called the "heat equation."d wave be reduced to the sum of seemingly many incompatible shapes: square waves and v-shaped waves have corners, while sinusoids are smooth. but over time, mathematicians affirmed fourier's discovery and came to refer to the unique set of simple waves that combine to form a more complicated wave as the wave's fourier series. so we're here with liz stanhope, professor of mathematics at lewis & clark college, and liz's research expertise lies at the intersection of fourier analysis and geometry. hi, liz. >> hi, dan. >> we're going to talk a little bit about fourier, and my understanding is that when fourier introduced this at that time, i guess, it was an impossible idea that any function could be represented as a sum of sines and cosines. people didn't really believe it. >> yeah, it seemed sort of surprising to do arithmetic with waves. i mean, you're adding and subtracting things that aren't functions. that seems like a surprising idea to come up with. >> and it was even more than tha

here's the equator. the equator. there's the sun. this is not the scale. but i'm gonna label one of these, june or december? if one is june, so the other is december. and you guys, look and see which one he gonna put down june and which one he gonna put down december. check with the neighbor and see what neighbor say. okay, gang, what did you pick? how many say this should december? how many say this should be june? yehey, the whole class. all right. you'd be knowing these things. see? this is gonna be june, right? because what happens in june? we're down in here. look who's catching more energy, huh? what happens six months later? well, take a place that's up a little higher about like san francisco or denver, colorado or oklahoma city, somewhere like that in the mainland, yeah? let's look over here. there down in the summer time, they're getting the energy pretty flushed in, yeah? six months later, over here. all right. now, here they are. but now it's nighttime. this part is a nighttime, isn't it? not here around the day. but look over here. oh, they're

by that equation, wouldn't it be changing its density? i'm changing--well-- because the weight stays the same with the volume. it's just the clay became bigger. so--and so the volume got-- the volume of the boat is way thicker than the water than you put it on. effectively, the density of that which does the displacing becomes less. the problem is that, well, the clay has the same density no matter what you do. that's true. but the volume of clay that displaces the water, that density becomes less because now a lot of it is that air. so in a sense, we're effectively changing the density. the density of a ship is a lot less dense than the density of iron and metal, because the ship has that open space in the middle. see? so the volume is way bigger by not increasing the weight if you hold the weight the same. do you see that these equations are nice ways to think about things? see? if you hold the weight the same to change the volume, then you'll change the density. see, there's all kinds of ideas and considerations to think about with any

it equates to a false equivocation. on the one hand, you have the most evil expression of man's inhumanity to man in the history of humanity that took place in american slavery. where black bodies were violated, where people had no right, simply because of the color of their skin. and as a consequence, you had many lives lost. millions of lives that have been lost. and so evidently, our dear misguided friends on the right did not go far enough in terms of what they want to equate the affordable health care act. maybe they should equate it to the emancipation proclamation. but, of course, their ignorance does not take into the account that, again, so many lives were aborted and lost, so many lives% treated. families were torn asunder, and i recommend all of them to read not only orlando patterson, but the life of a slave, in which he compares slavery. you want to look at words for slavery synonymous, check out bar barety, such as human fraud. check outwards such as evil. those are the words that you equate with slavery,

congressman allen grayson after pictures surfaced from a fundraising appeal that uses burning crosses and equates the tea party to the klu klux klan. the e-mail went out from the 2014 re-election campaign and the caption suggests this t stands for the tea party. caption reads now you know what the t stands for. they asked grayson and house democrats to pull down this appeal and return any money that it raised as fundraising effort, calling the tea party basically the kkk. fox news contacted the congressman a couple hours ago to see if he wanted to disavow the e-mail. he went on to launch new attacks. we will have those with reaction from former florida congressman and marine lieutenant colonel allen west who is furious about this in moments. >>> but first, there is breaking news. an obama care bombshell. health and human services secretary giving an interview in the last hour about epic failures in the health care rollout and who is responsible. she was asked to appear before congress, she declined, had to go to some gala, but she sat down and gave an interview moments ago. she was asked specific

