I'm Heart, your friendly neighbourhood admin!

[Kelly]

Congratulatons, Heart!

[Kelly]

[Calligraphette_Coe]

I used to like to drive myself crazy with one called Laplace's Demon. Someone eventually disproved it as a possibility because the amount of data needed to be processed by even a computer that could process operations at the speed of a Planck length would take more time than has elapsed in the universe so far. In essence, you couldn't run the simulation.

And that led to another profound quote about simulacra and simulation:

The simulacrum is never that which conceals the truth—it is the truth which conceals that there is none. The simulacrum is true

I sometimes think that applies to gender, too. And that you Heisenberg it when you try too simulate it with any kind of precision.

[Heart]

So true! Gender really does follow a certain uncertainty law, doesn't it? If you try to measure where it is too precisely, you loose track of where you're going... The best thing is to only ever squint at gender, eh? ;)

And thanks Kelly for the cartoon! My labmates gave a look when I laughed out loud while eating my lunch here :P

It's good to see you back around here, to both Kelly and Calli ^_^

[Dodecahedron314]

I had to Wikipedia both of these things because I couldn't remember them off the top of my head, and I'm glad I did.

I just looked this up, and I have to say that I find this image from the Wikipedia article for Maxwell's Demon inordinately amusing:

I used to like to drive myself crazy with one called Laplace's Demon. Someone eventually disproved it as a possibility because the amount of data needed to be processed by even a computer that could process operations at the speed of a Planck length would take more time than has elapsed in the universe so far. In essence, you couldn't run the simulation.

And that led to another profound quote about simulacra and simulation:

The simulacrum is never that which conceals the truth—it is the truth which conceals that there is none. The simulacrum is true

I sometimes think that applies to gender, too. And that you Heisenberg it when you try too simulate it with any kind of precision.

Computational power of the entire universe? Now that's a mind-blowing thing I'd never thought of. Although I suppose it makes sense, in a way--we can calculate objective trajectories of particles and atoms as much as we want, but in a universe with things as complex and abstract and messy as gender, I don't know that there's any way to really, truly understand those things in the same completely and utterly logical way. It's digital versus analog--no matter how many data points you have, you'll never be able to say with absolute 100% precision that you've got a continuous function just by connecting the dots. Music in bits versus magnetic tape--sure, one can be analyzed down to its tiniest component by working directly with its data, but the other has a very distinctive timbre that it may well be impossible to recreate digitally, and isn't that really the essence of music in a way? The intangible color that suffuses the sound? Or is it really all just down to strictly notes and their frequencies? What of musical emotion?

Sometimes I wonder if AIs would have genders, or if aliens who reproduce by cloning or some other means would. It all eventually comes back to the question of what even any of this gender stuff is, anyway. I'm pretty sure I personally will most likely never understand it, and I'm not sure humanity as a whole ever will either. But then, the same thing has been said of many, many things, the study of a great number of which is considered old hat by now, so who knows? The Laplace's Demon of a universe with infinite computational power, perhaps, but even about that I have my doubts.

...aaaand I think it's clear from all this rambling that it's far too late for me to be on AVEN, especially with a math pset for tomorrow and a physics pset for the day after. Get back to work and then go to sleep, Dodec :P

[Heart]

Good luck on your math and physics dodec!! What's a psec by the way? I assume it's some kind of test, and it is in fact midterm season in North America, so perhaps it is like a midterm?

Anyways, I want to pop in and say that there are those who believe that the universe IS a giant computer, where "reality" is just the result of computations and every single particle is just a piece of information, like a bit from your classic desktop computer. What we perceive and measure is simply the results of that computation, the entirety of reality is simply one big computation.

And they're not necessarily wrong either. The argument is based in sound logic and physics. One day, if you feel like going down a wormhole of awesome and have time on your hands, try looking up "holographic universe" and see where you get ;) Information theory is fascinating in its own right. The wikipedia article is pretty good, but in typical wiki style, very complex and not necessarily beginner-friendly. But it's a starting point to get you on the right track

[Dodecahedron314]

Good luck on your math and physics dodec!! What's a psec by the way? I assume it's some kind of test, and it is in fact midterm season in North America, so perhaps it is like a midterm?

Anyways, I want to pop in and say that there are those who believe that the universe IS a giant computer, where "reality" is just the result of computations and every single particle is just a piece of information, like a bit from your classic desktop computer. What we perceive and measure is simply the results of that computation, the entirety of reality is simply one big computation.

