Skip to main content

What was it like to meet Richard Feynman? Anecdote by Neil King

I sat in on Physics X at Caltech for a year: This is where Feynman would take questions from freshmen and sophomores, and try to answer them. He didn't like the more 'formal' questions that upper-division and grad students would ask: he wanted questions driven by real curiosity.

I had a lot of fun in Physics X: One time I mentioned something that had bugged more for a long time: "Why is the gamma function generally considered the 'natural generalization' of n-factorial (n!)?". He didn't answer directly; instead, he turned to the classroom and issued a challenge: "Over the break, think about this: 'What is (1/2)!, the factorial of (1/2)?' OK, Merry Christmas!"

Three students actually thought about this over the break. One girl pointed out that (d/dx)^n[x^n] = n!; I thought something could be done with that. Another fellow expanded the factorial function in a complex power series about z = (1/2,0), imposing the conditions that (z +1)! = (z+1)*z! and also that 1! = 1 = 0!; he carried this out to more and more terms.

I picked up the idea about the repeated differentiation, and combined it with the fact that a repeated integral also incorporates the factorial function. (See ml ; you'll need to remove the space).
For integer values, the relationship between n! and the nth repeated integral is just true. I co-defined non-integral values of n! AND non-integral repeated integrals so that the relationship would still be true. I then proved that relationship between the gamma function and the beta function (See:
also held for my extension of the factorial. I was 95% of the way there, but I got stuck on one point: once I could figure out one value, for n = 1/2, I could immediately show that any continuous function that was defined in my way had to be the famous gamma function.

On the first Monday evening of the new calendar year, only 4 people showed up: the three factorialists and Feynman. Feynman was delighted at what we had found: It all reminded him of things he had worked on previously. I think he pointed out something very easy that I hadn't finished thinking through (basically integration by parts; I can't find my notebook to see why that would have been a problem), and then boom!, I had (1/2)! = sqrt(pi)/2; knew my definition of n! = gamma(n+1); and had a definition for non-integer iterations of integration and differentiation, all together.

Feynman dug it. Then he gave me a bit of advice: "Don't tell anyone. Just wait. Someday, someone will have a problem, and this will be the answer to it. Just bring it out then. And then when they ask you, 'How did you figure that out?', you just say, 'Oh, I discovered that when I was just a kid.'!"

I ran into Feynman at the Caltech cafeteria, and he invited me to join him for lunch three different times. This was the highlight of my year at Caltech.


Popular posts from this blog

How the Python import system works

How the Python import system works From: If you ask me to name the most misunderstood aspect of Python, I will answer without a second thought: the Python import system. Just remember how many times you used relative imports and got something like  ImportError: attempted relative import with no known parent package ; or tried to figure out how to structure a project so that all the imports work correctly; or hacked  sys.path  when you couldn't find a better solution. Every Python programmer experienced something like this, and popular StackOverflow questions, such us  Importing files from different folder  (1822 votes),  Relative imports in Python 3  (1064 votes) and  Relative imports for the billionth time  (993 votes), are a good indicator of that. The Python import system doesn't just seem complicated – it is complicated. So even though the  documentation  is really good, it d

On working remote

The last company I worked for, did have an office space, but the code was all on Github, infra on AWS, we tracked issues over Asana and more or less each person had at least one project they could call "their own" (I had a bunch of them ;-)). This worked pretty well. And it gave me a feeling that working remote would not be very different from this. So when we started working on our own startup, we started with working from our homes. It looked great at first. I could now spend more time with Mom and could work at leisure. However, it is not as good as it looks like. At times it just feels you are busy without business, that you had been working, yet didn't achieve much. If you are evaluating working from home and are not sure of how to start, or you already do (then please review and add your views in comments) and feel like you were better off in the office, do read on. Remote work is great. But a physical office is better. So if you can, find yourself a co-working s

Todo lists are overrated

My tasks come from a variety of sources: 1) Tasks from emails  2) Meeting notes with details of people who participated  3) Project related tasks that can have a long format and can be tagged/ delegated  4) Scratchpad for unrefined ideas  5) Detailed documentation for completed technical tasks / ideas  6) FIFO list of high priority small daily tasks No one app has been able to map all the requirements above, and I have tried a lot of them! In my lifetime I’ve tried a dozen todo apps. In the beginning they all seem different, novel and special. Slick UI, shortcuts, tags, subtasks, the list goes on and on. But all our stories were the same: I start using the new app, then after awhile I stop using it. Up until the last week I thought the problem was in myself (you probably think so too). After all, David Allen seems to have figured this shit out. Also there are people leaving long 5 star reviews on every major todo list app, they discuss them on forums, recommend them to friends. But the