it is when you mix the two, and equate the two, and conflate the crisis linking the two, as prominent democrats have, you have done something that is far worse. you, for example, mr. president, powder gasoline on your own fire and risk blowing the entire country to smither evens. it's like shouting fire in a crowded athleteter and there's no fire act least yet. people still panic and rush out the doors, like anyone that invests in this country would do, take they're money and run. it's stupid, wrong, dangerous, and unforgive able, far worse than calling the other side names. it's the equivalent of burning down the entire country because you want win an argument. this is what hasn't on wall and broadway when you do that. the dow sliding 1 0 points today on growing fears this going to happen. the more the president talks up the possibility of a default, the more these guys worry, hey, this is out of control. craig smith is the chairman of smith america and says i guess official live it is out of control. what do you make of this? >> you know, neil, it just amazes me. you just laid it ou

is so many areas of non-traditional credit that is extended to people every day that people don't equateith having to impact on their credit score but they can. >> many people don't realize when they don't pay a fine to a municipality or government for something like a parking ticket or speeding ticket or overdue library book it goes through a same process. they will continue to turn a blind eye he it goes to a credit agency. >> it appears on a credit report before it's secretar sent to co. >> it's that credit report that can have an impact. >> that impact can be big. >> one single payment can hurt your score by 50 or 100 points. i know that comes as a shock to a lot of people. >> they think it's a one time event and i will get dinged so severely. the truth is, yes. that is why small bills like library bills and parking tickets do have to be handled promptly and on time. >> if you receive a collection notice due to a fine or municipality, the first thing you need to do is pull your credit report. you can get a free copy once a year at www.annualreport [.com. www.annualreport.com. if you

get trading out of the equation. get management fees out of the equation.u own american business and you hold it forever: that's what indexing is. own a fund that owns the entire u.s. stock market, does no trading, and has a cost of one percent a year to own. and that is the only way to do it. then you are the creature of the market and not of the casino. >> smith: index funds buy and hold a broadly diversified basket of stocks that match the holdings of a market index: the s&p 500, the wilshire 5000, or maybe a bond or commodity index. they don't eliminate market risk, they ride the market up and down, but they are much cheaper because there is no active manager. >> you can guarantee to the shareholder that they will capture their fair share of the stock market's return, for better or for worse. if you want to gamble with your retirement money, all i can say is be my guest. but be aware of the mathematical reality. maybe you have a one percent chance of beating the market over time. it has been proven right year after year after year because it can't be pr

let's think about the basic gdp equation.he economy grows because consumers spend, businesses spend, government spends and trade. consumers are not spending a lot unless it's for a few phone. the state and federal government is coming back, the companies are hoarding cash, and so what you have got going on here is an austerity plan that is not well timed and fiscal policy not being part of the equation. >> do guys like you have a chance to look over at europe and what it did, particularly the uk or other countries and somehow transfer some of that knowledge on to what we should be doing here? >> guys like me, yes. the problem is i don't hold office or have to run for reelection. and those are the folks that don't want to believe those lessons are necessarily applicable in the united states. these are the same people who said the default on the debt won't have much impact. i have been calling these the flat earth society. >> let's find out what happens if we go past october 17th. what is your guess as to what happens? >> first

