Mathematics Thread

[Soloman Tump]

 

theres a book "chaos theory" by james gleick that goes into feigenbaum constants, not too many equations and stuff in it, more like a look at how things in the maths community evolved from when these things were discovered and how they came into the mainstream and talks about the people behind them. rly good read. i think a paper titled "period three implies chaos" by yorke and li touches on it, cant remem tho

 

 

This, together with "Universality" by Mark Ward were the books that got me hooked on fractals and chaos theory.

 

My masters degree project was on space/time intermittency, so turbulent flow along a hose, the onset of chaotic behaviour, percolation limits.  All great stuff.  I carried on my research well after graduation and kept in touch with my tutor for a while, but I feel that I have forgotten a lot of it now.

 

Couple map lattices ftw:-

 

[Guest]

The basic problem is that it's a divergent series so it does not have any definite sum since it does not converge toward any value.

 

For convergence you should be able to pick a value arbitrary close to -1/12 so that a finite subsum of the series 1+2+3+4+...would be closer to than the picked value and then adding any amount of values from the rest of the series wouldn't move the sum further away from.

 

So, let's see the series 1/2+1/4+1/8+1/16+...=1: We can pick a value arbitrary close to 1, like 0.99. There's now a finite subsum 1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128 that is closer to 1 than 0.99 and adding up values from the rest of the series to that, for example 127/128+1/256+1/512=511/512, will only get us closer to 1.

 

Going back to the original series in question, I should be able to pick a value like 0 that is 1/12 away from the -1/12. Now how do I pick a finite subsum of 1+2+3+4+.. that is closer than 0 to -1/12? Any finite subsum like 1+4+6=10 or 1+2+3+..+100=5050 is higher than 0 and definitely further away from -1/12 than 0. Adding any number of values from the rest of the series is going to move the sum even further away from it. The series does not converge towards -1/12 or any other value.

I completely understand this reasoning. By all means the result should be divergent, but the fun trickery presented, in more than one way, into getting -1/12 is too amusing to ignore despite how illogical it seems! I'm too ignorant to profess some deeper work happening, but -1/12 being applied in quantum physics gives the result SOME clout, doesn't it?

Edited June 28, 2018 by Guest

[cruising for burgers]

Edited June 28, 2018 by THIS IS MICHAEL JACKSON

[zkom]

 

The basic problem is that it's a divergent series so it does not have any definite sum since it does not converge toward any value.

 

For convergence you should be able to pick a value arbitrary close to -1/12 so that a finite subsum of the series 1+2+3+4+...would be closer to than the picked value and then adding any amount of values from the rest of the series wouldn't move the sum further away from.

 

So, let's see the series 1/2+1/4+1/8+1/16+...=1: We can pick a value arbitrary close to 1, like 0.99. There's now a finite subsum 1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128 that is closer to 1 than 0.99 and adding up values from the rest of the series to that, for example 127/128+1/256+1/512=511/512, will only get us closer to 1.

 

Going back to the original series in question, I should be able to pick a value like 0 that is 1/12 away from the -1/12. Now how do I pick a finite subsum of 1+2+3+4+.. that is closer than 0 to -1/12? Any finite subsum like 1+4+6=10 or 1+2+3+..+100=5050 is higher than 0 and definitely further away from -1/12 than 0. Adding any number of values from the rest of the series is going to move the sum even further away from it. The series does not converge towards -1/12 or any other value.

I completely understand this reasoning. By all means the result should be divergent, but the fun trickery presented, in more than one way, into getting -1/12 is too amusing to ignore despite how illogical it seems! I'm too ignorant to profess some deeper work happening, but -1/12 being applied in quantum physics gives the result SOME clout, doesn't it?

 

 

Well, in pure mathematical sense it's still provably wrong. You need a particular physical model and twist it a bit to get that particular result.

 

There are more common cases where the strict mathematical definition is not used in real life problems. For example in mathematics 0^0 is undefined, but sometimes in engineering and physics it's defined as 0 or 1 depending on what's practical. But mathematically 0^0 is still strictly undefined.

[mcbpete]

0^0 == ascii owl looks up.

[Guest]

 

 

The basic problem is that it's a divergent series so it does not have any definite sum since it does not converge toward any value.

