");vwo_$('head').append(_vwo_sel);return vwo_$('head')[0] && vwo_$('head')[0].lastChild;})("HEAD")}}, C_940895_66_1_2_0:{ fn:function(log,nonce=''){return (function(x) { try{ var _vwo_sel = vwo_$("`); !vwo_$("head").find('#1738257835657').length && vwo_$('head').append(_vwo_sel);}catch(e) {console.error(e)} try{}catch(e) {console.error(e)} try{const DEAR_READER_HEADING_HTML="

Dear reader,

",DEAR_READER_BODY_HTML="\n

Political debates with family or friends can get heated. But what if there was a way to handle them better?

You can learn how to have civil political conversations with our new e-book!

Download our free e-book, Talking Sense: Have Hard Political Conversations, Better, and learn how to talk without the tension.

\n",DEAR_READER_CTA_TEXT="Get your free ebook »",DEAR_READER_CTA_LINK="https://cloud.connect.mpr.org/mprnews-cfw03-01-talking-sense?utm_campaign=cfw_talkingsense&utm_term=dearreader_co";!function(){const e=async function(r,t=100,n=1e4){t=Number.isInteger(t)&&t>0&&t<=100?t:parseInt(t);let a="Array";if("NaN"==t)return console.error("Invalid refresh interval:",t);Array.isArray(r)||"string"!=typeof r||(a="string",r=[r]);let o=e=>document.querySelector(e),i=e=>e.every(e=>!!o(e));return new Promise((l,s)=>{let c=(e,r=null)=>(r&&clearInterval(r),l("Array"==a||e.length>1?e.map(e=>o(e)):o(e[0]))),d=a=>{console.error(`${a.name}: ${a.message}`);return s(a,()=>e(r,t=100,n=1e4))};try{if(i(r))return c(r);let e=setInterval(()=>{if(i(r))return c(r,e)},1e3/t);setTimeout(()=>{try{if(!i(r)){clearInterval(e);let r=Error(`Failed to find matching elements within ${n}ms`);throw r.name="Timed Out",r}}catch(e){return d(e)}},n)}catch(e){return d(e)}})};e("article").then(e=>{e.insertAdjacentHTML("beforeend",`

