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wasoxygen  ·  3 days ago  ·  link  ·    ·  parent  ·  post: Primer on complex numbers

I am trusting you on the trig identities used to get z³ in part 1.3, because the list is too long and ctrl-f doesn't work for images.

The power series expansion in 1.4 a) looks familiar, but also requires a bit of faith since I could not hope to derive it myself.

The only step that left me really perplexed is 1.5 2). Are you just rearranging the equations and substituting? I didn't follow.

From there it is clear how you get to cos(i) = 1.543..., and I suppose I should not be surprised that this falls outside the usual range of [-1, 1] for cosine.

I was pleased with how much sense I was about to make from your notes, thanks for putting it together.

Devac  ·  3 days ago  ·  link  ·

trig identities

The only ones you need here are the ones about the sum of angles:

sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y)

cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y)

EDIT: By the way, while Wikipedia's list is amazing most of them are there only for the sake of completeness. Let me put it like that: my typical day consists of crunching weird maths for at the very least four hours (even more during weekdays since, you know, classes). Aside from having to find if an expression like sin(3pi/17) has an exact value or needing to see before my eyes if something that I'm calculating is similar to what's in the list of identities (surprisingly not as often as you could think) I don't really have much use of it. On the other hand this list once memorised in junior high serves literally 99.9% of my trigonometric needs to this day. It's actually more than enough for the purposes of this primer.

Power expansion

In this case it's a Maclaurin series (which is literally the Taylor series with a = 0).

The only step that left me really perplexed is 1.5 2). Are you just rearranging the equations and substituting? I didn't follow.

Take the first equation, add the other, divide by two. You've found the cos(x). Sine can be obtained by subtracting the second equation from the first and dividing by 2i.

From there it is clear how you get to cos(i) = 1.543..., and I suppose I should not be surprised that this falls outside the usual range of [-1, 1] for cosine.

Well, we are no longer working on real numbers. We made an extension of the existing definition. It will still work for real values as intended. That's pretty much maths in essence: we have used existing formulas (power series, sin/cos functions) in an unusual context, and our definitions got somewhat updated. ;)

EDIT: By the way, note that in normal sine and cosine we use real numbers as arguments!

wasoxygen  ·  4 days ago  ·  link  ·    ·  parent  ·  post: Trump - Will it be awful? Will it be successful? What are your predictions?

I don't think I am well-informed enough to have a confident opinion.

My default expectation is that things will go on about the same as they have been going, which seems to mean that cooperation and bonhomie will be roughly proportional to visibility: conspicuous coordination in space, begrudging tolerance and sniping in official channels, rivalry and maneuvering in proxy war states, and unrestrained battle in arms racing and cyberwarfare.

While I was bottom-feeding on music videos and dashcam highlights recently, YouTube recommended something a little different: a speech Putin gave to some wonks at an economic forum. I was rather surprised to see the evil empire cartoon strongman speak in calm, measured tones, telling a version of history from the other side of the curtain. It's hard to know how to parse a prepared talk from a KGB man, but if his goal was to unsettle the audience with the image of a reckless bully upsetting delicate balances and toying with disaster, it worked; I was unsettled. (There is some analysis here and there and at that other place, all at standard Internet quality.)

We don't worry about the Bomb very much anymore. Well, most of us. It's hard to judge the risk of unlikely events with very large consequences. I haven't seen good evidence that our next commander in chief is more likely than his opponent to stumble into apocalypse. It's hard to know how to parse bluster and bloviating too.

If there is any signal to read amid all the noise, it seems to indicate that Russian leadership favored this outcome. I don't know if there was a "personal beef" (as was certainly true among many voters) or if Trump seemed more friendly, or manageable, or if it was thought that he would weaken a superpower rival. Maybe they thought it would be good for a laugh (or лулз?).

We haven't had a world war all century and it would be nice to keep it that way.

What do you think?

ThatFanficGuy  ·  4 days ago  ·  link  ·

I, myself, am not quite well-versed in the matter, hence asking the question, but I did see some things around.

Ever since I'm in the home city, I keep hearing what the news are saying; not the least amount of airwaves go to Trump these days. The news treat Trump in a defensive tone pretending to be neutral, which itself is unsettling, given the shit the old prez said over various media. I can't give you any examples (mostly because I didn't want to listen closely), but something was said about Trump being "constantly under attack" by his opponents for things he says, as if he's the poor victim of unjustified offences by the evil men and women that he's done nothing to wrong.