. >> i don't think doing that means that -- it doesn't change the underlying equation. the underlying equation is that you are insisting on not just good-faith negotiations, but negotiations with hostages. in your willingness to let the occasional hostage out while holding the other hostages, doesn't change that fundamental principle. i think that's fundamentally wrong and fundamentally un-american. >> shelton, the house has passed 14 bills to fund vital government priorities. all 14 of them are sitting on harry reid's desk. he won't allow the senate to vote. let me ask the question -- if you voted to fund the men and women in the active military, why are democrats blocking funding the v.a.? do our veterans not deserve the same treatment that the acti active-military do? >> i'll concede that -- that this is a -- the active military was a good thing to pay for. >> but why not the veterans? >> no matter how many individual hostages we decide to let go, there will still be others. it doesn't change right now but then you still have other people who are getting the central

by that equation, wouldn't it be changing its density? i'm changing--well-- because the weight stays the same with the volume. it's just the clay became bigger. so--and so the volume got-- the volume of the boat is way thicker than the water than you put it on. effectively, the density of that which does the displacing becomes less. the problem is that, well, the clay has the same density no matter what you do. that's true. but the volume of clay that displaces the water, that density becomes less because now a lot of it is that air. so in a sense, we're effectively changing the density. the density of a ship is a lot less dense than the density of iron and metal, because the ship has that open space in the middle. see? so the volume is way bigger by not increasing the weight if you hold the weight the same. do you see that these equations are nice ways to think about things? see? if you hold the weight the same to change the volume, then you'll change the density. see, there's all kinds of ideas and considerations to think about with any

this is called the "equation of exchange.", the economic question facing the monetary authorities like arthur burns was, what would happen to the economy when you changed the money supply, m? roughly speaking, congressional critics were saying that you needed a bigger increase in m, on the left-hand side, to get a bigger increase in q -- more output, jobs, employment. what burns was saying was that you could get this bigger increase in q without such a large increase in the money supply because v, velocity, would also be going up. but then, unfortunately, another problem comes up. suppose both m and v are increasing? how can we be sure that the effect will be on q and not mainly on p? will we get more q -- output and jobs -- or simply a higher price level, p? will the fed's actions bring us prosperity or simply more inflation? by the late 1970s, inflation had taken over again, and there was a widespread feeling that the fed had to exercise restraint on the economy. but how? up until this period, most economists felt that the b

we're talking about the demand side of the leak equation.journalists get to make this decision and not the government? >> we depend on journalists to make decisions like that all the time to decide what is news and what's not news? to gather as much truth as they possibly can in a very careful way, report it as carefully as they can and quite honestly if not a journalist, who? because if they're not out there asking questions every day and reporting them to the public so that the public can make informed decisions at the ballot box and elsewhere, there is going to be no ability in this country to hold anybody that we've elected to congress or appointed to an agency accountable. this is all about accountability. >> one thing that strikes me is that you mentioned before that we're now having a debate that's useful. the president said this. some of your former top colleagues have said this. these debates wouldn't have occurred in the absence of edward snowden's major leaking to "the washington post" and the colleagues at the guardian. how do yo

how does it effect the equation? yes, i have not seen any -- i don't think we have that information yet. based on good old economic 101. it it's clearly a negative in the equation. a quick point. all of the things we're talking about here, the bottom line it's an additional negative. you debate how much it is for various businesses and rake from business to business. this this environment, where are we going down the path in the first place? >> i think figures that jumped out at me the one in your testimony. you mentioned 76% of the small businesses are likely not to hire in the next six months. and other numbers in here with regards to how many are pulling back the number of employees they have as well as cutting your hours. whenever you look at small businesses as being the driver of our economy, that just, i mean, that just immediately shows there's a blanket of -- over the entire economy with regards to generating jobs. and, you know, i think you probably could extrapolate from that there's not at lough new job c

how does that equate? >> it doesn't equate.l, the number sounds outrageous to begin with. what's the purpose? what are we trying to accomplish? >> somebody has to take the fall for -- >> for what? >> -- the 2008 crisis, is what people will push back. >> the government ought to look in a mirror. >> in other words, they weren't policing? >> they weren't policing. they initiated many things. they wanted more individuals to own homes, and so they changed the terms. they've lowered the standards. they were encouraging it. so, it's not -- it's not one-sided. >> so does business have no sort of retaliation? i mean, you know, you actually have taken on government, suing the government. but can -- you don't see that very often, hank. >> you don't see that very often. but, you know, you have to fight for what you believe in. we have a constitution. a constitution has a provision against unlawful taking by the government. if you don't fight back, you deserve what you get. >> earlier today i sat down with tiger management's julian robertso