Dear reader,

\n ${DEAR_READER_BODY_HTML}\n \n \n \n

`)})}();}catch(e) {console.error(e)} return vwo_$('head')[0] && vwo_$('head')[0].lastChild;})("head")}}, R_940895_66_1_2_0:{ fn:function(log,nonce=''){return (function(x) { try{ var ctx=vwo_$(x),el; /*vwo_debug log("Revert","content",""); vwo_debug*/; el=vwo_$('[vwo-element-id="1738257835657"]'); el.revertContentOp().remove(); } catch(e) {console.error(e)} try{ var el,ctx=vwo_$(x); /*vwo_debug log("Revert","addElement","body"); vwo_debug*/(el=vwo_$('[vwo-element-id="1738257835659"]')).remove(); } catch(e) {console.error(e)} return vwo_$('head')[0] && vwo_$('head')[0].lastChild;})("head")}}, GL_940895_66_pre:{ fn:function(VWO_CURRENT_CAMPAIGN, VWO_CURRENT_VARIATION,nonce = ""){try{!function(){try{var e=function(e){return Object.keys(e).find((function(e){return e.startsWith("__reactInternalInstance$")||e.startsWith("__reactFiber$")}))},n=function(e,n){if(e&&n)return e[n]},t=function(e,n,t){var i=(i=e.nodeName)&&i.toLowerCase();n.stateNode=e,n.child=null,n.tag=e.nodeType===Node.ELEMENT_NODE?5:6,n.type&&(n.type=n.elementType="vwo-"+i),n.alternate&&(n.alternate.stateNode=e),e[t]=n},i=function(e,n){var t=Date.now();!function i(){var l=Object.keys(n).find((function(e){return e.startsWith("__reactProps$")}))||"",r=Date.now();if(l&&n[l])switch(e.name){case"href":n[l].href=e.value;break;case"onClick":n[l].onClick&&delete n[l].onClick;break;case"onChange":n[l].onChange&&n[l].onChange({target:n})}l||3e3 table:nth-of-type(1) > tbody:nth-of-type(1) > tr:nth-of-type(1) > td:nth-of-type(1) > div:nth-of-type(1) > div:nth-of-type(1) > h2:nth-of-type(1) > span:nth-of-type(1)"); vwo_debug*/(el=vwo_$(".stylingblock-content-margin-cell > table:nth-of-type(1) > tbody:nth-of-type(1) > tr:nth-of-type(1) > td:nth-of-type(1) > div:nth-of-type(1) > div:nth-of-type(1) > h2:nth-of-type(1) > span:nth-of-type(1)")).vwoRevertHtml();})(".stylingblock-content-margin-cell > table:nth-of-type(1) > tbody:nth-of-type(1) > tr:nth-of-type(1) > td:nth-of-type(1) > div:nth-of-type(1) > div:nth-of-type(1) > h2:nth-of-type(1) > span:nth-of-type(1)")}}},rules:[{"tags":[{"metricId":0,"id":"metric","data":{"type":"g","campaigns":[{"c":66,"g":1}]}}],"triggers":["13099398"]},{"tags":[{"metricId":959033,"id":"metric","data":{"type":"m","campaigns":[{"c":48,"g":3}]}},{"metricId":959033,"id":"metric","data":{"type":"m","campaigns":[{"c":64,"g":2}]}},{"metricId":959033,"id":"metric","data":{"type":"m","campaigns":[{"c":63,"g":2}]}}],"triggers":["8536415"]},{"tags":[{"metricId":959027,"id":"metric","data":{"type":"m","campaigns":[{"c":48,"g":5}]}},{"metricId":959027,"id":"metric","data":{"type":"m","campaigns":[{"c":64,"g":4}]}},{"metricId":959027,"id":"metric","data":{"type":"m","campaigns":[{"c":63,"g":4}]}}],"triggers":["8536409"]},{"tags":[{"metricId":959030,"id":"metric","data":{"type":"m","campaigns":[{"c":48,"g":4}]}},{"metricId":959030,"id":"metric","data":{"type":"m","campaigns":[{"c":64,"g":3}]}},{"metricId":959030,"id":"metric","data":{"type":"m","campaigns":[{"c":63,"g":3}]}}],"triggers":["8536412"]},{"tags":[{"metricId":951908,"id":"metric","data":{"type":"m","campaigns":[{"c":48,"g":1}]}},{"metricId":951908,"id":"metric","data":{"type":"m","campaigns":[{"c":64,"g":1}]}},{"metricId":951908,"id":"metric","data":{"type":"m","campaigns":[{"c":63,"g":1}]}}],"triggers":["8639604"]},{"tags":[{"metricId":951905,"id":"metric","data":{"type":"m","campaigns":[{"c":48,"g":2}]}},{"metricId":951905,"id":"metric","data":{"type":"m","campaigns":[{"c":64,"g":5}]}},{"metricId":951905,"id":"metric","data":{"type":"m","campaigns":[{"c":63,"g":5}]}}],"triggers":["8459768"]},{"tags":[{"priority":4,"data":"campaigns.48","id":"runCampaign"},{"priority":4,"data":"campaigns.66","id":"runCampaign"},{"priority":4,"data":"campaigns.64","id":"runCampaign"},{"priority":4,"data":"campaigns.63","id":"runCampaign"}],"triggers":["10589191"]},{"tags":[{"id":"checkEnvironment"}],"triggers":["5"]},{"tags":[{"priority":3,"id":"prePostMutation"},{"priority":2,"id":"groupCampaigns"}],"triggers":["8"]},{"tags":[{"priority":2,"id":"visibilityService"}],"triggers":["9"]},{"tags":[{"id":"runTestCampaign"}],"triggers":["2"]},{"tags":[{"id":"urlChange"}],"triggers":["75"]}],pages:{"ec":[{"1625289":{"inc":["o",["url","urlReg","(?i).