All of which, I suppose, is to say that official Russian media paint Trump as a friendly figure to the Double-Headed Eagle (which is the Russian coat of arms), much like it was before the election (I remember my groupmate asking me, after I told her the results of the election, "That's good, right? He's good for Russia, isn't he?"). If Trump's to be as bold as his pre-election speeches implied (which seems to be false now that he's in the office), Russia-US trade is going to improve, which would mean lower prices for US produce. For an average Russian, it's an obvious improvement, but I can't see how trading that for a narcissist at the wheel of the country of most powerful military in the world is worth it; I'd rather pay the same and have someone like Hillary - a cold-blooded politician but not sick in the head - in the position.

I believe it was rd95 who said in a different thread that people nowadays look for ways to feel safer through validation or assurance because of Trump. I guess I'm looking for the same as far as the two countries' relationships go. I know nothing, and I'd like to know something for certain; or, to put it in better terms that you've used, to have a more confident opinion.

(or лулз?)

No idea how you've found that, but kudos.

jadedog  ·  4 days ago  ·  link  ·

I happened to stumble on an AskReddit asking:

Russians of Reddit, how is Donald Trump being portrayed in your Media?

There were answers from both Russians in the US and in Russia.

If you're interested, I'll leave the link.

https://www.reddit.com/r/AskReddit/comments/5ng6fu/russians_of_reddit_how_is_donald_trump_being/

snoodog  ·  3 days ago  ·  link  ·

Some of the better quotes:

"Fellow Russian (ukranian, actually) here. My family all voted trump too. My parents told me it's because Clinton and the democrats were trying to rebuild the soviet union but in america."

"A lot of communities of legal immigrants sympathize him because he says that legal immigration is OK and illegal immigration is not OK."

"Some chose him because of the belief that Hilary would start a war with Russia. Others chose him because of his business background, and feel like he would improve the economy. Many chose him because they hate obamacare. I'm not saying the Russian community loves him or anything, but given the two options, almost all chose trump."

ThatFanficGuy  ·  2 days ago  ·  link  ·

"A lot of communities of legal immigrants sympathize him because he says that legal immigration is OK and illegal immigration is not OK."

Man, that's some solid logic right there.

Russia does have a problem with illegal immigrants, though: people from the poorer southern countries (Azerbaijan, Tajikistan etc.) come to work in Russia illegally en masse. There's a certain disdain for "churka" (a derogative term for people of skin more brown than that of a typical Russian; plural "churki") among the general population, and many people want them gone out of the country because they take jobs that most would scoff at anyway (street sweeper, janitor etc.). There are even measures to make illegal immigration from those countries more difficult.

...wait.

ThatFanficGuy  ·  4 days ago  ·  link  ·

Thanks. Some of the replies were interesting, like the Mongolian guy getting Russian news in his country.

Mostly everything I expected to hear, otherwise. Clinton's bad, Trump's good. Clinton = war, Trump = good businessman = good economy (somehow).

wasoxygen  ·  4 days ago  ·  link  ·    ·  parent  ·  post: Calling Bullshit

The item on data visualization is pretty good too. veen loves this stuff.

veen  ·  4 days ago  ·  link  ·

Hah! That's just perfect.

A while ago I thought there was a good and a bad way to represent data. Over the years and through some experience I've come to understand that just like any other form of communication, data visualizations tell a story first and foremost. Sure, there are plenty of bad ways to tell a story but there is not a good way to graph any phenomenon. The key to calling bullshit I think is to see the discrepancies between what the data says and what story its graph says.

wasoxygen  ·  4 days ago  ·  link  ·    ·  parent  ·  post: Calling Bullshit

If you are leading us through the 11 week course, I am in.

Creativity  ·  4 days ago  ·  link  ·

I might check the website from time to time to see new content but I'm not planning to follow it religiously week after week

wasoxygen  ·  5 days ago  ·  link  ·    ·  parent  ·  post: 0.2078795763

Oh, sorry to hear that, but thanks for making the effort. There is plenty at MathWorld to keep me occupied until old age.

Devac  ·  5 days ago  ·  link  ·

Nah, sorry for raging here. It wasn't called for, and I want to apologise about this whole situation. But I'm not going to lie, it felt like a complete waste of time. It wasn't, I was enjoying all the time while I was talking, but just something broke inside me when I've launched the recording and saw how it suddenly stops refreshing the video. I wanted to believe that it was just something about this program. When it failed to deliver on different five media players, I was done.

After thinking for a moment I have one more thing to add that I did not flash out in my would-be recording. Roots of unity and their properties are not crucial but provide certain insights into operations on complex numbers.

wasoxygen  ·  5 days ago  ·  link  ·    ·  parent  ·  post: 0.2078795763

An interpretation in some physical context sounds cool, especially if you can do it in words of two syllables or less.

Devac  ·  5 days ago  ·  link  ·

Fuuuuuuck.

I've recorded forty minutes long explanation and camera froze less than a minute in. And people can't even blame it on Linux being shit, that was on Windows. "It has better multimedia support" my arse…

I'll scan my notes and add some commentary, but later. I'm too furious to deal with anything right now.

