Muslims and Mexicans

I'm writing this here because my thoughts on the subject won't fit in a Facebook status.  Perhaps you've heard the news, or perhaps you haven't, that Señor Trump has recently announced his plan to bar Muslims from entering the United States.  I've been hearing and watching the stream of vitriol from this particular candidate for the past months with growing alarm.  I have a good deal of friends who could and might already be affected by the venom this viper spews, and it is for them I write this.

First of all, Mexicans, or Latin Americans in general.  I have a Mexican-born friend who had to leave school suddenly, with no explanation, and I only found out later it was for immigration reasons.  She is not an illegal immigrant.  She was getting a graduate degree, working towards making herself a citizen of great value.  And yet she had to put that all on hold so she could remain legal. About half of the students in my department are from Central or South America.  I have several friends in Mexico, students at the university I visited as a guest lecturer for a week, who are wonderful people, who helped me function with my limited Spanish and awed me with their prowess and skills.  What would they face if they came to my country?  What about the girl I met in the bus station in Mexico,  when I was alone near midnight in a bus station in Guadalajara, I was the only white girl in the station, and I couldn't understand the announcements in the bus terminal, and she immediately took me under her wing, making sure I got on the right bus and got to my destination safely?  Were our places reversed, would she receive the same welcome in my country?  Or would she be treated like a criminal?  Sadly, I think the latter is more accurate.

See, what scares me most is not so much Trump - he is one man spewing crazy.  It is these people who keep supporting him in the polls.  Or even the people who don't support him all the way, but perhaps are quietly grateful for his crazy because it legitimizes their racism and prejudice by contrast.

These people put my friends in danger.  I am legitimately scared for some of my friends, especially my Muslim friends, now.  Or heck, even those who look vaguely Muslim.  Because white people are stupid and can't tell the difference, as the tragic events in Wisconsin show.

Muslims are my friends, they are my teachers, they are my colleagues, they are my neighbors.  And I am scared for them.  I am scared that my friends I met in Canada will never be able to visit me in the United States without fear.  I am scared that some crazy white person could storm one of my classes at Mines, which can easily be half Middle Eastern students.  I am afraid for my friends who are Arab Christians, because white crazy is just going to assume that they are Muslim too.  I am afraid for the Iraqi Christian family at my church, because for the same reason they too are at risk, they who are already refugees, and came to my country as safe haven.  I pray that will not turn into a sick irony.

It was a conversation with one of my dear Muslim friends that got me going back to church after a long hiatus.  Talking with her about her religion made me realize how important mine was to me.   This same friend remembered me on the worst birthday of my life, bringing me a cupcake and a song when I had chained myself to my desk to work after yet another emotional breakdown over my thesis.  And it was an Iranian Muslim friend who quietly told me at a department party that there are still some in world who view America as a good place, an example to the world.  It makes me sick that there are so many in my country who would exclude him unconditionally.  An Arab Christian is helping me survive one of my hardest courses to date now.  Will he be in danger if he doesn't openly wear a cross? I was overjoyed to run into a Turkish friend, who I don't even know if he's Muslim or not, at a scientific conference.  He's also now at risk whenever he comes into my country.

I have heard from some of these friends of extra searches at airports, the difficulties of getting an American visa to merely visit family.  And now we've got this idiot candidate rousing up all the white crazies like the one who recently shot up a Planned Parenthood in Colorado Springs.

I am terrified for my friends.  I am terrified that it's only a matter of time before their rights start getting restricted, before I start hearing of them getting killed for wearing hijab or being in a mosque or looking Arab.  Oh wait, that's already happened, there were the three students in North Carolina.

And no, I am not going to debate the "there are Muslim terrorists!" and "Muslim governments do terrible awful things!" part right now.  I am not talking about terrorists.  I am not talking about governments.  I am talking about people, my people, people I love and respect and admire and care about very, very deeply.

So please, if you as a white/Christian/American person hear someone ranting about "those damn Muslims", shut them down.  Maybe even say something to law enforcement, if you think it's warranted.

Keep my people safe.

A Fading Fear of Faith

I WANT THIS ON MY CAR. NOW.

So I wanted to write about church.  Yup, I go to one.  That seemed like a way scarier statement to make when I lived on the West Coast, than now, where a lecture on campus given by a priest was very nearly standing room only... that was weird for me!  Anyway, I think because I did my undergrad and master's on the West Coast, where things are just a *bit* more liberal in general, I kind of have this skewed vision of how science and religion get along, which may or may not conform to reality.  It actually seems pretty normal at Mines to be religious, at least moderately so.  We don't seem to attract any traveling fire-and-brimstone preachers, anyway.  I kind of miss them... It's way too quiet on this campus without an atheist vs. traveling preacher stand-off now and then!

I've probably just completely undermined my point here, but I wanted to write about the whole I-go-to-church thing because I do think there is a pervasive perception that science and religion aren't compatible.  I think that's true in some cases, for some strains of religious belief, but not for mine.  I think if you believe that the Bible (or other holy text of your choice) is literal, unfailing truth...yeah, science is going to be a bit problematic for you.  That whole "the Earth is 6000 years old thing".... going to cause some issues.

I'm a progressive United Methodist.  I grew up in this church (the "progressive" part came more recently), and I was lucky enough to not grow up in churches that were particularly prone to fire and brimstone.  No one in the church ever told me I couldn't be a scientist!  To be honest, the churches I grew up in were pretty mum about anything controversial.  Oh, there were the usual calls to slow down, spend time with God, be nice to people, but nothing you could really argue with.  I often wishes the churches I grew up in could have been just a little more feisty about...something.  Anything.

The messages I heard, that you couldn't be a scientist and be religious, always came from outside, usually from the world of science.  I'd often hear statements like "Oh, those Christians and their young-Earth ideas"... and I'd always kind of bristle because no church I'd ever attended had preached such things!  But I can definitely understand where science might be just a bit skeptical of faith, Christianity in general.  Though it is now centuries past, the Church's treatment of Galileo still rankles.  And let's not even start on evolution.  Oh dear.  But it's also just a bit hard to swallow, how can a person of faith profess to believe outlandish things like a virgin birth, water from rocks*, and people coming back from the dead, and then still do good science, which rests on the foundation that things must be able to be tested and proven?

*Well, okay, I can see that one being some divinely-inspired geological know-how on Moses's part....

My personal answer to this is that my faith is not just a checklist of things I do and don't believe.  I'll be 100% honest, I have a really hard time wrapping my head around the physical reality of the virgin birth, or Jesus' resurrection, two events that are pretty dang essential to my faith!  I do believe in God, though, that I'm pretty sure of.  For me, the belief in God is the sense of a presence that I simply know to be there.   Even when I realize I'm probably never going to accept the resurrection as physical, unassailable fact, I know I can't shake the feeling that there is a God.  I've come to accept that there are certain elements of my faith that I'll probably never be able to come to terms with, but this doesn't mean I can't have a faith.  I am also lucky enough to have found a church here that makes it very clear that there is no litmus test of faith required to be a part of the church - I am allowed and encouraged to think, reason, and disagree.

Speaking of my church brings me to discuss the real reason I'm often nervous to share with people that I'm Christian and that I attend church.  The church I currently attend is a Reconciling United Methodist Church, meaning that this is a United Methodist Church that is actively working to fully include LGBTQ+* persons in the life of the church.  This means they are welcome to church, to communion, to being married in the church, to everything that any straight, cis-gendered person person would be able to access in the church.

*Please forgive me if I use any incorrect terminology for the rest of this article.  It is not my intent to harm by using language that has become hurtful over time, but I'm not always as on top of things as I should be.  If I have used any language that is now considered hurtful or offensive, I welcome any corrections in the comments.

