Anyone here into math?

[Guest [ch...]]

Excellent, L-free.

 

It's amazing how many formulas for pi there are.

 

[[Lo...]]

Oh, wow. Had no idea there are so many series and sums for calculating it. I've learned something new today. Thanks, cp.

[Guest [ch...]]

There are actually even more than that. See https://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80 .

[Guest [ou...]]

I hereby excuse myself from this thread.

 

Since Kpin99 appears to have left us I'm thinking about posting the answers to my open problems.

 

I remember learning programming and writing a program in Pascal back in high school for calculating pi

 

Miss those days

 

As both you and chessplayer seem to be interested in programming as well,

I'm also thinking about posting algorithmic problems.

 

1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... = pi/4

 

What's more interesting is how an infinite sum of rationals may be irrational.

[Guest [ba...]]

I hereby excuse myself from this thread.

 

Threads are like the Hotel California.  You can check out anytime you want, but you can never leave. 

[[Lo...]]

I hereby excuse myself from this thread.

 

Threads are like the Hotel California.  You can check out anytime you want, but you can never leave. 

 

Now, you're going to be stuck with us doing math problems, badsocref 

[Guest [ba...]]

I solved an early time/distance problem, then 'cheated' (according to outis) to answer (or partially answer) two other questions.  So I'm stuck here too. 

 

There are certain types of problems that I'm quite good at, and there are other problems that I haven't tried to solve for 40 years or more.  If the right question is posed, I'll give it a try, but I'm not gonna spend an hour trying to solve anything.

[[Lo...]]

Makes sense. I guess I am using this as a sandbox, really. Trying to remember some knowledge I haven't used in decades. I always liked math, but ended up working on programming projects where advanced knowledge of math wasn't required, so yes, I am in the same boat as far as the ability to solve problems. It's hard doing any of this with bad anxiety and significant brain fog, so I think just having a thread like this is a good start.

 

At least, we can all agree that 4 + 4 = 8

[Guest [Kp...]]

What's more interesting is how an infinite sum of rationals may be irrational.

no outis. an infinite sum of rationals can never be irrational.  any sum of rationals will generate only a countable number (ergo, rational). what you get by your formula is only a finite sequence of pi. you can't write the whole pi, even if you used all the digits of natural and repeatedly, because pi's decimal expansion carries on even after you can no longer count, write or even imagine. the number of digits in your finite decimal expansion will map 1-1 to the set of naturals. you will reach the infinity of naturals but pi's decimal expansion will still continue relentlessly. you can say this is the definition of real, or a problem innate to any discrete coordinate plane that is ordered, or that it took cantor to show this to us (we used to think natural numbers and real, both, have the same infinity).

 

if you can write pi's full decimal expansion, then that is one of the algorithms to generate pi (being able to write a number is itself an algorithm to generate it and it is the least complicated algorithm by syntax) and irrationals have no algorithm (you cannot even write them).

[Guest [ch...]]

What's more interesting is how an infinite sum of rationals may be irrational.

no outis. an infinite sum of rationals can never be irrational.  any sum of rationals will generate only a countable number (ergo, rational). what you get by your formula is only a finite sequence of pi. you can't write the whole pi, even if you use all the digits of natural and repeatedly, because pi's decimal expansion carries on even after you can no longer count, write or even imagine. the number of digits in your finite decimal expansion will map 1-1 to the set of naturals. you will reach the infinity of naturals but pi's decimal expansion will still continue relentlessly. you can say this is the definition of real, or a problem innate to any discrete coordinate plane that is ordered, or that it took cantor to show this to us (we used to think natural numbers and real, both, have the same infinity).

 

if you can write pi's full decimal expansion, then that is one of the algorithms to generate pi (being able to write a number is itself an algorithm to generate it) and irrationals have no algorithm (you cannot even write them).

 

No, kpin. All those formulas for Pi are valid, as is the one below. So outis's statement is correct.