Anyway, if you want a short version/spoiler, it involved conformal mapping and a circle-shaped capacitor.

kleinbl00  ·  5 days ago  ·  link  ·

Recording anything for 40 minutes is asking for trouble, and I've worked on 1-take films involving Red Epics and six figures worth of media.

Devac  ·  5 days ago  ·  link  ·

I guess you are right on that one. Usually, I try (and mostly succeed) to stay under fifteen minutes with any such recordings, but this time I didn't even notice for how long I was talking.

To add insult to injury, it was probably the first time in a long while when I could pass as an eloquent speaker. Aside from a single 'um' at the beginning, it felt like this impromptu recording has been in rehearsal for weeks. No pauses, no need for corrections, nothing to show in the end. This was simply the straw that broke the camel's back, hence the (uncalled for) reaction.

kleinbl00  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work. Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better. Unless you've got a dedicated hard-coded time-synched recorder it's all spitting shit every which way and it'll drop frames, lock up, whatever. If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

Devac  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work.

Thanks! I was vaguely aware of that, but never really noticed. As I said earlier, my recordings are usually under fifteen minutes. Plus I'm not recording my face, so it's not like I can realistically estimate how much my mouth and voice desync. Few frames here or there aren't much when discussing physics. But if what you say is true, forty minutes would probably look like complete shit. Hundred millisecond difference is probably bearable in my wannabe Khan Academy format, but extrapolating from your numbers it would get to be around full second(s) by the end. That's indeed too much.

Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better.

Hah. I know, codecs and their standards don't really depend on the OS (to my knowledge at least, I'll gladly be corrected). They can be harder to implement or port, but it's largely independent. That's, again, my annoyance showing.

But I'm not gonna lie, after years of people telling me that you can't do anything with video on Linux and the second ever recording that I made on Windows went tits up (and first wasn't really a success either)… I felt a kind of a vicarious pleasure at this failing. Lizard brain of sorts, I guess. Bit shame that at my expense though ;).

If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

If that's the case, are there any affordable solutions? Baring in mind that I live quite comfortably while making about 480-500 USD per month in total (that is stipends + tutoring) and the fact that in Poland most of the specialist electronics are about 10-30% more expensive on average. Would a mid-tier camera on a tripod recording on memory card cut it, or am I in a wrong ballpark?

No rush. I'm mainly just curious. It's not like I'm recording more than maybe two or three hours per month. That said, if I would get some sensible job for my senior year it wouldn't hurt me to get at least acquainted with quality video work and editing.

Thank you in advace!

kleinbl00  ·  5 days ago  ·  link  ·

The cheapest thing to do is learn to cut every minute or so. Next time you watch a show on television, pay attention to how often they switch angles or change scenes. It's actually pretty atypical to go longer than six or seven seconds without cutting to a different angle.

I recognize that this approach doesn't work for streaming screencasts but if you can find places to stop and start it'll improve your flow and save you money.

wasoxygen  ·  5 days ago  ·  link  ·

Oh, sorry to hear that, but thanks for making the effort. There is plenty at MathWorld to keep me occupied until old age.

Devac  ·  5 days ago  ·  link  ·

Nah, sorry for raging here. It wasn't called for, and I want to apologise about this whole situation. But I'm not going to lie, it felt like a complete waste of time. It wasn't, I was enjoying all the time while I was talking, but just something broke inside me when I've launched the recording and saw how it suddenly stops refreshing the video. I wanted to believe that it was just something about this program. When it failed to deliver on different five media players, I was done.

After thinking for a moment I have one more thing to add that I did not flash out in my would-be recording. Roots of unity and their properties are not crucial but provide certain insights into operations on complex numbers.

wasoxygen  ·  5 days ago  ·  link  ·    ·  parent  ·  post: 0.2078795763

Devac  ·  5 days ago  ·  link  ·

Do you want a proof of i^i ∈ ℝ or an interpretation of it in some physical context?

wasoxygen  ·  5 days ago  ·  link  ·

An interpretation in some physical context sounds cool, especially if you can do it in words of two syllables or less.

Devac  ·  5 days ago  ·  link  ·

Fuuuuuuck.

I've recorded forty minutes long explanation and camera froze less than a minute in. And people can't even blame it on Linux being shit, that was on Windows. "It has better multimedia support" my arse…

I'll scan my notes and add some commentary, but later. I'm too furious to deal with anything right now.

Anyway, if you want a short version/spoiler, it involved conformal mapping and a circle-shaped capacitor.

kleinbl00  ·  5 days ago  ·  link  ·

Recording anything for 40 minutes is asking for trouble, and I've worked on 1-take films involving Red Epics and six figures worth of media.