This, for me, is huge.  I'm cis-gendered and straight, by the way.  But for a very long time, I was reluctant to openly identify as Christian because, as far as I knew, all Christians were supposed to be against homosexuality or anything of that sort because it was a sin.  This seemingly institutionalized hatred, to me, always seemed far more of a sin than being born gay or lesbian, or being trans.  This also seemed to fly in the face of how my parents had taught me to treat people.  So, for a long time, it seemed to me that to be Christian was a form of sin in itself, because to be Christian required to me to exclude certain persons in a way that seemed very out of touch with what I had thought Christ had taught.  I have friends and family who are gay or lesbian, and the last thing I wanted was for them to feel unwelcome, excluded, dirty, because of my faith!

So for most of undergrad I stayed away from Christianity, although I missed the hymns and ceremony of the church services that had been such a consistent part of my childhood.  I also never quite gave up on God - I stopped really thinking about Him much for a while, but I never quite lost the feeling that He was there.

I'm having a hard time remembering when this started to change.  I think some time around the beginning of grad school, I began to hear bits now and then that a different kind of Christianity existed.  I had a few friends from high school who were openly Christian, and I think they may have posted a few things on Facebook suggesting a different interpretation of the relationship between homosexuality and Christianity.  I think the watershed moment was when I ran across the documentary "Fish Out of Water".  I was quite literally bawling when I came to the end of the film, in fact, I'm tearing up now having watched only the trailer!  The film documents the struggles of Christian gays and lesbians, but most crucially, offers alternative interpretations of the Biblical texts used to condemn homosexuality in the church, and documents the works of churches already working to fully include gays in lesbians in the church, including allowing them to marry the people they love.  This film showed me a way out.

The way that was shut to me now seemed open again.  I could be Christian and not be evil!  It may sound ridiculous to some to say such a thing, but before I learned about this new progressive Christianity it really did seem to me that to be Christian was to be forced to be evil, was to be required to be unwelcoming and hurtful.  Now I had learned that I could practice my faith, and actually follow the teachings of Christ, not in shunning or trying to reform "sinners", but rather in welcoming those who had been previously marginalized and shut out.

Around the same time, I encountered a fellow graduate student in Earth sciences who let slip that he was actually an Evangelical Christian.  Wait, what?? That was possible?  To be Christian and a scientist?  An Earth scientist??? That was allowed??  Suddenly more Christians in our department appeared from the woodwork, and we actually had a small Bible study going, still the only one I've ever attended in my life.  It was awesome - we had three Evangelicals, three Catholics, a Serbian Orthodox, and me, the random United Methodist.  I was absolutely terrified to bring my Bible to campus, and oh, the walk down the hall to the little room where we met, trying to hide the little black book all the way, oh that was awful.  I was quite literally in a cold sweat the whole time.

But it was worth it - for the first time, I was finally able to ask questions, and even if they often weren't answered, we at least had discussion, questioning, talk, the kind of conversation I'd never had when I was growing up.  I'm sure that was at least partly an age thing, but I think it was also the church I went to  - as a youth, Christianity seemed to be presented as more about rock and roll church and singing praise songs than discussing faith and learning theology.  I was always the weird one, so I never felt included or confident enough to ask questions.  Yet now, I had a small community of faithful just as weird as me, who weren't afraid of my questions, and didn't force their own faiths down my throat, as I'm (still) always afraid of when meeting other Christians.  They shared their views, and I mine, and we had long, winding discussions, and it was wonderful.

I eventually found a church in Vancouver, where I was living at the time.  It ending up a rather  hilarious situation... Because I had never felt comfortable in modern churches, I purposely sought out a more traditional church.  Having an organ was a requirement!  The first church I visited in my area, I think one person talked to me.  The second church I visited was in a completely different part of town, but I ended up staying there, because immediately at the end of the service I had about 5 people coming over to talk to me!  In hindsight, this was probably mostly because I was a 23 year old who had just showed up in a church where the average age was about 65....

That was a wonderful church, though.  I loved the old-style hymns they played, I was recruited into the choir my second week there by the choir director who had the most amazing dry wit, and the sermons were both progressive and mentally stimulating.  Best of all though, I found what I had never experienced before in a church - a community.  Even though I was about 40 years younger than most of the people at the church, I felt included in a way I had never before.  Despite the older demographic, I was also in a welcoming and accepting church - the second pastor who came while I was there was openly gay, and the head of the United Church at that time was also openly gay.  The people at the church loved the pastor, and didn't hide it.  They also loved me, and didn't hide that either!

When I moved back to Denver for grad school round two, I knew I needed to find a church like the one I had left behind in Vancouver.  By this time I had heard about the Reconciling movement in the United Methodist Church, so I knew this was where I needed to search.  My search algorithm was pretty simple - Reconciling, and has an organ.

I found what I was looking for at Christ Church United Methodist.  This is actually the only church I ever visited in Denver, but I've never felt an urge to look elsewhere.  Just as with my church in Canada, I was recognized as new on my first visit and welcomed by several people.  And, oh, they had a real pipe organ! And they played it, too!  I also got a good read on the culture of the church my first Sunday - it was Super Bowl Sunday, and all the choir had made orange stoles to go with their blue robes, and I think there may have been confetti...  The sermons were intellectually engaging and morally stimulating, engaging with Biblical texts in ways I had never heard before.  I think it was on my second or third visit that the pastor reminded the congregation that he would be performing same-sex marriages, in defiance of the official doctrine of the United Methodist Church.  This is the church I'll be joining, officially, on Sunday.

These amazing women have actually gotten married something like 7 times now, as marriage laws have changed over time in the different places they've lived.  I think this photo is likely #6, at my church!

I'm getting a bit better about being scared to announce that I'm Christian, because I'm much more comfortable about what that means now.  It doesn't mean I sweep under the rug all the pain that has been caused by my religion both now and in the past - I acknowledge it, and it grieves me deeply.  I do not deny that to call myself Christian connects me with countless acts of hate and cruelty across the ages.  What I know now is that it is my duty as a Christian to undo what I can of that pain, by trying to live out what Christianity should be - welcoming, loving, and affirming of all peoples.  I need to witness to the reality that my faith can be welcoming to those that have been marginalized in the past, that we can do our best to listen and make better.

Claiming my identity as a Christian also gives me that much more purpose in my work as a scientist.  Because I am Christian, I am charged to make the work that I have been called to do the very best I can.  This means I must be ethical and honest in my work, and give accurate results that will be good and useful for others.  It means I must support my fellow scientists.  It means that as a female scientist, I must stay the course so that I can hold open the door so that others like me can follow, and keep it open for others for whom it is now only barely opening.  Science isn't just something I do because I love it and it pays a decent salary, it's something I do because I feel called it.

And oh my goodness, science is where I have so many of my religious experiences!  Fourier series, GCV, wavelets, inversion, VOLCANOES, agh, to think that we have a world where these things work!  Isn't that amazing???

....*Hem*, okay reigning in the slightly crazy religious fanatic here.  Although I suppose raving about God in the context of Fourier series is slightly better than eternal damnation?

I hope I haven't come across as trying to convert anyone with this post.  That wasn't the intention.  I simply wanted to share something I'm really excited about, and if it's something that makes you excited too, great!  We can go babble about the holiness of inversion together.  But more seriously, I wanted to share my story because I've realized in this past year how important stories can be.  Stories give us options, stories give us understanding, insight onto new perspectives we might not have encountered before.  Before I started to hear stories about progressive Christianity, I despaired of ever being able to practice my faith with integrity again - now I don't.  More recently, before I heard the life stories of some of the amazing women in my field, I feared getting stuck on an oil and gas track for life - now I don't.  So I hope this little outburst of mine perhaps helps someone out there realize - there are options.  There are alternatives.  There are many stories to be told.

Feelings on Feminism

I actually wrote this about a month or so ago, but am posting it now because the (male) professor in my "Intro to Research Ethics" class (not actually as dry as it sounds) praised the fact that I had written about how being a woman in a traditionally male-dominated field is actually a pretty big driving force propelling me forward in geophysics.  I felt pretty intensely uncomfortable about being "revealed" publicly as a feminist, even in a positive sense.  The conflicting feelings I felt today - wanting to stand behind what I wrote, but feeling a great deal of trepidation over being "outed" as a feminist, reminded me of this post I wrote some weeks ago.  Also the fact that I actually had something of a night off, for once... 