 

pi = 3 + 1/10 + 4/100 + 1/1000 + 5/10000 + 9/100000 + ...

 

Irrational just means it cannot be expressed as a/b. Rationals have a repeating decimal expansion, irrationals do not. Transcendentals are a subset of the irrationals that are not the root of some polynomial. Pi is transcendental. There is also a notion of non-computable numbers which is a subset of the transcendentals. Pi is computable since there exists an algorithm to compute its digits, but there are non-computable numbers. See https://en.wikipedia.org/wiki/Computable_number

 

Cantor's proof of the uncountability of the real numbers is a diagonalization proof. It relies on the fact that every real number *does* have a (countably) infinite decimal expansion. See

https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

 

 

 

[Guest [Kp...]]

No, kpin. All those formulas for Pi are valid, as is the one below. So outis's statement is correct.

 

yes the formula is valid and true but it cannot be solved and outis is still wrong. pi is the sum of numbers rational and irrational. to be more technical, pi is the limit of that sequence of rationals and irrationals. thus that sum (or limit) cannot be computed and thus that formula can never be solved.

 

then what good is the formula?

well you can get approximate solutions or partial sums of the series. approximates will help us in calculations about the universe because at no point of time are we zoomed into the infinitesimal scale of the universe. so our scale or snapshot of the universe at any point of time is anyway always an approximation (till we prove string hypothesis right). so approximations are very useful.  if i use the first rational of lorazepamfree2015's series then pi is approx. 4. that is good enough on a blurred scale. if i use the first two rationals of the series, i get 2.8. that is good enough at focus scale. then i can compute more decimals and increase my zoom to keep maintaining accuracy of pi as a function of the zoom or scale.

 

why can't we write the sum of the series that defines pi?

the entire sum cannot be written and thus cannot be computed.  it is called uncountable.

 

if a number like pi cannot be written, then how do we even know that it is a number? just anything that cannot be written cannot be a number!

well we do know that the infinite series has a sum and it is pi. that means that even though we cannot compute the entire sum, we do know its order -- that is, what number it is greater than and what number it is smaller than. the necessary and sufficient condition for anything to be a number is only its order. it is just too bad that it has no name (meaning the full decimal expansion cannot be written).

 

why can it not be written?

because your decimal expansion will reach infinity. let us call infinity N_i. at that point you will run out of paper, ink, space and every discrete object in the universe (and mind) because nothing can be greater than N_i, or, so it will seem.

 

so isn't that the end of pi?

unfortunately no. because there is an even bigger infinity after that infinity -- as hard it may be to imagine or believe. let us call this bigger infinity R_i.  and that infinity or R_i is so massive that N_i pales in comparison to it, to the extent that in terms of spatial distance N_i is pretty much "not visible" when compared to R_i. and the decimal expansion of pi continues to that R_i. note that after  N_i, rational numbers no longer exist, so the conclusion "irrational pi is the sum of rationals" is not true because after that point in the series, we encounter irrationals. so the meaning of "..." in the series is very tricky. in other words, the formula is true and not true but since that is never a good way of stating anything, let us just say that the formula is true but it cannot be computed nor its sum be written. let's try once more: the formula is true because it describes the visible (rational) portion of pi and describes the invisible portion (the irrational part) by "..." the formula is not true because it does not tell us how to compute the invisible or irrational portion, that is the "..." portion. now i am sure you will not accept "pi = ..." for a formula but that is exactly what this formula is doing.

 

wait, how can there be two infinities?

see, if you accept that at the speed of light or singularity, the beginning and end of the universe is one event and that space does not exist and that all laws of nature break down, then you should accept this also. the universe and mind are scary but they are also hilarious. it is your attitude that determines if you find these truths funny or vertigo inducing.

 

ok, what determines one's attitude? does it too have a formula? maybe i can change it.

your attitude is a function of, or is determined by pi. since you know its formula, you can now change it.