Devac  ·  5 days ago  ·  link  ·

I guess you are right on that one. Usually, I try (and mostly succeed) to stay under fifteen minutes with any such recordings, but this time I didn't even notice for how long I was talking.

To add insult to injury, it was probably the first time in a long while when I could pass as an eloquent speaker. Aside from a single 'um' at the beginning, it felt like this impromptu recording has been in rehearsal for weeks. No pauses, no need for corrections, nothing to show in the end. This was simply the straw that broke the camel's back, hence the (uncalled for) reaction.

kleinbl00  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work. Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better. Unless you've got a dedicated hard-coded time-synched recorder it's all spitting shit every which way and it'll drop frames, lock up, whatever. If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

Devac  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work.

Thanks! I was vaguely aware of that, but never really noticed. As I said earlier, my recordings are usually under fifteen minutes. Plus I'm not recording my face, so it's not like I can realistically estimate how much my mouth and voice desync. Few frames here or there aren't much when discussing physics. But if what you say is true, forty minutes would probably look like complete shit. Hundred millisecond difference is probably bearable in my wannabe Khan Academy format, but extrapolating from your numbers it would get to be around full second(s) by the end. That's indeed too much.

Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better.

Hah. I know, codecs and their standards don't really depend on the OS (to my knowledge at least, I'll gladly be corrected). They can be harder to implement or port, but it's largely independent. That's, again, my annoyance showing.

But I'm not gonna lie, after years of people telling me that you can't do anything with video on Linux and the second ever recording that I made on Windows went tits up (and first wasn't really a success either)… I felt a kind of a vicarious pleasure at this failing. Lizard brain of sorts, I guess. Bit shame that at my expense though ;).

If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

If that's the case, are there any affordable solutions? Baring in mind that I live quite comfortably while making about 480-500 USD per month in total (that is stipends + tutoring) and the fact that in Poland most of the specialist electronics are about 10-30% more expensive on average. Would a mid-tier camera on a tripod recording on memory card cut it, or am I in a wrong ballpark?

No rush. I'm mainly just curious. It's not like I'm recording more than maybe two or three hours per month. That said, if I would get some sensible job for my senior year it wouldn't hurt me to get at least acquainted with quality video work and editing.

Thank you in advace!

kleinbl00  ·  5 days ago  ·  link  ·

The cheapest thing to do is learn to cut every minute or so. Next time you watch a show on television, pay attention to how often they switch angles or change scenes. It's actually pretty atypical to go longer than six or seven seconds without cutting to a different angle.

I recognize that this approach doesn't work for streaming screencasts but if you can find places to stop and start it'll improve your flow and save you money.

wasoxygen  ·  5 days ago  ·  link  ·

Oh, sorry to hear that, but thanks for making the effort. There is plenty at MathWorld to keep me occupied until old age.

Devac  ·  5 days ago  ·  link  ·

Nah, sorry for raging here. It wasn't called for, and I want to apologise about this whole situation. But I'm not going to lie, it felt like a complete waste of time. It wasn't, I was enjoying all the time while I was talking, but just something broke inside me when I've launched the recording and saw how it suddenly stops refreshing the video. I wanted to believe that it was just something about this program. When it failed to deliver on different five media players, I was done.

After thinking for a moment I have one more thing to add that I did not flash out in my would-be recording. Roots of unity and their properties are not crucial but provide certain insights into operations on complex numbers.

wasoxygen  ·  5 days ago  ·  link  ·    ·  parent  ·  post: 0.2078795763

≈ 1 / √(e^π)

wasoxygen  ·  5 days ago  ·  link  ·

Devac  ·  5 days ago  ·  link  ·

Do you want a proof of i^i ∈ ℝ or an interpretation of it in some physical context?

wasoxygen  ·  5 days ago  ·  link  ·

An interpretation in some physical context sounds cool, especially if you can do it in words of two syllables or less.

Devac  ·  5 days ago  ·  link  ·

Fuuuuuuck.

I've recorded forty minutes long explanation and camera froze less than a minute in. And people can't even blame it on Linux being shit, that was on Windows. "It has better multimedia support" my arse…

I'll scan my notes and add some commentary, but later. I'm too furious to deal with anything right now.

Anyway, if you want a short version/spoiler, it involved conformal mapping and a circle-shaped capacitor.

kleinbl00  ·  5 days ago  ·  link  ·

Recording anything for 40 minutes is asking for trouble, and I've worked on 1-take films involving Red Epics and six figures worth of media.

Devac  ·  5 days ago  ·  link  ·

I guess you are right on that one. Usually, I try (and mostly succeed) to stay under fifteen minutes with any such recordings, but this time I didn't even notice for how long I was talking.