The few weeks during which there was an uproar over a certain shirt were a bit jarring for me.  Mostly, because I was just shocked at the denial that the shirt was sexist*, in such tones as to suggest that this denial was simply common sense. I’m not going to jump into the argument over whether or not the shirt was sexist, because I’ve already done that, and that’s part of why I felt the need to write this.  I feel the need to explain a bit about why I keep posting all those articles, why I don’t post some other articles, why I am feminist, and why I felt a bit queasy about writing that last phrase.  

*The context in which the shirt was worn being a HUGE part of this

First, what I post and what I don’t post.  I would like to point out that the article I posted about the blankety-blank shirt was actually an attempt to move on from the issue.  The article I posted described how a female scientist saw the shirt, and did her own remake by photo-shopping the visages of notable female scientists onto the shirt, transforming the shirt from a symbol of latent sexism and microagression to a celebration of women’s contributions to science.  This is the kind of article I like to post, because there are few things that turn me off more than an angry diatribe*.  Mostly, though, I feel there are plenty of articles floating around about all the things that are wrong, and not enough about what to do about it.  I may be disadvantaged in terms of my gender, but this is very much not the case where race is concerned.  From my white perspective, I know how frustrating it is to be told always what NOT to do, and be always be wondering what I could possibly do to help and not hinder.  So when I find articles that offer helpful instruction, or information about methods that work to lessen the obstacles that women face in today’s society, those are the ones that I try to share. 

*although sometimes those are very much needed.

I also delight in sharing encouraging stories, when I can, about awesome women doing awesome things.  The article I posted related to the @#$@#$ shirt falls in this category.  One of my qualms about many of the feminist articles I read is the overall tone of doom and gloom (more on this later), and so I try to alleviate this when I can, as much for my own sake as anyone else’s.

Of course, I’m human, so I will occasionally go on a brief (say, two or three) article posting spree.  I actually just took a spin through my Facebok feed from the last nine months or so, and was somewhat confused to find very few posts on feminism.  So either I don’t post as much as I think I do or Facebook is hiding things.  Not really sure.  ANYWAY, most of the articles/videos/etc that I avoid posting are the gut-reaction ones, you know, the pictures that have some poignant picture and some sassy one phrase statement.  I may get a kick out of them sometimes, but I generally avoid sharing them because I don’t think they help.  I think they give those of us “in the feminist club” a thing to chuckle about, and give those “outside the club” another thing to get pissed off at.  So nothing is really accomplished.  I’d much rather help people see a reason to listen, and make them think.  Unfortunately, this strategy means posting a bunch of long articles I’m pretty sure not a lot of people read. 

So why care?  Well, for one, selfish interests.  I’m a woman in a male dominated field.  For most of the time I’ve worked there, my office has had one woman in the building – me.  We’ve recently hired a full time female geophysicist*, so now that’s increased to all of two.  Out of about twenty five or so humans in the whole building.  I will say right now that any bad experiences I’ve had related to my gender have been very, very mild, mostly just loneliness and a sense of having to be extra awesome to adequately represent my gender.  But there is something really off about these gender ratios!  Other selfish interest – I haven’t faced much gender discrimination or violence yet, but that doesn’t mean I won’t sometime in the future.  I’ve already had the experience of having a stalker for several years,  I regularly have to strategically avoid certain men at social dance events, and our advisors had to specifically tell the women in our research group to be aware of bad situations prior to our sponsors' meeting.**  I’ve had friends who have faced worse – leaving their careers because of hostile work environments, abuse, rape.

*Who did the survey planning for a 4-D gravity survey I may end up studying, fan girl swoon.

**I will say I’m very glad they were open about this, instead of sweeping it under the rug as a shameful thing that was only the women’s fault.  This shows awareness and integrity, and I salute them for it.

It is hard to un-see a thing once it is seen.  I have read so many articles on the challenges women face, particularly in science, that it is hard now not to automatically notice gender ratios at a conference, see who is presented as “successful” in an article*, notice who professors will praise and who they only mention, notice how all the founding scientists of geophysics are men.  I get tired of noticing all the extra things I have to think about as a female – is it safe to walk down this street?  Is this guy talking to me a threat or just friendly?  Do I need to stop dancing with this guy before he gets “ideas”?  

*All men, surprise. Should really have saved that article link, sorry.

It all gets me just a bit riled up.  It’s hard for me, sometimes, to imagine a reality in which I wouldn’t have to think about these things as a matter of daily life – the reality of a white male.  He only has to think about these things if he decides to, for me, it’s my reality all the time.  And I know it is so, so much worse for other women.  I’ve been rather ridiculously lucky to have the worse thing to happen to me be a few minor stalking episodes.  I can’t imagine having to deal with the trauma of something worse, AND being the only one around who will speak up about the societal systems that make such things common.  So because I have been relatively unscathed, I feel it’s my duty to speak up, as someone who’s “made it” so far.

And now for why I cringe at calling myself “feminist”.  Part of it’s a personality quirk.  I’m extremely contrarian by nature, so I instinctively hate associating myself with a label or a group.  For the same reason I cringe at calling myself “environmentalist”, even though I probably for all intents and purposes am*.  But on a deeper level, I worry about what all this does to me, on both an internal and external level.  I don’t deny that feminism needs to be a thing.  There’s too much stupid stuff in the world that just needs to change.  However, it gets exhausting being angry so much.  It is hard to un-see things, and harder to know that if I want to call them out I’m going to have to fight an uphill battle against very entrenched mindsets.  The anger is insidious, and more than once I have felt the danger of it poisoning friendships and relationships.  I am not a vindictive person, and I do not like finding I am angry at someone.  But because I am a faulty human being, I often find it hard to separate a person from their views, when those view run counter to something that is so very important to me, both as an issue and as a reality of my life. 

*which is just FUN when the research you love is funded by the extraction industries….

I also worry how my feminist views affect how people see me.  I wonder if employers, who is my field are pretty likely to be older white males, are going to find out about my feminist views and associations and think, oh, here is a white hot flaming feminist, she won’t do good work in our mostly male company. She is emotional and irrational, we don’t want her.  I wonder how my friends see me – do they see me as fiery emotional feminist firebrand on fire?  It is so important to me that people be able to talk to me, and the idea that people might not talk to me for fear of being attacked distresses me, all the more so because I know what that feels like in my identity as a White Upper-Middle Class Anglo Saxon Protestant American.  I don’t want to inflict that on my friends!  

Nonetheless, there are the people who quietly tell me that reading some article I posted empowered them, or helped them realize a difficult situation wasn’t actually just them being weak.  I’ve had older women tell me on more than one occasion to keep fighting, to not let slide the gains they made in their generation.  And that is very heartening.  But I am a pacifist at heart, and I find it hard to come to terms with the fact that sometimes conflict is necessary in order to fix things that need fixing.

So why am I still feministing?  Well, I’m a very stubborn optimist, and a lover of history.  At the SEG, we had a panel of prominent women in geophysics speak about their experiences in geophysics.  Something I have been thinking about a lot lately, when I am feeling overwhelmed by all the stupid resistance one can get for daring even to criticize a @%^% shirt:  would these women, one of whom was the first ever female PhD in EM (electromagnetism) and another who still remains the only female president of the SEG, have believed that one day I’d be in a geophysics research group that was slightly over 50% female?  Would they have believed that I would make it to the second half of my master’s before I realized, oh wait a minute, some people think I’m not supposed to do this?  I’d like to think they would have.  So I’m going to stubbornly believe that today’s trolls will be tomorrow’s history lessons, that the idea of not having equal numbers of women and men at an engineering school will be something for my children to gasp and giggle at.  That someday, I won’t have to explain to a man why a shirt is sexist, and I won’t even see the shirt in the first place.  I’m hoping that some day I’ll have some really hair-raising stories, and that they will be just that – stories, and no longer reality.

Tortuous Translations

I'm rather certain the sender of this email on one of my listservs did not intend this to be the message.... nonetheless, I do hope you enjoy Google's automated translation of the garble of Chinese characters I received in my inbox.  I've bolded my favorite bits....Pigwash soup, anyone?