 

For convergence you should be able to pick a value arbitrary close to -1/12 so that a finite subsum of the series 1+2+3+4+...would be closer to than the picked value and then adding any amount of values from the rest of the series wouldn't move the sum further away from.

 

So, let's see the series 1/2+1/4+1/8+1/16+...=1: We can pick a value arbitrary close to 1, like 0.99. There's now a finite subsum 1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128 that is closer to 1 than 0.99 and adding up values from the rest of the series to that, for example 127/128+1/256+1/512=511/512, will only get us closer to 1.

 

Going back to the original series in question, I should be able to pick a value like 0 that is 1/12 away from the -1/12. Now how do I pick a finite subsum of 1+2+3+4+.. that is closer than 0 to -1/12? Any finite subsum like 1+4+6=10 or 1+2+3+..+100=5050 is higher than 0 and definitely further away from -1/12 than 0. Adding any number of values from the rest of the series is going to move the sum even further away from it. The series does not converge towards -1/12 or any other value.

I completely understand this reasoning. By all means the result should be divergent, but the fun trickery presented, in more than one way, into getting -1/12 is too amusing to ignore despite how illogical it seems! I'm too ignorant to profess some deeper work happening, but -1/12 being applied in quantum physics gives the result SOME clout, doesn't it?

 

 

Well, in pure mathematical sense it's still provably wrong. You need a particular physical model and twist it a bit to get that particular result.

 

There are more common cases where the strict mathematical definition is not used in real life problems. For example in mathematics 0^0 is undefined, but sometimes in engineering and physics it's defined as 0 or 1 depending on what's practical. But mathematically 0^0 is still strictly undefined.

 

 

Interesting, what examples are there where 0^0 would be 0 or 1?

[auxien]

http://www.thisiscolossal.com/2018/07/kinetic-sculpture-based-on-the-fibonacci-sequence

 

[zkom]

Interesting, what examples are there where 0^0 would be 0 or 1?

 

Well, generally speaking, if you consider a continuous real-valued functions like 0^x and x^0 and their limits at x=0, you would get either 0 (0^x) or 1 (x^0). So basically in the case of continuous real function the value is usually considered as the limit of the function at 0^0. So for example if you had a real valued function (2x)^(3x) the limit at x=0 would be 1 so an engineer would probably use that value.

 

In discrete mathematics it often makes more sense to value it as 1. If you consider that 5^0=1 because 5^n = 1*5*..*5 where the number of 5s in the multiplication is n, and then 5^0 = 1 because there are no 5s. Then 0^n = 1*0*..*0 and 0^0=1.

 

On the other hand if you have a system that has m parts that have n possible states each, the total number of possible states would be n^m. If every part has 0 (n=0) possible states then 0 parts (m=0) would have still have 0 possible states and m^n=0^0=0, unless.. you consider the stateless state a state.

 

Quickly checking.. Google gives 0^0=1. Python gives 0**0=1, also math.pow(0,0)=1. Chrome JavaScript console gives 0**0=1. WolframAlpha, which is more "orthodox" gives "undefined". So, maybe 1 is the most common value in programming languages.

 

tl;dr: Whatever makes the most sense in the given use case.

Edited July 4, 2018 by mokz

[Guest]

 

Interesting, what examples are there where 0^0 would be 0 or 1?

 

Well, generally speaking, if you consider a continuous real-valued functions like 0^x and x^0 and their limits at x=0, you would get either 0 (0^x) or 1 (x^0). So basically in the case of continuous real function the value is usually considered as the limit of the function at 0^0. So for example if you had a real valued function (2x)^(3x) the limit at x=0 would be 1 so an engineer would probably use that value.

 

In discrete mathematics it often makes more sense to value it as 1. If you consider that 5^0=1 because 5^n = 1*5*..*5 where the number of 5s in the multiplication is n, and then 5^0 = 1 because there are no 5s. Then 0^n = 1*0*..*0 and 0^0=1.

 

On the other hand if you have a system that has m parts that have n possible states each, the total number of possible states would be n^m. If every part has 0 (n=0) possible states then 0 parts (m=0) would have still have 0 possible states and m^n=0^0=0, unless.. you consider the stateless state a state.