To add insult to injury, it was probably the first time in a long while when I could pass as an eloquent speaker. Aside from a single 'um' at the beginning, it felt like this impromptu recording has been in rehearsal for weeks. No pauses, no need for corrections, nothing to show in the end. This was simply the straw that broke the camel's back, hence the (uncalled for) reaction.

kleinbl00  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work. Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better. Unless you've got a dedicated hard-coded time-synched recorder it's all spitting shit every which way and it'll drop frames, lock up, whatever. If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

Devac  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work.

Thanks! I was vaguely aware of that, but never really noticed. As I said earlier, my recordings are usually under fifteen minutes. Plus I'm not recording my face, so it's not like I can realistically estimate how much my mouth and voice desync. Few frames here or there aren't much when discussing physics. But if what you say is true, forty minutes would probably look like complete shit. Hundred millisecond difference is probably bearable in my wannabe Khan Academy format, but extrapolating from your numbers it would get to be around full second(s) by the end. That's indeed too much.

Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better.

Hah. I know, codecs and their standards don't really depend on the OS (to my knowledge at least, I'll gladly be corrected). They can be harder to implement or port, but it's largely independent. That's, again, my annoyance showing.

But I'm not gonna lie, after years of people telling me that you can't do anything with video on Linux and the second ever recording that I made on Windows went tits up (and first wasn't really a success either)… I felt a kind of a vicarious pleasure at this failing. Lizard brain of sorts, I guess. Bit shame that at my expense though ;).

If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

If that's the case, are there any affordable solutions? Baring in mind that I live quite comfortably while making about 480-500 USD per month in total (that is stipends + tutoring) and the fact that in Poland most of the specialist electronics are about 10-30% more expensive on average. Would a mid-tier camera on a tripod recording on memory card cut it, or am I in a wrong ballpark?

No rush. I'm mainly just curious. It's not like I'm recording more than maybe two or three hours per month. That said, if I would get some sensible job for my senior year it wouldn't hurt me to get at least acquainted with quality video work and editing.

Thank you in advace!

kleinbl00  ·  5 days ago  ·  link  ·

The cheapest thing to do is learn to cut every minute or so. Next time you watch a show on television, pay attention to how often they switch angles or change scenes. It's actually pretty atypical to go longer than six or seven seconds without cutting to a different angle.

I recognize that this approach doesn't work for streaming screencasts but if you can find places to stop and start it'll improve your flow and save you money.

wasoxygen  ·  5 days ago  ·  link  ·

Oh, sorry to hear that, but thanks for making the effort. There is plenty at MathWorld to keep me occupied until old age.

Devac  ·  5 days ago  ·  link  ·

Nah, sorry for raging here. It wasn't called for, and I want to apologise about this whole situation. But I'm not going to lie, it felt like a complete waste of time. It wasn't, I was enjoying all the time while I was talking, but just something broke inside me when I've launched the recording and saw how it suddenly stops refreshing the video. I wanted to believe that it was just something about this program. When it failed to deliver on different five media players, I was done.

After thinking for a moment I have one more thing to add that I did not flash out in my would-be recording. Roots of unity and their properties are not crucial but provide certain insights into operations on complex numbers.

wasoxygen  ·  5 days ago  ·  link  ·    ·  parent  ·  post: 0.2078795763

≈ 1 / √23.14069

wasoxygen  ·  5 days ago  ·  link  ·

≈ 1 / √(e^π)

wasoxygen  ·  5 days ago  ·  link  ·

Devac  ·  5 days ago  ·  link  ·

Do you want a proof of i^i ∈ ℝ or an interpretation of it in some physical context?

wasoxygen  ·  5 days ago  ·  link  ·

An interpretation in some physical context sounds cool, especially if you can do it in words of two syllables or less.

Devac  ·  5 days ago  ·  link  ·

Fuuuuuuck.

I've recorded forty minutes long explanation and camera froze less than a minute in. And people can't even blame it on Linux being shit, that was on Windows. "It has better multimedia support" my arse…

I'll scan my notes and add some commentary, but later. I'm too furious to deal with anything right now.

Anyway, if you want a short version/spoiler, it involved conformal mapping and a circle-shaped capacitor.

kleinbl00  ·  5 days ago  ·  link  ·

Recording anything for 40 minutes is asking for trouble, and I've worked on 1-take films involving Red Epics and six figures worth of media.

Devac  ·  5 days ago  ·  link  ·

I guess you are right on that one. Usually, I try (and mostly succeed) to stay under fifteen minutes with any such recordings, but this time I didn't even notice for how long I was talking.