Xi Shi ⁍ Jinaipiejing  confused Lian Mei Chung  Tianlieniumei Huichaoceonlang ഊ 7 Jinaipiejing 䁷 Yingshenkemeng ਍੔ desert hunting pull Juanyoumoshao ⁵ Clocks Bishouwuden ⁶ Yu ⁴ bridge ⁗ pigwash soup ⁗ Congmojujian ⁶ Mei Shi Jue ഊ 2 ⼯ gushing sound of water gushing 渮 askance peg ⹥ She ⽭ Lian Yi Rui Mei worry destination time Yingshengtajia Fangxiaoqinqu 9 climb ⁶ Yu ⁥ gushing peg Ⱐ Jiaoshi ⁡ Ai Xi to ⁷ Shiren hunting Mensantianshao ⁢ Run Otaki ⁴ Guo Jing Ci ❨ ਉ Jiafangxiaoqin Dongfang Nanaiyuni Yi ⹥ She ഊഊ Huoqingjianqu Fangguanrenjin Mixunmuchao  Lvhuichuying Jinmogumeng ⁡ Li ਉ Jiafangyaoqin Dong decanted away Tuchuangniyi ⹥ She ഊഊ lump Xia ⁲ Shuxiongchuben ⁰ Jiqianmike Di ⁹ Sajuluanmen Santiangutu ⁳ desert Di ⁩ Ceon Wu Fang ⁳ Quan Dinner criticize ੴ radial tear drainage ≒ Yi ⁃ tide Wenbanceonliao ⁍ Jinaisanjing ⁤ Yang Ai Yun Zhi Cong ⸮∍਍਍੔ ❳⁔ collapse frieze masked civet ഊഊ † ‱ ⸠ 䕬 scattered tinkling of gems tide ⁍ frieze Guxiaohuangmi 䱡䵡 to Cheng Yu Zhi Bojiaomanshe ⁓ Liexiayingmeng ⁰ Tudidunqu ო ਠ †† ⁒ Meiminiejie ⁅ Man & T. ⁓ Liexiawanshan different Rui Shi Yan Ying Chuan 䑡 ⤍਍਍ਭ ⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭო ਍੍ Aixi㨠 ㄍ ੄ to deter Ke Yi ⁗ Ⱐ㈳⁊ SHE '〱 㐠 ㄴ 㨴 〺㈶〵〰ഊ 䙲 Tan 㨠 Shanruijiaoying 䑡 Shi Chuan different! Shanruiyanling 䑡 different Shi Chuan 䁲 Meinangkezai ഊ Luanmensanfa ⁛ 䵹 Fangxiaoqinru ⁅ Zhizongguqu 䵩 Juankuiguden ⁌ slow ⁍ consider Hui knock ⽒ Aiyirensaeng ਉ wine container 楥 Ban Mei Tian Denghuiyingchao ⁒ Meiminiejie ⁅ Man & T. ⁓ Transition Xia Jia Wan ഊ Boom 㨠 Fangshan Qintingniyi ⹥ She ഊ 䵥 angry dog ​​Hui Li 䥄 㨠 㰵 ㍄〰 䙁 䄮 㠰 ㅀ matter Wan ⹥ She 㸍 ੃ ⵔ Ban Chao Wen Gao Yi Sheng ⁴ Shuquanpianpanglian ⁣ 㴢 entire radial Mu Shi Lu Chuan ㄲ 㔲 ∍਍੄ decanted away 䅬 Shui Yi Ju ഊഊ ⡷ Direndiegai Shenweitanzhen 楥 Ceonjingjutong Bian Yu Ji Tu ⁰ Ying Chung ape ഊഊ Zhou Mi. 䕡 contravene Ren wine container 楥 Zhimin Mi. 䑥 Lan contravene wet Ban ⁡ Tian left Wan ⁕ Dongzhengmuti Cimei  Au Bu Yong ⁴ Desert Dinner Jing ⁴ bridge ੰ Tu Tichunqulao ⁅ Jizong Guqusihuang Mi. 䵩 volume expansive 䅮 Kee Jin knock 䕐 䵁 ⤠ Wuchemulang  special consideration Hui knock ⼠ ഊ Fangjiaomanshe ⁳ Liexiayingmeng ⁴ Moheiqiaojiao Mijinmikui knock Shedunqulao ⁡ apply `⵳ Quanzong Guyiwenju 䩅 Ci ੊ Lei ⴸ 㔳 u ⁆ 楥 soup ⁅ Haoruchunqu 䕬 scattered tinkling of gems tide ⁍ frieze Guxiaohuangnang ⁔ bridge ⁅ Jizongguqu 䵩 Juankuiguden ੌ slow ⁍ knock consider Hui Shi from forming dark ⁓ Liexiayingmeng ⁷ peg Chu Shui ഊഊ 㼠 䵡 ⁡ Shi Shi Chu Mu Wen Quan  ⁡ apply ⁊ 䕏 䰠 䩘 䄭 㠵 ㌰ 䘠 䙩 King stabbed 䕭 Mei Hui Chao ⁅ Zhisongguqu ഊ 䵩 volume collapse revolves Alto ഊ 㼠 Zilianqulv Shuoqianhuimeng ⁲ Ai Yirenqiaomu ⁡ Zhao Shi ⁳ Tangpanceonchu ⁴ ⁵ Jiao bridge  Yingjinmochu Mengqianyaban ഊ 㼠 Siheisongmo hunting Huishaotianjing Jushuowenjian Qin Tang Hao picked ⁡ Naolvshuochu Sumengwujin ⁵ Jiaomu  Mi. ഊ & T. Chu Ying Mengqianyaban ഊ 㼠 䵡 ⁡ Chu Chu Shi Shi Zhen Jing ⁤ tumultuous collapse ⁡ Yu Ying Jianshenmenglv Xi Mang Lai Hui ਿ⁍ consider Mojinmichu Mengqianyaban ⁵ Xi to ⁳ Shekeyulan ⁢ peg confused Chung Ⱐ Lvshuojinmo Buliegushu ⁷ dare Huiwen ഊ 㼠 䍯 Shaomoyuwen ⁡ Jing ⁶ Xiazhijujiao Quanmeimojing Jujinmochu Mengqianyapan Cheng Lai ਿ⁁ Didunyushen Fangningchaohui Kuoguyingai  ⁤ Zhi Zhen Han Tang Zhimin ⁩ Jingkuiyaban  Yingtumianlv Jin Gai Jin Mei ੰ Gulangdaoqu ਍੅ Sha knock 楥 Minmolvjin Qichuyinglai Tanzhenmeijin ⁡ ⽯ Shi Ju Zhuqiaojuchu Shemengwujin  Sheqiaoyubian ⁢ Ci ഊ 䕍 Cheng ⁩ Ceonai Jiaobanyudan ⁓ Tanmoshuquan matter Xia Lian