 

Quickly checking.. Google gives 0^0=1. Python gives 0**0=1, also math.pow(0,0)=1. Chrome JavaScript console gives 0**0=1. WolframAlpha, which is more "orthodox" gives "undefined". So, maybe 1 is the most common value in programming languages.

 

tl;dr: Whatever makes the most sense in the given use case.

 

Cool, thanks for the insight!

 

On the 'stateless state a state' bit, it would seem to keep in line with 0! = 1! as well.

[usagi]

2 + 2 is 4

-1 that's 3

quick mafs

[Soloman Tump]

This was a numbers quiz I put in Snare/Rush zine #3

 

If anyone can come up with the correct answer, you win a lollypop

 

 

Put a number to each letter!

Do some maths with the numbers!
Get the answer and receive enlightenment by the achievement!

1. Number of circles of Winnipeg according to Aaron Funk

2. -ism, BOC

3. Cylobs music system #

4. John Peel acquired number of headaches from Autechre

5. Number of men in the Hellfish sonic attack force

6. Monkeytown sublabel was a quantity of weapons

7. Ufabulum opening track

8. Debut album by woob

9. The unilaterally agreed BPM of all dubstep

10. The year Tresor Records was founded

11. Number of Analord records

12. Kieren Hebden

G - J  - L = O

A * K * F = L

(I * D) = M         

(ed: sorry, couldn’t resist….)

B * ( C - E - H) = N

L + O - M - N = ……………??

[auxien]

^that looks fun but I don't know near enough IDM lore to answer it

 

Here to post this: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

[luke viia]

^that looks fun but I don't know near enough IDM lore to answer it

 

Here to post this: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

Thanks for posting this!

[EdamAnchorman]

^that looks fun but I don't know near enough IDM lore to answer it

 

Here to post this: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

Just biked in here to post this but was beaten to it. I wish I understood this stuff but it really seems logical that a math that describes everything should really be more simple than complex...

[Candiru]

I pretend to be blue collar, but solve highly advanced equations when the mood strikes me. When I reveal my true intellect, people call me to set up meetings and fawn over me and ask me to work in clandestine government think tanks. I turn down the offers because I need to be challenged. I've never even used a calculator. I've never failed to distinguish Coke from Pepsi and I can roll burritos in origami shapes that illustrate how to solve the crisis in the middle east. I've taken apart my car on the side of the highway fast enough to lose the cops during a chase, and then put it back together in time to escape. I once had to emergency land a commercial passenger jet on a sandbar in French Polynesia while a mother gave birth to twins onboard. They were both named after me and I'm paying their college tuition with everything I made selling meth in a Hell's Angels bar in Missouri while evading FBI surveillance. I once debated a Branch Davidian type cult and made them all atheists, while simultaneously convincing them that Santa Clause exists and is actually Samoan. Math is boring.

[YangYing]

I pretend to be blue collar, but solve highly advanced equations when the mood strikes me. When I reveal my true intellect, people call me to set up meetings and fawn over me and ask me to work in clandestine government think tanks. I turn down the offers because I need to be challenged. I've never even used a calculator. I've never failed to distinguish Coke from Pepsi and I can roll burritos in origami shapes that illustrate how to solve the crisis in the middle east. I've taken apart my car on the side of the highway fast enough to lose the cops during a chase, and then put it back together in time to escape. I once had to emergency land a commercial passenger jet on a sandbar in French Polynesia while a mother gave birth to twins onboard. They were both named after me and I'm paying their college tuition with everything I made selling meth in a Hell's Angels bar in Missouri while evading FBI surveillance. I once debated a Branch Davidian type cult and made them all atheists, while simultaneously convincing them that Santa Clause exists and is actually Samoan. Math is boring.

who's stronger? candiru or µ--ziq?

[auxien]

 

 

 

^that looks fun but I don't know near enough IDM lore to answer it

 

Here to post this: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

Thanks for posting this!

For sure :)

 

Just biked in here to post this but was beaten to it. I wish I understood this stuff but it really seems logical that a math that describes everything should really be more simple than complex...

