Anyone here into math?

[Guest [Kp...]]

could you please give the solution to your open prob. question(s)? 

[Guest [Kp...]]

(to digress a bit but it is related to nature vs innate -- are you familiar with the double slit experiment in physics? it is recent but it shows how creepy nature can get!)

 

nature knows what you know and influences outcome based on your knowledge. the universe can be thought of as an algorithm with a simple logic gate:

 

if human_observer knows then outcome A else outcome B.

 

Edit. Zero observer effect in above statements / assumptions.

[Guest [Kp...]]

indian vs greek

orient vs occident

hindu-arab numerals vs roman

 

(sorry.. no more frivolity)

[Guest [ou...]]

i disagree. probability is 100% based on nature.

but let us be clear that my stand is that nature never mimics theories/hypotheses of science -- it is always the reverse.

do you still hold on to your opinion that nature mimics probability and not the other way around?

 

It seems we have a misunderstanding.

Of course physics attempts to approach (mimic) reality.

I was talking about the philosophical question of

whether math was discovered or invented, which has no answer.

Personally, I choose to believe the former, seeing that math is the language of the cosmos.

 

a coin toss in normal circumstances is perfectly random.

 

Depends on your definition of randomness.

If random means you couldn't theoretically predict the outcome, then it is.

If random means you can't practically predict the outcome, then it is not.

 

if human_observer knows then outcome A else outcome B.

 

It doesn't work quite like that. It's more like:

IF Observer=Present THEN Probably A ELSE Probably B.

 

i again disagree. the sum of the triangular series is infinity.

the sum of the divergent series 1-1+1-1+1... = 1/2

1/2, we know, can never be its sum. its sum can either be 0 or 1.

 

Disagreeing with a fact doesn't change the fact that it is a a fact.

 

Fact: The series 1−1+1−1+... has no sum in the usual sense (it diverges).

Fact: If we have to assign a value to its sum, it should be 1/2 (neither 0 nor 1).

Fact: You aren't the 1st to struggle with infinity; Cantor ended up in an asylum.

 

could you please give the solution to your open prob. question(s)?

 

I will in due time. I'm planning on posting an easier problem to lure in some people,

and then wait and see if anyone wants to give the harder ones a try.

[Guest [ou...]]

The only unanswered problem as of yet is Russian roulette.

Since it's a hard one, I'm reposting it along with an easier one.

 

 

Russian roulette problem

 

Assumptions & Rules:

1. There are 2 players.

2. The revolver contains 1 bullet.

3. The cylinder consists of 6 chambers, though you could try generalizing to N.

4. Each player takes a shot at the opponent in turn.

 

Which player should go 1st in each variant:

1. The game ends after 2 turns, possibly resulting in a draw.

2. The game does not end until we have a winner and the cylinder is

either A. spun after each turn or B. not.

 

 

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

[Guest [Kp...]]

if human_observer knows then outcome A else outcome B.

 

It doesn't work quite like that. It's more like:

IF Observer=Present THEN Probably A ELSE Probably B.

 

what is the difference between

 

observer = present

 

AND

 

observer knows

 

please explain in laymen terms... i am unable to differentiate between the semantic meanings.

 

Disagreeing with a fact doesn't change the fact that it is a a fact.

 

100% agree. my disagreement is likely to end in an agreement (with you) with a probability of 0.99. thus this exercise...

 

Fact: The series 1−1+1−1+... has no sum in the usual sense (it diverges).

Fact: If we have to assign a value to its sum, it should be 1/2 (neither 0 nor 1).

 

1/2 is the cesaro summation, which is not the sum (ref: mathologer). the sum is either 0 or 1. 

 

can we agree on this?

 

edit. if we do not agree, i will accept your interpretation. i think the difference is purely interpretational. call the figure (1/2 or -1/12) a sum or a constant (ramanujan called it "constant" not "sum") -- it is the same difference.

 

Fact: You aren't the 1st to struggle with infinity; Cantor ended up in an asylum.