 

isn't math weird?

not really because even human language is weird. the counterpart of pi in language is the liar's paradox -- "i am lying said the liar." godel proved this equivalence. so if you think language is not weird, then neither is math. 

 

what about the links i gave?

everything stated in the links is true. yet they do not contradict anything i just said.

 

 

 

 

 

 

 

[[Lo...]]

 

Kate Bush - "Pi"

 

 

Sweet and gentle sensitive man

With an obsessive nature and deep fascination

For numbers

And a complete infatuation with the calculation

Of PI

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

 

3.1415926535 897932

3846 264 338 3279

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

But he must, he must, he must

Put a number to it

 

50288419 716939937510

582319749 44 59230781

6406286208 821 4808651 32

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

 

82306647 0938446095 505 8223...

[Guest [Kp...]]

 

Kate Bush - "Pi"

 

 

Sweet and gentle sensitive man

With an obsessive nature and deep fascination

For numbers

And a complete infatuation with the calculation

Of PI

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

 

3.1415926535 897932

3846 264 338 3279

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

But he must, he must, he must

Put a number to it

 

50288419 716939937510

582319749 44 59230781

6406286208 821 4808651 32

 

Oh he love, he love, he love

He does love his numbers

And they run, they run, they run him

In a great big circle

In a circle of infinity

 

82306647 0938446095 505 8223...

 

:laugh: :laugh: you crack me up! you made my weekend. bye... i got to forget all this else i'll ruin the day.

 

edit. i've never heard this song. the lyrics are awesome. let me listen to the song and google kate. thanks!

[Guest [Kp...]]

I always liked math, but ended up working on programming projects where advanced knowledge of math wasn't required, so yes, I am in the same boat as far as the ability to solve problems.

 

count me in the same boat lorazepam! pascal was the first language i was taught in comp. sci. in school. that was 1989. i loved pascal. pascal was never meant to be used commercially and its intended purpose was its use as an educational language to introduce data structures to students. but now kids get exposed to programming much earlier in life, so pascal has lost its relevance. my kids were taught blue java, i think, in school, when they were maybe 10! so they don't need to learn pascal. also many new, better languages have been developed in the interim.

 

yes, comp. sci. does not require much math knowledge. i agree with you. i have a friend who spent his life lecturing in various universities in india and US. he holds a double phd in comp. sci. and electrical engineering. when i was confused with cantor, a few days ago, i ran to him. he told me in no uncertain terms that he was not a phd in math and that he was as much a novice in number theory as i was. for comp. sci., he said, he needed mostly predicate calculus and not number theory.  it then took me a good number of days to understand these concepts on my own. and i have only scratched the surface!

[Guest [ba...]]

I also took a course in Pascal - at Cal Davis back in around 1982 or 83, I think.  We had a 16k Apple II computer (upgraded to 48k) that we used for DNA cloning and sequencing analysis, and we had a Pascal compiler for that computer.  Researchers actually wrote DNA software using Pascal, and we could (and did) freely modify it.  Very interesting times.  I enjoyed writing 'screensavers' that generated geometrical shapes (kind of like a spirograph does).  I'd stare at them for hours at night (probably explains my insomnia today). 

[[Lo...]]

I always liked math, but ended up working on programming projects where advanced knowledge of math wasn't required, so yes, I am in the same boat as far as the ability to solve problems.

 

count me in the sane boat lorazepam! pascal was the first language i was taught in comp. sci. in school. that was 1989. i loved pascal. pascal was never meant to be used commercially and its intended purpose was its use as an educational language to introduce data structures to students. but now kids get exposed to programming much earlier in life, so pascal has lost its relevance. my kids were taught blue java, i think, in school, when they were maybe 10! so they don't need to learn pascal. also many new, better languages have been developed in the interim.