And they're not necessarily wrong either. The argument is based in sound logic and physics. One day, if you feel like going down a wormhole of awesome and have time on your hands, try looking up "holographic universe" and see where you get ;) Information theory is fascinating in its own right. The wikipedia article is pretty good, but in typical wiki style, very complex and not necessarily beginner-friendly. But it's a starting point to get you on the right track

Pset is just short for problem set (homework). It is indeed midterm season though...at my school, midterms basically last all the way through finals because professors just schedule everything whenever they want :p

The holographic universe idea is really cool--my aunt gave me a book about it a couple of years ago, and even though I never managed to finish it before high school and college put an effective end to my pleasure reading, I still definitely got through enough of it to see just how amazing it is, and how deep the implications can be. I was hoping to get an internship at Fermilab to work on the Holometer over the summer, but the application deadline for that already passed and my university's job application platform has a bunch of requirements that it's really easy to forget about until you're already in the middle of trying to apply for something...and they don't actually tell you what they are unless you go to the career advancement office and ask. :/ Hopefully I'll be able to get some funding for a few other opportunities I'm looking into, though. One way or another, I WILL spend this summer sciencing or mathing. :p

[Heart]

Yeah, it took me a few summers in my undergrad too to untangle the process for applying to a summer research program. The process in Canada's a bit different, but equally confusing :P Governments, eh?

Don't be hard on yourself. What I do is write down the deadlines in a calendar somewhere that I keep for the next year. Every year, the deadlines seem to usually be the same or similar, so it gives you a "head start" on next year. If you know when the deadline was this year, write it down somewhere you'll still have it next year, so that'll be a reminder that it's coming up. With that note, you can also include things like the requirements and such.

Google calendars is a good place for that too, because you can just go ahead and put it in for next year. I used to put it in a month before the actual predicted deadline, just in case it changed a bit or I needed time to gather the required materials ;)

But you can still email professors directly, it's never too late to try that. The internet is a great place for that! Every researcher will have some kind of website describing what they do, so choose someone that's doing something you think you'd be interested in, and fire off an email. I know it's intimidating, but that's the only way I've ever gotten a science job :P It never hurts to try!

[Calligraphette_Coe]

So true! Gender really does follow a certain uncertainty law, doesn't it? If you try to measure where it is too precisely, you loose track of where you're going... The best thing is to only ever squint at gender, eh? ;)

And thanks Kelly for the cartoon! My labmates gave a look when I laughed out loud while eating my lunch here :P

It's good to see you back around here, to both Kelly and Calli ^_^

Awww, thanks for the thought, Heart. It's been a bad winter, and these last few days felt like Groundhog Day for me. I came out of hibernation, poked my head out of the burrow, and am still trying to decide between Spring or Six More Weeks. I want to be humming The Beatles' "Here Comes the Sun", but then I get to work and go all facepalm at my desk when a procession of managers rain on my parade with the latest list of Missions Impossible, and I get to thinking of the lyrics of Monty Python's 'Galaxy Song', instead.

So I just engage my Androgyny Cloaking Device, and keep moving around in the CisGender Neutral Zone.

I think that's what I like about the Universe... it has some duality, but it's open to being somewhat androgynous itself. And it defies being defined and labelled with a most mysteriously wonderful aplomb.

[Heart]

The shades of grey are what make life interesting ;) I find myself the most engaged when exploring the grey zones, in just about every aspect of life, be it gender or debate or politics, or even a particle's position and momentum. No wonder I'm a physicist; it's practically my job to investigate the few remaining grey areas we don't already know everything about in nature!

Edit: The pun on the movie/book title escaped me when I wrote that... for reference, there are far more than 50 of them, and I was not intentionally referring to that :P

It truly is good to have you back. Life sometimes gives us lemons, but that's part of life. It's good to hear you're doing better now though

[Kelly]

[Heart]

Once again, Kelly, you are responsible for making me laugh out loud in my lab! My labmates must be getting used to it by now; they don't even look over any more :P ;)

[Kelly]

What is not to love about the Riemann Zeta function?

Let's get nerdy.

Math Music

For fun, we can play some notes and make some chords and see what we get.

Since we like the Riemann Hypothesis here, we can play the non-trivial zeros of the Riemann Zeta function.

As we know, they all have real part equal to one half, and the imaginary parts are seemingly randomly spaced. For instance, the first five above the real axis are located here:

½ + i14.134725142
½ + i21.022039639
½ + i25.010857580
½ + i30.424876126
½ + i32.935061588

And they are also in the same places below the real axis.

