Science & Mathematics Unanswerable questions

[cormick]

My friend and I have had many philosophical debates on questions that cannot be answered. As you do. The main one is reasonably famous (as below). Post your own for others to debate or mull over.
Cheers

Monkey @ the typewriter

If there was a monkey placed at a typewriter, destined to hit random keys for eternity, would he one day type out the complete works of Shakespeare?



Hole in gravity This one can be answrred!

If I dug a hole through the middle of the earth, would I come out feet first (as I started, but therefore upside down) or head first (therefore wrong way from the start, but right side up)?

 

[Pie eyed]

My friend and I have had many philosophical debates on questions that cannot be answered. As you do. The main one is reasonably famous (as below). Post your own for others to debate or mull over.
Cheers

Monkey @ the typewriter

If there was a monkey placed at a typewriter, destined to hit random keys for eternity, would he one day type out the complete works of Shakespeare?





Hole in gravity This one can be answrred!

If I dug a hole through the middle of the earth, would I come out feet first (as I started, but therefore upside down) or head first (therefore wrong way from the start, but right side up)?

Monkeys.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.
In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces a random sequence of letters ad infinitum. The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa. The probability of a monkey exactly typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time of the order of the age of the universe is minuscule, but not zero.
From Wiki.

Even if the observable universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one in 10183,800. As Kittel and Kroemer put it, "The probability of Hamlet is therefore zero in any operational sense of an event…", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on thermodynamics, the field whose statistical foundations motivated the first known expositions of typing monkeys


Holes.
Your shovel would surely have melted by the time you hit the core (5000 degrees roughly). Of course you would have been dead for some time when this happened.

Here's one.

If you are on a platform moving at close to the speed of light (99%) and fired a cannon which launched a projectile at close to the speed of light (99%) in the direction you are travelling what would happen?

 

[tucker777]

Monkey @ the typewriter

If there was a monkey placed at a typewriter, destined to hit random keys for eternity, would he one day type out the complete works of Shakespeare?

But what type of monkeys would they be? Because if they were a marmoset then clearly their fingers would be too small to type on the keys but if it were a gorilla or chimpanzee then they would be too large and it would hit multiple keys and it would just come out as rubbish.
But if you did find the right monkey for the job wouldn't it make sense that the monkey would type in a more modern idiom than Shakespeare?

Thankyou Bill Bailey.

 

[scooterb]

If you're interested in the infinite monkey theorem, the birthday paradox will make you shit bricks.

In probability theory, the birthday problem, or birthday paradox pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday. Such a result (for just 23 people, considering that there are 365 possible birthdays) is counter-intuitive to many.

 

[Pie eyed]

If you're interested in the infinite monkey theorem, the birthday paradox will make you shit bricks.

You mean annual birth date...no?

Just as aside...in the mid 90's a 2 year study in the US into teenage pregnancy actually found that teenage girls were as much as 90% more likely to have a teenage pregnancy than non-teenagers of either sex. The was absolutely no data published in regard to boys, teenage or otherwise.

Some people study the most ludicrous things.

 

[EFL Boy]

How long is a piece of string?

 

[TheStinger]

You mean annual birth date...no?

Just as aside...in the mid 90's a 2 year study in the US into teenage pregnancy actually found that teenage girls were as much as 90% more likely to have a teenage pregnancy than non-teenagers of either sex. The was absolutely no data published in regard to boys, teenage or otherwise.

Some people study the most ludicrous things.

Hold on there Sparky. Is this saying that the probability of a TEENAGE pregnancy by a TEENAGE girl is 90% more likely than a NON-TEENAGE person of either sex? I would have thought it would be 100%....or am I missing something here?

 

[Pie eyed]

Hold on there Sparky. Is this saying that the probability of a TEENAGE pregnancy by a TEENAGE girl is 90% more likely than a NON-TEENAGE person of either sex? I would have thought it would be 100%....or am I missing something here?

No you got it right.

Do you think you or I could have saved two years and who knows how much money and had a stab at the findings?

 

[TheStinger]

No you got it right.

Do you think you or I could have saved two years and who knows how much money and had a stab at the findings?