*"]]}},{"2183589":{"inc":["o",["pg","eq","141375"]]}}],"pc":[{"141375":{"inc":["o",["url","urlReg","(?i)^https?\\:\\\/\\\/(w{3}\\.)?mprnews\\.org\\\/story.*"],["url","urlReg","(?i)^https?\\:\\\/\\\/(w{3}\\.)?mprnews\\.org\\\/episode.*"]]}}]},pagesEval:{"ec":[1625289,2183589],"pc":[141375]},stags:{}}})(); ;;var commonWrapper=function(argument){if(!argument){argument={valuesGetter:function(){return{}},valuesSetter:function(){},verifyData:function(){return{}}}}const getVisitorUuid=function(){if(window._vwo_acc_id>=1037725){return window.VWO&&window.VWO.get("visitor.id")}else{return window.VWO._&&window.VWO._.cookies&&window.VWO._.cookies.get("_vwo_uuid")}};var pollInterval=100;var timeout=6e4;return function(){var accountIntegrationSettings={};var _interval=null;function waitForAnalyticsVariables(){try{accountIntegrationSettings=argument.valuesGetter();accountIntegrationSettings.visitorUuid=getVisitorUuid()}catch(error){accountIntegrationSettings=undefined}if(accountIntegrationSettings&&argument.verifyData(accountIntegrationSettings)){argument.valuesSetter(accountIntegrationSettings);return 1}return 0}var currentTime=0;_interval=setInterval((function(){currentTime=currentTime||performance.now();var result=waitForAnalyticsVariables();if(result||performance.now()-currentTime>=timeout){clearInterval(_interval)}}),pollInterval)}}; var pushBasedCommonWrapper=function(argument){var firedCamp={};if(!argument){argument={integrationName:"",getExperimentList:function(){},accountSettings:function(){},pushData:function(){}}}return function(){window.VWO=window.VWO||[];const getVisitorUuid=function(){if(window._vwo_acc_id>=1037725){return window.VWO&&window.VWO.get("visitor.id")}else{return window.VWO._&&window.VWO._.cookies&&window.VWO._.cookies.get("_vwo_uuid")}};var sendDebugLogsOld=function(expId,variationId,errorType,user_type,data){try{var errorPayload={f:argument["integrationName"]||"",a:window._vwo_acc_id,url:window.location.href,exp:expId,v:variationId,vwo_uuid:getVisitorUuid(),user_type:user_type};if(errorType=="initIntegrationCallback"){errorPayload["log_type"]="initIntegrationCallback";errorPayload["data"]=JSON.stringify(data||"")}else if(errorType=="timeout"){errorPayload["timeout"]=true}if(window.VWO._.customError){window.VWO._.customError({msg:"integration debug",url:window.location.href,lineno:"",colno:"",source:JSON.stringify(errorPayload)})}}catch(e){window.VWO._.customError&&window.VWO._.customError({msg:"integration debug failed",url:"",lineno:"",colno:"",source:""})}};var sendDebugLogs=function(expId,variationId,errorType,user_type){var eventName="vwo_debugLogs";var eventPayload={};try{eventPayload={intName:argument["integrationName"]||"",varId:variationId,expId:expId,type:errorType,vwo_uuid:getVisitorUuid(),user_type:user_type};if(window.VWO._.event){window.VWO._.event(eventName,eventPayload,{enableLogs:1})}}catch(e){eventPayload={msg:"integration event log failed",url:window.location.href};window.VWO._.event&&window.VWO._.event(eventName,eventPayload)}};const callbackFn=function(data){if(!data)return;var expId=data[1],variationId=data[2],repeated=data[0],singleCall=0,debug=0;var experimentList=argument.getExperimentList();var integrationName=argument["integrationName"]||"vwo";if(typeof argument.accountSettings==="function"){var accountSettings=argument.accountSettings();if(accountSettings){singleCall=accountSettings["singleCall"];debug=accountSettings["debug"]}}if(debug){sendDebugLogs(expId,variationId,"intCallTriggered",repeated)}if(singleCall&&(repeated==="vS"||repeated==="vSS")||firedCamp[expId]){return}window.expList=window.expList||{};var expList=window.expList[integrationName]=window.expList[integrationName]||[];if(expId&&variationId&&["VISUAL_AB","VISUAL","SPLIT_URL"].indexOf(_vwo_exp[expId].type)>-1){if(experimentList.indexOf(+expId)!