Anyone here into math?

[Guest [Kp...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

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.

 

Variants:

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

 

go second.

 

probability of success in first turn is 1/6 = 0.17

probability of success in second turn is 1/5 = 0.20

 

[Guest [ou...]]

Let us call the area of an "equilateral triangle" of N dots T(N).

2 copies of such a triangle form an Nx(N+1) rectangle.

It follows then that T(N)=N*(N+1)/2.

Q.E.D.

 

if by N you mean each side of the eq. triangle is N dots then

 

2 copies of T(N) = 2 * T(N) = 2 * √3/4 *  N²  = √3/2 *  N²  = N *√3/2 N <> N * (N+1)

 

what am i missing?

 

Any 2 sides share a dot, which is why I said "equilateral triangle",

which in turn is why 2 copies form a rectangle rather than a rhombus.

 

you have assumed that each dot denotes a square of area 1 sq.

 

if you make a similar arrangement using dots/circles to arrange them as an equilateral triangle or rhombus ((T(N) X 2) - area N dots/squares), then you have to subtract the area of the open spaces because dots or squares of 1 sq area will not tile into an equilateral triangle densely.

 

The dots' area can be considered infinitesimal in the case of a rectangle,

but not in the case of an "equilateral triangle" since any 2 sides share a dot.

It is in the latter case where you should add some area A

to the area of an equilateral triangle of side N to get the answer.

 

Problem: Which player should go 1st in a game of Russian roulette?

 

Variants:

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

 

probability of success in second turn is 1/5 = 0.20

 

That's incorrect.

 

PS - Do you have any background in math?

[Guest [Kp...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

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.

 

Variants:

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

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

 

if A -- go first. you do not want to lose the first chance of killing your opponent because the game ends in that event.

 

if B -- go second -- reasoning same as previous question.

[Guest [Kp...]]

PS - Do you have any background in math?

 

i did undergrad in comp. sci. & philosophy from XXXX in 1989. so you can say college level. but i haven't revisited math since  for i am (and have been since graduation) an entrepreneur in steel (industry).

 

edit. removed name of college. reason - TMI

[Guest [Kp...]]

The dots' area can be considered infinitesimal in the case of a rectangle,

but not in the case of an "equilateral triangle" since any 2 sides share a dot.

It is in the latter case where you should add some area A

to the area of an equilateral triangle of side N to get the answer.

 

i agree. but making the dot infinitesimal does not change things. we run into the same problem as with unit 1 squares (as you state in the next lines). since i am looking at it from the laymen perspective, i think it becomes necessary to state the assumption (infinitesimal or unit 1 square) only when directly comparing it with an equilateral triangle's area in your answer.

[Guest [Kp...]]

Let us call the area of an "equilateral triangle" of N dots T(N).

2 copies of such a triangle form an Nx(N+1) rectangle.

It follows then that T(N)=N*(N+1)/2.

Q.E.D.

 

if by N you mean each side of the eq. triangle is N dots then

 

2 copies of T(N) = 2 * T(N) = 2 * √3/4 *  N²  = √3/2 *  N²  = N *√3/2 N <> N * (N+1)

 

what am i missing?

 

Any 2 sides share a dot, which is why I said "equilateral triangle",

which in turn is why 2 copies form a rectangle rather than a rhombus.

 

you have assumed that each dot denotes a square of area 1 sq.

 

if you make a similar arrangement using dots/circles to arrange them as an equilateral triangle or rhombus ((T(N) X 2) - area N dots/squares), then you have to subtract the area of the open spaces because dots or squares of 1 sq area will not tile into an equilateral triangle densely.

 

The dots' area can be considered infinitesimal in the case of a rectangle,

but not in the case of an "equilateral triangle" since any 2 sides share a dot.

It is in the latter case where you should add some area A

to the area of an equilateral triangle of side N to get the answer.

 

Problem: Which player should go 1st in a game of Russian roulette?

 

Variants:

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

 

probability of success in second turn is 1/5 = 0.20

 

That's incorrect.

 

PS - Do you have any background in math?

 

probability of success in 2nd turn is 5/6 * 1/5 = 0.17

 

so no difference who goes first.

 

edit. go first -- same reasoning as case A.

[Guest [ou...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

Variants:

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

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

 

if A -- go first. you do not want to lose the first chance of killing your opponent because the game ends in that event.

 

if B -- go second -- reasoning same as previous question.

 

Your reasoning is incorrect. Probabilities are often counterintuitive.

 

The dots' area can be considered infinitesimal in the case of a rectangle,

but not in the case of an "equilateral triangle" since any 2 sides share a dot.

