Recent content by haruspex

Which means it is not a solution to the problem. Each player can anticipate the other’s strategy. If player 2 calculates player 1's best strategy then player 2 can reconsider her own strategy. But player 1 can anticipate that, and so on. Please read posts #17 and #20, and see...

Well, I have a result, but hard to be sure how accurate it is. R has probability of about 0.625 of winning. The strategy distributions are both, graphically, and with some smoothing The peak is at distance 0.56. Note the slight asymmetry. Some notes on my method: I divided the 1m distance...

Working on it, but I don’t see an analytic way and I can’t get an accurate numerical result before the program exceeds its execution time.

That does not define a stable solution. Exactly how long does L wait to decide R has failed to fire? If L waits for ##\Delta t## then R will delay ##\Delta t##, so L waits ##2\Delta t##… The problem is to find a pair of strategies, each a fixed probability distribution known to the other, such...

We have to make an assumption about realism. Can each duellist observe the other pulling the trigger and respond rapidly enough to achieve a dead heat (in terms of moment of firing) deliberately? If not, we can consider a dead heat effectively impossible. Either way, in general, we may need to...

The original text does not say "once". You added that in your instruction. But what does cutting once mean? It suggests a single straight cut, but that appears impossible. Do you mean one continuous line, but not necessarily straight? I can do that, but it seems too easy.

Bingo. As should have been obvious, it would not have been possible to time an individual transit since that is defined as the period Io is invisible in consequence of Jupiter's shadow. From Earth, that can be observed at one end of the transit only; at the other, it will be hidden from Earth...

You're right - I was looking at the first line of the body of the post, the bit to the right of the"TL;DR". I just assumed the title was the same. So the puzzle is, which did @gronk mean? The difference is that "how can it be" is asking for an explanation whereas "how it can be" is offering...

I have a suspicion that some respondents are reading the thread title as "How can light be a wave and particle at the same time" instead of "How light can be a wave and particle at the same time". As I read it, the OP is suggesting that whether it behaves like a wave (as we experience waves at...

That’s reading too much into the way the diagram is drawn. The distances 1-2 and 3-4 will be about the same, but not exactly. Suppose the transit takes time T and Earth's average velocity from Io in going from 1 to 2 is v. Light leaves Io to reach 2 time T later than the light that reached 1...

The text is clarified somewhat by the caption on the figure: "When the Earth moves away from Jupiter during a transit." I.e. it’s not the speed of the movement but rather the extent of the movement over the interval.

Infinity is to do with things. How you can discuss things rigorously without developing a theory of sets eludes me.

We are: The normal force between two bodies is, by definition, normal to the plane of contact of the bodies (if that is well defined). The question setter seems to expect you to assume the platform the person sits on is parallel to the plane, though that is not necessarily the case...

"not moving at all" may be misleading. Its instantaneous velocity is zero, but it is accelerating upwards.

What if we define ##f(x)=1+\ln(x)##, ##g_{n+1}(x)=f(g_n(x))##, ##h_{n+1}(x)=h_n(x)g_n(x)##, with suitable settings for ##g_0, h_0##, for ##x>=1##? Does ##g_n## converge for all x? If so, is the limiting function slower than ##x^{1+\epsilon}## for all ##\epsilon>0##?