. >>> today oakland police will be tackling the flip side of the human trafficking equation. >> firstinternational. >> they are hitting the track in a reverse sting operation, targeting the men whose continuing patronage drives the underground sex trade. >> the male johns, the customers. >> we're going after the johns. a lot of times in these operations you see we're going after females. females are a major part of the problem, but they're also victims. if we can attack this, if we can address this situation by going after the customers, well, then i think it's our duty to try and address this big problem on all sides of the coin. >> undercover officers will be wendy. everybody take a look. and felicia. >> two veteran female officers prepare to go undercover as street walkers. >> you want it through your bra or -- >> okay. >> stick it underneath the straps. you should be fine. >> they are wired for sound -- >> yeah, that's working. >> -- and must also brace themselves for the very real danger that comes from playing prostitutes out on the track. >> i've been doing undercover work for

we always talk about corruption south of the equator, but this is north of the equator.y. oil business is -- that's just the way we get things done. no more. there's a transparency revolution happening, and it's a great thing, because all over the continent of africa, developing world, there's young smart leaders, tech-savvy, even phones are checking in and holding their governments to account. >> you've dealt with so many different leaders around the world. who has impressed you? >> the great man nelson mandela is at home now. he was -- he was a towering figure for me in so many ways. i've been working for him since i was 18. we did our first antiapartheid concert. desmond tutu. he's my other boss, i so admire him, but even president clinton, who i imitated, to my chagrin -- i was trying to cover for him. >> what happened? >> he was off doing some stuff, and sheryl sam burg, from facebook says you had to do something. so i pretended to be him. >> when i first met bono, he walked into the oval office, and actually i thought it was a member of his own road crew. >> what d

so wayne, as lisa mentioned, a lot of people equate drones with foreign policy and military strikes,nd we just talked about steve saying how they use drones for animal protection. talk us to about how some these drones are also used in other areas in the united states. >> the first thing i would like to say is in my area we don't use the d word. because the d word has a very negative connotation associated with it. so we call them unmanned aerial systems on our manned aerial vehicles. once the faa decides on the integration of usa's into our national air space system, 85% of the use of these uas's will be for agriculture and public safety. firefighters -- our wild land fires that we have in utah, california, and arizona, are getting more widespread and more intense, and the way that we might those wildfires now is really the dated technology. it's a little bit better than what we had 40 years ago when an airplane would actually fly over a fire and drop a tube with photos that that airplane had taken. now they can detect areas where the fire right move and areas where firefighters can

i'm just saying that she has a very simple equation in her head. by the way, she has written a very important paper, these very complicated equations that back up her feeling. >> i hope she gets backed up. last one, steve liesman, does janet yellen care about the dollar exchange rate? does she care about the exchange rate? >> i think that she does care about the dollar exchange rate, but i think she would disagree with you, as does i think, larry, no disrespect, the consensus of the board that the dollar should not be the focus of policy for the federal reserve. >> i understand. that's been true for decades. that's why those guys are all wrong. that's why their models are wrong. don't move a second. we have alex young with s&p capital i.q. and brian kelly founder of brian kelly capitol. janet yellen. does this change your investment strategy? >> no, it doesn't. the best thing is we have some kind of certainty coming out of watching ton. that's t washington. i think everybody expected it to be yellen. easy monetary policy. taper is off the table. at

knowing that that is part of the equation, what do you think went wrong on the -- i don't want to say the democrat side but the administrative side where this great opportunity to roll out this the incredible initiative for health care goes so south when it could have really, not put the nail in the coffin of obstructionism but demonstrated this is what we're talking about in terms of being able to be helpful to the citizens. >> any time you have a major change in any system like the health care system, we know there are going to be kinks and bumps. and there have been with the rollout of the affordable care act. but at the end of the day what we should be -- we all have ato agree on one basic premise that everybody has the right to access to affordable quality health care and because we can't steam get republicans to agree on that basic premise they are hell bent on threing every obstacle in the path of trying to make sure that that happens. yes, there's kinks but in my experience in government, when you have a little bit of trouble implementing a will you, you work together to iron