 

please do not say such things. euler and ramanujan did not end up in a sanitorium. cantor was genuinely schizophrenic. he was also persecuted by his peers for his cardinality theorem (though that did not cause his schizophrenia but it might have made his life hell).

 

edit. i will respond to your statements on randomness after we resolve the above issue (about observer edit. and about "probably"). one of us is wrong in his understanding of probability and randomness. i am still not convinced it is me.

[Guest [Kp...]]

if human_observer knows then outcome A else outcome B.

 

It doesn't work quite like that. It's more like:

IF Observer=Present THEN Probably A ELSE Probably B.

 

is that "probably" or a typo?

 

if it is not a typo then i am afraid i have no idea what you mean by the statement.

[Guest [ou...]]

what is the difference between

observer = present

AND

observer knows

 

human_observer_knows implies a conscious observer,

whereas a rock could be considered an observer.

Anthropocentrism hasn't worked very well in the past (Ptolemy's geocentric model).

 

is that "probably" or a typo?

if it is not a typo then i am afraid i have no idea what you mean by the statement.

 

IF Observer=Present

THEN (Probably A but Possibly B)

ELSE (Probably B but Possibly A).

 

With or without an observer the probabilities are still there.

 

1/2 is the cesaro summation, which is not the sum. the sum is either 0 or 1.

can we agree on this?

 

No. Usual summation gives no answer. Cesaro summation gives 1/2.

There is no rigorous summation that gives either 0 or 1.

 

please do not say such things. euler and ramanujan did not end up in a sanitorium. cantor was genuinely schizophrenic. he was also persecuted by his peers for his cardinality theorem (though that did not cause his schizophrenia but it might have made his life hell).

 

Sorry. Just trying to make a point. Didn't know the whole story.

[Guest [Kp...]]

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

 

total weight = 1 kg + 99 kg = 100kg

assume 98% of water remains or .98 * 99 kg = 97 kg

total weight with rock now = 1 kg +  97 kg = 98 kg

assume 98% of water+rock remains = 0.98 * 100 kg = 98 kg

 

ans. 98 kg

 

 

[Guest [ou...]]

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

 

total weight = 1 kg + 99 kg = 100kg

assume 98% of water remains or .98 * 99 kg = 97 kg

total weight with rock now = 1 kg +  97 kg = 98 kg

assume 98% of water+rock remains = 0.98 * 100 kg = 98 kg

 

ans. 98 kg

 

Nope. I said easier, not less tricky. Give it some more thought.

[Guest [Kp...]]

what is the difference between

observer = present

AND

observer knows

 

human_observer_knows implies a conscious observer,

whereas a rock could be considered an observer.

Anthropocentrism hasn't worked very well in the past (Ptolemy's geocentric model).

 

is that "probably" or a typo?

if it is not a typo then i am afraid i have no idea what you mean by the statement.

 

IF Observer=Present

THEN (Probably A but Possibly B)

ELSE (Probably B but Possibly A).

 

With or without an observer the probabilities are still there.

 

no. probability function collapses in double slit if observer knows. but this is not like schrodinger's cat because there is no observer effect and i cannot emphasize this enough.

 

Anthropocentrism hasn't worked very well in the past (Ptolemy's geocentric model).

 

i agree. i am arguing for a particularly anthropocentric model. "sentience" matters. science says probability function collapses with sentience and that is a perfectly valid scientific explanation. but science does not say why the probability function collapses with sentience.

 

science does not answer why nature behaves the way it does. it only shows us how it behaves.

 

i am sorry but i think i cannot explain the results of double slit any further. i can only attempt to respond to your criticisms of my explanations.

[Guest [Kp...]]

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

 

total weight = 1 kg + 99 kg = 100kg

assume 98% of water remains or .98 * 99 kg = 97 kg

total weight with rock now = 1 kg +  97 kg = 98 kg

assume 98% of water+rock remains = 0.98 * 100 kg = 98 kg

 

ans. 98 kg

 

Nope. I said easier, not less tricky. Give it some more thought.

 

ok give me the rest of the day. sorry but i am slow and i will be able to return to it only in the evening. (others are free to solve, of course.)