==-1){firedCamp[expId]=variationId;var visitorUuid=getVisitorUuid();var pollInterval=100;var currentTime=0;var timeout=6e4;var user_type=_vwo_exp[expId].exec?"vwo-retry":"vwo-new";var interval=setInterval((function(){if(expList.indexOf(expId)!==-1){clearInterval(interval);return}currentTime=currentTime||performance.now();var toClearInterval=argument.pushData(expId,variationId,visitorUuid);if(debug&&toClearInterval){sendDebugLogsOld(expId,variationId,"",user_type);sendDebugLogs(expId,variationId,"intDataPushed",user_type)}var isTimeout=performance.now()-currentTime>=timeout;if(isTimeout&&debug){sendDebugLogsOld(expId,variationId,"timeout",user_type);sendDebugLogs(expId,variationId,"intTimeout",user_type)}if(toClearInterval||isTimeout){clearInterval(interval)}if(toClearInterval){window.expList[integrationName].push(expId)}}),pollInterval||100)}}};window.VWO.push(["onVariationApplied",callbackFn]);window.VWO.push(["onVariationShownSent",callbackFn])}}; var surveyDataCommonWrapper=function(argument){if(!argument){argument={getCampaignList:function(){return[]},surveyStatusChange:function(){},answerSubmitted:function(){}}}return function(){window.VWO=window.VWO||[];function getValuesFromAnswers(answers){var values=[];for(var i=0;i=timeout;if(toClearInterval||isTimeout){clearInterval(interval)}}),pollInterval)}}window.VWO.push(["onSurveyShown",function(data){commonSurveyCallback(data,argument.surveyStatusChange,"surveyShown")}]);window.VWO.push(["onSurveyCompleted",function(data){commonSurveyCallback(data,argument.surveyStatusChange,"surveyCompleted")}]);window.VWO.push(["onSurveyAnswerSubmitted",function(data){commonSurveyCallback(data,argument.answerSubmitted,"surveySubmitted")}])}}; (function(){var VWOOmniTemp={};window.VWOOmni=window.VWOOmni||{};for(var key in VWOOmniTemp)Object.prototype.hasOwnProperty.call(VWOOmniTemp,key)&&(window.VWOOmni[key]=VWOOmniTemp[key]);;})();(function(){window.VWO=window.VWO||[];var pollInterval=100;var _vis_data={};var intervalObj={};var analyticsTimerObj={};var experimentListObj={};window.VWO.push(["onVariationApplied",function(data){if(!data){return}var expId=data[1],variationId=data[2];if(expId&&variationId&&["VISUAL_AB","VISUAL","SPLIT_URL"].indexOf(window._vwo_exp[expId].type)>-1){}}])})();; ;var vD=VWO.data||{};VWO.data={content:{"fns":{"list":{"vn":1,"args":{"1":{}}}}},as:"r5.visualwebsiteoptimizer.com",dacdnUrl:"https://dev.visualwebsiteoptimizer.com",accountJSInfo:{"ts":1744623768,"noSS":false,"pc":{"a":0,"t":0},"rp":30}};for(var k in vD){VWO.data[k]=vD[k]};;var gcpfb=function(a,loadFunc,status,err,success){function vwoErr() {_vwo_err({message:"Google_Cdn failing for " + a + ". Trying Fallback..",code:"cloudcdnerr",status:status});} if(a.indexOf("/cdn/")!==-1){loadFunc(a.replace("cdn/",""),err,success); vwoErr(); return true;} else if(a.indexOf("/dcdn/")!==-1&&a.indexOf("evad.js") !