It is in the latter case where you should add some area A

to the area of an equilateral triangle of side N to get the answer.

 

i agree. but making the dot infinitesimal does not change things. we run into the same problem as with unit 1 squares (as you state in the next lines). since i am looking at it from the laymen perspective, i think it becomes necessary to state the assumption (infinitesimal or unit 1 square) only when directly comparing it with an equilateral triangle's area in your answer.

 

You seem to have a point. Either way I'm not that good with geometry.

You mentioned earlier of a Part II. I wanna see that.

 

PS - I don't mean to be indiscreet or try 'identifying' you but may I ask:

a. Male/Female? b. Where from?

Just like having a mental picture of who I'm talking to.

Obviously, you don't have to answer.

[Guest [Kp...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

Variants:

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

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

 

if A -- go first. you do not want to lose the first chance of killing your opponent because the game ends in that event.

 

if B -- go second -- reasoning same as previous question.

 

Your reasoning is incorrect. Probabilities are often counterintuitive.

 

yes, probabilities can be counter intuitive but they are empirically well established. they are observations of nature.

 

it does not matter, over n turns, who goes first.

 

answer -- it does not matter who goes first (for all questions).

[Guest [Kp...]]

You mentioned earlier of a Part II. I wanna see that.

 

sir, part 2 will require a long explanation from you. if i leave the forum, i will not be able to access the "off-topic" section as a guest and will forever be tortured to know if my question has been answered. i will nevertheless post my question so that you can compose the answer in your mind but please do mail me a copy of the answer at my email address sent to you in private. the email address is again not my real name so be it known that i am not compromising my personal information.

 

part II -- the euler-ramanujan summation of the infinitely divergent triangular series is -1/12. how can the sum of positive integers be negative?

 

PS - I don't mean to be indiscreet or try 'identifying' you but may I ask:

a. Male/Female? b. Where from?

Just like having a mental picture of who I'm talking to.

Obviously, you don't have to answer.

 

no, no, it is ok. i am glad to share these details.

 

M 52 from kolkata, india, residing in kolkata, india. i am married with 2 sons, aged 23 and 21. older is an electronics and communications engineering graduate and in business with me  (he is into drones). younger is in 3rd year mechanical engineering (he is into hybrid automobiles and formula cars). my wife is... damn... i think 48? thereabouts!  maxima f(wife_age) = 49!

 

edit. born & raised in kolkata. 5 years in US (college). f(wife_age) is a parabolic function. 

[Guest [Kp...]]

actually i have an explanation for part II? but i do not know if i am right? either you explain or i say what i think and you can correct/refine my understanding. your choice.

[Guest [ou...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

Variants:

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

 

probability of success in second turn is 1/5 = 0.20

 

That's incorrect.

 

probability of success in 2nd turn is 5/6 * 1/5 = 0.17

 

so no difference who goes first.

 

That's "closer" to the truth, meaning the spirit of the question.

Upon further consideration, I believe Variant 1 is boring.

So I shall give the answer and then proceed to rephrase the question.

 

part II -- the euler-ramanujan summation of the infinitely divergent triangular series is -1/12. how can the sum of positive integers be negative?

 

NO! Not that. I shall refer you to

.

 

M 52 from kolkata, india, residing in kolkata, india. i am married with 2 sons, aged 23 and 21. older is an electronics and communications engineering graduate and with me in business (he is into drones). younger is in 3rd year mechanical engineering (he is into hybrid automobiles and formula cars). my wife is... damn... i think 48? thereabout!  maxima f(wife_age) = 49!

 

LOL. Too much info!

 

PS - Please don't call me Sir. I'm 26 and it makes me feel older than I already feel!

[Guest [Kp...]]

NO! Not that. I shall refer you to

.

 

ROFL! i have watched many many such videos -- they were no help. but let me watch this one -- if it doesn't help i will write what i think and you can have a go at my "explanation."

 

PS - Please don't call me Sir. I'm 26 and it makes me feel older than I already feel!

 

you are a young lad, probably a strapping young lad! sir honorific was in deference to your superior knowledge of math, but i agree with you -- no more sir (because of the age difference)!

[Guest [ou...]]

 

ROFL! i have watched many many such videos -- they were no help. but let me watch this one -- if it doesn't help i will write what i think and you can have a go at my "explanation."

 

you are a young lad, probably a strapping young lad! sir honorific was in deference to your superior knowledge of math, but i agree with you -- no more sir (because of the age difference)!

 

1. That video is the exception.

2. Thanks for the honor. I can accept its use in that context.

3. I need some sleep now after 24h.

[Guest [Kp...]]

puzzle #1 (no googling please):

 

 

probabilities are empirically well established. they are observations of nature.

