Let's go.........RANDOM!

[xander]

0.999... = 1

Now I am curios.

I can see how nothing fits in between both notations, but if I apply the rounding rule, they behave differently:

1.4999.... -> 1
1.5 -> 2

Or am I wrong?


But I think the notation serves as a coin flip here.

No. 1.4999... is exactly equal to 1.5, so when you apply normal rounding rules, it rounds up to 2.

xander

[bert_the_turtle]

NeatNit, since one of your troubles seems to be that the 1/2, 1/4... subdivision of the process is arbitrary, try this different problem:

Consider an idealized bouncing ball in a vacuum (no air friction). Assume the bounce is instantaneous, it skips the compression/expansion phase. But it is not lossless: each jump reaches only sqrt(0.5) times the height of the previous jump (which means the air time will be half of that of the previous jump). The ball is also allowed to rest still on the ground.

Drop the ball from 1.25 m height. After 1/2 a second, it will hit the floor (let's arbitrarily define that as our zero point in time, t=0s) and bounce back up, reaching only, umm, about 0.8 m height, and hit the floor 1/2 s later. The next jump will reach 0.625 m and last only 1/4 s.

So, summing up, the first jump finishes at t=1/2 s. The second jump at t=3/4 s. The third jump at t=7/8 s. And so on, the n-th jump concludes at 1-0.5^n. What happens at and after t=1 s?

Well, obviously, the ball is not jumping any more at t > 1s. Each jump demonstrably concludes before t=1 s. So it must be resting on the ground. (*) When did the transition between jumping and resting happen? Again, obviously, at t=1.

And now, the really important question is: How did the transition happen at t=1?

Sub-Question: Was there a last jump that ended at t=1?
Clearly, there must have been, because at t<1, the ball is jumping and at t>1 it is resting. So it stopped jumping at t=1. So there was a jump that ended then.
But equally clearly, there can't have been. All jumps end before t=1, none ends precisely at t=1.
So.... now what?

And before you claim that the model is incomplete and insufficient: Yes, it is. However, a full model, when you afterwards take the limit to infinitely fast bouncing without compression, yields precisely the same motion. The full model gives one result you would need to wrestle from the simplified model: the speed of the ball at t=1 s is zero. You are allowed to use that.

*: You may be tempted to evade by saying the ball was blown up by the increasing frequency of impact shocks. You would be wrong.Yes, their frequency approaches infinity, but their magnitude approaches zero in such a way that any average containing more than one shock has a finite average force bound by about twice the ball's weight. If you want to blow up ideal bouncing balls in thought experiments, put one between two mercilessly converging plates. Or trains.

[NeatNit]

Trying out a new avatar.

Might become permanent.

Sick of the flashiness of the old one (though it made it a lot easier to find myself everywhere).

If anyone's interested in what it is, it's a concept art related to a cool game called Plain Sight.

http://www.beatnikgames.com/plain-sight/

Which you should have heard of by now.

Anyone up for a game?

[xander]

In the style of the every idiotic Insane Clown Posse (and mirroring the attitude of my students):

Implicit differentiation. How the FUCK does that work?

xander

[Jackdapantyrip]

Currently drinking an inversion ipa. For the price and quality you can't do much better.

[NeatNit]

Montyphy, you evil bastard...

[bert_the_turtle]

So I'm in a game. I have object A. Bad Guys have object B in their lair. We all know A and B combined is going to give a clue. I enter the lair, find curious random object C right next to B. The clue given by A and B hints at object D, which for some reason I expect to be in the same room, and indeed it is! After the inevitable escape scene, turns out C and D combined with some conclusion jumping tells me where to go next! What a lucky coincidence!

For one, I will be disappointed if it turns out in the end the Bad Guys were NOT using me the whole time to do the dirty work for them, because otherwise, this would not make a bit of sense. Would also explain the goons obviously ordered to do the job of killing me not very well.

[xander]

Currently drinking an inversion ipa. For the price and quality you can't do much better.

For an IPA, Inversion is not bad. My first impression was that it was really bland and inoffensive---I tend to think of IPAs as being quite hoppy and bitter (which is how I like them). However, I had another bottle a few days later, and was quite surprised to notice that the beer had a pleasant peachyness to it and some nice floral notes. I should not have doubted Dechutes Brewery.

That said, I think that the Black Butte Porter is about the best beer ever made.

xander

[NeatNit]

So I'm in a game. I have object A. Bad Guys have object B in their lair. We all know A and B combined is going to give a clue. I enter the lair, find curious random object C right next to B. The clue given by A and B hints at object D, which for some reason I expect to be in the same room, and indeed it is! After the inevitable escape scene, turns out C and D combined with some conclusion jumping tells me where to go next! What a lucky coincidence!

For one, I will be disappointed if it turns out in the end the Bad Guys were NOT using me the whole time to do the dirty work for them, because otherwise, this would not make a bit of sense. Would also explain the goons obviously ordered to do the job of killing me not very well.

What game is this?

[bert_the_turtle]

That would be a potential spoiler, so:
SPOILERUSPOILERSPOILERSPOILER
SPOILERSPOILERSPOILERNSPOILER
SPOILERSCPOILERSPOILERSPOILER
SPOILERSPOILERSPHOILERSPOILER
SPOILEARSPOILERSPOILERSPOILER
SPOILERSPOILERSPOIRLERSPOILER
SPOILERSPOTILERSPOILERSPOILER
SPOILERSPOILERSPOILERSPOILER
SPOIELERSPOILERSPOILERSPOILER
SPOILERSPOILERSPOIDLERSPOILER
SPOILERSPOILERSPOILERSPOILER
SPOILERSPOILETRSPOILERSPOILER
SPOILERSPOILERSPOILERHSPOILER
SPOILERSPOIRLERSPOILERSPOILER
SPOILEERSPOILERSPOILERSPOILER
SPOILERESPOILERSPOILERSPOILER

Not a bad game, mind you. They just seem to be making an effort to hit as many cliches as possible. I guess it's an homage?

[Endless]

I have been reading this thread from beginning since the 7th, and have now made it.
Would make a great book.

[NeatNit]

I have been reading this thread from beginning

oh god why

Would make a great book.

Too bad books can't be updated in real time.

[Endless]

I have been reading this thread from beginning

oh god why

Would make a great book.

Too bad books can't be updated in real time.

As a state trooper you get a lot of down time.

[Jackdapantyrip]

I have been reading this thread from beginning

oh god why

Would make a great book.

Too bad books can't be updated in real time.

As a state trooper you get a lot of down time.

Have you ever smelled what the Rock is cooking?

[Feud]

I have been reading this thread from beginning

oh god why

Would make a great book.

Too bad books can't be updated in real time.

As a state trooper you get a lot of down time.

Depends on the state, I'd imagine. A friend of mine does accident investigations, he keeps fairly busy.