== -1){loadFunc(a.replace("dcdn/",""),err,success); vwoErr(); return true;}};window.VWO=window.VWO || [];window.VWO._= window.VWO._ || {};window.VWO._.gcpfb=gcpfb;;var d={cookie:document.cookie,URL:document.URL,referrer:document.referrer};var w={VWO:{_:{}},location:{href:window.location.href,search:window.location.search},_vwoCc:window._vwoCc};;window._vwo_cdn="https://dev.visualwebsiteoptimizer.com/cdn/";window._vwo_apm_debug_cdn="https://dev.visualwebsiteoptimizer.com/cdn/";window.VWO._.useCdn=true;window.vwo_eT="br";window._VWO=window._VWO||{};window._VWO.fSeg={};window._VWO.dcdnUrl="/dcdn/settings.js";window.VWO.sTs=1744398902;window._VWO._vis_nc_lib=window._vwo_cdn+"edrv/nc-22652eff7f31b5ce957ea182f3b00d90br.js";var loadWorker=function(url){_vwo_code.load(url, { dSC: true, onloadCb: function(xhr,a){window._vwo_wt_l=true;if(xhr.status===200 ||xhr.status===304){var code="var window="+JSON.stringify(w)+",document="+JSON.stringify(d)+";window.document=document;"+xhr.responseText;var blob=new Blob([code||"throw new Error('code not found!');"],{type:"application/javascript"}),url=URL.createObjectURL(blob);window.mainThread={webWorker:new Worker(url)};window.vwoChannelFW=new MessageChannel();window.vwoChannelToW=new MessageChannel();window.mainThread.webWorker.postMessage({vwoChannelToW:vwoChannelToW.port1,vwoChannelFW:vwoChannelFW.port2},[vwoChannelToW.port1, vwoChannelFW.port2]);if(!window._vwo_mt_f)return window._vwo_wt_f=true;_vwo_code.addScript({text:window._vwo_mt_f});delete window._vwo_mt_f}else{if(gcpfb(a,loadWorker,xhr.status)){return;}_vwo_code.finish("&e=loading_failure:"+a)}}, onerrorCb: function(a){if(gcpfb(a,loadWorker)){return;}window._vwo_wt_l=true;_vwo_code.finish("&e=loading_failure:"+a);}})};loadWorker("https://dev.visualwebsiteoptimizer.com/cdn/edrv/worker-b31b97f8c2fb7582cde37c6681f5aeadbr.js");;var _vis_opt_file;var _vis_opt_lib;if(window.VWO._.allSettings.dataStore.previewExtraSettings!=undefined&&window.VWO._.allSettings.dataStore.previewExtraSettings.isSurveyPreviewMode){var surveyHash=window.VWO._.allSettings.dataStore.plugins.LIBINFO.SURVEY_DEBUG_EVENTS.HASH;var param1="evad.js?va=";var param2="&d=debugger_new";var param3="&sp=1&a=940895&sh="+surveyHash;_vis_opt_file=vwoCode.use_existing_jquery&&typeof vwoCode.use_existing_jquery()!=="undefined"?vwoCode.use_existing_jquery()?param1+"vanj"+param2:param1+"va_gq"+param2:param1+"edrv/va_gq-3c5e403756405f46fc0d721428dbc45cbr.js"+param2;_vis_opt_file=_vis_opt_file+param3;_vis_opt_lib="https://dev.visualwebsiteoptimizer.com/dcdn/"+_vis_opt_file}else if(window.VWO._.allSettings.dataStore.mode!=undefined&&window.VWO._.allSettings.dataStore.mode=="PREVIEW"){ var path1 = 'edrv/pd_'; var path2 = window.VWO._.allSettings.dataStore.plugins.LIBINFO.EVAD.HASH + ".js"; ;_vis_opt_file=vwoCode.use_existing_jquery&&typeof vwoCode.use_existing_jquery()!=="undefined"?vwoCode.use_existing_jquery()?path1+"vanj"+path2:path1+"va_gq"+path2:path1+"edrv/va_gq-3c5e403756405f46fc0d721428dbc45cbr.js"+path2;_vis_opt_lib="https://dev.visualwebsiteoptimizer.com/cdn/"+_vis_opt_file}else{_vis_opt_file=vwoCode.use_existing_jquery&&typeof vwoCode.use_existing_jquery()!=="undefined"?vwoCode.use_existing_jquery()?"edrv/vanj-944ef786aed805499ec94f3cef25ed99br.js":"edrv/va_gq-3c5e403756405f46fc0d721428dbc45cbr.js":"edrv/va_gq-3c5e403756405f46fc0d721428dbc45cbr.js"}window._vwo_library_timer=setTimeout((function(){vwoCode.removeLoaderAndOverlay&&vwoCode.removeLoaderAndOverlay();vwoCode.finish()}),vwoCode.library_tolerance&&typeof vwoCode.library_tolerance()!=="undefined"?vwoCode.library_tolerance():2500),_vis_opt_lib=typeof _vis_opt_lib=="undefined"?window._vwo_cdn+_vis_opt_file:_vis_opt_lib;var loadLib=function(url){_vwo_code.load(url, { dSC: true, onloadCb:function(xhr,a){window._vwo_mt_l=true;if(xhr.status===200 || xhr.status===304){if(!window._vwo_wt_f)return window._vwo_mt_f=xhr.responseText;_vwo_code.addScript({text:xhr.responseText});delete window._vwo_wt_f;}else{if(gcpfb(a,loadLib,xhr.status)){return;}_vwo_code.finish("&e=loading_failure:"+a);}}, onerrorCb: function(a){if(gcpfb(a,loadLib)){return;}window._vwo_mt_l=true;_vwo_code.finish("&e=loading_failure:"+a);}})};loadLib(_vis_opt_lib);VWO.load_co=function(u,opts){return window._vwo_code.load(u,opts);};;;}}catch(e){_vwo_code.finish();_vwo_code.removeLoaderAndOverlay&&_vwo_code.removeLoaderAndOverlay();_vwo_err(e);window.VWO.caE=1}})();