 

yes, comp. sci. does not require much math knowledge. i agree with you. i have a friend who spent his life lecturing in various universities in india and US. he holds a double phd in comp. sci. and electrical engineering. when i was confused with cantor, a few days ago, i ran to him. he told me in no uncertain terms that he was not a phd in math and that he was as much a novice in number theory as i was. for comp. sci., he said, he needed mostly predicate calculus and not number theory.  it then took me a good number of days to understand these concepts on my own. and i have just scratched the surface!

 

I think I really first started with BASIC, as so many do. Then in high school we had courses in BASIC, Pascal and later Fortran, which I never used. Then going to college, the introductory course was Pascal, then C, then C++. Then I also learned COBOL as well, which actually ended up being very handy (knowing legacy and new languages was a big asset to my career for a long time). But I really liked when Borland created Delphi, and I remember working with Visual Basic and SQL Server, and playing around with Delphi and realizing how much more evolved and elegant programming platform was than either Microsoft Visual Basic of MS Visual C++ MFC and ATL. But companies used to stick with Microsoft because "no manager ever got fired for buying Microsoft". So anyway. I transitioned from Visual Basic to VB.Net, which really was a totally different language. Of course, I learned some html and vbscript and ASP and javascript on the way too. Then I had some interesting experiences, working on languages such as PowerBuilder and Visual FoxPro. PowerBuilder was unique and interesting, but I never liked Visual FoxPro much. Then, of course, the unavoidable MS Access and more .NET (VB.NET and ASP.NET). My .Net knowledge got really good in the 00's and had switched to working on C# around 2010. Also had a chance to work on Oracle DB with PL/SQL for a year or so. After that, it was back to ASP.NET, VB.NET and SQL Server again.

 

Honestly, I'll always love Pascal/Delphi. I know that Pascal has sort of been thought of as a university language and not meant for writing commercial code, Borland's Delphi had lots going for it, and a lot of Microsoft .Net programming technology was built by ex-Borland engineers (Anders Hejlsberg comes to mind). And it's amazing how much Oracle's PL/SQL borrows from Pascal in terms of creating units with interface and implementation section.

 

I actually thought that the whole Microsoft COM interface borrowed heavily from Pascal/Delphi, PowerBuilder.

 

Even though being a Visual Basic programmer in the 90's paid decent, it never ceases to amaze me how there were so much better rapid development languages available that companies were afraid to purchase. But then again, Microsoft was not going anywhere, so there was that safety.

 

I keep looking back at my career choices, and wonder what would have happened if I ditched Microsoft and just went to work on Oracle and PL/SQL. It would have been lot less stressful, as the platform doesn't change as much, and it would have given me more time for personal life aside from work, rather than learning every new Microsoft's iteration and permutation of everything.....

 

[Guest [Kp...]]

occam's razor says it is futile to do with more things that which can be done with fewer, which means that i should shut up now because i have said all that is relevant. cantor, godel, turing, church, mises used the occam's razor in their proofs. but i am not as brilliant as them. i am a layman who gets easily excited and it is my wont to act as a layman:

 

so it is possible that when we reach the string level (the putative end), we will find we need further magnification, equivalent to the work of the last few hundred years of mathematicians & physicists, to reach the real end.

 

and at the real end... (you can now understand what "..." denotes)

 

so what is happening here? infinite recursion is happening. that is it! "now" i know the secret of the universe or the sum of the pi series. the sum is infinite recursion. then outis comes and tells me that he can create an infinite, self reflexive series to define 2. so is 2 the secret of the universe? i realize that 2 cannot be the secret so i search for an additional qualifier to distinguish this phenomena from 2... till i wake up to the reality that i am trying to define something which, by definition, is not definable! the problem is with our definition of real numbers -- the definition is that all this should happen. the problem is that there is no other way to define real numbers. and i knew this, yet i had forgotten it. so what is happening is that i keep forgetting. i keep getting tempted. physics keeps going forward. but is it really going any forward?

