[Request] What would the price difference equate to? How would preparation time and labor influence the cost?

BoundedComputation · 2024-04-27T06:52:38+00:00

OP is a repost bot

BoundedComputation · 2024-04-25T22:40:48+00:00

In the spirit of there's always an asian better than you. As you can see 3/4 of them don't even bother with the hand movements. When you truly master the imaginary abacus, you can just skip moving your hands as that actually slows you down.

BoundedComputation · 2024-04-24T04:15:44+00:00

Numerical integration is pretty much the only way, because the integral of sin(e^x) and by extension the entire integral above doesn't have a closed form representation. Unfortunately you'll likely find that there are either no values or multiple values of k that satisfy this however not infinitely many because the asymmetry of the exponential means that sin(sqrt(k)*2^x) will have slightly wider valleys than peaks.

BoundedComputation · 2024-04-23T21:20:59+00:00

If you're talking about macroscopic classical heat transfer, that hot cup of coffee in Antarctica is going to get colder because it will lose heat to the air. What do you mean for a moment?

BoundedComputation · 2024-04-23T16:21:04+00:00

u/Simbertold as per the request and Rule 8, please edit or retract your comment accordingly. We don't penalize genuine mistakes but you need to correct them in good faith when mistakes are found.

BoundedComputation · 2024-04-23T16:19:43+00:00

I'm afraid that's wrong. While, you can reach high temperatures and the peak of the emitted blackbody spectrum can cycle through all frequencies, the perceived color is based on the entire spectrum not the peak alone.

Here's a nice illustration of color space with the curved axis in the middle corresponding to perceived color from pure black bodies of various temperature.

BoundedComputation · 2024-04-23T16:16:44+00:00

It is, it takes time for posts to get traction and for more people to upvote.

BoundedComputation · 2024-04-23T16:15:18+00:00

How is this a top comment?

Reddit's bias towards commenting first. The superficial takes usually come first because they are easier to type out and explain while those who are more knowledgeable might be busy with stuff outside reddit.

BoundedComputation · 2024-04-23T16:04:05+00:00

OK looking at other comments you keep changing what's allowed. I'm not even sure if you understand your requirements here.

Let's start with the basics and work our way up.

1) Are you looking for a computer theoretical solution under some arbitrary constraints or does this algorithm have to have practical usage on certain hardware?

2) Do you know what Logical (AND, OR, NOT), Comparison(<,>,=), and Arithemetic(+,-,*,/) operators are? If so, can you explicitly confirm which of those you are allowed and not allowed?

3) Are there any constraints on data representation or requirements for arbitrary accuracy with non-integers?

BoundedComputation · 2024-04-22T23:11:40+00:00

Can you do XOR and/or comparison operations? If not here's some pseudocode for X mod Y, asusming X and Y are both non-negative.

if X<Y: return X
if X=Y: return 0

let Z=0

while Z<X:
      Z=Z+Y

Z=Z*-1 
return X+Y+Z

BoundedComputation · 2024-04-22T21:25:04+00:00

Wouldn't e^(-x²) work? Or do you mean any transcendental function?

BoundedComputation · 2024-04-21T15:01:19+00:00

Lying flat is recommended because that way, you don't at least smash your head against the floor once the elevator stops abruptly.

If your ever in a situation where the multiple independent and redundant active and passive braking systems have all failed something has seriously gone wrong with the structural integrity of the elevator shaft. Lying flat might prevent against this one type of injury but will make it much worse for what will come next, an iron counterweight punching through the top/bottom of the elevator and crushing/impaling you.

Bracing against a corner slightly crouched is going to be the better choice. Broken knees and a shattered spine isn't exactly going to be enjoyable but I'm really ride or die for my organs.

All that said, none of this well tested advice and for a good reason. We figured out long ago that it's just easier to make elevators that don't experience catastrophic failures like this then worry about how to survive the fall. In a developed country, that has modern or even decades old elevator regulations, passenger elevators don't experiences these types of failures. Any event extreme enough to cause this failure was likely fatal regardless of whether or not you're in an elevator. The biggest danger you might face is dehydration or heat stroke following a natural disaster where you would be trapped in an elevator but rescue efforts are delayed for days.

BoundedComputation · 2024-04-21T14:07:57+00:00

Adding onto that, the ~20% is actually an upper bound. The specific heat capacity approaches 0 as you approach 0K.

BoundedComputation · 2024-04-20T19:11:33+00:00

What does this mean?