I definitely can see that argument. But the article rings true in its own way: to describe higher dimensional behavior accurately, one may need math that operates in higher dimensions. Makes perfect sense...but also, they did point out that they think some alternate version of the octonions (or some bridging maths? I forget) may ultimately be the key that gets them there. Anyway, I just mention that because it's still in relation to the more normal numbers and maths, it's not like anything they're talking about would negate the maths that have gotten physics to where it is, but it may be necessary to jump the gap into string theory level shit, describing the complexities of subatomic particle interaction and such. Physicists have been working at that for fucking decades and still haven't broken through in the ways they know they need to, not because they're not all very intelligent and creative and great at what they do, but they've just been ignoring those tools of octonions (or whatever else). ^total layman's speculation

 

I don't understand the stuff beyond complex numbers, but I assume it takes some getting used to. Had a class that we briefly touched on quaternions in, but I didn't put the time in to begin to grasp it (though the concept is simple enough). What I'm trying to say is I'm sure you could understand it if you wanted, all the examples they're giving it just sounds like they're not doing much more complex than algebra, but just with the different number classes and some altered rules. I didn't look into the videos referenced in the article, did anyone check them out?

[jaderpansen]

got a B on recent CS math test because i identified 0 as a root with a multiplicity 1 instead of 2 ((x-0)² anyone? duh) in the characteristic polynomial of the homogenous solution of a 2nd order partial differential equation and now i feel like a complete failure . i know it's first world prob material par excellence but i'm seriously bummed out i missed a perfect grade because of such a stupid and unnecessary mistake.

at least i still know how to calculate the average score i'd need in the next 24 tests to overall get under 1.3, which i'd need for an honorary degree: 1.22174. whatever, not gonna make it anyway, too many subjects i'm not super fond of, like software engineering and business studies.

blah.

i enjoy uni math, especially the discrete variety, abstract algebra, number theory... and stochastics. my last grade in high school was a straight F, then i dropped out. it's fascinating how much just depends on intrinsic motivation and practice, math is kinda like sports, non? i used to think my brain just wasn't made for it or whatever.

[usagi]

same, I also enjoyed discrete at uni, as well as statistics. it was the first time I felt like I was really getting "good" at math, I'd always been disinclined toward it in high school and started to think I was just congenitally bad at it.

[EdamAnchorman]

I wish I was better at math, it would make me much more valuable at my job.  Don't get me wrong, I bring a lot to the table (niche measurement scientist), but I have a gigantic dataset from a recent study and I'm having to rely on unreliable data scientists to process everything when I just want to get in there and do the dirty work myself, but lack the skills.

I bought myself Tukey's Exploratory Data Analysis book for Xmas and am going to try to learn as much as I can.

[iococoi]

46 minutes ago, randomsummer said:

Tukey's Exploratory Data Analysis

phunny.. i´m just going through Visualizing Data and The Elements of Graphing Data, both by Cleveland

lol

otherwise

Quote

Everything counts in large amounts

btw.

Quote

It's a competitive world

 

[usagi]

y'all use R or what?

[EdamAnchorman]

2 hours ago, usagi said:

y'all use R or what?

I'm trying to learn Python.  I love to code, since my brain is very logic-based, but I hate learning syntax.

[Freak of the week]

nice logic workoutKoshelevKreinovich-FUZZY INTERPRETATION OF QUANTUM MECHANICS MADE MORE CONVINCING_ EVERY STATEMENT WITH REAL NUMBERS CAN BE REFORMULATED IN LOGICAL TERMS.pdf

[zazen]

Profile of Yitang Zhang

https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

Quote

“No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game,” Hardy wrote. He also wrote, “I do not know of an instance of a major mathematical advance initiated by a man past fifty.”

He has a talent for long, deep thinking.

At 58 (in 2013) he published groundbreaking stuff on bound gaps ("there are infinitely many pairs of prime numbers that differ by less than 70 million")

In November (at 67) he announced he had achieved the solution to the Landau-Siegel zeros conjecture, which caused quite a buzz because it relates to the Riemann hypothesis, one of the most important unsolved problems in Maths. People are still picking through the 111 page proof so its still up in the air at the moment

Edited January 5, 2023 by zazen