 

aside: this sounds a lot like fractals and the mandelbrot set doesn't it? the problem is that the moment i say it sounds like the mandelbrot set, i am trying to define pi -- which is not possible. this is what i mean by "temptation." the mandelbrot set is countable; irrational numbers are not.

 

so is it that physics is never going forwards because there is no end?

 

i don't know because i don't know if there is an end -- maybe string theory is the end. but i do know that if we reach the end then we will have the mathematical equations to "create consciousness," or, at the very least, "understand consciousness." but i do not know if the universe is countable or uncountable -- not that it matters. but i know that science never gives up. hawking isn't giving up. if hawking isn't giving up, who am i to accept defeat? i have to fully trust his wisdom, knowledge and optimism.

 

so what is the solution?

 

i don't know. maybe we need a new math that is "complete" and not based on peano axioms to describe (map) nature at the sub quantum level -- i really don't know. the math probably has to be "consistent" too. a "complete" math will have no irrationals. godel showed us all this.

 

 

[Guest [Kp...]]

I think I really first started with BASIC, as so many do. Then in high school we had courses in BASIC, Pascal and later Fortran, which I never used. Then going to college, the introductory course was Pascal, then C, then C++.

 

my story is the exact same. i too loved pascal. i thought pascal was much like the syntax of human language. then i had to learn lisp. lisp was so hard -- too many recursive elements. ironically lisp was invented for AI so logically it ought to resemble human language more. but i never felt so. it makes sense because math resembles human language closely, but how many great writers love math or how many mathematicians write great?

[[Rr...]]

Lorazepamfree, I am on the same dose of Metoprolol.  How about some fun easy math? 

[[Lo...]]

Ok

 

5! = 5 * 4 * 3 * 2 * 1 = 120

 

5!! = 5 * 3 * 1 = 15

[[Lo...]]

x + y^2  = 25

x = 5

 

y^2 = 25 - x

y^2 = 20

y = sqrt(20)

 

y approx. 4.47

[[Rr...]]

Thanks.  Hi there kpin99. 

[Guest [Kp...]]

Thanks.  Hi there kpin99.

 

:laugh:

 

 

[[Lo...]]

Calculate the sum of numbers from 1 to 100:

 

100

99 + 1 = 100

98 + 2 = 100

97 + 3 = 100

....

85 + 15 = 100

51 + 49 = 100

50

 

So, there are 49 pairs and each equals 100, meaning that 49 * 100 = 4900

then add 100

then add 50

4900 + 100 + 50 = 5050

 

[[Lo...]]

A day in a life of a mathematics student:

 

Day 1: 12x12 = 144

Day 2: takes a 1mg ativan: 12x12 = 144

Day 3: takes a 1mg ativan: 12x12 = hmm, wait 12x10 = 120 and then add 12x2 = 24. It's 144

Day 3: takes a 1mg ativan: 12x12 = Oh, I can't do this. What's the point? 12x12 = Blood pressure goes up. It's 100 and something. Isn't that good enough

Day 4: takes a 1mg ativan: 12x12 = ? panic sets in.

Hello, advice nurse? 

Are you having symptoms of chest pain?

Shortness of breath?

No, but when I try to multiply 12x12, my blood pressure goes up

So, how much is it?

144/100

That's not too bad

But why is my pulse 150?

Oh, we recommend you get the immediate medical attention

"Must relax, 2 + 2 = 4, 2 + 2 = 4, 2 + 2 = 4"

Pulse down to 145

Stops taking ativan, goes to ER

"1mg Ativan adminstered, with an advice. Why don't you go home, have a nice burger, and keep solving more math problems. It will bring the anxiety down"

 

 

At home: no ativan

day 1: 12 x 12 = ??

day 2-7, stays in bed

day 8, 12 x 12 = 144, yay! what just happened to me?

 

Ativan: "when your math skills get good, it's the only way to prevent that from happening"