you don't have to put that equation up on your post. >> when it e caquals four, plea post that. >> yeah so we can correct you. >> i've done all of them. >> that was the annoying part. now, let's look at the genius part. it's friday. it's time to talk to our staff and viewers to find out who is to follow on twitter. >> first, our newest reporter in west palm beach florida. ashley porter has a pick that will crack you up.&báo >> i like to follow big ben clocks. this one gets pretty much to the point. some say bong. some same bong, bong, bong, bong, bong, bong. >> when you follow big ben, you know exactly what time it is in london. you also know when you've wasted an hour on twitter. but with nearly half a million followers, how would you go wrong? i will warn you big ben duoes nt follow anyone back. >> let's see what cooking expert chef matt has to say. hands down, thomas keller. he is the world's greatest chef. he posts pictures of the food that he makes and this stuff is so incredible. i mean, it's dynamic. it's colorful. you have different textures. you can taste it through the pictur

to our concerns about translation on this website site we look forward to work with the assuring equate to communities generated websites. >> (speaking foreign language.) >> the b cc appreciates the accountability data that has been generated for the students progress. this initial data has helped to engage our dialog with the district >> (speaking foreign language.) >> the l l d report card it is important for communicating progress to our families. we appreciate that k through 5 implementation happened last year. >> (speaking foreign language.) >> we like to honor and recognize the work and commitment to a bbc member who served for many years and recently passed away. thank you >> thank you cindy. >> so, now in our packet you have the copy of the bilingual observation report for the observations we made in 2012 and 2013. this is a report that we submitted to the internal oversight committee. i'm not going to read through this but i want the opportunity to highlight a couple of things. they visited the school sites and they represent did bilingual folks. they met with the administratio

because their state their government they are also poor but the couple to for i don't agree i don't equate that at all in fact we have to talk of the value of the medicine not the price of the medicine because water the value all seeing the smile in a mother's face when the child disappeared from a life threatening disease waters a value that you put on improving life expectancy from forty years to eighty years what are the economic value if that person had been at your place and you had been in the place and that person had been selling their drugs at such a high place that you were not able to afford it. and would i would you have liked it i. don't. how do i received if. it didn't already. for maybe a bit more but i use it as it suits the i know that. this particular piece. out. the. principle multi-nationals should. really be. in richmond instead of the springs and the city. to be. clear today the supreme court is to issue its verdict and put an end to the sensational court battle of novartis india that has lasted for seven years. the court's verdict will be the one to determine whether

together we equate this if it is the military, since it's mandatory, when i was 18, i met a lot of peoplefferent people than where i grew up. and we wear the same uniform. but under the uniform, we're different people and this makes us so special. >> and i think our military is a volunteer military in this country -- is a volunteer military. do you see that if your country? >> we may have it some day. but right now it creates a lot of equality and friendship and it also helps our economy. some of those friendships that tend spirit that is created there, the networking that comes out of it is very supportive of that. >> thank you very much. we'll come back in a moment and continue our conversation. join us back here on mosaic in a moment. >>> for nor information about the israel conflict in the pacific northwest, you can good to israeliconsulate.org or give them a call. welcome back to mosaic. we're in the middle of a great conversation. so what are some of the local program that's the general gets involved with in the bay area? >>i say that what concerns me most is how can we give back to