Skip to Main Content
Skip to audio player to listen live

Create a Free MPR

news profile

for you

Already have an account?

By submitting, you consent that you are at least 18 years of age and to receive information about MPR's or APMG entities' programs and offerings. The personally identifying information you provide will not be sold, shared, or used for purposes other than to communicate with you about MPR, APMG entities, and its sponsors. You may opt-out at any time clicking the unsubscribe link at the bottom of any email communication. View our Privacy Policy.

Welcome back

to news for you

New to MPR News?

Welcome back

to news

for you

Reset Password

Still require assistance or not sure what your User Name is?

Welcome back

to news

for you

Email Verification

A verification code has been emailed to

Still awaiting the code?

St. Paul, Minn.

November 28, 2007 4:36 PM

U of M math video is a Web hit

A still image from the "Moebius Transformations Revealed" video.
Image courtesy of YouTube

Go Deeper.

Create an account or log in to save stories.

Like this?

Thanks for liking this story! We have added it to a list of your favorite stories.

Show me!

About 40 YouTube clips will get featured in Wednesday's CNN debate. However, it's almost guaranteed that none of them will get as many views as a math video produced at the University of Minnesota.

In the video, "Moebius Transformations Revealed," you'll see what looks like a rainbow-colored square grid spinning twisting around the screen. The video was created to illustrate the concepts of a mathematics formula.

Douglas Arnold directs the Institute for Mathematics and its Applications at the University of Minnesota and he's one of the creators of the "Moebius Transformations Revealed" video. He joined All Things Considered host Tom Crann to talk about the video, which has been viewed by more than 900,000 people on YouTube.

Gallery

1 of 1

Turn Up Your Support

MPR News helps you turn down the noise and build shared understanding. Turn up your support for this public resource and keep trusted journalism accessible to all.

Dear reader,

Political debates with family or friends can get heated. But what if there was a way to handle them better?

You can learn how to have civil political conversations with our new e-book!

Download our free e-book, Talking Sense: Have Hard Political Conversations, Better, and learn how to talk without the tension.

Dear reader,

Dear reader,

Turn Up Your Support

Dear reader,

News you can use in your inbox