[Guest [Kp...]]

i am sorry but i think i cannot explain the results of double slit any further. i can only attempt to respond to your criticisms of my explanations.

 

with this unresolved, i think we should drop the "randomness and laws of probability" discussion.

[Guest [ou...]]

IF Observer=Present

THEN (Probably A but Possibly B)

ELSE (Probably B but Possibly A).

 

With or without an observer the probabilities are still there.

 

no. probability function collapses in double slit if observer knows.

 

Anthropocentrism hasn't worked very well in the past (Ptolemy's geocentric model).

 

i agree. i am arguing for a particularly anthropocentric model. "sentience" matters. science says probability function collapses with sentience and that is a perfectly valid scientific explanation.

 

1. Observation isn't always absolute. There are degrees of measurement.

2. There are other - more or less - equally valid interpretations of quantum mechanics.

 

PS - I was gonna say we're getting off-off-topic here, but you beat me to it!

[Guest [Kp...]]

IF Observer=Present

THEN (Probably A but Possibly B)

ELSE (Probably B but Possibly A).

 

With or without an observer the probabilities are still there.

 

no. probability function collapses in double slit if observer knows.

 

Anthropocentrism hasn't worked very well in the past (Ptolemy's geocentric model).

 

i agree. i am arguing for a particularly anthropocentric model. "sentience" matters. science says probability function collapses with sentience and that is a perfectly valid scientific explanation.

 

1. Observation isn't always absolute.

2. There are other - more or less - equally valid interpretations of quantum mechanics.

 

double slit... double slit.

 

in double slit observation is absolute (P function collapses... heisenberg and QM comes to a halt) and free of observer effect. period. let us agree to drop this subject and randomness and probability. you can however have the last word in a rejoinder and i won't answer unless phrased as a question.

 

---------------the other issue-------------

 

the series 1-1+1-1+...

 

let us use velocity and acceleration (please correct me wherever my analogy is wrong -- i am only going to use simple terms and a bit of poetic license... you are free to use calculus notations in your reply)

 

assume a car moving at 20km/hr and 1 means 1 metre north and - 1 means 1m S back to pole position ---- (sorry.. please insert correct terms for velocity here)

 

so the car is 1 m N and then moves to pole position and then 1m N and repeat... harmonic motion

 

the car's acceleration is the cesaro summation, viz. it looks for delta (d / t) r by making a sequence of partial sums and then the average of the n partial cesaro summations to find if the new sequence has a limit. to put it crudely, this is somewhat like the slope/derivative of the series. (of course, the native series 1-1+1-1.. has no limit (of velocity) though and that's why it is divergent.)

 

now acceleration <> sum of all velocities of the car

 

sum of all velocities of the car =  either pole or 1m N (depending on last velocity)

 

but acceleration says something about the sum of all velocities regardless of whether the car ends at standstill or 1m N

 

we can have acceleration 0.5 even when the car is at the pole at n turns or infinite turns and thus it seems it hasn't moved and has 0 for sum of all velocities (or 1N in the other case). but the acceleration tells us A LOT about the activity of the car, during this period, despite its 0 displacement over a long period of time.  the fact that acceleration is the same regardless of what n is in the nth partial sum also means that acceleration <> sum of n velocities (because no two partial sums of the same series can be the same)

 

similarly -1/12 is not the sum of the tr. series. the word "sum" here is a mistake of language that just serves to confuse us.-1/12 is an "aspect" of every partial sum of the series and also its infinite sum (as is it's derivative or rate at which it explodes).

 

 

 

[Guest [ou...]]

in double slit observation is absolute.

 

---------------the other issue-------------

 

1. Agreed on the double slit. Subject closed.

2. Simply put, you're wrong on the other issue.

Cannot elaborate now. Body commands me to sleep.

[Guest [Kp...]]

2. Simply put, you're wrong on the other issue.

Cannot elaborate now. Body commands me to sleep.