 

 

if the above is true, how do computers generate random numbers? how can an algorithm to generate random numbers ever be random ("algorithm to generate random numbers" sounds like an oxymoron)? even the decimal sequence of an irrational number like π (pi) is not random!

 

puzzle #2 (googling allowed)

 

explain this joke (as a math or comp. sci. concept):

 

 

 

 

[Guest [ou...]]

Problem: Which player should go 1st in a game of Russian roulette?

 

answer -- it does not matter who goes first (for all questions).

 

That's also incorrect.

 

[Guest [ou...]]

 

puzzle #1

 

how can an algorithm to generate random numbers ever be random ("algorithm to generate random numbers" sounds like an oxymoron)? even the decimal sequence of an irrational number like π (pi) is not random!

 

puzzle #2

 

explain this joke:

 

http://preview.ibb.co/hPYWBG/Whats_App_Image_2017_10_10_at_12_17_09_PM.jpg

 

First of all, let's talk a bit about randomness.

Nothing in nature (quantum mechanics aside) is truly random.

We just can't know the initial conditions (chaos) to determine the outcome.

Algorithms generate pseudorandom numbers based on some seed (initial condition).

We don't know yet whether the digits of most irrational numbers are random.

On the contrary, computers have led us to believe that most of them are.

 

Now for 2nd one.

There are 2 types of people:

1. Those who can extrapolate from incomplete data and

2. those who can't,

thus being (un)able to understand the joke/statement which itself is incomplete.

[Guest [Kp...]]

outis, you are 26. may i ask what your background is? academic + professional + married or not + city?

 

1st gen immigrant from greece? age?

[Guest [Kp...]]

 

puzzle #1

 

how can an algorithm to generate random numbers ever be random ("algorithm to generate random numbers" sounds like an oxymoron)? even the decimal sequence of an irrational number like π (pi) is not random!

 

puzzle #2

 

explain this joke:

 

 

First of all, let's talk a bit about randomness.

Nothing in nature (quantum mechanics aside) is truly random.

 

(let us approach this as Q&A if you would oblige. that way i too will learn as we go along)

 

QM is a 20th century phenomena. probability is an older theory. does your statement then claim that probability is a priori and not based on how nature works?

 

(i will return to the rest of your answer after we reach a consensus on the above)

 

Now for 2nd one.

There are 2 types of people:

1. Those who can extrapolate from incomplete data and

2. those who can't,

thus being (un)able to understand the joke/statement which itself is incomplete.

 

your explanation is a good and valid explanation.

 

the way i saw it though was as the age-old liar's paradox (the microsoft windows of comp. sci? something that got reinvented again and again and is still current?) - "i am lying" said the liar. this self reflexive paradox was rephrased, polished, chiseled over centuries and now exists as the church-turing theorem or the turing halting problem. cantor's "diagonal slash" proof that cardinal number of reals > cardinal of naturals is an older version (godel's was the version right after cantor's by the way).

 

it would be most succinct to present this in the cantor theorem version:

 

in today's age, by "number" we mean real numbers (before we discovered real, we meant integers by "numbers" and before zero, we meant natural numbers by "numbers").  therefore "data" is a set of real numbers. cantor proved that real numbers are literally uncountable. if you attempted counting them on your fingers (in other words mapping every real number with a natural number:  1 --> 0.000001, 2 ----> 0.00002...), and if god gave you infinite fingers, you would run out of fingers and still have real numbers left to be count.

 

so, in this joke, the first category is easily established (data analysts extrapolate from incomplete data and they have no qualms about the way they extrapolate). in order to state that the second category exists, we can imagine that a team of data analysts who "can extrapolate from complete data" went out to collate all data (# of data = # of real numbers). they haven't returned yet! we also know (cantor's theorem and more sophisticated godel/turing) that they will never return! thus the joke will forever be incomplete.

[Guest [ou...]]

outis, you are 26. may I ask what your background is? academic + professional + married or not + city?

 

1st gen immigrant from Greece? age?

 

I have a diploma in Applied Mathematics and Physics from Athens Polytechnic.

Currently unemployed due to benzo withdrawal. Not married.

 

Why would you assume I'm an immigrant?

Everyone in my family tree is Greek, going back 4 generations.

[Guest [Kp...]]

part II -- the euler-ramanujan summation of the infinitely divergent triangular series is -1/12. how can the sum of positive integers be negative?

 

I shall refer you to

.