Wan  Banliantongyong ⁡ Qujingsanqiang tide  Mei Mei Guxiaohuangmo ੰ Fanghanmuyang Miyutiantang Tianyunfangnan Weiyangxiacong ⁔ bridge ⁩ Nanqiangyuxia Tian Lu Jing ⁴ indignant desert canal Alto  䩅 Ci ੳ knock scabies Wan ⁣ Chaoqiangguantian Lvshuoxunyi ⁡ Wumutianlao  Weijinluolao Zhi Qiangliantongyong ⁩ Ceonshuoxunzong Ke ⸍਍੅ Gumayangmo Laozhi Jianshisongshe ⁡ Fang Ai Sha ⁥ Sanwenshuolang ⁨ Tan stabbed consider ⁍⹓⸠ dig into account pigwash ⁡⁐ Er 䐮 ੤ Qifangmichu ⁧ Min Veterinary 楥 Mianmolvshuo Zhuqiaojufang Wuwenshuomo Shouyugutu Ceonchuquwen Chuyingbowen matter Jinceon ഊ Fangjiaomanshe ⸠ Boom ⁡ gray tumultuous Ⱐ Jianshisongshe Ai ⁳ Yingsheshuobei ⁴ desert 㼍 ਍2 Jue Hui 㨯 ⽪ Huangxianwuwan ⹥ She ⽡ Huigujianpan Tuanshengyingdu Manke PLAY Tushishungang 䩯 Shang whole Lianbianwennou ⹪ hunting 㽰 Tu Chung Ying 䥤 㴱 㜹 ㈲ 㐠 ഊഊഊ Lvshuosheshi homes ⁡ ⁣ Hei knock  entire Wen climb ⁃ suck ⁳ Shiwenyapan  Yingfangjiaoman homes ⁩ Banqiaoaicuo Ⱐ consider stabbed ഊ Yu Yatuandaoban Guantianchujing Si Shedunqulao ⁴ quince knock Xia Yan ⁲ London Wan Xian ⁁ gray Gujianyingchao ⁲ 楥 Zhen Ji Mian Lu Jing Chu  ੢ Drainage Xi Hongyangdenju ㄬ '〱 㐬 ⁡ Shen Shi ⁷ peg Daobanchulue ⁵ ⁴ bridge ⁰ peg Ban Tu Dichunqumei 0 peg Zhili ⁔ bridge ⁥ Shasanwenshuo Mengmantianxi Wen ⁦ pigwash ⁴ bridge ⁰ Tu Tidunqumei ⁊ consider Gai special ‱ Ⱐ㈰ ㄵ ⸍਍੔ bridge ⁳ Shi dark ⁳ Liexiayingmeng ⁷ peg Shen Alto ⁥ Gumayangmi Lang ⁡ gray tumultuous ⁦ pigwash ⁥ Huaqiaoyushen Fangjiaomanshe 0 ⁡ Shi Chung Mu Mount ⁴ bridge ⁰ Tuti Shunqulujing ⁰ revolves scabies Tang  Huishaozhaodong Ai Ying Chao She ⁦ pigwash ⁣ Song Chu Ying ഊ Chutangxunshi Xia Tian Hui Fangjiaomanshe ⁵ ⁴ Bay Bridge ⁅ Jing Shen Ti 䄠 energy efficient compact fluorescent  ⁷ & T. knock ⁦ accustomed peg Qing Lian Shi 楥 Ceon ഊ Wuyangmoshe ⁒ frieze Nang ⁏ knock ⁥ & T. Chemengchuying Bulieguying 䕡 contravene Tian Ren Ai ⁡ wine container 楥 Hunmolvshuo three remaining Wan Han Tang Zhimin⁉ 䍐 ⵍ Carpenter ⡷ Direnwujiao Yu ⁦ Guanqiadici Jingjuqiangguan Mijingyangxia Tian consider Shuomeizhukui frieze ੡ Yuxiongjiaowei ⁰ Langqubengu Mei Shi Shi  SHE knock ⁡ ⁡ Quan Ying Zhen Mei Ai ⁦ peg ⁤ pigwash ⁳ Gaojinaimei  ੐ ⵔ⁳ sooner Ying Yang Huo pile Ai Ⱐ 䙔 䥒 Ⱐ quiet gushing measured ⁓ 䕍 ⁔ 䕍 Hedgehog Hedgehog Hedgehog ⁘ cut the throat ⁘ Wo ⁦ pigwash ⁶ Man Dun jyo ⁳ sooner Xiangxi Mi. ഊ Shemanguanwen Wuseyingchao Ⱐ Jing Shen energy efficient compact fluorescent ⁷ ⁷ elata Mimuyongmo flooded ⁣ Tan Jin Ling Shi Ying Chao Shi 楥 ⁦ accustomed peg offer ഊഊ 䙯 Chu Ju Ju Qi Jing Si contravene bridge canal consider deterrence Dun Nan stabbed knock 楥 hedgehog ⁣ tide Ou Tang Shi Song ⁒ number / compact fluorescent pestle Hong Ou Tang number resentful ഊ ⡒ ⹄ Qianchuhongxie matter Wan ⹥ She ⤮ഊഊ left Wan ⁕ Tongzhengmushi Cimei ⁡ Drainage 䕱 Gaishenbaideng contravene Mu Shiying 䅦 Dinner Sishejiemo 䅣 Ying Chao ⁅ Lianhongxiangpao ഊഊഊ Yan Ze ਍ਭ ჰ ഊ ⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭო ੒ Ou Tang number / compact fluorescent pestle Hong Min Min Yu Wen ⁐ ਍ੁ angry dog ​​angry dog ​​revolves Han pigwash ഊ 䑥 contravene wet Ban Lan Ying 䕡  contravene Ren 楥 Zhimin wine container lintel Mi. Nie Ying Jie ੒ knock Huishu ഊ 㘱 〰⁍ canal but Lian Fang entire Ⱐ 䵓 ‱ ㈶ഊ 䡯 jyo Lang measured ⁔ Baihe 㜷 〰 㔬 ⁕ ten ഊ Ci 㨠 ⬱ⴷ ㄳ ⴳ 㐸 ⴲ 㘶 㐍 ੆ Chi 㨠 ⬱ⴷ ㄳ ⴳ 㐸 ⴵ㈱ 㐍 ਍2 Jue sound of water ⼯ Gaijuanyishi ⹲ Meinangkening number contravene ഊ ⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭⴭო ਍ਭ ⴭⴭⴭⴭⴭⴭჰ Quan Hua Tu ⁰ Mantian