I think we could have taken the money and submitted the findings in 2 minutes, not two years.

Here's one of those perennial questions, If a tree falls in the forest and no-one is around to hear it, did it make a sound?

I have read one answer which states that sound is only a perception by the auditory senses of sound waves created by something. So if no-one is around to interpret the sound waves then it would therefore have not been converted into sound.

Interesting concept anyway.

 

[Pie eyed]

I think we could have taken the money and submitted the findings in 2 minutes, not two years.

Here's one of those perennial questions, If a tree falls in the forest and no-one is around to hear it, did it make a sound?

I have read one answer which states that sound is only a perception by the auditory senses of sound waves created by something. So if no-one is around to interpret the sound waves then it would therefore have not been converted into sound.

Interesting concept anyway.

I don't really agree, but I'm no philosopher.
A sound is still a sound regardless of whether there is a huamn ear to detect it. The ear is designed to detect sound waves, which the brain can process and therefore hear. If you have a painting on your wall and there is no-one there to look at it is it still a picture? Same principle really.
There are many, many sounds we cannot hear and the dog right beside you can. Is that a sound then?
At the same time if a tree fell in the forest and there was not a living creature close enough to detect either a sound as you would regard a sound or the vibration (of the actual sound wave or sympathetic waves through another medium other than air, solid or liquid.) then it would a forest resplendent and possibly unique in it's lack of life.

Then there is the quandary of the cricket bat theory.

When is the sound of leather on willow a sound, when the batsman hears it , several milliseconds later when you hear it on the boundary or up to 6 seconds later when I hear it on the ABC in Canberra?

 

[Wally Carter]

1. Yes.

2. Feet first.

 

[cormick]

Gotta start off by admitting I have no grasp of the concept of "infinity". I know what it's supposed to mean, but I can't get my head around it. Therefore take my completely uneducated musings are that the monkey wouldn't type out the works of Shakespeare. Although it is, as the second post states, more a metaphor than a concept, the argument put forward that it will type them out - from my friend, anyway - is that every possibility that could happen, will happen. My counter argument, silly as it is, is that, as soon as the first letter is typed (presuming the typewriter has just the 26 letters & Space bar), then 25 (or 26 inc. space) possibilities are gone. Say, for example, the monkey types out "A" first up. As that's done, the possibility of "B" being typed out for eternity (remembering that it's random selection each time) - or "C", "D" etc - is gone.

Probably makes as much sense to everyone here as it did to him - none - but he says I have no grasp on "eternity" as a concept - which is true - but I find he has no grasp on the concept of "random selection". Just my take.

 

[Pie eyed]

1. Yes.

2. Feet first.

Free at last...free at last.

1. Explain.
2. Why?

Get back into the infinity thread asap.

 

[Wally Carter]

Free at last...free at last.

1. Explain.
2. Why?

Get back into the infinity thread asap.

1. An infinite number of key combinations would sooner or later arrive at the complete works of Shakespeare.

2. For the same reason that dirt doesn't fall out of the ground.

 

[Pie eyed]

1. An infinite number of key combinations would sooner or later arrive at the complete works of Shakespeare.

2. For the same reason that dirt doesn't fall out of the ground.

In reality, if it were theoretically possible to dig through the earth ( hmmm realistically and theoretically in the same statement is there a ruling on that?) , gravity would prevent you from falling through at all. You would have to climb out from the core in any direction. So unless you are climbing feet first, uphill then no. There is no place on any planetary object which exerts gravity on your mass which would allow you to fall out of a hole in the ground. A cliff face sure.

If you were to, theoretically, cut the greater portion of one hemisphere of an object away, and pre-drilled a hole of the right size, you could conceivably jump in and get "shot out the other side due to the proportional variation in the gravity, but you would eventually fall back to the surface on the same side you were shot out of.

 

[Wally Carter]

In reality, if it were theoretically possible to dig through the earth ( hmmm realistically and theoretically in the same statement is there a ruling on that?) , gravity would prevent you from falling through at all. You would have to climb out from the core in any direction. So unless you are climbing feet first, uphill then no. There is no place on any planetary object which exerts gravity on your mass which would allow you to fall out of a hole in the ground. A cliff face sure.