To add insult to injury, it was probably the first time in a long while when I could pass as an eloquent speaker. Aside from a single 'um' at the beginning, it felt like this impromptu recording has been in rehearsal for weeks. No pauses, no need for corrections, nothing to show in the end. This was simply the straw that broke the camel's back, hence the (uncalled for) reaction.

kleinbl00  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work. Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better. Unless you've got a dedicated hard-coded time-synched recorder it's all spitting shit every which way and it'll drop frames, lock up, whatever. If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

Devac  ·  5 days ago  ·  link  ·

h.264, which is the protocol most cameras record to, isn't even synchronous. There's no mandated field length within the codec. Which means for those of us who record audio, h.264 will drift by at least a frame after less than 5 minutes of recording. More than ten minutes and you can be off by three frames or more. After that it's all kinda wooly; the video recording is dumping data where it fits and speeding up or slowing down to make the audio work.

Thanks! I was vaguely aware of that, but never really noticed. As I said earlier, my recordings are usually under fifteen minutes. Plus I'm not recording my face, so it's not like I can realistically estimate how much my mouth and voice desync. Few frames here or there aren't much when discussing physics. But if what you say is true, forty minutes would probably look like complete shit. Hundred millisecond difference is probably bearable in my wannabe Khan Academy format, but extrapolating from your numbers it would get to be around full second(s) by the end. That's indeed too much.

Meanwhile it's spitting out a secondary path for monitoring which Windows is playing with asynchronously as well. Linux is no better.

Hah. I know, codecs and their standards don't really depend on the OS (to my knowledge at least, I'll gladly be corrected). They can be harder to implement or port, but it's largely independent. That's, again, my annoyance showing.

But I'm not gonna lie, after years of people telling me that you can't do anything with video on Linux and the second ever recording that I made on Windows went tits up (and first wasn't really a success either)… I felt a kind of a vicarious pleasure at this failing. Lizard brain of sorts, I guess. Bit shame that at my expense though ;).

If you're using a webcam it doesn't much matter because we accept that webcams are going to be shit. But if you're recording, you're in for a bad time.

If that's the case, are there any affordable solutions? Baring in mind that I live quite comfortably while making about 480-500 USD per month in total (that is stipends + tutoring) and the fact that in Poland most of the specialist electronics are about 10-30% more expensive on average. Would a mid-tier camera on a tripod recording on memory card cut it, or am I in a wrong ballpark?

No rush. I'm mainly just curious. It's not like I'm recording more than maybe two or three hours per month. That said, if I would get some sensible job for my senior year it wouldn't hurt me to get at least acquainted with quality video work and editing.

Thank you in advace!

kleinbl00  ·  5 days ago  ·  link  ·

The cheapest thing to do is learn to cut every minute or so. Next time you watch a show on television, pay attention to how often they switch angles or change scenes. It's actually pretty atypical to go longer than six or seven seconds without cutting to a different angle.

I recognize that this approach doesn't work for streaming screencasts but if you can find places to stop and start it'll improve your flow and save you money.

wasoxygen  ·  5 days ago  ·  link  ·

Oh, sorry to hear that, but thanks for making the effort. There is plenty at MathWorld to keep me occupied until old age.

Devac  ·  5 days ago  ·  link  ·

Nah, sorry for raging here. It wasn't called for, and I want to apologise about this whole situation. But I'm not going to lie, it felt like a complete waste of time. It wasn't, I was enjoying all the time while I was talking, but just something broke inside me when I've launched the recording and saw how it suddenly stops refreshing the video. I wanted to believe that it was just something about this program. When it failed to deliver on different five media players, I was done.

After thinking for a moment I have one more thing to add that I did not flash out in my would-be recording. Roots of unity and their properties are not crucial but provide certain insights into operations on complex numbers.

wasoxygen  ·  6 days ago  ·  link  ·    ·  parent  ·  post: Trump - Will it be awful? Will it be successful? What are your predictions?

When I see the word "prediction," I think of something like this:

"It will be a very dramatic change in the sky, as anyone can see it. You won't need a telescope to tell me in 2023 whether I was wrong or I was right," Molnar said at the presentation

I don't see many clear, measurable, falsifiable predictions here. Some of the predictions are already true. How will we know if we had any understanding of current events if we can't check our hypotheses later? Saying "it's going to be a disaster" and claiming validation every time something bad happens is too easy.

Bryan Caplan has recorded a number of bets, some concerning Trump.

Scott Alexander has published a list of predictions for 2017 and keeps a scorecard. He also made ten specific predictions about Trump. Some paraphrased examples:

Total hate crimes incidents will be not more than 125% of their 2015 value at any year during a Trump presidency.

The U.S. Muslim population will increase throughout Trump’s presidency.

The Trump cabinet will be at least 10% minority.

No large demographic group will be forced to sign up for a “registry.”

Other sources make some predictions, but the ones I saw were often fuzzy and unclear, like talk of "impeachment" without specifying whether Trump would be removed from office.

Here are my guesses. In brief, I predict more of the same.

The Wall

There are now "more than 580 miles (930 km) of barriers in place" along the 1,954-mile (3,145 km) long Mexico-U.S. border.