ⴭⴭⴭⴭⴭⴭⴭ ഊ═ 䑆 ⴱ⸵ ഊ┿ 㼍 ਱〠〠 Huang Ze ਼ 㰯 䱩 Tumanrouke ‱ a still "㜳 㠲 ⽏ ‱ ㈯ 䔠 ㌲ 㜹 ㄯ Qiu ㄯ bark ㌷〸〯 䠠 Can 㐵 㠠 ㄵ ㉝ 㸾 ഊ Xia Zhi palpable ഊ ††††††††† ഊ ㄷ ‰  palpable ഊ 㰼 ⽄ Sanrunchenman Yi Yu Nan Shan 㰼 ⽃ ‴ contrast Fangmozongshao ‱ ㈾㸯 䙩 Bian dirty knock ⽆ unwinding Tang Wen 䑥 Month 䑛 㰲 〱 䄵 㤸 䕆 䌸 㠶 㙃 ㅅ 䍅 䉂 ㉅㉁㉄ 㤸 䌳 㘾 㰲 䐱 〷 䕄 㔶 䉄 䐸 〴 㜹 䘱 䅄 㔷 㠱 㐱 䔲 䘲 㠾 Yin 䥮 Tangceok ㄰ ‱ 㙝 Month Sheng desert 㤠 〠 Geng 䱥 Chung & T. `㘯 Cai Zhen" 㜰 㠱 ⽒ Xun Tian ㄱ ‰ ⁒ from forming Rou Mi. ㈶ running water Gaozhishidun ⽗ Mun '‱ Yao 㹳 tinkling of gems Yi Si 2 㽢 twitch Guai fork ഊ Ȓ ౾ 䀿㼑 㼇 ␿ 㼉 㼿 㼿 troubled 䠉 ̣ Nai 㼀 Ć 㼇 㽥 Shimengfangyin ഊ palpable Xia Zhi Xuan ഊ Mengmanbinfang ਰ ഊ┥ 䕏 䘍 ਠ ††† ਲ 㔠 〠 Bian Huang Ze ਼ 㰯 䙩 knock ⽆ dirt Wen 䑥Month ‸ 㤯 䰠 unwinding Tang Xia Qianren 㘸 㜳 a still from forming "㠾 㹳 tinkling of gems Yi Si 2 㽠 Guaiqueyihuai 㼿 㼿 జ ഊ 㼿 Qie 㼿 㼿 㽢 㼿 ݐ 㼿 㼿 ᤿ ഊ 㼀 Shu Xia ࠭ഊ Kouqiangyisi ੥ Shi Huang Huang Ze Ze ਱ ㄠ 〠 ਼ 㰯 䵥 Shi Xi Shi '‰ ⁒ contrast Hui Dimanjingceon 㘠 〠 Gengzhanlaiceon 㠠 〠 Geng Yi Quan ⽃ deterrence Qinzhen 㸾 ഊ Xia Zhi palpable ഊ ㄲ ‰  palpable ഊ 㰼⽃ Chaowenbanceon ㄴ ‰ ⁒ ⽃ Guzeshanying ‰ "ㄲ ‷ 㤲 Yin 䵥 Moyongshanying ‰" ㄲ ‷ 㤲 Yinzhanfangban ‸ ‰ ⁒ ⽒ Aisarenai ‱ 㠠 〠 Gengfushiwen ‰ running water Gaozhizhanlai 㸾 ഊ Xia Zhi palpable ഊ ㄳ ‰  palpable ഊ 㰼 ⽆ peg Wencheng 䙬 Shewusanrun support 䙩 Mutian 㐸 a still Qiu Xia Qian Ren 㔹 ㄯ 㜯 Yiquan ⽏ palpable but send 㹳 tinkling of gems Yi Si 2 㼿Wan 㼔 㼿 㼿 manually ≕ 㼠 ჭ 㼿 㼿 㼇 㝸 㼩 ᜿ 㼚 㼕 㼿 䥼 basket 㼿 㽠 䍠 㼇 Ping 㼃 㼿 㠿 ⸅ 㼝 ɷ 㼿 㼿 ഊ 㼿 㼿 㼞 Juan 㼼 䘑 㼿 㼿 㼿 㼴 㼿 ᭞ 㑵 㽈 㼤 㼿 䤿Geng 㘲 Hou 㼿 㽩 㼿 La 㼿 㼿 㼿 Qian alkali children create ㍠␙ Meng ؿ Dai 㽆 Gui 㽴 㽤 㼠 ᰲሿ 㼿 pulp ഊ ᠿ 㼿 ᬚ Fan ℶⴸ 㼿 grid 㼿 㼰 Jiangxi 㼿 㼔 䬿 㼿 Wu 㼗 diarrhea 㼿 ⴿ ὸ 㽋 beast 㔿 㼨┱ ᄝ 〿 䔲 䭍 ⡑ 㽔 㼿 㼔 㽱 㵙 㔿 ᘳ Hu 㽑 㼩 ⑐ 㼨 humble Jiu Ba 㼿 㼌 㼿 㽦 䐿 㼪 㼿 㼡 Gui 㔿 㽸 㼿 㼿 Ἦ 䁎 㼿 ి 㼯 ഊ 㼿 㼴 㼿 㼿 㽋 㼿 㼿 㽿 㼿: ᨿ 㽄 㼿 ୃ ⴮〿 㼱 㽣 㼿 FILE ᘿ Hey 㼱 㽽 Tian Կ SDWK 㽽 political 㥰 ༿ Jian 㼿 㽉 ⽘ 㽧 㼿 㼿 㼿 䀿 㼺 㼿 㼿 㼿 䘿 gall 㼿 ፾ 㽧 㼿 㼈 ∿ 㼙 ᘭ 㼿 㽺 ܿ ؿ times ਿ Ć 㼿Shu ੥ Shimengfangyin ഊ Xia Zhi palpable ഊ ㄴ ‰  palpable ഊ 㰼 ⽆ peg Wencheng 䙬 Shewusanrun support 䱥 Chung & T. '㐶 㤾 㹳 tinkling of gems Yi Si 2 yrs old 㽘 㼕 㼿 䔿 㼿 㼿 㼿 㽌 㽀 ␤Π䠿 ‿ plug 㼿 㼑 㼿 Luo 㼿 ᭽ 㽴 㼿 alkali 㼿 㽩 㼿 OilPainting 㼿 㽠 ᬿ 㽾 㼿 䐳 㼿 䝳 㘿 㼿 㼻 㼿 㼿 ᘿా 㽴 㼿 㽤 㽍 㼿 㽤 Sao 㼿 㼿 㽫 ☷ 㼷 㼿 㼿 㼿 㼿 ᤿ 㼿 㽸 㽜㼿 㽂 㼋 㼹 ⱳ 㼾 㼂 㼿 ጿ 㽮 㼿 㼿 㼿 㤿 㽾 Jia 㼿 POINT 㼿 㼹 Ṋ 䕙 㼿 㼿 㼧 㼎 㼬 Pie 㼿 Yan Hui 㙪 㽛 㼿 㼖 㼿 ᘿ 㼿 ጽ basket Kuangxian 㼿 㼿 㼿 〹 㼿 㼿 㼿 Xiang draft 㼿 wail ㄯ 㽵 㽇 㼿 ጲ E miasma 㽙 㼿 㼿 㼸 ༸ 㼿 䜿 cat 㼳 Ը 㼿 ᐿ 㼿 Jian 㼣 ဈ Kuang 㼿 ୋ ഊ Yan 㼿 㥗 K 㼖 alkali ⬿ paint 㼰 㽹 㼉 Hey 㽚 㼿 㼿 㼕 㼿 㼿 Nai 㼿 䤿Houlu 㽥 㼿 㼿 㼿 㼿 䩖 㼗 ͹ Mu 䤑 Liu 㼿 㼿 ᘧ 㼕 hinder ࠿ 㽫 ࠿ declare The 㼿 alkali ⵞ ొ 㼐 㼍 ਿ 㽓 㽝 㼳 㼿 㽲 㽇 POINT 㼮 㽓 㼿 㼿 㼿 㼘 㼿 ⸿ 㽘 㼿 ᠿ Sao 㼥 㽛 ⰿ ㈿ഊ 㼴 䁀 ؿ 㼿 Bai Yu 㬛 㼿 㼿 㼠 㕨 㽭 㸿 E 㼿 㼜 㼦 ሿ 穨 㼿 㼍 ਼℟ 㼨 䐿 public bathhouse 㼍 ੻ 䨈 㼿 㼡 䍍 Fu Hu ̿ children ㈿ 㼿 ㈞ book 㽸 㔿 㽩 㽫 㰿 㼿 㽅 Կ㼿 ဿ ⼵ Ḵ 㼿 㽊 ape genus 㼕 Mo ㈿ 㘿 ̿ thiophene advocate 㼔 㼂 㕒 㨣 㼿 㽶 ؝᰿ 㽩 㽒 㼿 㽋 㼒 㼫 㼱 㼿 㼿 Gou 㼿 䁑 ഊ 㼿 Hey 㼿 㽺 ✿ POINT ᜕ 㼿 㼿 alkali children ᄿ 㼿 㼛㼿 Ga ⌙ 䜿 㼩 㽅 not hide 㜹 ᤿ 㽯 㼿 ⸿ 㼿 discontented with oneself 㼿 㼼 㽢 㠿 䐛 㼿 㽎 㼯 㼿 ‿ 㽹 ᄿ 㼞 㼿 㼿 㼻 㼣 ि 㼿 㼆 ฿ ㌩ 㼿 Mo debt 㼿 㽓 Wuchengyingxiao ṍ Fan 㼿 㼿㼮 willing Chan 㤿 㼍 ਿ Chuang 㼚 ഊ⥄ 㼿 䜿 㼿 morpholino 㼚 㽟 ᐿ paper it 7 㼿 ᠿ 㽮 㼿 ഊ ȕ 䤿 ㈿ Fu hide 㼿 ape 㽶 㽴 㼿 Fu Shan 䕯 㤿 㼿 㼿 㼿 㼁 䈁 㼿 㼐 㼿 Yi ape ȿ 㼿☿ᬿ Ba Shan 㼿 㼿 㼨 㽊 㼿 㼎 ᘔ Da 㼹 㼿 CANCEL POINT 䤱 㼿 ℓᱜԿ 㼿 Yan 㽲 㼍 ਃ 㼎 㼿 political ᰔ 㼿 ᨿഊ 㽒 㼼 ✿ᠿ 㽪 㼿 㼿 ㈽ goblet Etan ⴿ Peng 㼿 㽼 㼿 㘿 cliff 䬿 ᴿ㼿 㼿 Jiu 䬎 㼿 㼿 The factory 㽺 㽭 㼈 㼿 ⌿ Dai Xiang ugly ┿⑻ⅽ 㼿 each ᄿ 㤿 㽵 㬿 㼿 ᰿ 㼿 㼿 㽎 㼿 Yan Yue 㼿 ✿ You 㼸 㼃 㼿 㼒 㽭 square 㼿 discontented with oneself 