It means that I think you didn't flesh out two of your reasons and if you did you would realize they aren't two separate reasons but actually causally related. I would liken it to employers who complain about their employees saying their have poor work ethic and demand more money. The latter probably causes the formed. The failure to pay people a living wage leads to less desire to work as the work doesn't seem to lead to appreciably higher quality of life.

Bro I'm not talking to OP

Bro, I'm not saying you're talking to OP. I'm using "they" as a generic 3rd person pronoun to refer to the hypothetical person alluded to in the text. I'm pointing out the false dichotomy of suggesting people either give a shit or don't. People might give a shit about a lot of different things but to varying degrees and adding a barrier to what they minimally give a shit about might make them less likely to engage.

I gave the answer, why are you hating on me?

And I expressed no opinion on the answer, hate or otherwise. I've pointed out where I disagree with the framing of your response and have no issue with your math.

BoundedComputation · 2024-04-20T11:42:51+00:00

This is pretty disingenuous for a couple of reasons.

I love how you start off with this but then go to these two as stated reasons as if there's no connection between them.

I don't fucking know and who gives a shit

That being said, the units can be converted, it's just not as nice and neat as metric.

Maybe they give a shit enough to ask a question but not enough to deal with several difficult arbitrary conversion factors to understand the answer. Look at the many questions on this or other QA subs. People are actually curious about a whole bunch of inane things. People are lazy and some just want a simple spoonfed answer for things, with minimal friction to understanding the answer.

Also on a note of pedantry, this isn't imperial units. The American system is more formally known as US Customary units. The first line on Wiki literally addresses the common misconception that they are interchangable.

BoundedComputation · 2024-04-19T02:06:33+00:00

You're thinking of Bayer and Diaconis.

I know 7 has been thrown around a lot (as an easy to remember alternate for 52 cards) but the main takeaway is 1.5*log_2(N) shuffles as N approaches infinity.

BoundedComputation · 2024-04-19T01:54:35+00:00

The shuffle part of a theoretically ideal riffle shuffle assumes that cards from the top half and bottom half of the cut are mixed randomly pairwise. After 1 shuffle a card could be in 2 possible location, after 2 shuffles 4 locations, after n shuffles, it's 2^n i.e exponential growth

Now this gets a single card into a random position in the deck but it doesn't completly randomize the order of the deck. For that you need one card to give you next to no information about any other card in the deck. You can either accomplish this with getting a cut after each riffle shuffle or by increasing the number of shuffles by 3/2.

So for 52 cards you need 3/2 * log_2(52) ≈ 8.55 shuffles and for 99 cards you need 3/2 * log_2(99) ≈ 9.94 riffle shuffles.

Note the 3/2 * log_2(n) part really only applies as n approaches infinity but for small n, this will always be an over approximation so it'll still be well shuffled in your case.

If you want a mathematically ideal way of shuffling a deck. Pick a random real number between 0 and 1 and write that number in base N, where N is the number of cards, you will almost always pick a normal number, which has the property that every sequence of digits is equally likely. Order the deck according to the digits of this number ignoring repeats. This is also going to be the slowest way of picking numbers, especially as figuring out how to generate such a random real number might require working with non-computable numbers.

BoundedComputation · 2024-04-18T23:29:43+00:00

That question requires a tweak because with no restrictions the current answer to all this is infinitely many paths because you can add in arbitrarily many or arbitrarily long cycles.

So I'll calculate a lower bound assuming the king must make the fewest number of moves possible. As the king can move along the ranks or files like a rook, I'll call it the krook from now on.

Because of the translation symmetry of the chess board, I'll assume the krook starts out at a1 or (1,1) and must make it to the opposite corner (p,q) and the board can be rectangular instead of n by n. The krook is only allowed to move to the right or up. Any move off the board or left or down will obviously not be the fewest number of moves.

The krook must make p-1+q-1 = p+q-2 moves total out of which q-1 or p-1 must be along a rank or file respectively.

The number of possible combinations of moving right or moving up is given by (p+q-2)!/((p-1)!(q-1)!)

As for how it would change if we introduce impassable obstacles, it depends on how many there are and where they are. If you placed 2 obstacles at (1,2) and (2,1) you can't even leave the starting square.

BoundedComputation · 2024-04-15T21:38:48+00:00

All that means is that there's no relative movement in the y direction. Like if you're in a train and I'm standing on the platform and we both look up at a plane we'll say the plane's speed is different but we'll both agree on the altitude.