 

watched it yesterday. it is an A+++ explanation. i am surprised why no video on youtube approaches this concept of the sum (actually a constant or an "aspect" of the sum, including its partial sums) with such clarity.  now i understand why a knowledge of riemann zeta functions and zeta regularization (to eliminate 0) and the concept of analytical continuations to complex numbers are necessary to understand this concept. (you can correct me if i am wrong.) the several sums (or seeming infinities) of divergent series probably have a number system in a higher mathematical system that is obvious in those higher math systems. geniuses like ramanujan and euler could "see" those number systems (ramanujan clearly could -- euler presaged that ramanujan would happen). now i know why ramanujan is called "the man who knew infinity." lastly, -1/12 is not a sum of the series just a 0.5 is not the outcome of a coin toss (the outcome of a coin toss is always either H or T and never 0.5H). yet 0.5H suffices (substitutes for a deterministic outcome as it tells us something important about the quality of the result that differentiates it from other scenarios) and we can plug it in calculations and travel to mars.

[Guest [Kp...]]

Why would you assume I'm an immigrant?

 

facetious answer -- because only ameri indians are not imigrants?

serious answer -- because you declared you are greek.

 

did you migrate right after the polytech education? was english your first language in greece?

 

i am very sorry to hear withdrawal has come in your way to employment. i was in a bad way earlier this year but with an AD & DLMT i do not feel the taper and have lost ~ 50%. it seems your cognition is not affected -- probably a good time then to catch up on math and physics.

[Guest [ou...]]

did you migrate right after the polytech education? was english your first language in Greece?

 

Why would you assume I migrated at all? Because of my proficiency in English?

I was born, raised and have lived in Greece all my life.

I've studied English since the age of 4 though, so I consider myself bilingual.

[Guest [Kp...]]

did you migrate right after the polytech education? was english your first language in Greece?

 

Why would you assume I migrated at all? Because of my proficiency in English?

I was born, raised and have lived in Greece all my life.

I've studied English since the age of 4 though, so I consider myself bilingual.

 

highly presumptuous of me!!! i thought you are american! actually, my brain, by default, approaches every member here as if he is american by extraction (until proven otherwise... extraction? is "american" an ethnicity? i'll have to think about that) because they form the largest population here! please accept my apologies.

 

oh, you are only 5 hours behind me!

[Guest [ou...]]

QM is a 20th century phenomena. probability is an older theory. does your statement then claim that probability is a priori and not based on how nature works?

 

your explanation is a good and valid explanation.

 

Quantum theory includes probability.

Probability is not based on nature; it is nature that is probabilistic.

However, true randomness disappears at large enough scales.

A coin toss is no more random than a pseudorandom integer in {0,1}.

 

Your explanation is valid but not as good.

William of Ockham would agree with me.

 

-1/12 is not a sum of the series just a 0.5 is not the outcome of a coin toss

 

Those 2 are not equivalent.

0.5 is the expected outcome of coin toss, whereas -1/12 can be the sum of 1+2+3+...

depending on your definition of sum or "..."

In the classical sense 1+2+3+...=infinity but it can be useful to change your definition

to avoid infinities, as is the case in string theory.

[Guest [Kp...]]

QM is a 20th century phenomena. probability is an older theory. does your statement then claim that probability is a priori and not based on how nature works?

 

your explanation is a good and valid explanation.

 

Quantum theory includes probability.

Probability is not based on nature; it is nature that is probabilistic.

 

i disagree. probability is 100% based on nature. if n random coin tosses gave H n/3 times, then probability of H would be 0.3H. we had radioactive decay before QM... even a coin toss in normal circumstances is perfectly random (until proven otherwise! ... this is an outrageous and arrogant statement and i might be wrong but i suspect it is true). 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? if you do then i will cite links in my next response. you are free to cite links in your response.

 

(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!)

 

Those 2 are not equivalent.

0.5 is the expected outcome of coin toss, whereas -1/12 can be the sum of 1+2+3+...

depending on your definition of sum or "..."

In the classical sense 1+2+3+...=infinity but it can be useful to change your definition

to avoid infinities, as is the case in string theory.

 

i again disagree. the sum of the triangular series is infinity. and there is no classical vs quantum sense of the sum.

 

the sum of the divergent series 1-1+1-1+1... = 1/2 (ref. your mathologer link)

 

1/2, we know, can never be its sum. its sum can either be 0 or 1. it looks like the average of 0 and 1 (it isn't though -- but similar -- like probability it is a relative quality of the result).

 

edit. string theory has 12 dimensions based on -1/12.... this has nothing to with non classical property of string theory.

 

edit2. sorry. n dimensions is by definition non classical.