Yet I am mindful that over time the powers of Gemini and its A.I. competitors will only continue to increase.

I can’t figure out which would be more worrisome: A future in which articles written by humans are replaced by inferior A.I. imitations, or a future in which those articles are replaced by superior A.I. imitations.

From an airplane window

I was on a flight this evening and the plane passed by Manhattan. I had forgotten just how incredibly lovely New York is, sparkling like a wondrous jewel in the moonlight.

As I took in the sight of the Empire State Building and the city’s many other architectural wonders, I had an epiphany. In spite ourselves, we humans are capable of incredible beauty.

The shutdown served its purpose

There was a lot of hand wringing on the left when the shutdown was shut down. To some it felt like a betrayal.

But I think it served its purpose. It gave our president a chance to show his true colors.

For anyone willing to pay attention, we learned that the Defecator in Chief not only doesn’t care about American citizens, but in fact saw the shutdown as an opportunity to actively starve American families and their children.

And why? What was the hill that the Republicans were willing to die on? Amazingly, it was so they could deny affordable health care to those same American families and their children.

The message was clear to anyone not completely locked into the Faux News fantasy world. Never before has an American administration shown such contempt and cruelty toward its own citizenry.

Future skills

I wonder what future skills will emerge in the age of A.I. Certainly it will make some professions of today obsolete, much as advancing technology started to make telephone operators obsolete in the 1970s.

But what new skills will emerge? Just as the skill of photography requires the technology of photographs, and cinematography requires the technology of movies, what skills that are not yet even on our radar will start to become important?

Related questions: How will education change in the age of A.I.? Will law schools and medical schools need to radically rethink their curricula?

Sure, A.I. can do a lot for us, but it does not replace us humans. It would be more accurate to say that it offers the promise of leveling up the superpowers that we already have.

In the long run, how will future expertise and education change for photographers, cinematographers, architects, engineers, mathematicians, recording engineers, financial planners, and so on?

These are hard questions to answer. But it is important that we start to tackle them sooner rather than later.