I predict that the wall will be improved, but will remain less than half the length of the border. I predict that Trump will not force Mexico to pay construction costs (talk perhaps, but not actions like garnishing money transfers or withholding aid). Aid obligations in 2015 were \$586 million, mostly for drug enforcement. The number varies a lot by year, but I predict it will not drop below the 2012 reported value of \$215 million during the next four years.

Jobs

There were 12,265,000 employees in U.S. manufacturing jobs in October 2016. The trend has been downward since the 1980s, though there has been some recovery since 2010.

I predict that this number will be lower than 12,265,000 by the end of 2020.

Other

Twitter will still exist and annoy in 2020.

Trump will remain president for a full four-year term.

The number of abortions induced, as measured by the CDC, will continue to decline as it has for years, with no conspicuous change in the next four years.

The U.S. will remain a signatory to the Paris Climate Agreement.

The number of mosques in the U.S. not be less than the 2,106 counted in 2011 during the next four years.

U.S. GDP growth will be positive for at least three of the four years from 2017 to 2020, and not lower than -2% in any year.

``  ``

Which of these do you think I got wrong? What are your concrete predictions?

ThatFanficGuy  ·  5 days ago  ·  link  ·

What are your thoughts on the Russia-US (and vice versa) relationship under Trump?

wasoxygen  ·  4 days ago  ·  link  ·

I don't think I am well-informed enough to have a confident opinion.

My default expectation is that things will go on about the same as they have been going, which seems to mean that cooperation and bonhomie will be roughly proportional to visibility: conspicuous coordination in space, begrudging tolerance and sniping in official channels, rivalry and maneuvering in proxy war states, and unrestrained battle in arms racing and cyberwarfare.

While I was bottom-feeding on music videos and dashcam highlights recently, YouTube recommended something a little different: a speech Putin gave to some wonks at an economic forum. I was rather surprised to see the evil empire cartoon strongman speak in calm, measured tones, telling a version of history from the other side of the curtain. It's hard to know how to parse a prepared talk from a KGB man, but if his goal was to unsettle the audience with the image of a reckless bully upsetting delicate balances and toying with disaster, it worked; I was unsettled. (There is some analysis here and there and at that other place, all at standard Internet quality.)

We don't worry about the Bomb very much anymore. Well, most of us. It's hard to judge the risk of unlikely events with very large consequences. I haven't seen good evidence that our next commander in chief is more likely than his opponent to stumble into apocalypse. It's hard to know how to parse bluster and bloviating too.

If there is any signal to read amid all the noise, it seems to indicate that Russian leadership favored this outcome. I don't know if there was a "personal beef" (as was certainly true among many voters) or if Trump seemed more friendly, or manageable, or if it was thought that he would weaken a superpower rival. Maybe they thought it would be good for a laugh (or лулз?).

We haven't had a world war all century and it would be nice to keep it that way.

What do you think?

ThatFanficGuy  ·  4 days ago  ·  link  ·

I, myself, am not quite well-versed in the matter, hence asking the question, but I did see some things around.

Ever since I'm in the home city, I keep hearing what the news are saying; not the least amount of airwaves go to Trump these days. The news treat Trump in a defensive tone pretending to be neutral, which itself is unsettling, given the shit the old prez said over various media. I can't give you any examples (mostly because I didn't want to listen closely), but something was said about Trump being "constantly under attack" by his opponents for things he says, as if he's the poor victim of unjustified offences by the evil men and women that he's done nothing to wrong.

All of which, I suppose, is to say that official Russian media paint Trump as a friendly figure to the Double-Headed Eagle (which is the Russian coat of arms), much like it was before the election (I remember my groupmate asking me, after I told her the results of the election, "That's good, right? He's good for Russia, isn't he?"). If Trump's to be as bold as his pre-election speeches implied (which seems to be false now that he's in the office), Russia-US trade is going to improve, which would mean lower prices for US produce. For an average Russian, it's an obvious improvement, but I can't see how trading that for a narcissist at the wheel of the country of most powerful military in the world is worth it; I'd rather pay the same and have someone like Hillary - a cold-blooded politician but not sick in the head - in the position.

I believe it was rd95 who said in a different thread that people nowadays look for ways to feel safer through validation or assurance because of Trump. I guess I'm looking for the same as far as the two countries' relationships go. I know nothing, and I'd like to know something for certain; or, to put it in better terms that you've used, to have a more confident opinion.

(or лулз?)

No idea how you've found that, but kudos.

jadedog  ·  4 days ago  ·  link  ·

I happened to stumble on an AskReddit asking:

Russians of Reddit, how is Donald Trump being portrayed in your Media?

There were answers from both Russians in the US and in Russia.