Multiple Magnificent Mathematicians

This is not a rant!  Nor is it a long-winded reflection on a topic of interest to me.  Nay, it is a fan tribute of the geekiest kind!

You see, I simply must tell you about two amazing mathematicians I encountered in recent ramblings on Wikipedia.  Well, I say ramblings, but really I was turning to Wikipedia in desperation for SOME sort of plain English description of two rather hairy (but very very cool) mathematical thingamabobs*.  Oh, and did I mention they're female**?

*I am absolutely certain there's a more correct term, but I am completely blanking right now on what that would be.  This is what two finals after three years of no exams will do to a person.
**The mathematicians.  Not the thingamabobs.  In English, at least, mathematical thingamabobs have no gender.  Also, the mathematicians do not appear to be particularly hairy.

Thigamabob #1: Wavelets.  Of the Daubechies kind.

Wavelets are COOL.  What is a wavelet, you cry?  Well, you know sine curves?  Those things you had to mess with in trig*?  Well, a wavelet is kind of like just a little part of a sine curve.  Sine curves, you see, don't end.  They just go on and on and on FOREVER going up and down, up and down, etc etc.  Wavelets, on the other hand, go up once (or a few times), down once (or a few times), and then they're done.  That's it.  That's all you get.

*For the record, I hated trig.  Although that was more to do with having a teacher who hated teaching, and was one year away from retirement.  I still, however, shudder when my sister asks me for help with trig identities...

THIS IS A SINE CURVE!  It goes on and on and on and on and on and on and on....

This is a wavelet.  It doesn't.

So WHY are they cool?  Well, first I have to tell you about a Fourier Transform.  DON'T PANIC.  They're awesome too.  Okay, who here plays a musical instrument/sings?  Oh heck, who here listens to music?  That would be everyone.  Okay.  Great.  SO.  A note is caused by something (Piano string, vocal chords, rubber bands, kazoos...) vibrating at a specific frequency.  If you were to track the position of that vibrating thing over time, and make a graph of the position of the thing as time went on, you would get a sine curve (or a cosine shifted by π/2, if you're feeling frisky).  The frequency of the sine curve, which is what determines what note you get, is the time (distance on the graph), between the bumps on the sine curve.  When the bumps are closer together, you get higher notes/higher frequencies, and when the bumps are farther apart, you lower notes/frequencies.

Okay, still with me?  So, say you have a chord.  A chord is made of different notes, so different frequencies.  So if you plotted the movement of the vibrating music thingy over time, you would get something that looks kind of complicated:

LIKE THIS.  Bit more complicated, eh?

So, what if we want to know what notes are in that chord, just by looking at that curve?  Well, it's pretty hard just looking at that curve.  You could make a guess, but it'd be hard.  This is where Fourier transforms come in!!  A Fourier transform takes your complicated sine curve, and turns it into a plot of the different frequencies, and how strong those frequencies are:

LIKE THIS.  See, the spikes tell you what the three notes are!

Ta da! Now we can see what notes were in that chord!  Cool, right??  FOURIER TRANSFORMS ARE AWESOME.  You can use them for all sorts of cool things, like filtering seismic data to see seismic signals that relate to magma moving around, or you can look at gravity data and figure out if you got a lot of deep stuff or a lot of shallow stuff.

*hem*.  So, what more could we possibly want?  Well, there's a rather crucial limitation to a Fourier transform - it assumes your sine curve goes on forever.  Well, what if it doesn't?  WHAT DO WE DO???

Never fear, the wavelets are here!!!  Wavelets don't go on forever, so we can use them to search for notes/frequencies that only pop up for a certain time, and then go away.  How do we do this?  Well, we take the the basic wavelet shape (there are different kind of wavelets, more on this later), and we stretch it, make it bigger, etc., and then run it across our signal and figure out which distortions of the wavelet fit where.  So if a signal had lots of low notes in the beginning, that's where all the way stretched out wavelets would fit well, and if we had lots of high notes in the end, that's where all the squished wavelets would fit well.

The thing on the left is the basic Haar wavelet.  The basic form is called the "mother wavelet".  The things on the right are the mother wavelet shifted and stretched, kind of like how kids might get a real mother all bent out of shape...

So a really simple kind of wavelet is the Haar wavelet.  That's the one above this paragraph.  It works pretty well for some things, but you'll notice it's pretty blocky.  What if our signal isn't particularly blocky?  The Haar wavelet might not work so well for analyzing it.

And now comes along the very much awesome Ingrid Daubechies.  She developed a class of wavelets (now known as, unsurprisingly, Daubechies wavelets) that are both more detailed, and easier to work with than Haar wavelets.  And here I must confess my knowledge runs thin, because although I've had great fun playing around with Haar wavelets, I don't know all that much about the nitty gritty details of Daubechies wavelets.  However, I DO know that they get used A LOT.  The way I encountered them first was through inversion of gravity data - some of the files used in the inversion program can get pretty huge in the computer's memory, which limits the size of the data sets you can deal with and how detailed the models are.  However, you can use Daubechies wavelets to compress these files, which allows us to get some pretty freaking cool looking gravity models.  The way you've likely encountered wavelets is through our friend the JPEG!  Daubechies wavelets are part of the standard algorithm for compressing JPEG images, so that all those photos of your cat only take up 50% of your computer space rather than 99.999999%.

This is a Daubechies wavelet!  See how it's got a lot more complicated features to it?  This makes it easier for the shifted and stretched version to match more complicated looking signals.

Thingamabob #2: Generalized Cross Validation

Okay!  You ready for some MORE math??? No wait, wait, come back!!  All right, for those of you who didn't just run screaming away from your computer, causing great consternation for your loved ones and roommates, I'll now tell you the tale of Generalized Cross Validation (GCV for short).  This will be a shorter explanation because I know less about it, other than I thought it was really cool when I first encountered it in the inversion course I audited*, I just wish I had actually gotten to play with it more so I would remember more about the specifics!

*With the professor who really didn't want me there, but I showed up anyway....

ANYWAY.  Now we get to talk about inversion!!!  Inversion is awesome!!!*  Okay. So you have gone out in the field and sweated and strained and come back with your gravity data clutched in your grubby fists.  Now what?  Well, maybe you made a nice contour plot of the data, but you're not really sure what this anomaly is telling you. How deep is it?  Is it tilted at all?  Is it shallow, or just really high density?

*I need a word other than awesome!!!

Enter inversion to answer most* of your questions!  So, if you've got a Dense Thing in less dense stuff under the ground, that causes an area where gravity is stronger than other areas - a gravity anomaly.  If we know the shape of the Dense Thing and how dense it is, it's a relatively simple problem to calculate what the gravity anomaly should look like - this is called the "forward problem".

*Always work with geologists.  Always.  They keep your geophysics connected to those rock things all geophysicists seem to be terrified of.

The orange line is what you measured out in the field, braving heat, steep slopes, high winds, killer bees, and angry cows.  That orange blob is the focus of all your efforts - how dense is it?  Where is it?  Is it going to explode? (That last being only applicable in volcanic situations, generally)

But we're not dealing with that, are we?  No, we have the data, and since we like trees and grass we're NOT going to go digging to figure out what that Dense Thing* looks like.  So, we do the process in reverse - we use the gravity data and do the physics backwards to get the shape and density of the Dense Thing.  This is called the "inverse problem".

*Otherwise known as a "density anomaly".  But I rather like the term Dense Thing for now, as it puts me in mind of a rock with a beard, a bandanna, and a peace sign pendant just chillin' beneath the ground.