If you were to, theoretically, cut the greater portion of one hemisphere of an object away, and pre-drilled a hole of the right size, you could conceivably jump in and get "shot out the other side due to the proportional variation in the gravity, but you would eventually fall back to the surface on the same side you were shot out of.

Who stated anything about "falling out"?

 

[Pie eyed]

Who stated anything about "falling out"?

Feet first?

 

[BomberGal]

You mean annual birth date...no?

Just as aside...in the mid 90's a 2 year study in the US into teenage pregnancy actually found that teenage girls were as much as 90% more likely to have a teenage pregnancy than non-teenagers of either sex. The was absolutely no data published in regard to boys, teenage or otherwise.

Some people study the most ludicrous things.

I think it's worded so that it sounds ridiculous, but it's perfectly reasonable. I think it means pregnancy specifically, not teen pregnancy. Yay abstinence-only sex ed in the US! They've got one of the highest rates of teen pregnancy in the Western world.

I
Here's one of those perennial questions, If a tree falls in the forest and no-one is around to hear it, did it make a sound?

This question is always thrown up as some philosophical thing, but why? It's a question of science and what your chosen definition of sound is. The sound waves are still present, so the air is vibrating in the same way. That to me is sound. There's just no-one around to perceive it. You may as well ask if the trees are still visible.

 

[Pie eyed]

I think it's worded so that it sounds ridiculous, but it's perfectly reasonable. I think it means pregnancy specifically, not teen pregnancy. Yay abstinence-only sex ed in the US! They've got one of the highest rates of teen pregnancy in the Western world.

The study was actually a front which enabled a US Government subsidy of a fundamentalist religious organisation's assault on publicly funded abortion clinics. They happily masquerade behind science to further their own self righteous ends.
The entire study was a fake. The money was used to target clinics and harass their clientele.



This question is always thrown up as some philosophical thing, but why? It's a question of science and what your chosen definition of sound is. The sound waves are still present, so the air is vibrating in the same way. That to me is sound. There's just no-one around to perceive it. You may as well ask if the trees are still visible.

Agree.

 

[Kerrby]

How long is a piece of string?

As long as you cut it.

 

[Rustin Cohle]

If you are on a platform moving at close to the speed of light (99%) and fired a cannon which launched a projectile at close to the speed of light (99%) in the direction you are travelling what would happen?

Nothing.

 

[Pie eyed]

Nothing.

Lazy answer there Atheist.

 

[Moonwatcher]

The cannon ball would recede away from the platform at 99% of the speed of light.

 

[Pie eyed]

The cannon ball would recede away from the platform at 99% of the speed of light.

Correct. The force required to push either object to the speed of light is so great as to be considered infinite. As you cannot apply infinite force you cannot reach the speed of light.

Unless you are talking about the speed of light on earth and not light in a vacuum.
http://www.jupiterscientific.org/sciinfo/slowlight.html

In which case you can apparently reach and even surpass the speed of light in a 1974 Vauxhall with one dicky spark plug.

 

[Moonwatcher]

Pie eyed what you really want to know is if the platform is moving at 99% of the speed of light relative to you (very important to know what your measuring it's speed against) and the cannon is fired in the same direction as the platform is moving. What is the cannon balls speed relative to you. ie do you see the ball moving at 198% of the speed of light, contradicting relativity.


ok , i couldn't actually remember how to do this but... using wiki

http://en.wikipedia.org/wiki/Specia...2C_coordinates_and_the_Lorentz_transformation

and using the equation in the Composition of velocities section

where

c is the speed of light

w(prime) is the cannon balls velocity relitive to you.

w is the cannon balls velocity relative to the platform ie 99% speed of light (c)

v is the velocity of you relative to the platform (this is important as in your question it is -99% c not positive 99%c

Then the answer to the question how fast is the ball moving relative to Pie Eyed is
99.994949750012625624968435937579% of the speed of light

as you can see this last 1 percent is very costly in energy, the person on the platform had to fire it at 0.99c just so you could see 0.009949c increase in velocity! and once more it would take an infinite amount of energy to send something to the speed of light. Relativity is safe for now i guess.