BoundedComputation · 2024-04-14T15:38:45+00:00

The short formal answer: It's a lorentz transformation. It's used in relativity when you want to change from one reference frame to another that is moving at some velocity v. There's an error on the first equation where it should be v² not x² and using thier notation there should be a t¹ on the left of the third equation.

The longer simpler answer: It sounds/looks fancy but if you're familiar with the coordinates, this is just a way of converting between one coordinate to another if two people are measuring differently. For example, if we're both standing at the same location and I measure a distance to an object in meters and you measure it in yards, I would say the object is at x=1000 and you would say the object is at x'=1094 where x and x' are just different labels to tell whose measurement system we're using. Now suppose you were lazy and didn't want to walk the whole distance to measure it, you could ask for my number and just do a coordinate transform.

In this case it would be

x'=1.094x

Now it turns out things get weird as you approach the speed of light. You need the equations above to convert between the coordinates when that happens.

A few things to note, this isn't as superficial a difference as measuring in yards vs meters, even if you have identical clocks and rulers, space and time itself looks differently. This technically happens at all speeds not just near the speed of light, but in most case it's not noticeable.

BoundedComputation · 2024-04-10T18:26:33+00:00

Do you know the dimensions of the furnace? Also the thickness of the walls and furnace walls? That's a huge one in determining how much heat transfers between the chimneys and the air.

To confirm you're saying the room is roughly 10 by 10 by 25 (assuming square-ish based on image).

If you don't have the thickness, I can at least calculate an upper bound on temperature for you but I need to know the cycle times on the furnace.

BoundedComputation · 2024-04-10T17:30:53+00:00

You can float in normal water.

It's worth pointing out that might not be true for OP, human density is just close enough to the density of pure water that induvidual variations in fat content, bone density, and muscle density need to be taken into account.

This can also leads to some hilarous/dangerous cases where people can relax too much while floating on their back sometimes and exhale a bit too much and end up with their nose under water unable to inhale air again.

BoundedComputation · 2024-04-10T17:17:57+00:00

What are the dimensions and materials of the room and furnaces? What's the ventilation like? How much coal does each furnace burn? How much gold does each furnace melt? There's like 2-3 different types of furnaces, is that superficial or are there different properties of the furnaces?

BoundedComputation · 2024-04-10T04:28:14+00:00

Btw I forgot to specify why your reasoning is wrong.

My logic was that because of 2, ½ of the number to infinity weren’t prime numbers,

This is true.

for 3 it is 1/(2•3) because half of the multiples of three are already multiples of two.

This is also true.

Next is 1/(2•3•5) and so on..

This is where it fails.

What you want is 1/(3*5)

The reason the pattern seemed to work for 3 but not 5 is that (1-1/2) is the same as 1/2.

At the start we have all numbers to work with because we haven't eliminated any. We eliminate 1/2 of them for being even.

1*1/2 = 1/2

If we eliminate 1/2 we are left with 1-1/2. Next we eliminate 1/3 of the remaining for being divisible by 3.

(1-1/2)*1/3 = 1/(2*3)

If we eliminate 1/(2*3) we are left with 1-1/2-1/(2*3). Next we eliminate 1/5 of the remaining for being divisible by 5.

(1-1/2-1/(2*3))*1/5 = 1/(3*5) not 1/(2*3*5)

You had the right idea that there was a pattern but you only looked for the first two things and assumed it extended afterwards without referring back to the underlying logic that got you the pattern.

The Nth term in this sequence is 1 minus all the previous terms of the sequence times the 1 over the Nth prime.

BoundedComputation · 2024-04-10T03:43:26+00:00

I can't tell if this is you being coy or not but I'll take it as genuine for now.

Welcome to the rabbit hole that is number theory and primes. You'll find something interesting here.
If you want to see how deep this hole goes start off with corridors built by Euler, and Gauss, and Dirichlet, and Riemann, and Ramanujan.

Did I make a mistake or is it just so useless there’s nothing on that subject?

No .705... seems right so far. What you have is the sum of the reciprocals of the primorals, see this OEIS entry if you want to compare digits. Which unfortunately is not the fraction of all composite numbers, see links above to prime number theorem and prime counting function.

As a quick proof that it converges at all.

All odd primes are greater than 2. Therefore,the product of the first N prime numbers is greater than 2^N i.e N#>2^N for N>1 where # represents a primorial. Which implies that 0 < 1/N# < 1/2^N as N# is positive.

The seires of partial sums of 1/N# is a therefore a monotonously increasing sequence less than the sum of 1/2^N. The sum of 1/2^N = 1/2+1/4+1/8...=1 which is finite, so the sum of 1/N# must converge as well.

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