So, how do we play one of these? Here is an idea. We can take one of these values (and their complex conjugates; we can call a value "rho" for short) and then, for all values x, plot:



"N" stands for note. The above looks easy to play, but it is somewhat tricky, but I can teach you how to do so in the spoiler.

Since each value has a complex conjugate, we add them, and that actually makes it easier. We have:



And that equals:



Where a is the real part, b is the imaginary part, and theta is the angle of the complex number. And, since the real part is always ½, we have:

So, let us play the first note (for rho = ½ + i14.134725142).

For x = 0 to 20, we have:



We have a cyclical signal that gets gradually louder and lower in frequency as x increases.

Let us try another one. This time, the fifth (for rho = ½ + i32.935061588):



It has a similar behavior, but the amplitude is lower and the frequency is higher, like an overtone.

We can make chords and such. First, an interval (an interval is two notes played together). Playing the first and fifth notes gives us:



We see that sometimes they make the signal louder, and other places, they interfere, as we expect. Further, we can see that the shape stays the same. The pattern continues, so the three bumpy peaks in a row look like the next three bumpy peaks in a row. We have a sound.

This is fun. Now, I wat to get real loud. I will play the first one hundred notes all together, and see what that chord looks like.

We have:



Interesting. We have a sort of saw tooth wave. My MiniMoog has a saw tooth waver generator. It sounds cool.

We see that the saw changes very quickly and with big values at 2, 3, 5, 7, 11, 13, 17, 19, and 23, and smaller changes at 4, 8, 9, 16, and 25.

Hold it. The big changes occur at prime numbers. Powers of primes create smaller changes.

And it looks as though the values got through zero right at the primes (and some prime powers).

Very interesting. It looks as though the Riemann Zeta zeros, although seemingly randomly distributed, clearly encode the prime numbers. Add them up in this manner and they always go to zero when x = a prime number (and sometimes a prime power).

The big thumps in the music of the Riemann zeros are all from primes. The orchestra of Riemann zeros "sounds" like primes.

And we clearly have a way to generate prime numbers and prime powers directly from the Riemann Zeta Function. Prime numbers are encoded in the Zeta function.

Fascinating, yes? :)

[Starry Sky]

My brain hurts... I don't understand this language you speak. I'm fascinated by how much you know, Kelly.

[Kelly]

There is a follow-up on the big Riemann zeta chord that gives the jumps at prime numbers. And that introduces the Von Mangoldt function and the Chebyshev function.

More geekiness:

The Von Mangoldt function, denoted by Λ(n), is defined as:



So, the first eleven positive integers give:

0, ln(2), ln(3), ln(2), ln (5), 0, ln(7), ln(2), ln(3), 0, ln(11)

Once can add them up, and that is known as the Chebyshev function:



So, the Chebyshev function: for 11 is:

0 + ln(2) + ln(3) + ln(2) + ln (5) + 0 + ln(7) + ln(2) + ln(3) + 0 + ln(11) ~ 10.23

We can plot the function:



It makes jumps at primes and prime powers with magnitudes equal to the log of the prime and is flat elsewhere.

Our saw-tooth-like plot (the chord of zeta zero notes) also makes jumps at primes and prime powers, and also by the amount near equal to the logs of the primes. But it is not flat elsewhere, it has a slope of about 1 or so (and is also wavy, but if we used more zeros and used more precision, it would straighten out).

Could our zeta zero chord be related to the Chebyshev function?

It is. One other was to define the function is:



The sum of the x to the rho divided by rho is our chord of all of the notes of the Riemann Zeta [non-trivial] zeros.

Taking this equation and using the plot from the previous post as the sum, we can plot it along side of the plot above:



So, that is a brief intro to the Chebyshev function and how the music of the Riemann zeta function is related to primes.

[Lightning Blue Ray]

Feels like I've walked into an IB student reunion after reading the second page. Can't wait for November.

[Kelly]

What is in November, Fluorine?

Oh, more ways to make Prime music:

There are other ways to play music with the Riemann zeta zeros (or any other number). The instrument that we used last time was:



We vary x from 0 to wherever, and the note is defined by the zeta zero chosen. We can then add more notes and get math music.

Here is a new instrument to play these zeros:



This is a rather easy instrument to play, for:



Where rho is the value of the imaginary part. For the first zeta zero, which has imaginary part at 14.1347251..., we have, for the sine portion:



We have just a sine function. It is a pure note that remains constant in volume and frequency. Our previous notes had increasing volumes and frequencies.

