concreteblock

The problem seems to have the same flavor as the Collatz conjecture. Simple dynamical system - very difficult to tell what happens in the long run.

Perhaps these things are too hard for (human) mathematics. I wonder if anyone has proved any theorems that make this precise. E.g. "Most cellular automata rules cannot be analyzed efficiently".

I don't know enough complexity theory/set theory to formulate this precisely.

In case anyone is wondering, the way to interpet the rules is as follows.

* The state of the system is a black-white assignment of colors to the grid.

* The rules tell you how to compute the next state of the system.

* To update the state at a certain cell x, you look at the colors of x-1, x and x+1. (left, self, and right). Then use use the table of rules to determine the new color of the middle cell. For instance, the first rule tells you that if you see three black cells in a row, then in the next time step the middle cell is white.

* This update is done simultaneously over all cells, so you compute all the new cell colors and then update them all at once.

Choosing to allocate most of your net worth in, e.g. cash, is a gamble too.

Many problems can be reduced to graph coloring problems if you look at it the right way. Try understanding the standard examples (see the applications section in Wikipedia), then it is really easy to come up with your own applications.

I agree with the first 3 statements.

Just to confirm, I am using 'almost surely' in the technical sense, which means 'with probability 1.'

Consider the following statement:

If you keep flipping a fair coin every day, it is almost sure that after some day you will have gotten a tails.

This is the same 'almost surely' that I am referring to.

You’re right. I made a mistake - I thought you were trying to contradict the theorem I stated. I’ve just realized you were saying something orthogonal.

As for the proof of my theorem, By taking logarithms, the process becomes an additive random walk with negative drift (log 1.6 + log 0.5 < 0). This is well known to converge to negative infinity almost surely. After exponentiating to undo the logarithm, this is exactly the statement I made.

It does not matter how many test subjects there are ( as long as there’s finitely many) because, informally speaking , you can just wait for each of them to become irrevocably bankrupt in turn.

The mean converges exponentially to zero with time. It doesn’t grow exponentially. So the theorem you cited also goes in the same direction of my statement.

No matter how many test subjects you use, if you run the experiment for a very long time, everyone goes bankrupt and will never recover.

More precisely there is a finite time after which no-one ever passes above $0.0000000000000001.

That is a mathematical theorem.

This doesn’t depend on the number of test subjects, and you can add as many zeroes as you want.

Therefore in the long run the mean outcome is 0.

Forgive me if I have misinterpreted what you are are trying to say.

Edit: I’ve just realized that I have indeed missed your point.

> I'd expect many candidates to think that you actually want them to generate all the permutations and then get bogged down in recursion.

Ideally the candidate should realize that this is computationally infeasible and quickly come up with a much more efficient solution, right? Perhaps they believe that this question filters out people who 1) don't have a feel for what is computationally feasible 2) will just dive into coding without spending 10 seconds to see if there's a significant optimization.

Some things can't be measured.

Do you have an actual argument or are you just going to nitpick word choices?

Curious, who drilled it into your head? Were you/are you a quant?

I see the 'house money' fallacy all the time (most commonly in the context of 'take out your initial investment').

A bit depressing to be an advertising, I think.

Those who did poorly at school, love to use this trite cliche.

Even when we're not even talking about teachers.

I did read the thread. Someone was saying how whiteboard prompts are scary and has a high false negative rate. You took that and turned it into "if you find interviews scary, that's a signal that you have unreasonable social skills and you are unable to think on your feet". In other words, you believe that the false negative rate is not so high, because you believe that the the stress induced by an interview is similar enough to the stress induced in other stressful situations that are common in the work place.

The only point I am trying to make is that yes, interviews are very different than the other scenarios that you mentioned.

Here's one reason: in an whiteboard problem solving session, the other person has explictly prepared something that they know more about than you. On top of that, you are both aware of this fact. This almost never happens in a normal work-collaboration. A collabaration happens because both parties have something to offer. If not, they'd be explaining to you, and not the other way around.

Sounds like stress doesn't impact you, even in interview settings. Good for you! Too bad it seems like you also lack the empathy to see why other people might find interviews different from normal work-collaboration duties.

And no, it's not your job to worry about other people's issues, but if you think that 'being stressed in an interview setting' == 'unable to collaborate' (this is what I read from your ridiculous strawmen), you're going to pass on a lot of good people.

Very interesting. Do you have any suggestions for reading more about this?

"It is actually one of the nice facts of life that as you dial up the local instability of a dynamical system you get a corresponding increase in the statistical stability."

I am a mathematician working in a tangentially related area and have never come across this before.

Feynman was brilliant but I don't think his skepticism of formailty sets him aparts from other good mathematicians or even a typical good mathematics student.

https://terrytao.wordpress.com/career-advice/theres-more-to-...

Can you explain why the lawyers needed mirror sites? Does mirroring a site mean making a local copy of it?

And then some other guy will object to your use of 'precise' or 'exact'. Just read the definition and move on.

> For a user named ketamine_ are you really questioning the well known efficacy of few-shot therapies for treatment resistant depression and PTSD?

Maybe they want to convince their friends?

You're right. I was 100% thinking of 'stat arb' when I wrote that comment. What I meant to say that the way 'arb' is used is completely meaningless.

Maybe a clearer comment would have been:

"If rentech's strategy can be considered an arb, then every strategy can be considered an arb".

2. No strategy can scale indefinitely.

3. Every strategy can be viewed as a sort of 'arbitrage'.

4. Applies to every strategy.

According to wikipedia,

"From his two known interviews, it is known that:

Mini-Microsoft is male (reported in both interviews). He is married (reported in both interviews and occasionally referred to on the site). At least one co-worker has figured out his identity (reported by Danny Westneat)."

Someone said, roughly, that X should be like Y. You immediately asked them why this was ethically optimal.

To me that seems like a non-sequiter.

There is no reason to suspect that the optimization (with respect to whatever objective you desire, e.g. total happiness) of a large, complex, chaotic, system (such as a society) can be best achieved by using 'ethical correctness' as the only criterion for decision making.

At least, that's my opinion. I hope that doesn't make me an indecent human being.

Why did you automatically bring "ethics" into this discussion? The person you replied to was probably using the word 'should' in reference to some other objective.

That's because (imo) numbers aren't intrinsic to the physical universe. They are (imo) an abstraction we humans invented to describe certain phenomena. You may not agree but hopefully you can at least see why some people would have this PoV, and especially the more general PoV that mathematics is not about (physical) nature, but about abstract ideas.

In your opinion, what are the important 'soft skills' that

1) Academics lack

2) Are hard to pick up

E.g. another commenter mentioned Git. Many academics don't use version control, but I think learning how to do this to an acceptable level is not very difficult, so it doesn't really count.

I'm asking because I might be trying to get a job in industry soon.

I don't think it's fair to characterize such people as "incapable of learning how to do new things" if they're not even being given the opportunity to learn.

I'm not saying that the OP should hire these people, or that they would even be good hires. Maybe they don't want to take the risk or time of training up a new employee.

It just seems like a bit wierd non-sequitur to draw conclusions on someone's learning capabilities based on their performance in an interview outside their usual domain.

That's a good point about the linguisitic connotations. faitswulff's comment reads so much better to me when you just replace the word 'privilege' with 'virtuous cycle' or 'snowball effect'.