If you're interested, I'll leave the link.

https://www.reddit.com/r/AskReddit/comments/5ng6fu/russians_of_reddit_how_is_donald_trump_being/

snoodog  ·  3 days ago  ·  link  ·

Some of the better quotes:

"Fellow Russian (ukranian, actually) here. My family all voted trump too. My parents told me it's because Clinton and the democrats were trying to rebuild the soviet union but in america."

"A lot of communities of legal immigrants sympathize him because he says that legal immigration is OK and illegal immigration is not OK."

"Some chose him because of the belief that Hilary would start a war with Russia. Others chose him because of his business background, and feel like he would improve the economy. Many chose him because they hate obamacare. I'm not saying the Russian community loves him or anything, but given the two options, almost all chose trump."

ThatFanficGuy  ·  2 days ago  ·  link  ·

"A lot of communities of legal immigrants sympathize him because he says that legal immigration is OK and illegal immigration is not OK."

Man, that's some solid logic right there.

Russia does have a problem with illegal immigrants, though: people from the poorer southern countries (Azerbaijan, Tajikistan etc.) come to work in Russia illegally en masse. There's a certain disdain for "churka" (a derogative term for people of skin more brown than that of a typical Russian; plural "churki") among the general population, and many people want them gone out of the country because they take jobs that most would scoff at anyway (street sweeper, janitor etc.). There are even measures to make illegal immigration from those countries more difficult.

...wait.

ThatFanficGuy  ·  4 days ago  ·  link  ·

Thanks. Some of the replies were interesting, like the Mongolian guy getting Russian news in his country.

Mostly everything I expected to hear, otherwise. Clinton's bad, Trump's good. Clinton = war, Trump = good businessman = good economy (somehow).

blackbootz  ·  6 days ago  ·  link  ·

Woah. Why have abortions steadily declined? Had we hit some zenith in the nineties? I thought the number of abortions would stay steady or increase. Have all the TRAP (targeted regulation against abortion) laws been working? Is this a result of the preaches and calls for abstinence?

francopoli  ·  6 days ago  ·  link  ·

Better sex ed. ADA made birth control free and/or low cost. Also with 'Plan B" over the counter there will be fewer unplanned pregnancies as well.

Funny, when women and girls don't get pregnant in the first place, they don't have abortions.

wasoxygen  ·  6 days ago  ·  link  ·    ·  parent  ·  post: Hubski Stickers in the states

Here's an old map, but I don't know if any of the stickers are still there:

http://goo.gl/XoBTSG

wasoxygen  ·  9 days ago  ·  link  ·    ·  parent  ·  post: The Dumbest User Interface of 2016

Okay, I agree that you disagree, though I'm not clear on why.

I've tried to add a little nuance, so my one-sentence position would be more like "Profit-seeking drives business behavior, and serving customer interests brings profit."

johnnyFive  ·  8 days ago  ·  link  ·

and serving customer interests brings profit.

Except where it doesn't....

wasoxygen  ·  9 days ago  ·  link  ·    ·  parent  ·  post: Pavlov dog

I recall that was another Laika effort in the Great Dogs of science series.

We have a guest arriving from Sweden that weekend, so we will probably pretend that everything is normal. In fact, that's my long-term plan too.

wasoxygen  ·  9 days ago  ·  link  ·    ·  parent  ·  post: Pavlov dog

Hope this isn't a spoiler, but I think you'll be pleased to find a very pretty lighthouse when you step back and look at your picture.

A friend is taking some oil painting lessons. He got some good results, despite little experience. So I shopped for some oils, looking for cheap primary colors to start. The nearest I could find is a set of eight or so colors, in very tiny tubes. Is paint such a big expense?

oyster  ·  8 days ago  ·  link  ·

A little tip, don't cheap out on your paint brushes. You don't need the most expensive ones but don't buy the cheap ones unless you want a million brush hairs on your piece.

mk  ·  8 days ago  ·  link  ·

It's not cheap, but a little paint goes a long way, and you can mix to get the range you want. You'll want some liquin and some linseed or walnut oil to mix with the paints to thin them and get different textures.

I paint on plywood because I think canvass is a pain.

We watched Tim's Vermeer last night. Really interesting. I have little doubt that Vermeer was doing something like that. It changes his art for me. Now I see it an amazing labor, but accessible.

More to come, no doubt...

The linked story does reveal a confirmation step, but it adds as much charm as it takes away.

According to Neitzel’s Amazon app, which she now uses to monitor her kids’ interactions with the gadget, Brooke asked Alexa, ” Can you play dollhouse with me and get me a dollhouse?”

After Alexa confirmed the order, the app shows Brooke responded, “I love you so much!”

The Neitzels said they saw this as a teachable moment. They have now activated parental controls requiring a four-digit code for purchases, and have set clear rules for their kids.