The cosine portion will be similar:



In order to listen to the note, we take the magnitude, which is:



That gives:



Not very interesting. Let us add the note from the fifth zero. The sine portion is:



It is just a sine function but has a higher frequency.

Adding the two notes together gives the following for the sine:



Note that it has a repeatable pattern and looks like the repeated pattern that we saw before when we played both of these notes together. The cosine portion looks similar.

Now, we can take the magnitudes of these two notes played together. We have:



Not very interesting yet. So, let us also add in the note from the 10th zero. The magnitude is:



That looks like it would sound rather nice. It shifts smoothly from one sound to another. It is not a repeatable pattern, but the theme continues and sounds very much the same as x increases.

Adding yet another note (from the 20th zero) gives this magnitude:



That is getting interesting. We have big spikes of varying distances between them, and varying smaller spikes in between, and ever changing.

Now, we can write a symphony.

I will be boring, but ambitious. I will add all of the notes from the first 2000 Riemann zeta zeros.

This what I have:



Very interesting. It is a series of big and not-so-big spikes, seemingly randomly placed.

It looks like it is getting crowded near the end. What I could do to spread it out is take the exponent of the x-axis and plot it that way.

The first half or so looks like this:



And the next part:



Now, the spikes are more spread out.

But, but...

The big spikes are on prime numbers! The smaller ones are on powers of primes.

Our orchestra, playing only the notes of the Riemann zeta zeros, with the instrument described, will make sound at the time of the logarithms of prime numbers and powers and no when else.

All of the sounds combine and they all cancel each other out all of the time, except when the time is a log of a prime or prime power, then all of the notes suddenly, at a log of prime time, the notes are all in phase and we have a loud sound, then all of a sudden all of those same notes cancel each other out and remain cancelling each other out, until the next prime or prime power, when again, all of a sudden, they are all in tune with each other.

That really is fascinating.

The zeta zeros (themselves irrational) seemingly pop up randomly along the critical line (where the real part equals exactly one half), but they are clearly placed there with pure rhyme and reason, and together, conspire to produce the prime numbers.

Does anyone know why the non-trivial zeros of the zeta function produce the prime numbers? I don't.

But this does show us how interesting the Riemann zeta function and the Riemann Hypothesis is so frigging interesting.

[Heart]

Kelly, it's SO NICE to have you back in this thread :D :D

I admit, I was studying Riemann Zeta functions for a few weeks back there before finals, but I feel like I only touched the tip of the iceberg, and I've never worked with the others. I'm so excited to spend some time this weekend with a pen and pad of paper and just play with this new math!

Also, welcome Fluorine! There are a surprising amount of IB and ex-IB students here! I was impressed myself too. We always seem to find each other, eh? ;)

[Lightning Blue Ray]

What is in November, Fluorine?

My final exams are in November, and that's when I'll finally be done with the IB.

Also, welcome Fluorine! There are a surprising amount of IB and ex-IB students here! I was impressed myself too. We always seem to find each other, eh? ;)

I know! Nothing like finding other IB students (graduated or not) to commiserate with ;)

[Heart]

Oh wow, good luck on your exams! Make sure to try to get lots of sleep, that was probably what helped me the most ;)

[Lightning Blue Ray]

Thank you

[Kelly]

I hope that you do well. :)

I am long done with exams, but still learn, and have fun at work.

If I did go back...

[Heart]

I LOVE THAT! I had thought I'd seen just about all things, but man. People are creative on exams! My students never fail to surprise me ^_^

[TheMartianGeek]

Well, I'm glad you've found happiness. You seem like an interesting and sweet person to me.

[Kelly]

I recall a band called Heart. I listened to them in the 70s, saw them live in 1977, and have a few of their albums, including:

[Heart]

Hehe. Kelly, it didn't occur to me until now that someone or band might have shared my name! The 70's were before my time, but of course a name so common would have been used before! I'm glad they're a good band, it's nice to share my name with such a talented group of people ;)

Well, I'm glad you've found happiness. You seem like an interesting and sweet person to me.

Aww, thank you! :)

[Dodecahedron314]

I grew up listening to Heart, actually, seeing as my mom is from Seattle. True story: my grandpa was a DJ in Seattle in the early 70s when they were just starting out, and he met them when he gave a talk for career day at their high school. To this day, they're still one of my favorite bands :D Particularly this song:

[Heart]

So you know your grandpa, who met the band Heart, who shares a name with me... That makes us connected by, what, three degrees of RL separation, right? ;)

I admit, I did not grow up listening to the band Heart (I still can't bring myself to say "I didn't listen to Heart", because it just feels so thoroughly like I'm saying "I didn't listen to myself"! :P ). But since discovering that this is a thing, I've been looking up their songs and listening to them for the past half hour. I really like them ^_^ I am, after listening to them, still honoured to share a name.