somehow the idea of being part culture appeared out of that equation. would say it is our fault as well because we kind of cultivated that image with these harley-davidson's. do i take from your statement now that you think there is too much conductor worship in our contemporary society? alone, but itor think that my industry, the classical music industry has been an industry of covers. so we do covers. with thecompare this rock and pop side, what is the most exciting event? it is the new album of a band or a singer-songwriter or whatever, and people are eagerly awaiting to hear the new piece, the new stuff. industry, we have turned it into this endless cover producing. and it is a pd. pity.is a the situation is changing about us, and it's people who work with these institutions, how we can find a balance, to be guardians of the legacy on one level. it really is a miracle how a piece by beethoven is completely alive today and how it still speaks to all kinds of people in all countries around the world and all that. that is a miracle, and we have to take

we are more in the scandal part of the equation.n the reform side, they are not tailing many wins right now, where is the folks who want more money coming in right now, absolutely, they have momentum. host: can we expect balanced news coverage from your organization, specifically on the issue of dark money question mark do you investigate folks on the left as well as the right? guest: absolutely. that is one reason i like this job. we go after both sides of the aisle. we recently wrote a piece, looking at some of the most the country,ems in and they are planning what they call a $40 million surged to push back against the conservative side of this, against mitch mcconnell in the senate, who has been a big leader in the campaign-finance effort. i can tell you from my e-mail that people i wrote about were far from pleased. but they were people on the progressive side. some of them i have been on c- span to talk about before. this is absolutely a bipartisan issue and we cover it exactly that way. aj is from memphis, tennessee on our li

martin bashir who has no love for the tea party or the right. >> he made it clear. >> he tried to equate party with racists even in his question. >> that wasn't good enough for congressman grayson. he needs everybody to support his use of the burning cross in a fund raising e-mail and referring to a group of people who buy bi and large stand for limited government. otherwise if you don't you are a coconspirator, potential racist, apparently. always interesting, mr. webb. >> never a dull moment. >> adios. >> sadly. >> coming up, new information in this decades-old murder mystery that grabbed headlines around the world. up next, mark furman explains why he thinks jon and patsy ramsey may indeed have helped cover up their daughter's murder. (dad) just feather it out. that's right. (son) ok. feather it out. (dad) all right. that's ok. (dad) put it in cond, put it in second. (dad) slow it down. put the clutch in, break it, break it. (dad) st like i showed you. dad, you didn't show me, you showed him. dad, he's gonna wreck the car! (dad) he's not gonna wreck the car. (dad) no fighting in the r

this time we may see a shift in that equation. we may see for a first time as a result in several decades that virginia breaks it's pattern for going to an opposite party in the year of the presidential vote. this would be historic and it would send a warning signal for their ability to retain majority in the south givent wha -- given to what happened with the shutdown and obamacare. >> this does sound like it's terry mccullough's race to lose. does that change his campaign strategy? >> he is running a cautious campaign. if you watch a lot of tv in the washington or virginia areas he does not appear in his own tv ads. averaged cuccinel limili's campaign puts him in them all. where he is wearing a hawaiian shirt. they are trying to make him look like a sleazy deal maker. a wheeler dealer. it's not working in part because mcculloff is no where to be seen. they run a tightly controlled message campain. it's fair to say, given the perceptions that that is still being vastly vast trumped by the anger they have over the government shutd

that equates to jobs and strengthens the middle class. i am hopeful that will be accomplished. >> outside the senate frustrated protesters demanded an end to the shutdown. >> these people are down here because things are broken. they are broken all the way around. i mean, i am tired of getting kicked around. i have lost money on this. >> the shutdown has lost all -- has left -- has lasted almost two weeks already and have left hundreds of thousands of americans without work. >> to syria where the violence continues. a car bombing today killed at least 12 people in the northern town of dark push -- of -- 12 of the dead have been identified. also, gunmen abducted seven red cross and red crescent workers. the nationalities of those workers has not been made public. for now there has been no claim of responsibility. there has been a call for the men and women to be released by the international red cross. >> we are here to serve the syrian people. we are delivering water. we deliver food, health. we do a lot of things, and that is for them, n