 

i tried...  :laugh:

 

it is an analogy and i know it is not an equivalent analogy but the conclusions are right. feel free to punch holes in it! (it won't matter much who is right because we are differing only on terminology. i want to call it a constant and you want to call it a "new definition of sum" -- and both of us are right -- but holes in my analogy will certainly help me understand the concepts better because there is a possibility that my analogy is not only wrong, it is also a very bad/dangerous analogy!)

[Guest [Kp...]]

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

 

1kg rock + 99kg water = 100kg

 

after evaporation, bucket contains  98% water

 

assume bucket contains x kg after evaporation

 

so 0.98 x = water_after_ev

so x = water_after_ev / 0.98

we also know that water_after_ev = x - rock = x-1

so x = (x-1)/0.98

so x = 50

 

ans. 50 kg  (good one!)

 

 

 

 

 

[Guest [Kp...]]

math puzzle #3 (googling allowed)

 

are the two puzzles in this post one and the same? 

 

rule - answer should be in yes or no. no explanation will be offered (nor reasoning asked) for the right answer. an explanation for the wrong answer will not be offered unless asked for and if it is offered, it shall be by links.

[Guest [ch...]]

Here's another probability one:

 

In an infinite sequence of coin tosses, which sequence will occur more often (and how much more often)? Or will they occur the same amount?

 

...HHHH...

 

or

 

...HHHT...

[Guest [ou...]]

Easy problem

 

You put a 1kg rock inside a bucket and fill it with 99kg of water.

You leave the bucket in the sun for the water to evaporate,

until it contains 98% water. How much does the bucket weigh now?

 

1kg rock + 99kg water = 100kg

 

after evaporation, bucket contains  98% water

 

assume bucket contains x kg after evaporation

 

so 0.98 x = water_after_ev

so x = water_after_ev / 0.98

we also know that water_after_ev = x - rock = x-1

so x = (x-1)/0.98

so x = 50

 

ans. 50 kg  (good one!)

 

Problem solved!

PS - Algebra >= Intuition

[Guest [ou...]]

math puzzle #3

 

are the two puzzles in this post one and the same?

 

1st puzzle concerns probabilities.

2nd puzzle concerns statistics (eg frequencies).

 

By the law of large numbers P=lim(F).

So the 2 puzzles are connected but not equivalent.

 

This forces me to reopen the subject of whether math was invented or discovered.

Statistics were invented to explain nature, then probability theory followed.

Now nature seems to obey probabilities, which implies that math was discovered instead.

[Guest [ou...]]

In an infinite sequence of coin tosses, which sequence will occur more often (and how much more often)? Or will they occur the same amount?

 

...HHHH...

 

or

 

...HHHT...

 

I'm guesstimating that the 1st sequence will occur more often with a ratio of 5:3.

PS - Do you play backgammon?

[Guest [ou...]]

i know it is not an equivalent analogy but the conclusions are right. feel free to punch holes in it!

 

How can you be certain that your conclusion is right when you know the analogy is inequivalent?

That said, there are 2 problems with your analogy.

 

1. There is no 'acceleration' in the series.

 

A better analogy would be using constant speed, going between 0 and 1.

Then the question becomes: "Where's the car after an infinite amount of time?"

The answer is it could be anywhere but on average you'd find it at x=1/2.

That's where you get confused; thinking of 1/2 as the average.

The problem is that this analogy (while better) is also bad.

 

2. There is not even 'velocity' in the series.

 

The partial sums alternate between 0 and 1.

Therefore, the best analogy would be using a teleporting car.

Then the question becomes: "Where's the car after infinite teleportations?"

Now the answer is less clear.

If the question asked for a finite amount of teleportations,

the answer would be either 0 or 1 depending on whether the amount was odd/even.

But infinity is neither an odd nor an even number so the answer is neither 0 nor 1.

The car would be in a 'transitional' stage represented by the value 1/2.

[Guest [Kp...]]

PS - Algebra >= Intuition

 

sir, what is PS?

 

How can you be certain that your conclusion is right when you know the analogy is inequivalent?

 

i cheated. all my conclusions are picked up from the mathologer video you gave me.

 

would you like to change your opinion about my conclusions now (but not about my analogy -- you know the two are different)?