[Heart]

I'm quoting you to talk to you , Dodec, because for some reason my PM inbox won't load and I'm getting impatient with it. Hopefully this summons you from the internet void :P

In any case, on a total tangential note (so tangential... it might even be normal *whispers* Oh so puny! ;) ); did you choose 314 after your name because it's pi? I admit that I just started playing Pokemon Go (yes, I'm a late bloomer in every area of life, but at least I'm consistent!), and when trying to pick a name my favourite one was taken. Someone other than me has already named themselves Heart, but who could blame them? I'm pretty awesome, I could understand wanting to steal my name. So anyways, I tried various variations, and just nothing was working. So for the first time in my life, I decided I might have to resort to throwing numbers on the end. So I asked myself what numbers would make me happy? If I'm going to resort to numbers anyways, might as well try for something "me", before I resort to random numbers.

I thought about e, but I haven't memorised enough digits to satisfy my nerd self (I only know 2 for sure, and I'm new to the smartphone world so I forgot that I could look it up while playing). Symmetry is far too important to me as a physicist; odd numbers of digits only, and 2 is not nearly as satisfying as if I'd just remembered the third digit of e! So I thought about Avogadro's number, and how satisfying that one is (6.023e23). Then I wondered if it wasn't a bit too chemistry-y, I kinda wanted a natural number. Not one that relies on human measurement decisions. So, what other than e is there? Pi, of course! It also reminds me of my cake vs pie analogy that I pull out every once in a while. It's so perfect! So I held my breath, and typed in Heart314, because periods or decimals are not allowed, and it worked!

So now I have to ask if you are also a 314 for pi's sake.

[Dodecahedron314]

I'm quoting you to talk to you , Dodec, because for some reason my PM inbox won't load and I'm getting impatient with it. Hopefully this summons you from the internet void :P

In any case, on a total tangential note (so tangential... it might even be normal *whispers* Oh so puny! ;) ); did you choose 314 after your name because it's pi? I admit that I just started playing Pokemon Go (yes, I'm a late bloomer in every area of life, but at least I'm consistent!), and when trying to pick a name my favourite one was taken. Someone other than me has already named themselves Heart, but who could blame them? I'm pretty awesome, I could understand wanting to steal my name. So anyways, I tried various variations, and just nothing was working. So for the first time in my life, I decided I might have to resort to throwing numbers on the end. So I asked myself what numbers would make me happy? If I'm going to resort to numbers anyways, might as well try for something "me", before I resort to random numbers.

I thought about e, but I haven't memorised enough digits to satisfy my nerd self (I only know 2 for sure, and I'm new to the smartphone world so I forgot that I could look it up while playing). Symmetry is far too important to me as a physicist; odd numbers of digits only, and 2 is not nearly as satisfying as if I'd just remembered the third digit of e! So I thought about Avogadro's number, and how satisfying that one is (6.023e23). Then I wondered if it wasn't a bit too chemistry-y, I kinda wanted a natural number. Not one that relies on human measurement decisions. So, what other than e is there? Pi, of course! It also reminds me of my cake vs pie analogy that I pull out every once in a while. It's so perfect! So I held my breath, and typed in Heart314, because periods or decimals are not allowed, and it worked!

So now I have to ask if you are also a 314 for pi's sake.

*materializes from the void, possibly in the TARDIS because they've been watching way too much Doctor Who lately*

Yep, I never use random numbers either, and the 314 is absolutely because pi. That's doubly significant in the context of my username because not only is it pi for pi's sake, but the Dodecahedron part comes from my obsession with the book Contact by Carl Sagan, which has a very nice ending scene involving pi that's always sort of perfectly summed up why I'm so into science and math. (And is anyone here surprised that someone like me is a complete and utter Carl Sagan fanby? No. The answer is no.)

Pi has also just been a thing for me since before I read Contact, though--by high school, I had memorized about 80 digits of it because I had nothing better to do with my life. That's since dropped to maybe 60something because I don't practice all that much anymore. Still, the ultimate goal is to get up to the Feynman point, but we'll see whether that pans out :P I only know e up to 2.7182818, though--I was planning on memorizing lots of digits of that, too, but never really got the chance.

I do occasionally use even numbers of digits in usernames though--the username I used for pretty much everything before I started going by my middle name IRL involved my first name and some other things, followed by 42 :P