So there are some tricky things about this.  We want whatever Dense Thing we end up finding through this inversion to produce gravity data that matches the data we measured.  BUT, not exactly, because we know this data has noise - that is, we know our measurements aren't exactly accurate.  Maybe a cow walked by and made the gravity meter unhappy.  Maybe that measuring line on the meter wasn't REALLY on the 2, it was on the 3.  So we want the Dense Thing we create to match the data, but not too well.

Second tricky thing - physics!  See, gravity is what is known as "non-unique".  There are, mathematically speaking, an infinite number of ways you could build your Dense Thing to get the same gravity data.  Oh gods, what now??? ALL IS LOST!!!  Nope! We gots math, and we gots geology.  See, we do know some things about this Dense Thing.  We know it should be smooth - that is, you don't have one part of it that has a density of 0.000001 and one part right next to it that has a density of 10000000.  Geology generally doesn't do that.  We also want it to be small - we're assuming the simplest shape is the best, because on the scale that gravity surveys can detect stuff, things tend to not be spiky*.  Spiky things are large, and smooth things are small.  So we put in a bunch of math that says, only choose Dense Things that have sane variations in density and aren't too spiky.

*TEND TO BE.  I heard you geologists and geochemists wailing just now.  Just bear with me, k?  Most of the time you know it's true....  And I know sometimes it isn't....

So when you run the inversion stuff, it's a balancing act between the two.  Dense Things that are really smooth and laid back might be nice, but they probably won't fit your data very well.  Dense Things that fit your data well will probably be too spiky.  We have thing called a "regularization parameter" that controls the balance between the two.  I'm going to call it Bob, because "regularization parameter" is just too dang much to write multiple times.  So if Bob is really high*, we get smooth Dense Things that don't fit the data too closely, and if Bob is really low, we get models that fit the data really really well, but are unbearably spiky.

*Oh dear.  Maybe this wasn't such a good idea after all....especially in this state....

So how best to choose Bob?  This is where Generalized Cross Validation comes in!  And you thought we would never get there...  GCV was developed by the amazing and wonderful Grace Wabha, who is apparently STILL an active professor of the University of Wisconsin-Madison, at the age of 80.  I want to be HER when I'm 80.  So anyway.  My rough understanding of the method, drawn nearly entirely from the very useful explanation by the UBCGIF group, is this:

1. Do an inversion with a certain value of Bob, but leave out one data point.
2. Calculate a number that says how close the Dense Thing your inversion gave you matches the original gravity data.
3. Do steps 1 and 2 for all the data points.
4. Sum up all those "how close you got" numbers from step 3.  This is called your "cross validation value".
5. Do steps 1 through 4 for a range of values for Bob.  This gives you a cross validation value for each Bob.
6. Figure out which Bob value gives you the lowest cross validation value.  This is the best Bob to use to get the best model of the Dense Thing!

Tada!  Now you have a Dense Thing that fits your data, but not too close, and is not too spiky.  Isn't GCV awesome?  Aren't we glad Grace Wabha is awesome?

So sometimes I get all discouraged when I read all the stuff about how being female in a STEM field can be tough.  And how it seems like all those scientists you hear about in class who made all those really important discoveries that define your field, well, they're all male, so I guess the females just had too much to fight to really contribute, so I guess everyone's going to assume women are too stupid to be good scientists.  But THEN I keep encountering these methods that are so fundamental to what I do, and hey, these really incredible women developed them!  So hey, maybe we can do cool stuff.  Maybe I can do cool stuff.  If they could make it, and I mean REALLY make it, in the face of what were undoubtedly much higher odds than I face today, then, heck, I can do this.  I can stay in, I can make lasting contributions to my field.  They gave me such amazing tools to play with, it's the least I can do....

Still haven't had your fill of nerdiness yet?  Well, check out these spectrograms of famous classical pieces!  Each vertical line is a Fourier Transform of about a second of the music.  High notes show up higher up in the image, lower notes show up lower down on the image.  Start with the Dvorak's 9th Symphony to get the idea, and then move on to The Imperial March to multiply the geekiness factor to eleventy-seven...

Bad Bus Behavior

No, you are not this guy.  This woman wants you to GO AWAY.

(And, as it turns out, this photo is actually from a film about just that...)

<rant>So I have no problem with talking to guys on the bus.  I have actually had a few great bus encounters recently with guys, including reminiscing with a guy about living in the Pacific NW, and then later running into him and his daughter, whom he had taken to see the film Lucy because he wanted her to see films with strong female characters (!), and then some time later having a great debate on geophysics vs. geology with a petroleum geologist I ran into.

I DO have a problem when a guy asks to take the seat next to me, and then I look up and notice there are plenty of other empty seats around me he could have taken.  By taking this seat, he has boxed me into my seat, blocking off an escape route, thus instantly making me edgy.  He then  proceeds to ask me if I believe in fate, because he saw me on the bus that morning and "wanted to compliment me on my hat" (so he was watching me all morning).  Meanwhile, I'm trying frantically to be VERY involved in poking my phone, hoping he'll get the hint (spoiler alert - he doesn't).  He pulls out a can of something that smells like beer and asks me do I have a particular seat I like to sit in.  I mumble something, wondering if I should get off a stop early, even though it's about 10˚F outside, just so I can make sure he doesn't follow me home.  At some point I give him the false name of "Rachel", all the while really, really hoping he doesn't try to follow me off the bus, and he doesn't start making this his normal route.  Thankfully, he doesn't follow me off, and by this point the friend I've been texting with calls me so I guess the guy at least knows someone knows where I am if he decides to try anything.... I got off at my normal stop, but walked a different route home... just in case.

And yes, I live in a lower income area, but it's not a scary one.  I like riding the bus, and I'm not planning on stopping because of one creeper.  This was probably just some guy who thought I was cute and wanted to try his chances.  Okay, fine.  BUT I DON'T KNOW THAT.  All I know is this guy has boxed me in and WON'T GO AWAY.  Guy probably thinks he's on a romantic encounter, I'm wondering if I've picked up (another) stalker.  You know those romantic comedies where the guy goes after the girl who obviously hates him in the beginning but he wins her over by the end?  I hate those movies. </rant>

<siderant>Venturing into dicey territory here, but I should point out that both of the great bus conversations I had were with black men.  My (God I hope) former stalker and this more recent creep?  Both white.  So, from a totally significant sample size of four, I can reasonably conclude that white men are to be avoided at all costs.</siderant>

<addendum>No, I'm not saying all men are creeps.  I'm not saying all white men are creeps.  The vast, vast majority of the white men I know are perfectly wonderful human beings, including my friend who called me to give me a conversation ending excuse.  I'm saying that based on my experiences thus far, my race's all-too-common back-of-the-mind fear of black men is looking pretty dang stupid.</addendum>

Geophysical Gems

I know, I know, I know I still owe the last installment of my Matlab series.  I do apologize, but grad school is happening again, as it does.  I'll get to it eventually, I swear...

However, these two gems were just too good to pass up:

Gem #1: In my mining geophysics course today, we learned the proper definition of a geophysicist, as originally published in Northern Mining:

"A geophysicist is a person who passes as an exacting expert on the basis of being able to turn out with prolific fortitude infinite strings of incomprehensible formulae calculated with micrometric precision from inconclusive experiments carried out with instruments of problematic accuracy by persons of doubtful reliability and questionable mentality for the avowed purpose of annoying and confounding a hopeless chimerical group of fanatics known as geologists who are themselves the lunatic fringe surrounding the hard-working mine operator."

Accurate, every word of it.  Although I am a little disappointed that I don't get to be "chimerical".

Gem #2: I also ran across the following when clearing my desktop of approximately 5 years worth of clutter.  I cannot attest confidently to its provenance, only to say it smacks strongly of a certain Male Parental Unit of mine....

"And lo for he who praises the Lord shall receive unto him proportional understanding of the mass which lay below his feet. And God spoke "Let the firmament have a multitude of kinds and shall each hill and valley be corrected as free-air, " and He saw it and it was Bouguer."

And now, if you'll excuse me, I have some lightening bolts to dodge.